The use of synchrotron radiation techniques in the characterization of strained semiconductor...

The use of synchrotron radiation techniques in the characterizationof strained semiconductor heterostructures and thin films

C. Lambertia,b,c,*

aDepartment of Inorganic, Physical and Material Chemistry, University of Torino, Via P. Giuria 7, I-10125 Turin, ItalybINFM UdR of Turin University, Turin, Italy

cINSTM UdR of Turin, Italy

Accepted in final form 15 December 2003

Abstract

In the last couple of decades, high-performance electronic and optoelectronic devices based on semiconductor

heterostructures have been required to obtain increasingly strict and well-defined performances, needing a

detailed control, at the atomic level, of the structural composition of the buried interfaces. This goal has been

achieved by an improvement of the epitaxial growth techniques and by the parallel use of increasingly

sophisticated characterization techniques. Among them, a leading role has been certainly played by those

Surface Science Reports 53 (2004) 1–197

0167-5729/$ – see front matter # 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.surfrep.2003.12.001

Abbreviations: AED, Auger electron diffraction; AFM, atomic force microscopy; ALE, atomic layer epitaxy; BEEM,

ballistic electron emission microscopy; CBE, chemical beam epitaxy; CTR, crystal truncation rod; DAFS, diffraction

anomalous fine structure; DFT, density functional theory; DOS, density of occupied electron states; EDC, kinetic-energy

distribution curve in a photoelectron emission experiment; ESCA, electron spectroscopy for chemical analysis; EXAFS,

extended X-ray absorption fine structure; FEL, free electron laser; FELIPE, free electron laser internal photoemission; GID,

grazing incidence diffraction; GIT, growth interruption time; GISAXS, grazing incidence small angle X-ray scattering;

GIXRD, grazing incidence X-ray diffraction; HXRD, high-resolution X-ray diffraction; IR, infrared; LASER, light

amplification by stimulated emission of radiation; LED, light-emitting diodes; LEED, low energy electron diffraction; MBE,

molecular beam epitaxy; ML, monolayer; MOCVD, metal-organic chemical vapor deposition; MOVPE, metal-organic vapor-

phase epitaxy; MQW, multi-quantum well; MS, multiple scattering; NEXAFS, near-edge X-ray absorption fine structure;

PDMEE, primary beam diffraction modulated electron emission; PL, photoluminescence; PES, photoelectron spectroscopy;

PEXAFS, photoemission extended X-ray absorption fine structure; QD, quantum dot; QW, quantum well; RHEED, reflection

high-energy electron diffraction; RBS, Rutherford backscattering; RSM, reciprocal space maps; RTA, rapid thermal annealing;

SEXAFS, surface extended X-ray absorption fine structure; SL, superlattice; SQW, single quantum well; SR, synchrotron

radiation; SS, single scattering; STM, scanning tunneling microscopy; TEM, transmission electron microscopy; UHV, ultra-

high vacuum; UPS, ultraviolet photoelectron spectroscopy; UV, ultraviolet; VCA, virtual crystal approximation; VCSEL,

vertical-cavity surface-emitting laser; XANES, X-ray absorption near-edge structure; XAS, X-ray absorption spectroscopy;

XPD, X-ray photoelectron diffraction; XPS, X-ray photoelectron spectroscopy; XRD, X-ray diffraction; XRR, X-ray

reflectivity; XSW, X-ray standing waves; WL, wetting layer* Tel.: þ39-011-6707841; fax: þ39-011-6707855.

E-mail address: [email protected] (C. Lamberti).

exploiting synchrotron radiation (SR) sources. In fact synchrotron radiation has distinct advantages as a photon

source, notably high brilliance and continuous energy spectrum; by using the latter characteristic atomic

selectivity can be obtained and this is of fundamental help to investigate the structural environment of atoms

present only in a few angstrom (A) thick interface layers of heterostructures. The third generation synchrotron

radiation sources have allowed to reach the limit of measuring a monolayer of material, corresponding to about

1014 atoms/cm2. Since, in the last decade, the use of intentionally strained heterostructures has greatly enhanced

the performance of electrical and electro-optical semiconductor, a particular attention will be devoted to

intentionally strained superlattices.

First the effect of strain on the band lineups alignments in strained heterostructures will be discussed deeply.

Then the attention will be focused on to review the most important results obtained by several groups in the

characterization of semiconductor heterostructures using the following structural SR techniques: (i) X-ray

absorption-based techniques such as EXAFS, polarization-dependent EXAFS, surface EXAFS and NEXAFS (or

XANES); (ii) X-ray diffraction-based techniques such as high-resolution XRD, grazing incidence XRD, XRD

reciprocal space maps, X-ray standing waves and diffraction anomalous fine structure (DAFS); (iii)

photoelectron-based techniques.

# 2004 Elsevier B.V. All rights reserved.

PACS: 61.10.-i; 61.10.Ht; 61.10.Kw; 68.49.Uv; 68.55.-a; 73.; 73.21.Cd; 73.40.Kp; 81.05.Dz; 81.05.Ea; 82.80.Pv

Keywords: Synchrotron radiation; Free electron laser; Crystal growth; Epitaxy; Quantum well; Superlattices; Semiconductor

heterostructures; Thin films; Band offsets; Strain; EXAFS; NEXAFS; XRD; DAFS; XSW; XPS; UPS

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1. The technological impact of semiconductor heterostructures: a brief overview. . . . . . . . . . . . 3

1.2. Strained heterostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3. Dynamic interplay among growth techniques, theoretical modeling and characterization

techniques in the design and improvement of semiconductor heterostructure-based devices . . . 10

1.4. Objectives and plan of the review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2. The effect of strain on the band profile of semiconductor heterostructures . . . . . . . . . . . . . . . . . . . 12

2.1. Band alignment in semiconductor heterojunctions: a brief overview . . . . . . . . . . . . . . . . . . . 13

2.2. Calculation of band profiles in strained layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3. The band offsets in strained QWs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4. Band profiles in unstrained or nearly unstrained SQWs with abrupt interfaces . . . . . . . . . . . . 23

2.5. Band profiles in strained SQWs with abrupt interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3. Interfacial layers in semiconductor heterostructures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.1. Interface characterization in real SQWs by means of conventional laboratory techniques . . . . 29

4. Application of EXAFS spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1. Basic concepts of EXAFS spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2. Pioneering works on bulk semiconductor alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3. Applications of EXAFS on semiconductor SL and thin films: the problem of epitaxial strain . . . 41

4.4. The joint role of alloying and epitaxy in determining the first shell bond distances in strained

thin epitaxial layers: the InxGa1�xAs/InP case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.4.1. Bond-length variation in pseudomorphic films . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.4.2. Bond-length variation in strain-released epitaxial films. . . . . . . . . . . . . . . . . . . . . . . 51

2 C. Lamberti / Surface Science Reports 53 (2004) 1–197

4.5. Interface mixing in InxGa1�xAs/InP short period SL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.6. Higher shell data analysis: the necessity of a multiple-scattering approach . . . . . . . . . . . . . . 54

4.7. Polarization-dependent EXAFS studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.7.1. Polarization-dependent EXAFS studies on NiO and MgO films on Ag(001) substrate . . . 64

4.7.2. Polarization-dependent EXAFS studies on conventional IV–IV, III–V and II–VI

semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.8. Surface EXAFS or SEXAFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.9. The near-edge structure: NEXAFS spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5. Application of high-resolution XRD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.1. Basic concepts of XRD applied to SL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.2. Few selected examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.3. In situ XRD studies during growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.4. XRD reciprocal space maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.5. Surface diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6. Application of DAFS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.1. Basic concepts of DAFS applied to SL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114


7. Application of XSW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

7.1. Basic concepts of XSW applied to SL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120


7.3. InxGa1�xAs/InP short period SL: a case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

8. Application of X-ray reflectivity: basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128


9. Application of photoemission spectroscopies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

9.1. Few selected examples using XPS and UPS synchrotron radiation sources . . . . . . . . . . . . . . 139

9.2. Space resolved PES experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

9.3. Internal photoemission spectroscopy: examples using free electron laser sources . . . . . . . . . . 153

9.4. Photoemission extended X-ray absorption fine structure (PEXAFS) . . . . . . . . . . . . . . . . . . . 154

Notes added in Proof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

1. Introduction

1.1. The technological impact of semiconductor heterostructures: a brief overview

III–V, II–VI and IV–IV heterostructures, single-, multiple-quantum wells (SQW, MQW) andsuperlattices (SL) are widely used in an always growing number of high technology devices operatingfrom the mid-IR to the UV regions of the electromagnetic spectrum.

III–V heterostructures have played, and still play, a dominant role in the realization of electronic andoptoelectronic devices employed in modern optical fiber communication systems at 0.9, 1.3 or 1.55 mm(corresponding to 1.38, 0.95 and 0.80 eV, respectively) [1–17] high electron mobility transistors[18–20], single-mode tunable lasers [21–23] and in general for all technological domains requiringremarkable electro-optical characteristics [24–27], mainly due to the optical non-linearities of quantumstructures [11,28–34]. This is mainly the domain of ternary and quaternary alloys of the type

C. Lamberti / Surface Science Reports 53 (2004) 1–197 3

Nomenclature

a lattice parameter of a film in its bulk state (A)ak lattice parameter of a strained film in the growth plane (A)Dak lattice mismatch in the growth plane (A)a? lattice parameter of a strained film in the growth direction (A)Da? lattice mismatch in the growth direction (A)as lattice parameter of the substrate (A)Ac, Av hydrostatic deformation potential of the conduction, valence bandAi(k) amplitude function of the scattering atom of the ith shell(A)n/(B)m superlattice formed by alternating n monolayers of semiconductor A with m

of semiconductor Bb bowing parameter (eV)bh horizontal size of the beambv vertical size of the beamB shear deformation potential for strain of tetragonal symmetry (eV)C11, C12 elastic stiffness constants (dyn cm�2)d periodicity of the standing-wave field (Section 7) (A)dh k l distance between atomic (h k l) planes (A)dinterface interface distance between film and substrate (A)Dexp(yj) experimental XRD pattern (counts)Dfit(y; xi;wi) theoretical XRD pattern (a.u.)E electric field vector of the incoming X-ray beam [N C�1] (only its direction is

relevant here)Eav average over the three uppermost valence bands (eV)DEc discontinuity in conduction band (eV)DECL EB

core � EAcore, energy separation between two core levels of two elements (EA

core

and EBcore) exclusively present in only one side of the heterojunction (eV)

Eexc exciton binding energy (eV)Eg unstrained energy gap (eV)DEg band gap energy difference between two semiconductors (eV)Ehv hydrostatic perturbation energy (eV)Elh, Ehh, Esplit-off lineups in valence band (light, heavy and split-off holes, respectively) for a

strained layer (eV)Et tetragonal distortion perturbation energy (eV)DEvlh, DEvhh,DEvsplit-off

discontinuities in valence band (light, heavy and split-off holes, respectively)

E0 K- or L-edge threshold energy (keV)E0

c unstrained conduction band edge (eV)E0b

c unstrained lineup in conduction band for a bulk-like barrier layer (eV)Ew

c lineup in conduction band for a strained well layer (eV)Ew

lh;Ewhh;E

wsplit-off lineups in valence bands (light, heavy and split-off holes, respectively) for a

strained well layer (eV)


E0lh;E0

hh;E0split-off unstrained valence-band edge (for light, heavy and split-off holes, respectively) (eV)

E0blh ;E

0bhh;E

0bsplit-off unstrained lineups in valence bands (for light, heavy and split-off holes,

respectively) for a bulk-like barrier layer (eV)F coherent fraction in XSW measurementsh Planck constant (eV s)hn energy of the incoming X-ray beam Planck constant (keV)Ie intensity of the electron yield (nA–pA)IF intensity of the fluorescence yield (counts)Il intensity of the monochromatic beam, transmitted by the sample (mA)I0 intensity of the monochromatic (before interaction with the sample) (mA)k photoelectron wavenumber (A�1)k wavenumber vector of the incoming X-ray beam (A�1) (only its direction is

relevant here)kf wavenumber vector of the scattered X-ray beam (A�1)ki wavenumber vector of the incoming X-ray beam (A�1)me, mlh, mhh, G-edge electron, heavy and light hole effective masses (m0)m0 free electron mass (kg)ni refractive indexes of the ith layerNi coordination number of the ith shellNk first shell coordination number in the growth plane for an epitaxial film (Section

4.7.1)N? first shell coordination number in the growth plane for an epitaxial film (Section

4.7.1)NSL number of wells in a SLOh octahedral symmetryP period of a heterostructure (A)P0 coherent position in XSW measurements (Section 7)q ¼ kf � ki transferred wavenumber vector in the scattering process (A�1)r first shell bond distance (A)r1,2(n1, n2) reflectivity coefficient of the interface between medium 1 and 2 (characterized by

refractive indexes of n1 and n2, respectively)rAl

AC; rAlBC first shell AC, BC bond length in the unstrained ternary AxB1�xC alloy (A)

rfAC; r

fBC first shell AC, BC bond length in a pseudo-binary thin film AxB1�xC (A)

r0AC; r

0BC first shell AC, BC bond length in the unstrained binary compounds AC and BC (A)

drAlAC; drAl

BC first shell AC, BC bond distances variation induced by alloying effect (A)

drfAC; drf

BC first shell AC, BC bond distances variation induced both by alloying and strainedeffects (A)

drstAC; drst

BC first shell AC, BC distances variation in a epitaxial film due only to tetragonaldistortion produced by strain (A)

R experimentally measured reflectivity R ¼ jrj2Rk first shell bond distance in the growth plane for an epitaxial film (A) (Section 4.7.1)DRk first shell bond distance variation in the growth plane for an epitaxial film (A)

(Section 4.7.1)


R? first shell bond distance in the [0 0 1] direction for an epitaxial film (A) (Section 4.7.1)DR? first shell bond distance variation in the [0 0 1] direction for an epitaxial film (A)

(Section 4.7.1)R(y) reflectivity (Section 7)T thickness of an epitaxial film (A) or (ML)Tc critical thickness of an epitaxial film before strain release (A)Td tetrahedral symmetryT0 kinetic energy of photoelectron (eV)T0 characteristic temperature of a laser devicew well width of a QW structure (A)x sample thickness (cm)Y(y) normalized XSW field intensity distribution

Greek lettersaf angle at which the X-ray beam scattered from the single crystal surface is collected

by the detector (8)ai incidence angle of the X-ray beam on the single crystal surface (8)g Poisson’s ratioD0 spin–orbit coupling (eV)ek parallel straine? perpendicular strainy Bragg angle (8)yi angle between the ith interface and the X-ray beam direction (8)y0 angle between the electric field vector E of the X-ray beam and the normal to the

crystal surface, usually the [0 0 1] direction; it is used in polarization-dependentEXAFS studies (8)

yh k l angle of the [h k l] Bragg reflection (8)Dy0 the angular difference between the substrate and the zeroth-order SL peak (8)l photoelectron mean-free path (A)l0 X-ray wavelength (A)m(E) or m(k) absorption coefficientm0(k) atomic like absorption coefficientn(y) phase between the incident and diffracted X-ray waves (Section 7)x force disorder parameterx0 known energy difference between the core-level binding energies of two elements

(eV)s roughness parameter of a surface (A)si Debye–Waller factor of the ith shell (A)f work function in an electron photoemission experiment (eV)ji(k) phase function of the couple absorber–scatterer in the ith shellw(k) overall EXAFS functionwi(k) contribution of the ith coordination shell to the overall EXAFS function


InGaAlAsP, because the energy gaps of the corresponding binary system, EgðInAsÞ ¼ 0:41 eV;EgðInPÞ ¼ 1:42 eV; EgðGaAsÞ ¼ 1:52 eV and EgðGaPÞ ¼ 2:87 eV, EgðAlAsÞ ¼ 2:15 eV and EgðAlPÞ ¼2:45 eV, allow to cover the whole range of interest for optical fiber communication. In this field, themost common systems are GaAlAs [35–41], InGaAs [35,36,38,41–46], InGaAlAs [35,36,44] andInGaAsP [21,23,47–51].

More recently, also the GaInNAs system has become of interest because the incorporation of verysmall amounts of nitrogen (a few percent) into III-As materials leads to a dramatic decrease in the bandgap energy1 [52–55] and has enabled the growth of GaAs-based laser diodes functioning in the 1.3–1.55 mm range, suitable for optical fiber transmission. Meanwhile, the smaller nitrogen atom reducesthe lattice parameter of these films, and reduces the strain in epilayers with respect to that observed forsystems containing the larger In or Sb atoms. Moreover, the presence of nitrogen strongly improve theelectron confinement as a consequence of the increased conduction band discontinuity (DEc)

2

[54,56,57], allowing the devices to work at much higher temperatures with respect to that ofconventional systems. As an example, GaInNAs/GaAs vertical-cavity surface-emitting laser (VCSEL)operating at 1.3 mm have been realized [58–60] with a characteristic temperature (T0) as high as 215 K[61], to be compared with T0 values in the 50–100 K range for the more conventional InGaAsP/InPlasers [54].

The realization of devices operating in the mid-IR region is important, not only fortelecommunication, but also for gas-sensing (environmental physical chemistry) and heat-sensing(military application). It can be achieved either by introducing the large antimony anion into theclassical InGaAsP semiconductor alloys or by using the II–VI HgCdTe ternary system [62,63]. As theenergy gaps of antimony-based binary systems given by EgðInSbÞ ¼ 0:17 eV and EgðGaSbÞ ¼ 0:73 eV,very low energy gaps can be obtained for the InGaSb ternary and InGaAsSb quaternary systems[64,65]. InAs/InAsSb heterostructures are the most powerful LED emitters beyond 5 mm (below0.25 eV) [66] and incoherent LED emission has been observed up to 11 mm (down to 0.11 eV) [67],but coherent laser emission has been achieved only in the narrow 3.3–3.8 mm (0.38–0.33 eV) region[68,69]. InAsSb/InAsSbP double heterostructure resulted in high power LED devices [70,71].

Coming to the II–VI HgCdTe ternary system [72], HgTe is a semi-metal with a negative energy gapEgðCdTeÞ ¼ �0:26 eV, while EgðCdTeÞ ¼ 1:57 eV, therefore very long wavelength operating devicescan be realized [73–75]. Potentially, the band gap of CdTe/HgTe SL is adjustable from 0 to 1.6 eVdepending on the thickness of the CdTe and HgTe layers [73]. Double-heterostructure HgCdTeinjection lasers emitting at 2.86 mm (0.43 eV) have been realized [76]. InGaAsSb quantum wells andInAs/InGaSb superlattices are found to be more promising laser candidates than HgCdTe superlatticesand InAsSb bulk ternaries. The calculated threshold current densities of InAs/InGaSb superlattices aresimilar to those of InGaAsSb active layers operating at 2.1 mm (0.59 eV), but are significantly lower atlonger wavelengths [63]. As far as low energy lasers are concerned, more recently, high-power quantumcascade lasers based on intersubband transitions in a MQW heterostructure have been realized in themid-infrared (IR) (l > 4 mm, hn < 0:31 eV) region mainly by the Capasso’s group [77–83].

1 The observed red-shift of the energy gap in the family of so-called ‘‘dilute nitrides’’, alloys (GaNyAs1�y, InxGa1�xNyAs1�y

and GaNyAs1�y�zSbz systems) contrasts the well-known chemical trend of conventional III–V alloys for which a smaller

lattice constant a results in a blue shift of the energy gap. The large electronegativity of N and its small ionic radius result in a

strong bowing parameter which, in turns, decreases the band gap of the alloy [52–55].2 For a more formal definition of DEg, DEc and DEv vide infra Section 2.3 and Fig. 5.


On the opposite side of the electromagnetic spectrum, wide-gap II–VI compounds such as ZnCdSSequaternary and ZnSSe ternary compounds [84,85] and group III nitride semiconductors [86] shear thefield of visible and UV light emitters. As for the II–VI ZnCdSSe system CdSe/ZnSSe quantum islandlaser [87] and ZnSe/ZnCdSe [88] QW lasers [88,89], have been successfully realized. Yellow-greenZnCdSe/BeZnTe II–VI laser diodes emitting at 0.56 mm II–VI laser diodes were successfully grown onInP substrates [90]. Great progress has recently been made in research and fabrication of optoelectronicdevices based on the group III nitride semiconductors [86]. One of the attractive features of the nitridesemiconductors is that their direct band gaps span most of the visible spectrum, into the UV, as theenergy gaps of the corresponding binary systems is: EgðInNÞ ¼ 1:89 eV; EgðGaNÞ ¼ 3:44 eV;EgðAlNÞ ¼ 6:28 eV. Appropriate alloying allows formation of ternary or quaternary alloys with bandgaps intermediate to those of the binary compounds. This feature is widely used in band-structureengineering of nitride-based devices; for instance, most light emitters contain an active regionconsisting of an InGaN layer with band gap lower than that of GaN [91,92]. The AlxGa1�xN system hasbeen used as cladding layer for LEDs in the UV region of the spectrum [93–95]. The GaxIn1�xN-basedquantum optoelectronic devices play an important role as light emitter and detectors from the UV to theblue/green region of the electromagnetic spectrum [92,96]. Finally, the AlxIn1�xN system is ofparticular interest, as it is lattice matched to GaN for x ¼ 0:83. High-performance AlGaN/GaInN QWlasers have been realized [97,98]. These are the reasons why, in a remarkably short space of time, thenitrides have caught up with and, in some ways, surpassed the wide band gap II–VI compounds(ZnCdSSe) as materials for short wavelength optoelectronic devices [86].

Finally, group IV materials, in sp3 hybridization, exhibit a band structure that moves from theinsulating diamond to the extremely narrow energy gap of tin: EgðCÞ ¼ 5:33 eV; EgðSiÞ ¼ 1:14 eV;EgðGeÞ ¼ 0:67 eV; EgðSnÞ ¼ 0:08 eV. The indirect nature of the band gap in group IV materials makessuch materials unsuitable for large-scale use in optoelectronic technologies up to now. However, severalattempts have been made to modify the band gap structure of group IV semiconductors in order toobtain direct gap materials [99–106]. It has been shown that alloying silicon with a few percent ofcarbon can render the band gap direct with strong optical absorption, provided the carbon atoms areordered [104]. The addition of carbon introduces a significant s character into the conduction bandminimum, resulting in a large dipole matrix element. The direct energy gap has been measured forcoherently strained SnxGe1�x alloys on Ge(0 0 1) substrates with 0:035 < x < 0:115 and film thickness50–200 nm [103,105]. The energy gap for coherently strained SnxGe1�x alloys indicates a large alloycontribution and a small strain contribution to the decrease in direct energy gap with increasing Sncomposition. These results are consistent with a deformation potential model for changes in the valenceand conduction band density of states (DOS) with coherency strain for this alloy system [105]. Yangand co-workers have very recently made great progresses in the synthesis and characterization of one-dimensional Si/SiGe SLs exhibiting great potential for applications in electronics because they couldfunction as a transistor, light-emitting diode, biochemical sensor, and heat-pumping thermoelectricdevice simultaneously [107]. The advantages of SiGeC/Si for optoelectronic devices are adjustablestrain, band gap, and band offsets; all of which come from tailoring the Si1�x�yGexCy composition. Itfelt that SiGeC would offer the same band offsets as SiGe/Si with less strain. Substitution of C atomsfor Ge atoms in SiGe/Si compensates for Ge-induced strain because of carbon’s smaller atomic size.Perfect compensation (zero net strain) occurs when the x–y choice gives a lattice match to Si [103].

On an other hand, with the rapid development of very large-scale integration technology, the numberof components per integrated circuit chip is increasing considerably and the power density increases


accordingly. Device performance and reliability degrade significantly when devices are overheated.Heat generation and thermal management are becoming one of the barriers to further increases in clockspeed and decreases of feature size. As SiGe is a good thermoelectric material for high temperatureapplications [108], SiGe/Si and SiGe/SiGe SLs structures are used to enhance the cooler performanceby reducing the thermal conductivity between the hot and the cold junctions [109,110] and by selectiveemission of hot carriers above the barrier layers in the thermionic emission process [111]. Si and SiGedevices can integrate directly with these coolers to achieve an high device performance [100,112,113].The SiGe technology has also found applications in the field of solar cells [114,115].

Finally, the development of SiC research is mainly supported and justified by the needs to elaborate anew generation of devices, which can work in very extreme conditions. Because of this need, SiC-baseddevices have been considered as an alternative to the silicon and silicon-based devices, which arecurrently playing an important role in modern semiconductor electronic, and optoelectronic device. Theheterostructure SiC/GaN/AlN is also guessed for laser devices applications emitting in the blue/ultraviolet spectrum which are characterized by high thermal conductivity, high breakdown electricfield, high forward current density, high saturated electron drift velocity, high electronic mobility andhigh blocking voltage [116].

1.2. Strained heterostructures

High quality devices can be realized only if the layers forming the heterostructure exhibit a perfectcrystallinity, a request that can in turn be fulfilled only if the lattice parameter of the epitaxial layer (a)is almost equal to that of the substrate (as). By ‘‘almost’’ we mean that ja � asj=a should be in the orderof few units in 10�4. In such a case we are under lattice match conditions and very thick films can begrown under pseudomorphic regime. Conversely, for ja � asj=a in the order of some units in 10�3, weare under lattice mismatch conditions and only thin epitaxial film can be deposited on the substrateunder pseudomorphic regime. The maximum growth thickness for a pseudomorphic film on a givensubstrate is called thickness Tc and its value decreases dramatically by increasing ja � asj=a. Such filmsare strained and the cell of their lattice is distorted to fit with the substrate cell. Notwithstanding thegreat technological problems related to the growth of pseudomorphic strained films, the use ofintentionally strained heterostructures has greatly enhanced the performances of electronic andoptoelectronic devices [117,118]. In fact, strain-based heterostructures offer further advantages in thatthe energy band lineups can be shifted by the strain (vide infra Section 2.2), giving an added flexibilityin the design of the devices [119]. The presence of strain reduces the crystal symmetry and modifies theenergy band lineups [15,117,118,120–125] (vide infra Section 2.2). This is the reason why the effectsof strain have been employed in the field of: InGaAs/InP [43,46,49,126], InGaAs/GaAs [127], InAsP/InP [128], GaAs/AlGaAs [37,129], InGaAs/AlAs [130], InGaAs/InGaAlAs [35], InGaAs/InGaAsP [48]QW lasers; compressive-strained InGaAsP QW lasers [44,131–133]; tensile-strained GaAs1�yPy/Al0.35Ga0.65As QW lasers [39]; alternating tensile/compressive (i.e. zero net strain) InGaAsP QW lasers[47,134]; InGaAs/InP avalanche photodetectors [135] (see also the recent review by Brennanm andHaralson [136]); InGaAs/GaAs high-transconductance p-channel field-effect transistors [137,138];AlGaN/GaN field-effect transistors [139]; AlInAs/InGaAs [140–142] and AlGaAs/GaAs [19] highelectron mobility transistors; strained InAs/InAsSb [64] and InGaAsSb/AlGaAsSb [65] mid-IR lasers;strain-compensated InAsP/InGaP electroabsorption modulators [143]; high-performance AlGaN/GaInN strain-compensated QW lasers [97,98]; InGaAsSb/AlGaAsSb QW mid-IR lasers [65,144];


and high power LEDs (mid-IR emitting) InAs/InAsSb strained SL [145]. Coming to IV–IV-basedheterostructures, Si1�xGex=Si strained alloys and SL results particularly attracting for the achievementof novel microdevices directly integrable in the Si-based technology [100,112,113], vide supra.

On the other hand, even for intentionally unstrained heterostructures, several studies [146–163] haveshown that undesirable strained monolayers (MLs) are present at the heterointerfaces. The presence ofstrained interface layers is related to the impossibility to realize, during the growth, instantaneousswitches between wells and barriers. This compositional interface chemical gradient, spreading over adistance of some MLs has been observed by several groups for different systems [40,45,127,146,158–167]. It is well known that the performances of the processed devices are influenced by the quality ofthe interfaces [42,168]. In fact, interface crystalline imperfections—such as planarity andcompositional grading [147]—cause scattering processes, yielding to a reduction of the exciton decaytime [169,170], to a limitation on the electron mobility [171] and to an increase of the non-radiativerecombination [127,172]. It is hence evident that a detailed characterization of the interfacial layers isvery important for their optimization. This implies again the need of studying the properties of strainedlayers. This is the reason why the consequences of strain on II–VI, III–V and IV–IV semiconductorheterostructures have been investigated so widely on both experimental and theoretical grounds[12,15,17,38,117,142,160,162–167,173–203].

1.3. Dynamic interplay among growth techniques, theoretical modeling and characterizationtechniques in the design and improvement of semiconductor heterostructure-based devices

Improvements in the realization of the devices above mentioned have been realized by a strictinterplay among the progress achieved on three grounds: (A) theoretical solid-state physics (or quantumchemistry) aimed to predict the characteristic of an ideal heterostructure [162–164,194,200,204–275];(B) epitaxial growth techniques aimed to realize heterostructure as close as possible to the desiredtarget [43,84,85,92,116,118,131,147,149,152,155,158,159,161,276–294] and (C) sophisticated char-acterization techniques aimed to verify the closeness between the target and the real heterostructure[147,158–161,164–167,188–191,279,281,287,288,291–313]. Of particular interest are the in situcharacterization techniques performed during heterostructure growth and thus combining directlytopics (B) and (C) [287,288,292–294,296,297]. In this field, beside the classical electron and ionsurface probes, used in laboratory, synchrotron radiation (SR) techniques have shown tremendouspotentialities [287,292–294,296,297].

The interplay among the fields (A), (B) and (C) can be basically schematized in the following flowchard: (i) theoretical solid-state physics predicts the physical properties of a given heterostructure; (ii)epitaxial growth techniques try to realize it; (iii) structural characterization techniques check whether theactually realized heterostructure corresponds to the desired one or not; (iiia) if not the growth parametershave to be optimized and step (ii) has to be repeated; (iiib) if yes, then optical, electrical and electroniccharacterization techniques check weather the desired heterostructure has actually the foreseen physicalproperties; (iva) if not then the level of theory used in step (i) has to be improved and the game has torestart again from the beginning; (ivb) if yes then, end of the story. Point (ivb) represents the final point ofthe scientific work and the future of the device lies now on an engineering/economical level where theproduction rate, the realization costs and the demand of the device are the main driving forces. Of course,the interplay can also move in the opposite direction, e.g. when theoretical models help in theinterpretation of previous non-understood (or wrongly interpreted) experimental results.


Stimulation for the improvement of each of the three branches (A–C) originates from the requestscoming from the remaining two. A short and non-exhaustive list of examples follows: the need ofrealizing short period SL has improved the realization of fast switches apparatus in the growthchambers; the need of having flat interfaces for testing theoretical models and innovativecharacterization techniques on an almost ideal heterostructure has stimulated the born of atomic layerepitaxy (ALE, which is useless on an industrial scale due to the too low growth rate); the need ofcharacterizing ML-thick interfaces has stimulated the development of sophisticated and powerfulcharacterization techniques (such as those based on synchrotron radiation); high quality experimentalresults have given important check values for ab initio models, while unexpected experimental resultshave asked for an improvement of the level of theory used so far, etc.

1.4. Objectives and plan of the review

It is evident that the global problem just mentioned in Section 1.3 is so large to need several books tobe faced. The aim of this review is then focused on a subset of topic (C), mainly synchrotron radiation-based techniques, which still remain a pretty large topic. In this domain we find both structural andelectronic characterization techniques i.e. what needed to face points (iii) and (iv) of the ideal flowchard discussed in the previous section. Of course, when needed the interplay between results obtainedfrom synchrotron radiation techniques and other characterization techniques, theoretical models andgrowth techniques will be underlined.

The important role played by synchrotron radiation techniques in the characterization ofsemiconductor heterostructures is due to the fact that synchrotron radiation has distinct advantagesas a photon source, notably high brilliance and continuous energy spectrum [314–326], see Fig. 1. Byusing the latter characteristic atomic selectivity can be obtained and this is of fundamental help toinvestigate the structural environment of atoms present only in a few angstrom (A) thick interfacelayers of heterostructures. The third generation synchrotron radiation sources have allowed reaching thelimit of measuring a monolayer of material, corresponding to about 1014 atoms/cm2.

The materials of interest are the semiconductor heterostructures (QW, MQW and SL) mentioned inSections 1.1 and 1.2 but, when needed, also thin films are discussed, because they represent a lesscomplex systems with respect to the heterostructures used in the devices, from which the fundamentalphysics of epitaxy and lattice strain can be learnt easier.

This review begins with a brief overview on the theoretical fundamentals of band alignment instrained heterostructures (Sections 2.1–2.3), followed by a detailed analysis of band profiles in idealsemiconductor heterostructures characterized by chemically abrupt interfaces (Sections 2.4 and 2.5). InSection 2, the effect that the parallel (ek) and the perpendicular (e?) strain have on the band alignment isdefined. In Section 3 the problems related with the growth of a real heterostructure are briefly discussedtogether with the consequences that the actual (non-ideal) composition of the heterostructure has on itsbands profile. The conventional characterization techniques used to investigate the interface quality isdiscussed in Section 3.1. The following five sections are devoted to describe five structuralcharacterization techniques that give direct information on ek, e? and on the interface mixing of theheterostructures: extended X-ray absorption fine structure (XAFS; Section 4); high-resolution XRD(Section 5); diffraction anomalous fine structure (DAFS; Section 6); X-ray standing waves (XSW;Section 7) and X-ray reflectivity (Section 8). Finally, Section 9, discuss the results obtained with X-rayphotoemission spectroscopies and closes the loop, giving access to the experimental values for the band


offsets, predicted in accord to the methods described in Section 2 for a given strain (which can bemeasured with the techniques described in Sections 5–8).

Each section is divided into subsection, whose content is briefly summarized at the begin of thesection. The different sections can be read separately, this allows the reader interested on a givencharacterization technique to focus his attention on the corresponding section only. There are severaltopics that are discussed along the review in the different sections because different characterizationtechniques have provided important information. In such cases, in all sections where the topic has beentreated reminds to the other pertinent sections are made.

2. The effect of strain on the band profile of semiconductor heterostructures

This section is divided into five subsections. The first one presents an overview of theoretical modelsof band alignment in semiconductor heterojunctions. Representing a good compromise between

Fig. 1. Comparison of calculated average spectral brilliance of the various synchrotron radiation sources. Reprinted from

S.M. Gruner, et al., Rev. Sci. Instr. 73 (2002) 1402, [315], with permission. Copyright (2002) by the American Institute of

Physics.


accuracy and simplicity, a brief description of the ‘‘model solid’’ method developed by Van de Walleand Martin [194,204–207,327] will be given in Section 2.2. The definition of the band offsets instrained QW structures is reported in Section 2.3. The application of the Van de Walle and Martin‘‘model solid’’ theory to the calculation of the band offsets in different unstrained and strainedsemiconductor QW structures is then reported in Sections 2.4 and 2.5, respectively.

2.1. Band alignment in semiconductor heterojunctions: a brief overview

A major problem in deriving the valence and conduction band lineups at heterojunctions is that, foran infinite (bulk) solid, there is no intrinsic (absolute) energy scale to which energies are referred[12,15,194,204–207,328,329]. The reason for this ambiguity is related to the long-range action of theCoulomb interaction, causing that the zero point of energy is undefined for a bulk semiconductor[194,205]. Kleinman [328] demonstrated this arbitrarity by showing that the zero value in the potentialenergy of a solid depends on how one performs the conditionally convergent Coulomb summation. Thearbitrary choice of potential energy zero is inconsequential in case of a bulk (infinite) semiconductor,but it introduces a problem when two dissimilar crystals are joined to form a heterostructure. In the latercase, it is essential to choose a common reference energy for both crystals.

If we imagine two semiconductors A and B, with EgðAÞ > EgðBÞ, then, when the heterostructureA/B/A is formed, A will act as barrier and B as well. In such a case, the band gap energy differencebetween the two semiconductor crystals, DEg ¼ EgðAÞ � EgðBÞ, is accommodated by both theconduction and valence bands. That is, DEg ¼ DEc þ DEv, where DEc and DEv are the conduction andvalence-band offsets, respectively (see Fig. 2) (see footnote 2). If we arbitrarily fix the bottom of theconduction band in A, then the top of the valence band in A is fixed by the Eg(A) parameter. Now, asdiscussed above, the problem comes when we try to put the bottom of the conduction band in B, andthus the top of its valence band, fixed by Eg(B). If it lies just below the bottom of the conduction band

Fig. 2. Pictorial representation of different ways how the energy gap difference DEg between the barrier (A) and the well (B)

can be shared between DEc and DEv in a A/B/A QW structure. (a)–(c) represent a type I band alignment, where both DEc and

DEv are positive; (d) represents a type II band alignment, where DEv is negative.


of A (Fig. 2a), then electrons will be poorly confined while holes will be well in B. Now, if we imagineto rigidly translate the bottom of the conduction band and the top of the valence band of B downwardswith respect to the corresponding levels of A, we progressively move to situations shown in parts (b)and (c) of Fig. 2, where the electrons confinement improves to the detriment of the holes confinement.Situations schematized in parts (a)–(c) of Fig. 2 are called type I band alignment since both DEc andDEv are positive. This is the case of, e.g. GaAs=AlxGa1�xAs (in the direct-gap range) [330],In0.53Ga0.47As/InP [162,331], In0.53Ga0.47As/In0.52Al0.48As [331], GaSb–AlSb [332], AlGaAs/GaAs[17], InAsP/InP [164], GIn0.65Ga0.35As0.983N0.017/GaAs [333], GaS/GaAs(0 0 1) [283] heterostructures.If we continue the downward translation of B levels, the top of the valence band of B will lie below thatof A, DEv becomes negative and the holes will be no more confined in B (Fig. 2d). In such a case we aredealing with a type II band alignment where the radiative recombination occurs between electrons in Band holes in A. This is the case of, e.g. InP/In0.52Al0.48As [334], InAs/GaSb [335], InAs/AlSb [336];GaInAsSb/GaSb [337], cubic GaN/hexagonal GaN [338], Ga0.7As0.3Sb/GaAs [333] and CdSe/ZnTe[339] heterostructures. It is so evident that the partition of DEg between DEc and DEv and the type ofthe band alignment strongly influences the physical properties of the heterostructure [12,15,267,310,311,329,330,339–344] and thus its knowledge is of fundamental importance.

The band lineups and related band offsets in semiconductor interfaces have been investigated byvarious experimental techniques, including: (i) capacitance–voltage [345–349]; (ii) photocurrent–voltage [350,351]; (iii) magneto-photoluminescence [352]; (iv) photoluminescence excitation [353]; (v)Raman spectroscopy [281,354–361]; (vi) admittance spectroscopy [362,363]; (vii) picosecond-resolvedtransient absorption spectroscopy [364]; (viii) internal photoemission [310,311,321,365–370], oftenperformed using free electron laser (FEL, vide infra Section 9.3) sources; and (ix) X-ray photoemissionspectroscopy [15,208,286,309–312,321,341,368,369,371–381], mainly performed with synchrotronradiation sources (vide infra Section 9.1). Several authors have been in search of an empirical scalingrule between the valence-band lineup and the band gap discontinuity for a large number ofsemiconductor heterostructures, i.e. DEv/DEg constant. The accuracy of this rule is only marginallysufficient for modern device engineering [199,208,260,346–348,354–359,362–364,376,378–380,382–384].

Beside this phenomenological approach, there exist in the literature more sophisticated theoreticalmodels for band lineup calculations [162–164,194,200,204–275]. The first theoretical approach fordetermining the band lineups was the electron affinity rule developed by Anderson [209], which is theequivalent of the Schottky model in the case of semiconductor–semiconductor heterojunction interfaces[385,386]. This rule and its improved versions [210,211] assume that the energy difference between theconduction band and the vacuum level (as measured from the surface) is a fixed quantity. Also worthmentioning are the Van Vechten’s dielectric model [213,214] and the common anion rule [212], whichstates that compound semiconductors with the same anion will form an interface with near zerovalence-band discontinuity. Harrison has certainly been one of the major contributing scientists in thisfield. He has developed a theory based on the linear combination of atomic orbitals (LCAO),establishing an absolute energy scale by referring all energies to the eigenvalues of a free atom[215,217]. His re-determination of the coupling parameters among atomic orbitals on neighboringatoms [216] (incorporating the additional atomic orbital perturbation theory developed by Louie [218])is able to fit in a stable way a large set of band parameters. Harrison has also introduced the concept ofoverlap repulsion among atoms in covalent and ionic solids [219,220]. He has also studied the Coulombeffects, including self-consistency and many-body enhancement of the energy gap in semiconductors


and insulators [221]. In a subsequent work, Klepeis and Harrison [223] have performed a self-consistent tight-binding calculation of the charge redistribution in semiconductor bonds in the presenceof substitutional impurity atoms, with the inclusion of Coulomb interactions, and later have extendedthe model to polar semiconductors. The effect of an interface dipole on the band lineups has also beeninvestigated, e.g. by Zur and McGill [225], Ruan and Ching [226] and Munoz et al. [254]. As anexample, Ishikawa and Bowers [260] have computed the band lineups of strained InGaAlAs/InP basedon the Harrison model [215,217]. In this regard the work of Bastard and Ferreira on the Ga(In)Al-basedheterostructures should also be mentioned [263]. Chen et al. have calculated band lineups and confinedenergy levels of strained Si on GaAs(0 0 1) via a pseudopotential method [387].

Frensley and Kroemer, using local pseudopotential calculations, have attempted to identify areference level in each semiconductor that would correspond to the vacuum level [227,228]; theresulting band lineups are independent of the crystallographic orientation of the heterojunction. Tejdorand Flores [229,230] and Tersoff [231–235] have introduced for each semiconductor an energyneutrality level, which will be aligned when an interface is formed, thus fixing the band offsets at theheterojunctions. In the context of the tight-binding theory, the neutrality level approach corresponds tothe average hybrid energies of each crystal [236]. Tersoff [231–236] has extensively discussed the roleplayed by interface dipoles in the determination of heterojunction band lineups. Also Zunger’s model[237] has to be mentioned. A few years later, Wei and Zunger have computed the valence-band offsetsof different AC/BC semiconductor heterojunctions from core-level energies [238]. They express DEv asa sum of a bulk contribution (characteristic of the two separate bulk crystals) and an interface-specific

contribution, which takes into account the charge transfer at the interface and subsequently the dipolestrength. They conclude that the latter term plays a minor role in the determination of DEv and can thus,to the first-order approximation, be neglected. Verges et al. [239] have developed, in the framework oflinear muffin-tin orbitals, a scheme to establish an absolute energy reference level for Si and Gesemiconductors.

Several groups have performed self-consistent pseudopotential calculations to determine the energyband structure of alternating binary compounds (AC)m/(BC)n strained SL, such as (InAs)m/(GaAs)m

[240–243], (AlAs)m/(GaAs)n [244,245,248] and (GaP)1/(InP)1 [249], as well as the GaAs/Ge SL[250,251,253,254].

The effect of biaxial strain on the valence bands in GaN/AlGaN QWs has been investigated by Niwaet al. [388] using the tight-binding method. Van de Walle et al. have investigated the band lineupsbetween GaN and InN, as well as InGaN alloys, using first-principles calculations with explicitinclusion of strains and atomic relaxations at the interface [91,389]. Bhouri et al. [390], on the basis of amodel solid theory, have calculated the band discontinuities for heterointerfaces between strainedAl1�xGaxN and relaxed Al1�yGayN over an entire compositional range. From first principles, Binggeliet al. [391] have examined the band offsets of zinc blende, wurtzite, or mixed zinc blende/wurtziteGaN/AlN, GaN/SiC and AlN/SiC, and their dependence on various structural and chemical propertiesof the interfaces. It was shown that a change from a cubic (1 1 1) to a hexagonal (0 0 0 1) polytypetransformation in nitride-based heterostructures, will selectively affect the conduction band offset andhave only a minor influence on the valence-band discontinuity. Bernardini and Fiorentini [392] havereported an ab initio calculation of prototypical polar interfaces of wurtzite III–V nitrides, showing thata large polarization-induced electric field exists in epitaxial nitride heterostructures. The determinationof the potential lineup has been obtained via a multipole decomposition of the macroscopicallyaveraged interface charge density. The authors also report a large strain-induced asymmetry of the


offset, and tiny interface formation energies. Growth conditions, optical properties, luminescencetransitions and band offsets of the GaInNAs/GaAS system have recently been reviewed by Pan [54].

In the last two decades, several refined theoretical models have been developed to solve the problemof electrons and holes confined in a QW. Among all, the envelope function theory [12,269,393–404]especially conceived for SL simulations is worth noticing. The most of the hereafter mentionedreferences uses the envelope function formalism. The transfer matrix method has been used by severalauthors [405–408]; also the finite element method proposed by Nakamura et al. [409] is based on thetransfer matrix method. Tang et al. [410] have solved both Schrodinger and Poisson equations using anon-uniform mesh size scheme combined with the finite difference method. A similar approach wasused by Abraham et al. for the Al0.46In0.54As/InP system [411]. Variational methods [412,413],particularly useful in the presence of an external electric field, have also given rise to good results; notethat the Monte Carlo method developed by Singh [414] is based on a variational approach. Also thestabilization method of quantum chemistry has been used to compute the quantized energy levels [415].Campi and Coriasso [30] have reported an analytical approximation of the optical properties ofelectron, heavy- and light-hole bands in an In1�xGaxAs/InP QW, based on an improved 2D version ofthe Elliott formula. The Elliott formula, initially developed for 3D systems [416], was reformulated forrather idealized 2D systems by Shinada and Sugano [417]. The Shinada–Sugano formula neglects thefollowing aspects [417]: (i) the broadening mechanism that causes the excitonic peaks to acquire afinite spectral width; (ii) the effects of a finite width of the QW on the binding energy and oscillatorstrength of the exciton and (iii) the splitting of the valence band into lh, hh and split-off subbands.Campi and Coriasso [30] have improved the Shinada–Sugano model by taking into account these threeeffects. The authors compare analytical results with numerical solutions achieved within a morecomplete many-body approach and with experimental results.

More recently, Delerue et al. [418] have reviewed the application of the empirical tight-bindingapproximation for complex semiconductor systems. Lin-Chung and Yang have performed tight-bindingcalculations of electronic structures for (0 0 1)-(InAs)n/(InSb)m strained superlattices [419]. Thedependence of the superlattice band gap energy on the band offsets between InAs and InSb has beenexamined. In the same year, Ivanov et al. [420] reported, for the first time, a new hybrid Al(Ga)Sb/InAs/Cd(Mg)Se heterostructures grown by MBE. In the quoted paper, the authors investigated the structural,luminescence and transport properties of the new heterostructure. Theoretical estimations of bandlineups in these structures predict type II band alignment for the InAs/CdSr interface, which transformsto type I with increasing the Mg content in a CdMgSe alloy. A valence-band offset as large as 1.6 eV isexpected at the InAs/Cd(Mg)Se interface. The results of electron transport measurements along theinterface are in good agreement with the theoretical estimation.

The surface passivation (saturation of surface dangling bonds) is an important process in therealization of high-quality and reliable semiconductor electronic devices because it avoids theformation of the undesired oxide layers [421,422]. Due to the importance of the S passivation of III–Vsemiconductor surfaces the band diagram of the GaS/GaAs(0 0 1), reported in [283], merits to beremarked.

For readers who are interested in the problem of band alignment in 1D (quantum wires) and 0D(quantum dots) systems, they are referred to Refs. [423,424]. The recent and exhaustive reviews ofShchukin and Bimberg [425], Reimann and Manninen [426] and Yoffe [427] represent excellentreferences for all scientists interested in semiconductor quantum dots and related systems on bothexperimental and theoretical levels. Note that Ref. [427] represents an update of Yoffe’s famous review


appeared in 1993 [428]. Also Acobi’s review, focused on InAs quantum dots on GaAs is worthmentioning [429].

Coming back to the Van de Walle and Martin work [194,204–207], they have presented a first-principle approach to derive the relative energies of valence and conduction bands at semiconductorinterfaces. They have performed self-consistent density functional calculation using ab initio non-localpseudopotentials allowing to derive the minimum energy structure and band offset for specificinterfaces, which are in reasonable good agreement with the experimental results. They have found that,within the accuracy of their model, band offsets are independent of interface orientation and obey thetransitivity rule. Moreover, based on a full-interface calculation [194], Van de Walle and Martin havedeveloped the model solid theory, which represents an excellent compromise between accuracy andsimplicity. First, a reference energy of each material is defined as the average pseudopotential in amodel solid, in which the charge density is constructed as a superposition of neutral pseudo-atomicdensities. The obtained reference level depends on the density of each type of atom and on the detailedform of the atomic charge density, which must be chosen consistently for different materials. Then thebulk band structures of the two semiconductors are aligned according to these average potentialpositions. A remarkable agreement is achieved [194] between the model solid approach and thecomputation-intensive, full-interface calculations. This method has been adopted to calculate the banddiscontinuity of the strained heterojunctions by several groups to study the dependence on strain of thevalence and conduction bands in several quaternary III–V semiconductors. Among all we remain withthe following systems: GexSi1�x/Si heterostructures on GeySi1�y(0 0 1) substrates by People and Bean[119]; In1�xGaxAs/InP by Wang and Stringfellow [173]; InAsyP1�y/InP by Lamberti et al. [164];In1�xGaxAsyP1�y/In1�vGavAswP1�w by Lamberti [162,163] and Krijn [430]. Using the model solid

theory, Cai et al. [141] have investigated the band alignment for lattice-matched AlxGa1�xSbAs/InGaAsheterostructures (0 � x � 1) grown on InP. In a subsequent work [351], Cai et al. have extended thestudy to AlxGal�xSbAs/InAlAs, again lattice matched to InP. The calculated offset values are inqualitative agreement with temperature-dependent current–voltage measurements.

2.2. Calculation of band profiles in strained layers

For both brevity and simplicity, this subsection is devoted to the band lineups in strained zinc blendeheterostructures. This choice is also justified by the fact that most of the binary, ternary and quaternarysemiconductor alloys exhibits the zinc blende structure.

Exception is made for a number of II–VI compounds, such as CdS, and for group III nitrides (AlN,GaN and InN, and related alloys) that crystallize preferentially in the hexagonal wurtzite structure.Note, however, that the cubic, zinc blende form is known for all the mentioned nitrides compounds andin particular cubic GaN has been widely investigated. It also appears that the cubic form of group IIInitrides gives higher electron and hole mobilities than the hexagonal form. The lower symmetry of thedominant hexagonal structure gives rise to three separate valence bands at the zone center even forunstrained layers. However, most of the group III nitrides materials consist of epitaxial thin films grownon non-lattice-matched substrates, in such cases the interpretation of the exciton spectra is even morecomplicated by the presence of strain that modifies the band edges positions. For a description on theband lineups in strained layers with hexagonal wurtzite structure, the reader is addressed, e.g. to thework of Van de Walle et al. [91] describing the effect of strain on the band lineups for the InxGa1�xNalloy grown on GaN. The problem of strain in cubic and hexagonal crystals has been discussed by


Yamaguchi et al. [92]. Of particular interest is also the review work of Orton and Foxon [86] who hasexhaustively described the impressive progress that has been made in the last years in understanding thephysics of strained group III nitrides films and who discussed the current position with regard to bandgaps, effective masses, exciton binding energies, phonon energies, dielectric constants, etc.

Coming back to cubic systems, as a result of strain-induced reduction of crystal symmetry, it isnecessary to distinguish a vector along the growth direction (the z or [0 0 1] direction) from that lying inthe growth plane (the x–y plane, where the lattice parameter of the epilayers is fixed to that of thesubstrate). Let as and a be the lattice parameters of the substrate and of the film in its bulk,‘‘unstrained’’ state, respectively. In a pseudomorphic epitaxial growth, the film has two different latticeparameters: ak ¼ as in the growth plane (0 0 1) and a? (<as or >as depending whether the strain istensile or compressive) in the growth direction [0 0 1], see Fig. 3.

As will be discussed in Section 5 of this review, the parallel (ek) and perpendicular (e?) strain arerelated to the lattice mismatch (Dak and Da?), given by:

ek ¼Dak

a¼

ak � a

a¼ �Da

a¼ � a � as

a(1)

(b)

(a)

x

z

y as

a//a

as

a//

a⊥

a⊥

as x

z

y

a

as

Fig. 3. Pictorial representation of the deformation undergone by a cell of cubic symmetry (unstrained lattice parameter a) by

the effect of pseudomorphic epitaxial growth on a substrate having a cell of the same symmetry but with different lattice

parameter (as). (a) Biaxial compressive strain: a > as; ak ¼ as; a? > as; (b) biaxial tensile strain: a < as; ak ¼ as; a? < as.

The differences between a and as have been exaggerated for the sake of clarity. Adapted with permission from E. Groppo,

degree thesis in Material Science, University of Torino, 2002 [431].


and

e?¼Da?

a¼ a? � a

a: (2)

According to the macroscopic elasticity theory [432], a? and ak are related through Poisson’s ratio

g ¼ þ 2C12

C11

; (3)

where C11 and C12 are the macroscopic elastic stiffness constants [198,433]. We thus have

a? ¼ ð1 þ gÞa � gak and thus e? ¼ �gek or e? ¼ � 2C12

C11

� �ek: (4)

The model solid theory [194,204–207,327], vide supra Section 2.1, allows to compute the band lineupsin strained semiconductor heterostructures in a straightforward way. Let us first consider the bandprofiles for holes. In the following, the |3/2, 1/2i, |3/2, 3/2i and |1/2, 1/2i valence-band maxima will bedenoted by E0

lh, E0hh, E0

split-off for the bulk and Elh, Ehh, Esplit-off for the strained layer, respectively.Following [173], the average of the three unstrained uppermost valence bands (Eav) is chosen as thereference energy level:

Eav ¼ 13ðE0

lh þ E0hh þ E0

split-offÞ ¼ 13ð2E0

lh þ E0split-offÞ; (5)

where the second equality arises from the degeneration of E0lh and E0

hh in a bulk material.The strained values of the band edges Elh, Ehh and Esplit-off are obtained by adding to Eav the

contributions of the hydrostatic perturbation energy Ehv (related to the cell volume variation), of thespin–orbit coupling D0 and of the tetragonal distortion Et [162–164,173,204,206,207,434,435]. Hencewe have

Elh ¼ Eav �D0

6þ Ehv þ

Et

4� 1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2

0 þ D0Et þ9

4E2

t

r(6)

for light holes in the mixed |3/2, 3/2i and |3/2, 1/2i valence band, and

Ehh ¼ Eav þ 13D0 þ Ehv � 1

2Et (7)

for heavy holes in the pure |3/2, 3/2i valence band, and

Esplit-off ¼ Eav �D0

6þ Ehv þ

Et

4� 1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2

0 þ D0Et þ9

4E2

t

r(8)

for split-off holes in the |1/2, 1/2i valence band. Note that the nomenclature of light- and heavy-holebands refers to the hole effective masses along the growth direction.

The hydrostatic perturbation energy in the valence band, Ehv, is given by:

Ehv ¼ �2AvðC11 � C12ÞC11

Da

a; (9)


where Av is the hydrostatic deformation potential of the valence band and C11 and C12 are the elasticstiffness constants. In Eqs. (6)–(8) the tetragonal distortion perturbation energy, Et, is defined as:

Et ¼2BðC11 þ 2C12Þ

C11

Da

a; (10)

where B is the shear deformation potential.Note that Ehv is proportional to the volume variation of the strained cell, i.e. to (2Dak þ Da?), while

Et is proportional to (Dak � Da?), being related to the symmetry decrease of the potential as describedby the ligand field theory. From Eqs. (6)–(8), it is evident that Elh and Ehh are degenerated for lattice-matched interfaces at an energy level of Eav þ D0=3. It is also evident that for any biaxial compressivestrain (i.e. Da=a > 0), the topmost valence band is Ehh (vide infra Section 2.5).

The unstrained conduction band edge E0c is computed by adding to the unstrained |3/2, 1/2i and |3/2,

3/2i valence-band levels (Eav þ D0=3) the unstrained energy gap Eg, i.e. E0c ¼ Eav þ D0=3 þ Eg. In the

presence of strain, because of the spherical symmetry, Ec is merely shifted from E0c by the hydrostatic

deformation potential Ehc (without tetragonal distortion):

Ec ¼ Eav þ 13D0 þ Eg þ Ehc (11)

and

Ehc ¼�2AcðC11 � C12Þ

C11

Da

a; (12)

where Ac is the hydrostatic deformation potential of the conduction band, similar to Av for the valenceband.

Fundamental material parameters for various binaries are listed in Table 1 [162–164,173]. In case ofa quaternary alloy (such as In1�xGaxAsyP1�y), a physical quantity Q(x, y) can be obtained, to the first-order approximation, through a linear interpolation:

Qðx; yÞ ¼ QInPð1 � xÞð1 � yÞ þ QGaAsxy þ QInAsð1 � xÞy þ QGaPxð1 � yÞ: (13)

Note that in general, Eq. (13) is not valid for Eg, for which an empirical non-linear expression should beused. The room temperature Eg of In1�xGaxAsyP1�y is reported by Kuphal [436]:

Egðx; yÞ ¼ 1:35 þ 0:668x � 1:068y þ 0:758x2 þ 0:078y2 � 0:069xy � 0:0322yx2 þ 0:03xy2 ðeVÞ(14)

The constant term 1.35 eV represents the 300 K energy gap of InP. When the computed band lineupsare compared with the experimental values obtained by low temperature experiments, the term 1.35 eVin Eq. (14) should be replaced by 1.423 eV (the 4 K InP band gap energy).

Eq. (14) represents a generalized version of the phenomenological equation usually used for ternaryalloys. Being Eg(AC) and Eg(BC) the energy gaps of AC and BC binary compounds, respectively, theenergy gap Eg(x) of the ternary A1�xBxC alloy will be given by:

EgðxÞ ¼ ð1 � xÞEgðACÞ þ xEgðBCÞ � bxð1 � xÞ; (15)


where b, measured in eV, is the bowing parameter of the A1�xBxC alloy and represents the deviationfrom linearity of the energy gap versus the chemical composition x of the ternary system[91,184,258,270,437–440]. For a given A1�xBxC alloy, the value of b can be determined eitherphenomenologically, by fitting with Eq. (15) a set of experimental data collected on samples withdifferent x values, or theoretically, by ab initio calculations.

In an effort to apply Eqs. (13)–(15) to other technologically important semiconductors alloys,Vurgaftman et al. [438] have compiled a comprehensive, up-to-date band-structure parameters of GaAs,GaSb, GaP, GaN, AlAs, AlSb, AlP, AlN, InAs, InSb, InP, and InN, along with their ternary andquaternary alloys. They also emphasize the quantities required for band-structure calculations, andtabulate the energy gaps, spin–orbit, and crystal-field splittings, alloy bowing parameters, effectivemasses for electrons, heavy, light, and split-off holes, Luttinger parameters, interband momentummatrix elements and deformation potentials, including temperature and alloy-composition depen-dences. The reader should refer to Ref. [438] for a more complete view on the topic.

2.3. The band offsets in strained QWs

A single QW consists of a thin layer of a narrow-gap semiconductor B (acting as well) sandwichedbetween two layers of wide-gap semiconductor A (acting as barrier). A single QW thus exhibits twoheterojunctions: first A/B, then B/A. In the case where the QW is grown on substrate A, the barrierlayers will be unstrained and strain appears only in the well layers. Fig. 4 shows the energy band profilefor an InP/InGaAs SQW.

We define E0blh ¼ E0b

hh, E0bsplit-off and E0b

c as the unstrained lineups in valence and conduction bands forthe bulk-like barrier layer and Ew

lh, Ewhh, Ew

split-off and Ewc for the strained well layer. These values have

been computed using Eqs. (6)–(8) and (11). The discontinuities in conduction and valence bands can be

Table 1

The 4 K lattice parameter (a); elastic stiffness constant (C11 and C12); Poisson’s ratio (g); shear deformation potential for strain

of tetragonal symmetry (B); spin–orbit splitting (D0); 4 K energy gap (Eg); the average over the three uppermost valence bands

at G (Eav); hydrostatic deformation potentials Av and Ac for the valence and conduction bands, respectively [181]; the G-edge

electron, heavy- and light-hole effective masses (me, mhh and mlh) are in the unit of the free electron mass m0 for selected bulk

semiconductorsa

Physical quantity Units GaAs InAs InP GaP

a A 5.65 6.05 5.87 5.45

C11 1011 dyn cm�2 11.88 8.329 10.22 14.12

C12 1011 dyn cm�2 5.38 4.526 5.76 6.25

g – 0.31 0.352 0.36 0.31

B eV �1.7 �1.8 �2.0 �1.5

D0 eV 0.34 0.38 0.11 0.08

Eg eV 1.52 0.41 1.42 2.87

Eav eV �6.92 �6.67 �7.04 �7.9

Av eV 1.16 1.00 1.27 1.3

Ac eV �7.17 �5.08 �5.04 �8

mhh m0 0.45 0.41 0.56 0.60

mlh m0 0.082 0.025 0.12 0.16

me m0 0.067 0.023 0.080 0.25

a The values have been taken from Refs. [163,164,173,194,204,206,207,260,441,442].


defined as (Fig. 5):

DEc ¼ E0bc � Ew

c (16)

and

DEvl ¼ Ewvl � E0b

vl ; where l ¼ lh; hh; or split-off: (17)

Using the standard sign convention, a positive value of DEc (DEvl) corresponds to the confinement ofelectrons (holes) in the energy potential well. The effects of strain on the well layer imply the presenceof three different discontinuities in valence band, which are identified with the index l in Eq. (17),adopting the same convention used in Eqs. (6)–(8) for the band lineups. It also implies the presence ofthree different strained band gaps in the well:

Ewgl ¼ Ew

c � Ewvl; where l ¼ lh; hh; or split-off; (18)

which leads to three band gap discontinuities DEgl ¼ E0bgl � Ew

gl, and as a result, three sets of (DEc, DEvl)values. For convenience, fractional band offsets are defined as:

Qcl ¼DEc

DEvl þ DEc

¼ DEc

DEgl

; where l ¼ lh; hh; or split-off (19)

and

Qvl ¼DEvl

DEvl þ DEc

¼ DEvl

DEgl

; where l ¼ lh; hh; or split-off; (20)

Fig. 4. (a) A 3D view of an ideal In0.53Ga0.47As/InP SQW heterostructure grown on an InP substrate; (b) a 1D view of the

band profile of the SQW along the z-axis, with DEc ¼ 0:226 eV and DElh ¼ DEhh ¼ 0:337 eV (type I band alignment). The

degeneracy of the light- and heavy-hole bands is evident from Eqs. (3) and (4), where Ehv and Et are both null when Da is set

to 0. Horizontal lines represent the eigenvalues for electrons and holes. Adapted from C. Lamberti, Comput. Phys. Commun.

93 (1996) 82, [163], with permission. Copyright (1996) by Elsevier.


where Qcl þ Qvl ¼ 1 for each l. Note that all quantities referred to the barrier and having l ¼ lh andl ¼ hh are degenerate in the absence of strain.

2.4. Band profiles in unstrained or nearly unstrained SQWs with abrupt interfaces

Epitaxially grown III–V SQW, MQW and SL on GaAs or InP substrates have represented the firstexample of artificial structures able to test the quantum mechanic rules. The quantized electron andhole energy levels in the well imply that the electron–hole energy transition depends on the width (w) ofthe confinement and the energy barrier height (DEc, DElh or DEhh, see Eqs. (16) and (17)) [443]. Thesestructures represent a real example similar to the exercise of ‘‘a particle in a box’’. The energyeigenvalues (e) and eigenfunctions (C) are obtained by solving the Schrodinger equation, subject to theboundary conditions along the growth axis at both interfaces (z ¼ 0 and z ¼ w in Fig. 4b) on theprobability density, |C|2, and on the probability density flux, j ¼ ½ih=ð4pm�Þ�½CrC� �C�rC� (i.e. onC and on (1/m�)@C/@z, where z is the growth axis and m� is the effective particle mass which change bychanging from barrier to well) [122,162,164,443].

The two de-coupled Schrodinger equations are solved for electrons in the conduction band and forholes in the valence bands separately, yielding ee, ehh and elh values for the corresponding eigenvalues.The predicted e ! lh and e ! hh transitions will thus be obtained by the following equations:

Ee!hh ¼ ee þ ehh þ Eghh; (21)

wglhE w

ghhE woffgsplitE −

bcE0

wcE

wvlhEwvhhE

bvhh

bvlh EE 00 =

woffvslitE −

boffvsplitE0

−

cE∆

vhhE∆ vlhE∆

offvsplitE −∆

boffgsplitE 0

−b

ghhb

glh EE 00 =

E A AB

Fig. 5. Pictorial representation of band lineups in a strained QW, with type I band alignment (barrier matched with the

substrate): E0bc , E0b

lh ¼ E0bhh and E0b

split-off indicate the unstrained lineups in conduction and valence bands for the bulk barrier

while Ewc , and Ew

lh, Ewhh and Ew

split-off represent the conduction and valence-band lineups in the strained well, computed

following Eqs. (6)–(8) and (11). Conduction- and valence-band discontinuities DEc, DEvlh, DEvhh and DEvsplit-off, see Eqs. (16)

and (17), have also been evidenced, as well as the three strained band gaps for the well, see Eq. (18), and the two unstrained

band gaps for the barrier. Adapted from C. Lamberti, Comput. Phys. Commun. 93 (1996) 53, [162], with permission.

Copyright (1996) by Elsevier.


Ee!lh ¼ ee þ elh þ Eglh; (22)

where Eglh and Eghh are the band gap energies of the well layer for the light and heavy holes,respectively, as defined in Eq. (18). Over the years, many researchers have developed computer codesthat are capable of solving electron and hole Schrodinger equations, including PLSIMUL [163], whichis available from the web site of Queen’s University of Belfast [444].

Eqs. (21) and (22) do not take into account the exciton binding energy, Eexc, which, depending on thechemical composition and on the width of the well, has a typical value of 5–15 meV for a 2D exciton[12,13,445–450]. Eexc has to be subtracted from the values reported in Eqs. (21) and (22) whencomparison is made with 4 K PL data.

Practically, such heterostructures become suitable for the realization of solid state lasers since theemission wavelength becomes a function of the well thickness. This characteristic allows to choosewell-understood and reliable semiconductors for light emission in a wavelength range unrelated to thematerial’s energy band gap. Moreover, the fact that both electrons and holes could potentially beconfined inside the active region of the device increases the emission efficiency.

In a non-strained QW, the mass effect (which implies that to the first order, the quantum confinementenergy is proportional to 1/m�) always results in Ee!hh < Ee!lh (Fig. 6); while in a strained QW, theband distortion can be so dominant to subvert the precedent statement (vide infra Figs. 7 and 8).

Fig. 6a shows for an unstrained In0.53Ga0.47As/InP system the positions of Hamiltonian eigenvaluescomputed by PLSIMUL [163], for the ground states of electrons, heavy and light holes as a function ofthe well width given in MLs. As discussed in Section 2.2, the absence of strain (Da ¼ 0) corresponds tothe valence-band degeneration condition. We thus expect that the heavy- and light-hole lineups aresuperimposed. Nevertheless, this degeneration is lifted by the quantum confinement effect, so thatheavy- and light-hole eigenvalues will converge only for very wide wells (bulk limit). As an example,for w 50 MLs (150 A), the difference between Ee!hh and Ee!lh transitions is less than 10 meV. It isevident from Fig. 5 that the ground state of heavy holes reaches the bulk limit for smaller well width ifcompared to the ground state of light holes.

Quaternary alloys lattice matched to InP—such as In0.59Ga0.41As0.90P0.10 with a bulk band gap of0.862 eV (1.55 mm)—are of great interest for InP-based fiber optic applications. Fig. 6b shows, for anearly unstrained In0.70Ga0.30As0.64P0.36/In0.59Ga0.41As0.90P0.10 heterostructure grown on InP, thePLSIMUL-computed Hamiltonian eigenvalues for the ground states of electrons, heavy and light holesas a function of the well width. The small strain (Da=a ¼ þ8:2 � 10�4), implies a difference betweenElh and Ehh of about 6 meV in the bulk limit. The heavy-hole valence band always lies above the light-hole band and the observed Ee!hh transition ranges from 1.007 eV for a 1 ML-thick well to 0.869 eVfor a 100 ML-thick well. The maximum difference between Ee!hh and Ee ! lh occurs for w ¼ 10 MLs(29 A) and is of about 55 meV. From Fig. 6b, it is evident that the confinement of electrons is verypoor (�14 meV), because nearly all the energy gap difference falls in the valence band.

2.5. Band profiles in strained SQWs with abrupt interfaces

Fig. 7a shows for the strained In0.60Ga0.40As/InP system the calculated Hamiltonian eigenvaluesusing PLSIMUL [163] for the ground states of electrons, heavy and light holes as a function of the wellwidth. Under biaxial compression (Da=a ¼ þ4:1 � 10�3), the hh lineup lies 28 meV above the lhlineup (i.e. the hh well is deeper: DEhh > DElh). In this system, the removal of the valence-band


degeneracy is due to both strain and quantum effects, acting in the same direction. As a consequence,for any w value Ee!lh is always greater than Ee!hh (i.e. no valence-band degeneracy) in In0.60Ga0.40As/InP. The strain effect implies that hh and lh Hamiltonian eigenvalues have two different bulk limits.

For comparison, in a tensile-strained In0.45Ga0.55As/InP SQW (Da=a ¼ �6:2 � 10�3), the hh lineuplies 45 meV below the lh lineup (DEhh < DElh), as seen in Fig. 7b. In this SQW, the effects of strain andquantum confinement act in opposite directions, resulting in Ee!lh > Ee!hh for narrow well width andEe!lh < Ee!hh for wide width. The |3/2,1/2> and |3/2,3/2> valence bands of strained In0.45Ga0.55As/InPintersect (degenerate) again for a width of about 25 MLs (w 73 A). The strain effects imply againthat hh and lh Hamiltonian eigenvalues have two different bulk limits.

Fig. 8a shows the lineups of the electron and holes bands of strained In1�xGaxAs/InP as a function ofthe Ga composition x. The computed ground states are also shown for a 25 ML-thick SQW. For such awell width, the degeneracy of the eigenvalues of hh and lh in valence band occurs at x 0:55, which isslightly larger than the degeneracy value of x ¼ 0:47 for bulk In1�xGaxAs ternary alloy.

From Figs. 7 and 8a, it is evident that both the Ga content x and the well width w play a role indetermining the energy level of the heavy-hole ground state relative to that of the light hole in

Fig. 6. (a) Energy eigenvalues computed by PLSIMUL [163] for the ground state of electrons (Ee þ ee), heavy (Ehh � ehh)

and light (Elh � elh) holes as a function of the well width given in monolayers in an unstrained In0.53Ga0.47As/InP SQW

(1 ML ¼ 2:93— at 4 K). Energy values are referred to the free electron. For this double heterojunction we have the following

band offsets: DEc ¼ 0:266 eV, DEvlh ¼ DEvhh ¼ 0:337 eV and DEvsplit-off ¼ 0:086 eV and the following ratios:

Qclh ¼ Qchh ¼ 0:44 and Qvlh ¼ Qvhh ¼ 0:56. (b) Calculated energy levels of the nearly unstrained In0.70Ga0.30As0.64P0.36/

In0.59Ga0.41As0.90P0.10 SQW, characterized by the following band offsets: DEc ¼ 0:014 eV, DEvlh ¼ 0:128 eV,

DEvhh ¼ 0:133 eV and DEvsplit-off ¼ 0:065 eV and the following ratios: Qclh Qchh ¼ 0:10 and Qvlh Qvhh ¼ 0:90. Adapted

from C. Lamberti, Comput. Phys. Commun. 93 (1996) 53, [162], with permission. Copyright (1996) by Elsevier.


In1�xGaxAs/InP, since the quantum confinement energy is inversely proportional to the effective mass[164,173,176]. The inset of Fig. 8a (adapted from [173]) displays for In1�xGaxAs/InP the contour ofvalence-band degeneracy in the x–w plane (for x > 0:47); above that curve Ee!lh < Ee!hh while belowEe!lh > Ee!hh. The degeneracy boundary can be generalized to a degeneracy surface in case of aquaternary In1�xGaxAsyP1�y, where x, y and w play a role in defining the valence-band ground state. Forany tensile-strained QW, there exits a particular well width w for which the heavy- and light-hole levelsare degenerate, whereas such a width value does not exist for a compressive-strained QW. Such a typeI ! II crossover has also been observed in other systems such as InxGa1�xAs/AlAs [451]. Thisphenomenon cannot occur for the InAsyP1�y system (Fig. 8b), being always under biaxial compression(Ee!lh > Ee!hh) for any y value [164].

Fig. 7. (a) Calculated energy levels of In0.60Ga0.40As/InP SQW with a compressive strain of Da=a ¼ þ4:1 � 10�3;

1 ML ¼ a=2 ¼ 2:94 A at 4 K. The following band offset values are obtained: DEc ¼ 0:290 eV, DEvlh ¼ 0:337 eV,

DEvhh ¼ 0:365 eV and DEvsplit-off ¼ 0:095 eV and the following ratios: Qclh ¼ 0:46;Qchh ¼ 0:44;Qvlh ¼ 0:54 and

Qvhh ¼ 0:56. (b) Calculated energy levels of In0.45Ga0.55As/InP SQW with a tensile strain of Da=a ¼ �6:2 � 10�3. The

following band offset values are obtained: DEc ¼ 0:237 eV, DEvlh ¼ 0:346 eV, DEvhh ¼ 0:301 eV and DEvsplit-off ¼ 0:072 eV

and the following ratios: Qclh ¼ 0:41;Qchh ¼ 0:44;Qvlh ¼ 0:59 and Qvhh ¼ 0:56. Note that, in both cases, the |3/2, 3/2i band

has a heavy mass along the z-direction, while the |3/2, 1/2i band exhibits a comparatively light mass. Adapted from C.

Lamberti, Comput. Phys. Commun. 93 (1996) 53, [162], with permission. Copyright (1996) by Elsevier.


Fig. 8. (a) Energy lineups of electron and holes bands of strained In1�xGaxAs/InP (solid lines) and quantized levels for a

25 ML-thick SQW (dashed lines) as a function of the Ga content x. Energy values refer to the free electron. The (bulk) lattice

constant of In1�xGaxAs varies from 6.05 A (Da=a ¼ þ3:15 � 10�2, biaxial compression) of InAs to 5.65 A

(Da=a ¼ �3:71 � 10�2, biaxial tension) of GaAs. Adapted from C. Lamberti, Comput. Phys. Commun. 93 (1996) 53,

[162], with permission. Copyright (1996) by Elsevier. The inset displays the contour of valence-band degeneracy in the x–w

plane. Adapted from T.Y. Wang, G.B. Stringfellow, J. Appl. Phys. 67 (1990) 344, [173], with permission. Copyright (1990) by

American Institute of Physics. Part (b) same as part (a) for the InAsyP1�y system strained on InP (solid lines) and quantized

levels for a 27 monolayers thick SQW (dashed lines) as a function of the As concentration y. Energy values, given in eV, are

referred to the free electron. This ternary alloy exhibit a lattice parameter which goes from a ¼ 5:85 A, for y ¼ 0,

corresponding to unstrained InP epitaxially grown on InP substrate (Da=a ¼ 0) to a ¼ 6:05 A, for y ¼ 1, corresponding to

biaxially compressed InAs on InP (Da=a ¼ þ3:15 � 10�2. Adapted from C. Lamberti, et al., J. Appl. Phys. 83 (1998) 1058,

[164], with permission. Copyright (1998) by American Institute of Physics.


The band structure of the InAsxP1�x ternary system strained on InP, computed by programBANDSTRAIN [162], is reported in Fig. 8b (solid lines) as a function of x. From Fig. 8b it is evidenthow, in valence band, strain removes the lh–hh degeneration resulting in a splitting between Elh, andEhh, which increases with increasing Da/a0, i.e., by increasing x. Also reported in Fig. 8b, for each Ascomposition, are the corresponding quantized levels for a 27 ML-thick SQW characterized by idealabrupt interfaces (dashed lines), as computed by program PLSIMUL [163]. All energy values are givenin eV, having the zero value referred to the free electron.

Finally, Fig. 9 reports the energy lineups of electron and holes bands in biaxially strained Ge as afunction of increasing strain as computed by Rioux and Hochst [452] according to the Van de Walle and

Fig. 9. Energy lineups of electron and holes bands in biaxially strained Ge as a function of increasing strain. The adopted,

from Ref. [327], shear deformation potential is B ¼ �2:9 eV, while the hydrostatic deformation potentials are as follows:

Av ¼ 1:24 eV, Aindirc ¼ �1:54 eV, Adir

c ¼ �8:24 eV. Reprinted from D. Rioux, H. Hochst, Phys. Rev. B 47 (1993) 1434. [452],

with permission. Copyright (1993) by American Physical Society.


Martin ‘‘model solid’’ theory [194,204–207,327]. This study predicts that biaxially strained Ge filmsbecomes a direct band gap material at ek ¼ 0:017 and a metal at ek ¼ 0:044.

Based on what was discussed above, it is evident that simulations performed under the assumption ofabrupt interfaces must be taken with caution, especially for narrow well width heterostructures.Nevertheless, the data reported in this context (Sections 2.4 and 2.5), related to the simulation of idealheterostructures, represent useful trends followed by real, chemically non-abrupt heterostructures,which will be discussed in Section 3.1.

3. Interfacial layers in semiconductor heterostructures

As a case study for the investigation of the interface quality in III–V semiconductor heterostructures,we will focus on InGaAs/InP. Notwithstanding this fact, the problems raised in this section are ofgeneral significance for any A/B system (see e.g. [117] for the InxGa1�xAs/GaAs and InyAl1�yAs/GaAssystems). Moreover, the InGaAs/InP system represents an excellent example for this review, beingwidely investigated by means of SR techniques, vide infra Sections 4.4, 4.5 and 7.3. As mentionedearlier, it has been shown that in metal-organic chemical vapor deposition (MOCVD), chemical- andmolecular-beam epitaxy (CBE and MBE) InGaAs/InP heterostructures, the non-intentional variationin composition at the real interfaces is associated to the switches from P to As and vice versa[45,146–163].

This compositional interface gradient, spreading over some MLs, can be partially reduced by theadoption of appropriate growth interruption times (GIT) [146,154–158,160–163,284,453–458]. TheGIT technique allows for the protection of the just-grown surface to avoid its decomposition and theexposure of InP and InGaAs surfaces to AsH3 (As2) and PH3 (P2) fluxes, respectively, before the growthof the next layer starts. These exposures lead to a partial substitution of P with As at the first interfaceand vice versa at the second interface, yielding the formation of InAsP at the first interface and ofInGaAsP at the second interface [45,146,158–167]. Although the problem of interfacial abruptness ispartially alleviated in atomic layer epitaxy [290], it suffers from a drawback of very low growth rates.

Fig. 10a represents schematically the cross-sectional profile of an ideal In0.53Ga0.47As/InP MQW.Fig. 10b represents the result obtained on a real heterostructure: the presence of interface layers impliesa systematic widening of the well in the real structure, if compared to the ideal one. Therefore, themodel of ‘‘a particle in a rectangular box’’ represents an approximation of the problem: the potentialprofiles for electron and holes are more complex than rectangular-shaped [162–164].

3.1. Interface characterization in real SQWs by means of conventional laboratory techniques

This subsection is devoted to give a concise overview to the most employed laboratory techniques inthe characterization of interfaces in real semiconductor heterostructures: 4 K PL and Ramanspectroscopies and TEM technique. Useful, but less popular techniques such as second-harmonicgeneration will just briefly mentioned and reference to recent specialized reviews will be made. XRDwill be completely ignored in this subsection, being treated in detail in Section 5.1. The same holds forEXAFS spectroscopy (see Section 4.5) and for XSW (see Section 7.3).

Fig. 11 shows the Ee!hh blue shift (solid line), i.e. Ee!hh–Eg(In0.53Ga0.47As), as a function of the wellwidth w computed by PLSIMUL for InGaAs/InP under the assumption of abrupt and ideal


heterostructures [163]. Various symbols represent the PL data reported in the literature [147,150,152,163,459,460]. The discrepancy between the experimental results and the theory is remarkable,especially at small well thickness. It is expected that for wide wells the interface mixing plays a minorrole. Indeed, the discrepancy in 4 K PL peak energy for a nominal 2 ML-thick SQW is over 200 meV,consistent with the fact that the 2 ML SQW is composed only of interface layers. With the exceptions ofthree data points from Lamberti [163] and of a set of data from Morais et al. [150], the whole set ofexperimental data lies below the theoretical curve computed for abrupt interface of nominalcomposition. In the former case, the remarkable additional blue shift of three samples was due to asignificant deviation from the ideal In0.53Ga0.47As chemical composition of the well layers, due to bothmemory and substitution effects resulting in an increase of the Eg of chemical and not confinementorigin. In the latter case, the experimental data (labeled by empty circles) would have been much bettercomparable with the theoretical curve and with the major set of experimental data if a scaling factorw ! sw (with s � 0:8) were applied to the abscissa. This could reflect an overestimation of the growthrate, resulting in a systematic overestimation of the widths w. This discussion, which is only aspeculative attempt to explain the literature data, underlines the importance of a combined PL and high-resolution XRD approach (performed on MQW grown by periodically repeating the growth proceduresadopted for the SQWs reported in Fig. 11) in the characterization of semiconductor heterostructures(vide infra Section 5.1).

Fig. 12 illustrates how the growth conditions affect the interface band profiles of a 7 ML-thick(w ¼ 19:075 A) In0.51Ga0.49/InP QW. Two simulated heterostructures, characterized by a first GIT atthe InP/InGaAs interface (1 s, same for both simulation runs) and by a second GIT at the InGaAs/InPinterface (10 s versus 1 s) are depicted in panels (b) and (c) and compared to the profile of the ideal

Fig. 10. (a) Ideal MQW characterized by abrupt interfaces. (b) The realization of the ideal heterostructure as depicted in (a)

implies the appearance of undesirable layers of InAsP (interface 1) and of InGaAsP (interface 2). The width (here tentatively

set at 10 A) and the chemical composition of those two undesired layers are hardly dependent upon the adopted growth

conditions [158–163]. This effect implies a systematic well width increase, yielding to a red shift in both Ee!hh and Ee!lh

transitions. Adapted from C. Lamberti, Comput. Phys. Commun. 93 (1996) 82, [163], with permission. Copyright (1996) by

Elsevier.


abrupt heterostructures, panel (a). At both interfaces of both samples, the compositional gradient isconfined within �10 A. The horizontal lines in Fig. 12 represent the quantized levels of electrons,heavy and light holes confined in the reported potential wells computed by PLSIMUL [163]. Noquantum mechanical simulation is performed on the split-off band (|1/2, 1/2i) owing to the difficultiesof: (i) estimating a reasonable value of the split-off hole effective mass; (ii) finding an experimentaltechnique able to verify the simulations. The simulated Ee!hh transitions are 1.103, 1.134 and 1.108 eVfor the profiles reported in Fig. 12a–c, respectively, while the simulated Ee!lh transitions are 1.193,1.208 and 1.183 eV, respectively. The low strain (Da=a ¼ �2:1 � 10�3) implies a difference betweenhh and lh holes lineups of 15 meV, barely visible in Fig. 12a.

Up to now, in this section, the problem of chemical gradient at the semiconductor heterostructureinterfaces has been treated in detail. There is a second main point that distinguish real from idealheterostructure, which is related to the well width fluctuation in the x–y growth plane (Fig. 13a). Suchan interface roughness [12] causes doublet and multiplet PL lines which are assigned to emission fromwell thickness fluctuating by 1 ML [158,159,163,164,169,171,361,403,457,461–467]. As an examplethe case a strained InAs0.60P0.40/InP heterostructure characterized by four single InAs0.60P0.40 wells of7, 14, 21 and 28 ML nominal thickness, taken from [164], is explicative. Fig. 13b, reporting the 4 K PLspectrum of the heterostructure, exhibits five different emission at 0.909, 0.934, 0.986, 1.090 and

Fig. 11. Electron to heavy-hole transition blue shifts from bulk value as a function of the well width w for an In0.53Ga0.47As/

InP SQW, i.e. Ee!hh � EgðIn0:53Ga0:47AsÞ. Simulation was performed by PLSIMUL assuming ideal, abrupt interfaces.

Experimental data are taken from Refs. [147,150,152,459,460,163]. Adapted from C. Lamberti, Comput. Phys. Commun. 93

(1996) 82, [163], with permission. Copyright (1996) by Elsevier.


Fig. 12. Electrons (solid line), heavy-hole (solid line), light-hole (dashed line) and split-off (dotted line) band profile

simulation of three 7 ML-thick In0.51Ga0.49As SQW structures grown on InP under different conditions: (a) ideal structure; (b)

real structure obtained after 1 s GIT at the first interface and 10 s GIT at the second interface; (c) real structure obtained after

1 s GIT at both interfaces. The three horizontal lines represent the ground states of electrons and holes confined in the

simulated profiles as computed by PLSIMUL [163]. No quantum simulation is performed on the split-off band. Adapted from

C. Lamberti, Comput. Phys. Commun. 93 (1996) 53, [162], with permission. Copyright (1996) by Elsevier.


1.108 eV. The last two emissions have been quite well simulated by Lamberti et al. [164] by adding oneInAs0.60P0.40 ML to the nominal composition profile, this means that in the 7 ML-thick (�21 A) well ofthe heterostructure, a þ1 ML fluctuation occurs. Even if not resolved, two shoulders are visible athigher and lower energy of the 0.986 eV peak. A band deconvolution approach results into threecomponents at 0.978, 0.986 and 0.997 eV (see Fig. 13c), values which are in full agreement with thehypothesis of a �1 ML fluctuation in the 14 ML (�42 A) well of the heterostructure. Lamberti et al.[164] concluded that the x–y plane the dimension of the regions having a width of w, w þ a=2 andw � a=2 is larger than the Bohr radius of the exciton. Both emissions at 0.909 and 0.934 eV, generatedby the 21 ML (�63 A) and 28 ML (�84 A) wells of the heterostructure have been satisfactorilyreproduced using only one Gaussian contributions; however, a �1 ML fluctuation in those wells cannotbe excluded due to the small influence on the PL emission of such well fluctuation for high well widths(see full line in Fig. 11).

High-resolution TEM investigations provide direct information on planarity of the interfaces, atomicinterdiffusion and possible presence of dislocations thus representing a complementary probe of theinterface quality [36,159,163,164,166,167,276,282,291,298,299,455,468–472]. Moreover, the parallel

Fig. 13. (a) Schematic representation of the well width fluctuation problem in real heterostructures. (b) Experimental 4 K PL

spectrum of a strained InAs0.60P0.40/InP heterostructure characterized by four single InAs0.60P0.40 wells of 7, 14, 21 and 28 ML

nominal thickness. Five different emissions are evident at 0.909, 0.934, 0.986, 1.090 and 1.108 eV. The two peaks at higher

energy are due to exciton recombination in wells of width w ¼ 7, 8 ML of InAs0.60P0.40, the composite peak at 0.986 eV in

wells of width w ¼ 14 � 1 monolayers, while the two emissions at lower energy are attributed to e ! hh transitions in 21 and

28 monolayer thick wells. (c) The composite nature of the peak at 0.986 eV is evidenced. It has been reproduced using three

Gaussian components centered at 0.978, 0.986 and 0.997 eV, attributed to exciton recombination in region of width 15, 14 and

13 ML, respectively. Parts (b) and (c) adapted from C. Lamberti, et al. J. Appl. Phys. 83 (1998) 1058, [164], with permission.

Copyright (1998) by American Institute of Physics.


use of high-resolution TEM and high-resolution XRD, with the relative simulation, permits us toestimate the chemical composition of the layers and to determine how the heterostructure period issheared between well and barrier lengths (vide infra Section 5.1). Fig. 14 reports, at two differentmagnifications, the cross-sectional TEM micrographs of a 40-period InGaAsP/InP SL with P ¼ 146 A.From the high magnification picture (part (b)) the presence of the two interface layers of InAsP andInGaAsP is evidenced, supporting the model schematized in Fig. 10b [163].

We will not address the high-resolution TEM studies of semiconductor heterostructures and a fewreferences will be quoted [36,159,163,164,166,167,276,282,291,298,299,455,468–472]. The sameholds for Raman spectroscopy [51,267,290,354,356,404,473–495] and second-harmonic generationtechnique [31] which have been very useful in the study of the interface quality in SLs.

Optical second-harmonic generation and sum-frequency generation, which arise from the second orhigher order non-linear optical susceptibility of the material, are the two non-linear optical techniquescommonly used for surface and interface studies [31,496]. Direct application are obtained forcentrosymmetric materials, such as elemental semiconductors because in the standard multipoleexpansion of fields, the electric dipole term is parity-forbidden for such materials, leaving only higherorder, non-local contributions (magnetic dipole and electric quadrupole effects). At a surface orinterface, the bulk symmetry is broken and electric dipole effects are allowed. Beside the study of theclean semiconductor surfaces, see e.g. the cases of Si [497,498], and GaAs [499,500], the technique hassuccessfully been applied in the investigation of the heterostructure interfaces such as the Sim/Gen

[501,502] Si(1 1 1)/GaP [503] and Si(0 0 1)/GaP [503] systems.

Fig. 14. (1 1 0) cross-sectional TEM micrographs of a 40-period InGaAsP/InP SL with P ¼ 146 A: (a) low-resolution

micrograph where InGaAs and InP layers appear as dark and clear lines, respectively. At this magnification no anomaly at the

interfaces can be detected. (b) In a high-resolution micrograph the presence of InAsP layers at the first interface and InGaAsP

layers at the second is evident. Adapted from C. Lamberti, Comput. Phys. Commun. 93 (1996) 82, [163], with permission.

Copyright (1996) by Elsevier.


Till now we have summarized the effects of strain on the band lineups of semiconductorheterostructures (Section 2) and we have underlined the structural (and thus electronic) differencesbetween ideal and real interfaces (Section 3). The last section is also devoted to a brief overview onthe laboratory techniques used to characterize the quality of the interfaces in semiconductorheterostructures. In the following sections the role played by SR techniques in the characterizationof the local (Sections 4 and 6) and long-range (Sections 5–8) structure and of the electronic structure(Section 9) of semiconductor heterostructures and thin films will be deeply discussed. Of particularinterest for this topic are the photoelectron microspectroscopy results described in Section 9.2,where local fluctuations in the band offsets have been singled out for different semiconductorinterfaces.

4. Application of EXAFS spectroscopy

The section devoted to EXAFS spectroscopy is divided into nine subsections. The first one,describing on a simple ground the physics of X-ray absorption, is addressed to scientists which areunfamiliar with the technique. Sections 4.2 deals with EXAFS experiments performed on bulksemiconductor alloys, while the subsequent one deals with thin semiconductor films, QWs and SLs,facing the problem of epitaxy. The joint role of alloying and epitaxy in determining the first shell bonddistances in strained semiconductor films, QWs and SLs is treated in Section 4.4 using the InxGa1�xAs/InP system as case study. The contribution of EXAFS spectroscopy in the study of interface mixing inQWs and SLs, already faced in Section 3.1, is discussed in Section 4.5 using InxGa1�xAs/InP shortperiod SLs as case study. In Section 4.6 the discussion is extended to the higher shell data analysis,underlying the necessity of a multiple-scattering approach. Section 4.7 deals with the selectivedetermination of the distances in and out of the growth plane performed by exploiting the polarizednature of the SR beam. Section 4.8 discuss the application of surface EXAFS. Finally, Section 4.9reports on the near-edge structure in X-ray absorption spectra.

4.1. Basic concepts of EXAFS spectroscopy

Starting from the late seventies, the progressively increased availability of synchrotron light sourcesallowed the execution of experiments requiring an high X-ray flux in a continuous interval [504].Among them X-ray absorption spectroscopy (XAS) is worth recalling [505–508]. Fig. 15 depicts the

(v) Fluorescence

(v) Second ionization

chamber

(iii) First ionization chamber

(ii) Double crystal monochromator

(iv) Sample (i) syncrotron

Fig. 15. Schematic picture of the basic set-up of a XAFS experiment, from left to right: (i) synchrotron; (ii) double crystal

monochromator; (iii) first ionization chamber for monitoring the intensity of the incident beam I0; (iv) sample; (v) second

ionization chamber for monitoring the intensity of the transmitted I1 or fluorescence detector sketched on top of the sample.


basic set-up of a XAS experiment, which can be summarized into four steps: (i) the white beam emittedfrom a synchrotron source is monochromatized with a double crystal; (ii) the intensity of themonochromatic beam I0 is measured with a first ionization chamber; (iii) the monochromatic beam ispartially absorbed by passing through the sample of thickness x; (iv) the intensity of the transmittedbeam I1 is then measured with a second ionization chamber. In such a way, the absorption coefficient mof the sample can be measured for any energy E selected by the monochromator according to theclassical law of transmission phenomena:

mðEÞx ¼ lnI0ðEÞI1ðEÞ

� �: (23)

For any sample, m(E)x is a monotonically decreasing curve superimposed on a few abruptdiscontinuities, which correspond to the K, L, etc. edges of the chemical elements present in thesample, as clearly seen in Fig. 16a for a GaAs polycrystalline sample. The first discontinuity across10,367 eV corresponds to the Ga K-edge, while the second one, around 11,867 eV, corresponds to theAs K-edge. Such abrupt jumps of m(E)x corresponds to the photoelectric effect done on a core electronfrom 1s orbital, for the K-edge of Ga and As atoms respectively.3 The selection of one of these twoedges allows to tune the technique to one specific chemical element only (Top curve in Fig. 16b and cfor Ga and bottom curve in Fig. 16b and d for As.) In the following we will focus the attention on theGa K-edge only. For energies higher than the threshold energy (E0 ¼ 10,367 keV for Ga K-edge),photons of the monochromatized X-ray beam have the sufficient energy (E ¼ hn) to extract the coreelectron (hereafter named photoelectron), which is ejected with a kinetic energy T 0 given by theEinstein equation: T 0 ¼ hn� E0. If the photoelectron is extracted from the 1s level, then it behaves as aspherical wave propagating from the excited atom with a wavenumber

k ¼ 2ph

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2m0ðhn� E0Þ

p; (24)

where h is the Planck’s constant and m0 the free electron mass. According to Eq. (24), for E > E0,m(E) can be expressed as a function of the photoelectron wavenumber k thus becoming m(k). Whenthe photoelectron interacts with the potential barrier of electron shells of the first neighbor (Asatoms in our case), it is partially backscattered. The backscattered wave will interfere with thespherical wave out-coming from the absorbing atom, affecting the value of the absorptioncoefficient m(k) of the sample. This interference can assume any configuration between fullconstructive and full destructive depending on the difference of phase between the two waves,which geometrical dependence is given by 2kr, where k is the photoelectron wavenumber, seeEq. (24), and r is the first shell bond distance (being so 2r the path difference). r being fixed anddepending k upon the energy hn of the incoming X-ray beam, it is evident that an energy scan of themonochromator will allow to measure along several periods this interference phenomenon, whichcauses oscillations in the absorption coefficient m(k)x after the edge, as visible in Fig. 16a. Theseoscillations represent the ‘‘fine structure’’ giving the name to the technique: extended X-rayabsorption fine structure (EXAFS).

3 The K-edge is the most frequently used edge for EXAFS experiments, however, also L-edges are sometime used,

particularly for high Z elements, corresponding to the photoelectric effect from one of the 2s, or 2p1/2, or 2p3/2 orbitals.


The EXAFS signal, usually labeled as w(k), has than to be extracted from the experimentallymeasured m(k) function by subtracting the background (both pre-edge and atomic-like absorptions)and by normalizing it to the edge jump to take into account the sample thickness x. Once the pre-edgehas been subtracted and once the signal has been normalized by the edge jump (proportional to thesample thickness x) than, for E > E0, m(k) is given by: mðkÞ ¼ m0ðkÞ½1 þ wðkÞ�, m0(k) being the atomic-like absorption (some time also defined as the bare-atom, background absorption). The EXAFS

11000 12000

5 10 15

2 3 4 5 2 3 4 5

0.25µx

(d)(c)

k (Å-1)

(b)

(a)

Energy (eV)

0.2 (Å-1)

Ga

As

0.1 (Å-2)

r (Å)r (Å)

0.1 (Å-2)

Fig. 16. (a) Absorption coefficient mx vs. the photon energy in the 10,250–13,000 eV range of a GaAs bulk polycrystalline

sample. The first discontinuity across 10,367 keV corresponds to the Ga K-edge, while the second one, around 11,867 keV,

corresponds to the As K-edge. (b) Ga (top) and As (bottom) K-edge EXAFS oscillations, kw(k), as a function of k, obtained

from the raw datum reported in part (a) after removal of the background adsorption and normalization to the jump edge. (c)

Fourier transform of the Ga K-edge kw(k) into r-space, where the contributions of the first (Ga–As), second (Ga–Ga) and third

(Ga–As) coordination shells around Ga can be distinctly observed around 2.2, 3.7 and 4.4 A, respectively. Note that these

distances are slightly shorter with respect to the actual ones since the Fourier transform has not considered the phase function

ji(k), see Eq. (26). (d) Same as part (c) for the As K-edge kw(k) function. Data refers to the GaAs sample measured as

reference by Boscherini et al. in their study of InGaAs/InP SLs reported in Ref. [160].


function is thus given by:

wðkÞ ¼ mðkÞ � m0ðkÞm0ðkÞ

; (25)

which is reported in Fig. 16b (top for Ga and bottom for As K-edges). In the frame of the singlescattering (SS) approach,4 the k2-weighted w(k) function can be modeled as follows [505–510]:

k2wðkÞ ¼X

i

NiAiðkÞr2

i

e�2ri=l e�2k2s2i sin½2kri þ jiðkÞ�; (26)

where l is the photoelectron mean-free path, the sum over i runs over the different coordination shellsaround the absorbing atom, Ai(k) the amplitude function of the scattering atom, ji(k) the phase functionof the couple absorber/scatterer, Ni the coordination number and si the relative Debye–Waller factor ofthe ith shell.

By performing a Fourier transform of the w(k) function, weighted by kn (n ¼ 1, 2 or 3) to empiricallybalance the lost of EXAFS signal in the high k region, it is possible to single out the contributions, inthe R-space, of the different coordination shells, as shown in Fig. 16c. The peaks around 2.2, 3.7 and4.4 A correspond to the first (Ga–As), second (Ga–Ga) and third (Ga–As) coordination shells aroundGa in GaAs. Note that the distances of the three peaks reported in Fig. 16c are slightly shorter withrespect to the actual ones since the Fourier transform has not considered the phase function ji(k), seeEq. (26). Contributions from the higher coordination shells are not observed because, due to the limitedvalue of l, the photoelectron has a too low probability to reach the fourth coordination shell, to bebackscattered and to come back to the absorbing atom before the core hole has been filled. This is theorigin of the local nature of EXAFS spectroscopy. Each observed single shell contribution can then beback-transformed into k-space to obtain a ‘‘single frequency’’ wi(k) function, which allows to optimizethe structural parameters Ni, ri, and s2

i , once that the Ai(k) and ji(k) functions have been independentlymeasured or ab initio computed. So, for each coordination shell, the coordination number, the atomicdistance and the thermal factor can be extracted from an accurate EXAFS study.

The procedure described in Fig. 16, top curve in part (b) and part (c), for the Ga K-edge can beduplicated for the As K-edge so obtaining complementary information on the local environment aroundAs of polycrystalline GaAs (bottom curve in Fig. 16b and d). Beside binary compounds, EXAFSspectroscopy can be, in principle, applied to the three K-edges of a ternary compound or to the four K-edges of a quaternary compound. In general, EXAFS can provide quantitative local structuralinformation on the environment of any selected atom [505,506].

Due to its atomic selectivity and to its local sensitivity, EXAFS spectroscopy has been widely beenemployed in the characterization of semiconductors in all cases where XRD, based on long-range order,fails. This is the case of amorphous semiconductors [511–518] or of doped materials, both during

4 The single scattering (SS) approximation assumes that only two body paths, involving the absorber and a single scattering

atom only, contribute to the EXAFS signal. The correct approach is based on the multiple scattering (MS) approach where all

paths starting and ending in the absorbing atom are considered, independently to the number of scattering processes undergone

by the photoelectron through neighbour atoms. The SS approximation is always correct for a first shell analysis, while care

must be done when higher shell analysis is performed, see Section 4.6, where the importance of MS contribution is briefly

discussed.


growth or post-growth by implantation techniques [511,519–527]. These materials are, however,borderline with respect of the main topic of this review, and will be only rarely discussed. The attentionis focused on the great advantage of this technique relevant to the characterization of thin filmheterostructures, which is its atomic selectivity, making EXAFS a technique of choice in theinvestigation of buried interfaces and layers. Moreover, when fluorescence detection is used (see upperpart of Fig. 15), its remarkable sensitivity to highly diluted species enable the collection of signalemitted from extremely thin interface layers composed down to a single ML.

4.2. Pioneering works on bulk semiconductor alloys

XRD experiments have shown since the twenties that in bulk semiconductor alloys (e.g. pseudo-binary alloys of the type AxB1�xC), the lattice parameter (a) varies linearly with composition accordingto the Vegard’s law [528]: aðxÞ ¼ xaAC þ ð1 � xÞaBC. The nature of XRD datum implies that themeasured a value is averaged over a huge amount of unit cells and the extent of atomic displacementsfrom ideal lattice sites is included in the diffuse scattering background, which is generally moredifficult to be experimentally quantified and analyzed. Till the beginning of the eighties, due to the lackof any direct experimental evidence on the local structure around anion and cations in AxB1�xC alloys,the virtual crystal approximation (VCA) [529,530], which assumes that all atoms occupy the averagelattice positions defined by X-ray lattice constants, was routinely adopted to predict semiconductorband structure such as Eg, that one would to vary with x in a predictable way. Now, vide supra Eq. (14),Eg varies smoothly with x but exhibits a significant non-linear behavior or bowing effect [162–164,270,436,441]. Mikkelsen and Boyce have reported the first EXAFS measurements on InxGa1�xAsalloys, so providing the first experimental structural local data to be used in modeling semiconductorband structure from a correct starting point [531,532]. Before starting the review of literature data, it isuseful to introduce an unique nomenclature. Let call r0

AC and r0BC the first shell A–C and B–C bond

length in the binary compounds AC and BC. In a straightforward manner rAlAC and rAl

BC will represent theA–C and B–C first shell bond length in the ternary AxB1�xC alloy, and finally, the bond-length variationinduced by alloying effect will be defined as drAl

AC ¼ rAlAC � r0

AC and drAlBC ¼ rAl

BC � r0BC.

Coming to the results of the seminal works of Mikkelsen and Boyce [531,532], a combined Ga, Asand In K-edge study on a set of InxGa1�xAs polycrystalline solid solutions with x ranging from 0 to 1has been reported. They actually observe a significant variation of both Ga–As and In–As first shelldistances versus x, being drGaAs ¼ þ0:04 A when Ga is present at 2% in InAs and drInAs ¼ �0:05 Awhen In is present at 1% in GaAs, see bottom and top data in Fig. 17. However, the measured distancesare much closer to the respective values in the pure GaAs and InAs binary compounds than to theaverage VCA distances, compare with the middle curve in Fig. 17. A bimodal distribution of secondshell As–As distances has been found, corresponding to Ga–Ga, In–In and Ga–In second shell distances(Fig. 18a). Conversely, the cation sublattice has a broadened single distribution centered at the averagelattice distance, as predicted by the VCA model (Fig. 18b). Mikkelsen and Boyce have so demonstratedthat the VCA is violated at the local scale, since it drastically underestimates the differences in the firstshell Ga–As and In–As distances, but it represents a reasonable good approximation for thecoordination shells higher than the second one, so in asymptotic agreement with the long-range dataobtained from XRD.

One year after the first paper by Mikkelsen and Boyce [531], Zunger was able to explain the twounequal anion–cation bond lengths RAC and RBC in AxB1�xC zinc blende semiconductor alloys, observed


Fig. 17. First shell bond distances, Ga–As and In–As (lower and upper curves, respectively) vs. In content in the InxGa1�xAs

alloy. The average cation–anion distance calculated from the lattice constant (a) measured with XRD (ffiffiffi3

pa=4), middle curve,

follows accurately Vegard’s law [528]. Reprinted from J.C. Mikkelsen Jr, J.B. Boyce, Phys. Rev. Lett. 49 (1982) 1412, [531],

with permission. Copyright (1982) by American Physical Society.

Fig. 18. (a) As–As second shell distances in InxGa1�xAs alloy as a function of In content. Two As–As distances are

observed, the shorter one corresponding to As–Ga–As bonds and the longer one corresponding to As–In–As bonds. The

middle curve represents the VCA As–As distance. (b) Same as part (a) for the Ga–Ga, In–In and Ga–In second shell distances.

The cation–cation distances approach the VCA values (solid line). Reprinted from J.C. Mikkelsen Jr, J.B. Boyce, Phys. Rev.

B 28 (1983) 7130, [532], with permission. Copyright (1983) by American Physical Society.


by EXAFS, applying the principle of conservation and transferability of chemical bonds [270]. Heshowed that this bond alternation, manifested as a structural distortion to a local chalcopyrite coordinationaround the anions, explains also most of the observed optical bowing in semiconductor alloys.

In the framework of the Keating potential [533], Mikkelsen and Boyce results have been related tothe fact that, in semiconductors, bond bending force constants are weaker than bond stretching ones:long-range order is maintained by distortions in bond angles which accommodate bond lengths. As aconsequence, bond lengths exhibit a strong tendency to remain close to their ‘‘natural’’, unstrained,value [534–536]. In interface alloy layers of epitaxial heterostructures the situation is more complex. Inthis case there are three factors that, depending on the system, may tend to distort the elementarytetrahedral building block: alloying, tetragonal distortion and interface strain [537,538]. While thealloying effect is the same as in the bulk there is little information available on how the tetragonaldistortion, due to epitaxy with the substrate, will affect bond angles and bond lengths. This point will bedeeply discussed in Section 4.4.

Since the pioneering work of Mikkelsen and Boyce [531,532] on the InxGa1�xAs system, thisphenomenon has been systematically observed in several pseudo-binary semiconductor bulk alloys upto now investigated; among it is worth recalling, e.g. InxGa1�xP [539]; InxGa1�xSb [539]; GaAsxP1�x

[539–541]; InAsxP1�x [164–166,301]; ZnSnxTe1�x [539]; CdxMn1�xTe [542,543]; Sn1�xMnxTe [544];Hg0.79Cd0.21Te [521]; GexSi1�x [513,545–547]. Focusing now briefly on semiconductor bulk alloys ofthe IV–IV group, the paper of Kaijyama et al. [545] reports that Ge–Ge and Ge–Si bonds relaxcompletely, being close to the sum of their constituent element atomic radii (2.45 and 2.40 A,respectively). A study on the coordination around a Ge atom in the alloys revealed that Ge and Si atomsmix randomly throughout the compositional range studied. Woicik et al. report an EXAFS study on theGexSi1�x (x < 0:5) system observing that the first shell rGe–Ge and rGe–Si distances are compositionallydependent [547]. This accurate measurement was made possible by utilizing the experimentally derivedGe–Si atomic phase shift from the isoelectronic compounds AlAs and GaP. Strain and Coulombcontributions to the bond lengths are also discussed. More recently, the local structure around Ge inepitaxial films of Si1�x�yGexCy alloy has been investigated by De Salvador et al. [548] by means of GeK-edge EXAFS. As far as nitrides bulk compounds are concerned, the following alloys will bementioned: InyGa1�yN [549] and AlyGa1�yN [549].

4.3. Applications of EXAFS on semiconductor SL and thin films: the problem of epitaxial strain

All the experiments briefly discussed in Section 4.2, referring to EXAFS measurements on bulkpolycrystalline semiconductor alloys, have been performed in transmission mode, which allows the bestsignal/noise ratio. The polycrystalline nature of the sample allows to optimize the thickness x of thesample, assuring a good edge jump with a sufficient intensity of the transmitted beam. This techniquecannot be applied to epitaxial films because of the presence of the substrate, which does not allow anysignificant transmission through the sample. In these cases the EXAFS experiments are performed influorescence mode, see upper part of Fig. 15. In this case Eq. (23) does not hold and the absorptioncoefficient m(E) is obtained directly as the ratio between the fluorescence yield IF(E) and the beamintensity I0(E):

mðEÞx ¼ IFðEÞI0ðEÞ

: (27)


In fact, X-ray fluorescence, being one of the disexcitation channels, is proportional to the photonabsorption (i.e. the physical quantity directly measured in transmission mode) and the fluorescence fluxemitted from the sample as a function of the energy of the synchrotron beam is an EXAFS-like signal.Of course, the fluorescence detector must be able to perform energy resolved measurements, in order tosingle out Ka and Kb photons emitted by the selected atomic species from those emitted by thesubstrate and from the elastically scattered photons. EXAFS spectroscopy in fluorescence mode can beapplied on samples where the absorbing atoms are highly diluted, in order to ignore reabsorptionphenomena. This detection mode is clearly complementary to the transmission mode, where the higheris the density of the absorbing atom, the better is the signal/noise ratio.

Impurities in semiconductor alloys are a typical example of diluted systems and several applicationsof the technique can be found, see e.g. work of Oyanagi et al. who investigated the local structurearound Ga and As impurities in InP [550] as typical example of one of the first works in this field. In thefollowing of the present subsection we shall, however, focus the attention on the first papers reportingEXAFS analysis on thin solid semiconductor films, MQW and SL because, even if such systems arehighly concentrated on a bidimensional ground, they are extremely diluted on the three-dimensionalground probed by X-rays and thus represents an ideal topic for applying fluorescence EXAFS.

Results reported in the previous subsection refer to bulk pseudo-binary semiconductors, where thereported first shell bond variation, with respect to the corresponding binary compounds, are due toalloying effect only. Now, a strained epilayer may be grown on a substrate having a slightly differentlattice constant, provided its thickness is kept below a certain critical value. In this case, the strain dueto the lattice mismatch is elastically accommodated by a tetragonal distortion of the grown layer(pseudomorphic growth). In the case of perfect epitaxy the film will have two different latticeparameters: ak ¼ as in the growth plane and a? in the growth direction, vide supra Fig. 3 and Eqs. (1)–(4) which define the relationships among Dak and Das, the parallel and perpendicular strains (ek and e?),and the g, C12 and C11 constants.

This subsection is devoted to the discussion of bond-length variation in strained epitaxial films andheterostructures. In the case of a pseudo-binary thin film AxB1�xC epitaxially grown on a substrate wewill deal with rf

AC and rfBC which represent the first shell A–C and B–C bond length measured, whose

variations drfAC ¼ rf

AC � r0AC and drf

BC ¼ rfBC � r0

BC will be due to the simultaneous presence of twoindependent factors: strain and alloying. This will add a further degree of complexity to the problem.

Among the first papers on the topic we shall recall [165–167,551–568] where the problem ofestablishing the local structure around cations and anions in strained epitaxial layers has beenaddressed. This problem is not only of academic interest, because, besides the fundamental interest indetermining the strain accommodation mechanisms in semiconductor epitaxial layers, a strongmotivation to obtain a local atomic description of the strained layer structures arises fromsemiconductor technology as the presence of strain reduces the symmetry of the crystal and modifiesthe band lineups of the charge carriers, see Sections 1.2 and 2.

As for group IV-based systems three papers report for SixGe1�x alloys epitaxially deposited onSi(0 0 1) the absence of a significant variation of the bond lengths around Ge with changing the relativecomposition x of the films [564–566]. Successively, Oyanagi et al. report surface EXAFS results on 1, 2and 4 Ge MLs epitaxially deposited on Si(0 0 1) [567,568] (vide infra Section 4.7.2). Woicik et al.[569] have performed a polarization-dependent EXAFS study on the first shell study of strained Ge–Silayers grown on Si(0 0 1). Ge–Si bond lengths deviate only slightly from their unstrained values,however, the distortion of the cubic-unit cell by strain leads to measurable polarization-dependent


changes in first shell coordination and second shell distances. We will return to this point in Section4.7.2, where polarization-dependent EXAFS studies will be treated in detail. Finally, the structure ofthin strained layer GenSin SL grown on Si(0 0 1) has been investigated in the Ge LIII-edge study ofCastrucci et al. [570] using a multiple-scattering approach. Of interest is to underline that, in the case ofvery thin Ge2Si2 samples, the formation of a single phase, chemically ordered, Si–Ge alloy where thewidely spaced (1 1 1) planes are occupied alternatively by the same atom type has been evidenced.

Coming to III–V compounds, Takeda et al. [561] have measured the Ga–P, Ga–As and In–As bondlengths in a number of thin films lattice matched to InP; they have found constant interatomic distances,compatible with measurements by Woronick et al. [553] on lattice-matched In0.53Ga0.47As/InP. Thesame group has also investigated InAs/AlSb SL [551,552]. Woicik et al. [562,563], combining EXAFSresults with an X-rays standing waves study (vide infra Section 7.1), have demonstrated that themacroscopic elasticity theory is valid at the monolayer level in a binary-on-binary system (InAs/GaAs);in fact, they measured bond lengths compatible with the value dictated for symmetry reasons bygeometry once the lattice misfit is fixed.

First EXAFS investigation on the As environment in InAsxP1�x/InP compressively strained SL werepresented in 1994 by Lamberti et al. [165,166]; the reported As–In bond length which varies at most0.02 A with As concentration at the interface, implying that epitaxy with InP is accompanied by localstructural distortions, such as bond-angle variations, which accommodate the nearly constant As–Inbond length. One year later, Shioda et al. [556] report similar results on single InAsP layer capped by20 A of InP and grown by exposing the InP surface to AsH3 flow as a function of the arsenic exposuretime. A complete work on the combined optical (4 K PL) and structural (high-resolution TEM, high-resolution XRD, and EXAFS) study on the InAsxP1�x/InP (0:05 � x � 0:59) SL by Lamberti et al.appeared later [164], confirming the results reported in the first works [165–167,556]. Extracted fromthe last work, Fig. 19 reports the EXAFS spectra, their k-weighted Fourier transform and In–As firstshell distance obtained from the data analysis. The same group, in a parallel work [301], has reported anin-depth study comparing the first three coordination shells in the same set of InAsxP1�x/InPcompressively strained SL and in bulk alloys. It has been clearly shown that differences between thestrained layers and the bulk samples increase with distance from the central atom, the first shell bondlengths being practically constant in this system. The evidence available so far thus suggests that latticestrain is accommodated mainly by bond bending variations rather than by bond stretching distortions, asituation common to bulk alloys. Results emerging from this work will be discussed in detail in Section4.6, as an example of higher shell EXAFS study.

Deviations from this picture have been reported in strained systems by three groups[554,555,557,558,571]. Kuwahara et al. [557,558] have reported an interesting study of bond lengthsin compressively strained InAs and InAs0.6P0.4 layers on InP as a function of thickness of the epitaxialfilm (from 3 to 1000 A). They report a small, gradual, increase of the first shell As–In bond length at athickness they identify with the critical thickness for strain relaxation; the value of the bond lengthsaturates at the bulk value. This study therefore suggests that changes in the first shell bond length dueto different strain values might exist and be observable. In a successive work, Kuwahara et al. [571]report on the rAs–In bond-length relaxation in InP1�xAsx MLs epitaxially grown on InP in the0:08 < x < 0:80 range. They claim that the rAs–In bond length shows an anomaly around x ¼ 0:5,deviating from the linear interpolation between the values in a dilute limit (x 0, As:InP) and thestrained InAs monolayer (x ¼ 1). This unexpected compression found for x ¼ 0:5 is still notunderstood. It has been investigated in short period for the Ga–As bond length in (InAs)m(GaAs)n


Fig. 19. (a) Experimental kw(k) for seven InAsxP1�x/InP superlattices of different composition, ranging from sample 32

(x ¼ 0:05) to sample 141 (x ¼ 0:59). (b) Modulus of the k-weighted Fourier transform of the EXAFS functions reported in

part (a). (c) As–In bond lengths derived from a first shell EXAFS analysis as a function of the local As concentration x, as

obtained from refinement of high-resolution XRD pattern. Open squares refers to data collected in fluorescence mode on

epitaxially strained superlattices, while open circles refer to data collected in transmission mode on unstrained polycrystalline

samples measured for comparison. All EXAFS data have been collected at the GILDA BM8 beamline at the ESRF, Grenoble,

France. The experimental data have been compared with the theoretical prediction of the VCA [529,530] and Cai and Thorpe

[535,536] models (dashed line and full line, respectively). Reprinted from C. Lamberti, et al. J. Appl. Phys. 83 (1998) 1058,

[164], with permission. Copyright (1998) by American Institute of Physics.


superlattices by Oyanagi et al. [554] and in In1�yGayAs/GaAs MQWs by Proietti et al. [555]. These twogroups find that the Ga–As bond undergoes substantial stretching (0.06 and 0.19 A, respectively,relative to the distance in bulk GaAs) much more than predicted by any existing theoretical picture. Theorigin of these unexpected findings is still unclear. In fact, for (InAs)1(GaAs)1 superlattices total energycalculations [538] show that the GaAs bond length is stretched, relative to bulk GaAs, but only by0.02 A. A theoretical attempt to give a macroscopic interpretation of the EXAFS results claimed in[555] has been reported by Bonapasta and Scavia, who have performed ab initio total-energy andatomic-force calculations on several strained structures of two ideal InnGa8�nAs8 (with n ¼ 2; 3)compounds [192]. The authors come to the conclusion that the second stretched Ga–As distancereported in [555] (2.45 A) cannot be explained in terms of strain-induced lattice deformation occurringin the In1�yGayAs layers epitaxially grown on GaAs and that it could perhaps only be related tointerface effects.

Woicik reported a random-cluster study aimed to determine bond lengths in strained semiconductoralloys [197]. He computed the In–As and Ga–As bond lengths in In1�yGayAs alloy grown on bothGaAs(0 0 1) and GaAs(1 1 1) substrates, comparing his theoretical results with several experimentalvalues obtained with EXAFS on different systems. Woicik found that in the In1�yGayAs/GaAs(0 0 1)system the In–As and Ga–As bond lengths exhibits an uniform contraction, with respect to their bulkalloy values, upon decreasing y. In the In1�yGayAs/GaAs(1 1 1) system strain is found to split the bondlengths: those along ½1 1 1� direction are less contracted than those along ½�1 1 �1�, ½1 �1 �1� and ½�1 �11�directions, however, their average behavior is similar to that of the In1�yGayAs/GaAs(0 0 1) system[197].

Finally, as an example of EXAFS study on doped SL, the recent paper of Boscherini et al. ismentioned [524]. The authors present a Si K-edge EXAFS study aimed to probe a periodic Si d-dopedstructure in GaAs, for equivalent Si thickness of 0.02, 0.2, 0.5, 1, 2, and 4 ML. The presence of bothSi–Si and Si–As (or Si–Ga) bonds was detected. The variation of the coordination numbers as afunction of the equivalent thickness of the Si layers has been reported. The Si–Si coordination numberwas found to gradually increase with increasing thickness, but Si–Si bonds were always detected, evenat equivalent Si coverages of 0.02 ML. This indicates that the preferred growth conditions for Si–GaAsSL lead to widespread Si clustering and self-compensation, and suggests that lateral growth of suchclusters to achieve coalescence may be the main mechanism for Si QW development.

While structural characterization of semiconductor interface layers is of great importance from anapplicative point of view (see Section 1) we note that the local structure of strained interface layers wasstill a debated argument in semiconductor physics even in the middle of the nineties. Two importantcontributions have then definitively clarified the situation [187,188], showing that, for thin epitaxialstrained layers, clear changes in the In–As and Ga–As first shell bond length are present, which actuallyreverse the slope of the distance versus concentration relationship with respect to the bulk (unstrained)case observed by Mikkelsen and Boyce [531,532], see Fig. 17 in Section 4.2. The next subsection willbe devoted to briefly summarize the work of Romanato et al. [188,190].

4.4. The joint role of alloying and epitaxy in determining the first shell bond distances in strained

thin epitaxial layers: the InxGa1�xAs/InP case study

Even after the first works reviewed in Section 4.3, there was a continuing interest in strained layersand interfaces of semiconductor alloys especially in view of the effects that strain can induce on the


band alignment in a heterojunction [162–164,572], and on the structural ordering processes [573], up tothe structural instability driving the mechanisms of defects nucleation [574]. Basic to this problem isthe description of the local structure inside the unit cell of strained pseudo-binary alloys. We still haveto keep in mind that for unstrained bulk alloys, Mikkelsen and Boyce [531,532] have demonstratedconclusively (vide supra Section 4.2) that the variations of the lattice parameter are accommodated at alocal scale mainly by bond bending, while bond stretching has a much weaker dependence on thecomposition.

4.4.1. Bond-length variation in pseudomorphic filmsIn order to investigate if the bond-length variations exist and how they are related to the tetragonal

distortion, Romanato et al. [188] have performed an EXAFS analysis of a set of InxGa1�xAs/InP thinepitaxial layers varying the In atomic concentration; in this way the biaxial strain can change fromtensile (x < 0:53) to compressive (x > 0:53) [162,302]. Basic for that investigation is the quality oflattice structure; only pseudomorphic samples have been selected by means of a structural andmorphological characterization in order to avoid possible effects on the local structure due to thepresence of defect strain fields. In particular, indium atomic fractions, film thickness and parallel strain(ek) have been determined after a cross-check of the high-resolution XRD and of the Rutherfordbackscattering (RBS) channeling measurements. High-resolution XRD analysis has been performed bycollecting (0 0 4) and (4 4 4) reflections, along both h1 1 0i in-plane directions [575]. In all thecomposition range a good agreement (within �0.5 at.%) was found between RBS measurements andhigh-resolution XRD results based on the validity of Vegard’s law for the average lattice parameter andon the assumption that the ratio between the perpendicular (e?) and parallel (ek) strains is given by theconstant of Poisson’s effect: g ¼ �e?=ek, vide supra Eq. (4). The surface morphology of the sampleshas been characterized by atomic force microscopy (AFM), which is a very sensitive technique todetect misfit dislocations through the surface roughness induced by strain fields [576] and to single outthe micro-cracks occurring in tensile-strained films. Among the different samples grown, Romanatoet al. [188] chose for XAFS measurements those characterized by no measurable strain relaxation andby good surface morphology.

Fig. 20a reports the modulus of the k2-weighted Fourier transform of Ga K-edge EXAFS signals offive out of the samples measured by Ref. [188]: tensile-strained epitaxial layer (T), compressive-strained epitaxial layer (C), lattice-matched epitaxial layer (M), epitaxial layer who has undergone astrain relaxation process (R) and a polycrystalline GaAs sample (GaAs). Part (b) of Fig. 20 reports thecomparison between the inverse Fourier transforms of the first shell peak relative to the Ga EXAFSspectra of the C and R samples. The difference of frequency in k-space reflects different Ga–As bondlengths between compressive-strained and strain-relaxed samples.

The values of the first shell Ga–As and As–In bond lengths found in the work of Romanato et al.[188], are reported in Fig. 21a and b both as a function of the In atomic fraction and of the misfit(bottom and top scales, respectively). As a comparison to the case of unstrained ternary InxGa1�xAsalloys, the linear fit of Mikkelsen and Boyce data [531,532] and the prediction of the virtual crystalapproximation [529,530] are also reported. Error bars take into account only the statistical errordetermined by EXAFS analysis. However, in order to confirm the absence of systematic errors,Romanato et al. [188] measured also three fully relaxed samples with different In compositions (x ¼ 0,0.735, 1) finding values of the first shell Ga–As and As–In bond lengths compatible with the linear fit ofMikkelsen and Boyce data (vide supra Fig. 17) and that clearly differs from those in strained epilayers


(see Figs. 20b and 21). Romanato et al. have so demonstrated that the strain of the epitaxial film inducesa variation of the mean nearest-neighbor distances additional to that induced by alloying.

To explain, on a quantitative ground, the results summarized in Fig. 21, the authors of Ref. [188] haveproposed the following model. For a strained film of a generic ternary alloy AxB1�xC the total variationof the bond lengths drf

IC (I ¼ A or B), can be written as the sum of two contributions:

drfIC ¼ ðrf

IC � rAlICÞ þ ðrAl

IC � r0ICÞ ¼ drst

IC � drAlIC ðf ¼ film;Al ¼ Alloy; 0 ¼ binary compoundÞ;

(28)

where drAlIC is the small average variation of the first shell distances in the unstrained alloy rAl

IC, withrespect to those in the binary compound r0

IC, while drstIC is the mean variation of first shell distances in

the epitaxial film due only to tetragonal distortion produced by strain. To understand the relativecontribution of bond stretching versus bond bending in accommodating tetragonal distortion it ishelpful to consider the case of the binary zinc blende compound IC, for which drAl

IC is null by definition.The symmetry properties of the zinc blende structure and Poisson’s effect allow to find generalrelationships between ek and the first-order expansion of the bond length rf

IC, and of the angle between

Fig. 20. (a) Amplitudes of the k2-weighted Fourier transforms of Ga K-edge EXAFS signals of five out of the samples

measured by Ref. [188]: most tensile (T), most compressive (C), lattice matched (M), relaxed with x ¼ 0:735 and x ¼ 1

(polycrystalline GaAs). (b) Comparison of the inverse Fourier transforms of the first shell peak relative to the Ga EXAFS

spectra of the C and R sample. The difference of frequency reflects different bond lengths. EXAFS data have been collected at

the GILDA BM8 beamline at the ESRF, Grenoble, France. Reprinted from F. Romanato, et al., Phys. Rev. B 57 (1998) 14619,

[188], with permission. Copyright (1998) by American Physical Society.


Fig. 21. Length of In–As (a) and Ga–As (b) bonds for the strained and relaxed InxGa1�xAs/InP films as reported by Romanato

et al. [188]. The VCA, the linear fit of Mikkelsen and Boyce data on polycrystalline samples, and the curves obtained according to

Eq. (32) with different x values are also shown. (c) The results of a similar experiment repeated by Woicik et al. [187] on three films

of the same system: In0.21Ga0.79As, In0.50Ga0.50As and In0.74Ga0.26As on InP. The dashed lines are the calculated cubic (bulk) bond

lengths and the solid lines are the calculated tetragonal (strained) bond lengths. Parts (a) and (b): reprinted from F. Romanato, et al.,

Phys. Rev. B 57 (1998) 14619, [188], with permission. Copyright (1998) by American Physical Society. Part (c): adapted from J.C.

Woicik, et al., Appl. Phys. Lett. 73 (1998) 2219, [187], with permission. Copyright (1998) by American Institute of Physics.


the [0 0 1] axis and the bond direction y:5

ð1 þ gðxÞÞ drstIC

r0IC

¼ 2 � gðxÞffiffiffi2

p dy; (29)

drstIC

aðxÞ ¼2 � gðxÞ

4ffiffiffi3

p ek: (30)

Eq. (29) refers to the relative roles of the force constants of bond stretching and bond bending, a and b,respectively. Let us consider two limiting cases: Pauling’s principle on one hand (i.e. rigid covalentbonds, a @ b) and the VCA approximation on the other hand (i.e. rigid tetrahedral angles, a ! b). Inthe former case, drst

IC ! 0 and, from Eq. (29), g ! 2. In the latter case, dy ! 0 yields g ! �1,reflecting a hydrostatic-like deformation for the unit cell. The experimental values of g for the majorityof the semiconductors range between 0.8 and 1.3, i.e. quite far from both these limiting values, eventhough closer to Pauling’s limit. Therefore, a contribution from both bond stretching and bond bendingis expected to accommodate strain in the binary alloy.

Eq. (30) can be used to directly relate the parallel strain to the variation of the nearest-neighbordistances. The value of drst

IC for pseudomorphic epilayers of GaAs and InAs on an InP substrate hasbeen calculated using the misfit as the input parameter (points S in Fig. 21). The same calculationrelative to the system InAs/GaAs yields drInAs ¼ �0:053 A, in perfect agreement with the experimentalvalue determined by Woicik et al. [563]. Another limiting case is represented by an In0.53Ga0.47Asepilayer grown lattice matched on InP [162,163]. For this film the tetragonal distortion is null, thereforedrst

IC ¼ 0 (points M in Fig. 21). In order to determine the variation of drstICðxÞ as a function of misfit,

Eq. (30) has been generalized to the case of ternary alloys:

x drstACðxÞ þ ð1 � xÞ drst

BCðxÞaðxÞ

� �¼ 2 � gðxÞ

4ffiffiffi3

p ekðxÞ: (31)

The hypothesis underlying Eq. (31) are the following: (i) small deformations (as in Eq. (29), drstICðxÞ is

described by a first-order expansion in the atomic coordinates); (ii) random distribution of atoms onthe chemically disordered sublattice; (iii) the tetragonal distortion of the unit cell is described byPoisson’s effect in the framework of macroscopic elasticity theory. Eqs. (28) and (31) allow tocompute the parallel strain using the EXAFS determination of the first shell bond distances and drAl

IC

values from linear interpolation of Mikkelsen and Boyce’s data [531,532]. Romanato et al. [188]compares the results of this calculation to the values measured by high-resolution XRD, finding that inall cases the data are compatible within error bars. Conversely, Eq. (31) cannot be inverted to getindividual values of drst

ACðxÞ and drstBCðxÞ starting from ek, the ultimate reason being that no

5 Let us consider an atom positioned in the origin of reference frame and the polar coordinates of a next neighbour atom. If

the distortion of the unit cell is purely tetragonal, only variations of the polar axis dy must be taken into account because

variations of the azimuthal angle are null: df ¼ 0. Then, two relationships relate y to the angle between two contiguous bonds

c: c ¼ 2y if the plane of c is perpendicular to the film interface, c ¼ arcos½�cos2ðyÞ� in the other cases. Eqs. (29) and (30)

are obtained taking into account the Poisson’s effect relating the first-order variations of the film lattice parameter a, in the

directions parallel and perpendicular to the epitaxial plane dak and da?, i.e. dak ¼ ð4=ffiffiffi3

pÞ½dr þ r dy=

ffiffiffi2

p� and

da? ¼ ð4=ffiffiffi3

pÞ½dr þ

ffiffiffi2

pr dy�.


assumptions about the microscopic forces have been introduced to derive it. To this purpose Eq. (30)is generalized as follows:

drstICðxÞ

aðxÞ ¼ek

4ffiffiffi3

p f2 � ½ð1 � xÞgðxÞ þ xgIC�g; (32)

where 0 � x � 1 is what has been called by Romanato et al. [188] the force disorder parameter. It isworth noting that Eq. (32) is compatible both with the constraints given by points S and M and withEq. (30), i.e. with hypotheses (i)–(iii), for any value of x.

The origin of Eq. (32) can be explained discussing the limit values of x. Absence of force disorder,x ¼ 0, corresponds to the assumption of the Kirkwood potential [577], according to which uniquevalues of the force constants a and b are used independently of the atomic configurations. Thishypothesis implies that all the tetrahedra, i.e. the smallest deformable elements of the zinc blendestructure made of an atom and its four nearest neighbor’s, have common topological rigidity

parameters (as defined by Cai and Thorpe [535,536]) independently of their atomic configuration. Thismeans that an external force drives on the average the same length deformation independently of thebond type, i.e. a unique (compositionally averaged) elastic constant g must be assumed. The limit x ¼ 0is reasonable when applied to the tetrahedra centered on the C atoms of the chemically orderedsublattice, around which an average configuration with mixed bond properties can be considered. Itcannot hold in the case of tetrahedra centered on the atoms (A or B) of the chemically disorderedsublattice, as they are surrounded only by C atoms and therefore have the same configuration of thebinary limit compounds. For these tetrahedra it is more appropriate to assign force constants belongingto the binary compounds; as they are randomly distributed this leads to the opposite limit of thedisorder of the forces, x ¼ 1.

The two limits of x represent the extreme cases where all the tetrahedra are considered as centered onI or C atoms. On the contrary, the symmetry properties of zinc blende structure imply that the averagevalue of x has to be 0.5 under the assumption that the tetrahedra are not interacting. This value has beenused in Eq. (32) to compare the resulting curves with the experimental data reported in Fig. 21.Deviations from x ¼ 0:5 are not expected as far as interactions coupling contiguous tetrahedra can beneglected. However, to illustrate the maximum effect that can be induced by x on drst

IC, in Fig. 21 alsothe curves obtained for its two limit values have been reported. Even though the difference betweenPoisson’s constant of InAs and GaAs is one of the highest among the most common III–V and II–VIzinc blende semiconductor compounds (gGaAs ¼ 0:90 and gInAs ¼ 1:09), the important qualitativedifference of the models represented by the two limit values of x is reflected in a small quantitativedifference that is still within the uncertainty given by the data error bars. If, on one hand, their excellentagreement with the experimental data does not allow to deduce further insights on the value of x, on theother, it confirms the important result stated by Eq. (32): the variation of the bond length in strainedternary alloys is proportional to the long-range averaged strain.

Romanato et al. [188] concluded their work by underlying that the variation of the first shell bonddistances is proportional to ek, which actually inverts the slope of the distance versus concentrationrelation found in bulk alloys in the pioneering work of Mikkelsen and Boyce [531,532], see Fig. 17,epitomizing the advances made in growth of controlled strained heterostructures on one hand, and inthe EXAFS technique on the other. The connection from short-to-long-range description of strainaccommodation, performed by Eq. (31), relies only on hypotheses (i)–(iii) concerning long-range


averaged properties that have been experimentally demonstrated for a large number of semiconductoralloys. On the contrary, the long-to-short-range connection is described by Eq. (32). Romanato et al.[188] have discussed its limits and its influence on bond-length variation showing that the analyticalmodel, thanks to the general validity of the assumptions, can be easily applied to a large variety ofstrained semiconductor alloys. Summarizing, they have demonstrated that nearest-neighbor interatomicdistances in strained film can be evaluated by applying the matrix of macroscopic strain down to theinteratomic scale and linearly summing this effect to that due to alloying.

A few months later, Woicik et al. [187] published a similar work reporting combined As and Ga K-edge EXAFS study on three InxGa1�xAs/InP thin films (x ¼ 0:79, 0.50 and 0.26) confirming that ek,imposed by pseudomprphic growth on InP, opposes the natural bond-length distortion due to alloying[531,532], see Fig. 21c. The agreement between the results independently reported by Romanato et al.[188] (see parts (a) and (b) of Fig. 21) and Woicik et al. [187] (see Fig. 21c) is remarkable. This relevantexperimental observation, is able to explain also the result of the EXAFS experiment of the Woicikgroup [185]. In [185], the authors report an In K-edge study on a buried, 213 A thick In0.22Ga0.78Aslayer epitaxially grown GaAs. They determined a first shell rIn–As bond length of 2:581 � 0:004 A,corresponding to a strain-induced contraction of 0:015 � 0:004 A relative to the rIn–As bond length inbulk InxGa1�xAs of the same composition. The same sample was successively subjected also to DAFSmeasurements (vide infra Section 6), giving rise to results fully compatible with the picture emergingfrom the EXAFS datum [186].

4.4.2. Bond-length variation in strain-released epitaxial filmsIn the successive years, Drigo’s group complemented their original work on the InxGa1�xAs/InP

system [188] (deeply reviewed here above) by extending the study in two main directions. The firstdirection consists in the use of the same set of pseudomorphic InxGa1�xAs/InP thin films investigatedby Romanato et al. [188] to study the effect of strain and alloying up to the third coordination shellaround Ga and As [578]. This important work will be discussed hereafter, in Section 4.7.2, as anexample of polarization-dependent EXAFS study. The second direction deals with the study of thickerIn0.25Ga0.75As/InP films in order to investigate by EXAFS the local structure in an epitaxialsemiconductor thin film undergoing strain relaxation due to extended defects when the criticalthickness for their introduction is exceeded [579]. In this case, the situation becomes even morecomplex with respect to that discussed in Section 4.4.1, because the first shell bond-length variation isdue to three main factors: (i) alloy; (ii) strain due to epitaxial constraint; (iii) strain due to plasticdefects. This means that Eq. (28) still holds if we keep in mind that the drst term includes thecontributions of both epitaxial constraint and plastic defects.

Drigo’s group [188] has carefully chosen the thickness of In0.25Ga0.75As/InP films to obtain a varyingdegree of relaxation, ranging from pseudomorphic growth to completely relaxed state. As done in theprevious work [188], the authors have thoroughly characterized the films with complementarystructural techniques measuring the residual strain by XRD. The effect of strain release in the first shellrGa–As bond length is immediately evident from the first shell filtered EXAFS data reported in Fig. 22a,where the longer period in k-space of the most relaxed In0.25Ga0.75As/InP film with respect of that of apseudomorphic film of the same composition is visible. Authors found that the rGa–As bond lengthexhibits a linear decrease with decreasing residual strain. Fig. 22b reports the values of drst obtained bysubtracting to the drf

Ga�As measured by EXAFS on the films the alloying contribution, drAlGa�As, vide

supra Eq. (28), and thus including the contributions due to both epitaxial constraint and plastic defects.


Fig. 22b shows that, when plotted as a function of the average strain e, the values of drst exhibit a clearlinear functional dependence (full circles), which obeys to Eq. (30) [579]. In Fig. 22b the functiondescribed by Eq. (30) appears to perfectly interpolate all the available data points.

The new result reported in [579] is that Eq. (30) is able to describe not only the pseudomorphicsamples (full circles), in which the strain is uniform, but also the relaxed samples where the strain isneither uniform nor biaxial (open squares). This experimental evidence can be understood by thefollowing considerations. For strain-released samples, the strain is not uniform but, except for thevolumes around the defect cores, has a modulation on a mesoscopic scale (i.e., on a length scale largerthan a lattice cell size, but smaller than the sample dimensions). It is therefore possible to divide thebulk of the layer in small volumes where the strain tensor can be considered constant and Eq. (30) canbe applied to obtain the corresponding bond deformation. In other words, Eq. (30) transforms the straindistribution in a corresponding bond lengths distribution. On the basis of this consideration, it is thenobvious that the mean values of the two distributions are still related by Eq. (30) even when the strain isnot constant over the measured volume. This is what the agreement with the experimental data shownin Fig. 22b actually means.

Fig. 22. (a) Comparison between the first shell filtered signal for the most relaxed (dotted line) and the pseudomorphic

(continuous line) In0.25Ga0.75As/InP films. (b) Variation of rGa–As bond length with respect to the corresponding values in bulk

InxGa1�xAs/InP for pseudomorphic (full circles) and relaxed (open squares) films. The data referred to relaxed In0.25Ga0.75As/

InP films undergo the same linear behavior given by Eq. (30) for those obtained on InxGa1�xAs/InP pseudomorphic films with

different compositions, data taken from the previous work of Romanato et al. [188]. Adapted from M. Tormen, et al., J. Appl.

Phys. 86 (1999) 2533, [579], with permission. Copyright (1999) by American Institute of Physics.


From comparison between the variation of the first shell Ga–As bond length obtained by Drigo’sgroup on the pseudomorphic In0.25Ga0.75As/InP films [188] and on relaxed In0.25Ga0.75As/InP films[579] (Fig. 22b), it can be concluded that the bond lengths have an identical behavior as a function ofthe mean residual strain independently from its elastic or plastic origin. This result is reproduced by ananalytical model based on the transfer of the mean macroscopic deformation at a local level. Finally,the broadening of the bond-length distribution induced by extended defects was also discussed butauthors concluded that it is not experimentally detectable with EXAFS experiments [579].

4.5. Interface mixing in InxGa1�xAs/InP short period SL

As extensively discussed in Section 3.1 when a periodic A/B heterostructure is epitaxially grown, theA to B and B to A interfaces are far to be perfectly planar and chemically abrupt [302]. As a significantexample of the use of EXAFS spectroscopy in the characterization of semiconductor heterostructuresinterfaces, the results of Boscherini et al. on InxGa1�xAs/InP short period superlattices (five sampleswhich periodicity lies in the range 30–60 A) has been chosen [160]. It is evident that the choice ofsuperlattices characterized by a short period allows to maximize the fraction of interface layers withrespect to InxGa1�xAs and InP layers. The combined use of EXAFS data, collected at both As and GaK-edges, allow the authors to prove that the coordination numbers around As and Ga deviatesignificantly from those expected in an abrupt superlattice structure even if interface bonds are takeninto account, demonstrating the presence of unwanted interface layers between InP and InxGa1�xAs.Based on the growth sequence employed and on indications from high-resolution XRD Boscherini et al.modeled the structure as composed by the periodical repetition of four different alloys: (i) InP, (ii)InAsxP1�x, (iii) In0.53Ga0.47As and (iv) In0:53Ga0:47As1�yPy. While the desired In0.53Ga0.47As (well) islattice matched with the InP (barrier) the two ‘‘undesired’’ interface layers (InAsxP1�x andIn0:53Ga0:47As1�yPy) are not and thus undergo a tetragonal distortion. This has been evidenced byhigh-resolution XRD measurements, performed at the D2AM beamline at the ESRF, which have foundvalues of e? in the range �0.14% to þ0.87%, depending whether prevails the InAsxP1�x (wherea? > aInP) or the In0:53Ga0:47As1�yPy (where a? < aInP) interface, vide infra Section 5.1. This picturehas been confirmed, on the local ground, by EXAFS spectroscopy, as demonstrated in Fig. 23a wherethe inverse Fourier transform of the first shell peak fitted with only Ga–As contributions (bottom) is notable to reproduce the experimental spectrum in the low k-region, i.e. exactly where the contributions ofa low scattering atom as P are expected to be observed. Conversely, once the fit of the experimental datais performed with a combination of Ga–As and Ga–P contributions (top) the agreement becomesexcellent. In this regard it is worth noticing that for a superlattice with chemically abrupt interfaces (nointerface layers) Ga–P bonds are expected only at the interface. Now, Boscherini et al. [160] havedemonstrated that the observed Ga–P coordination numbers are always significantly higher thanexpected in such ideal superlattices with periods equal to that of the measured samples. At the AsK-edge they detect As–In and As–Ga contributions; however, a significant excess of As–Incontributions is measured with respect the abrupt interface case, even if interface bonds are takeninto account. These evidences demonstrate the presence of interface layers between In0.53Ga0.47As andInP. The coordination numbers measured are related to thickness and concentrations of the interfacelayers and quantitatively justify the average lattice mismatch measured by diffraction, see Fig. 23b.

Along the whole set of samples authors found the first shell bond length in the following ranges:2:466 � 0:006— < rGa�As < 2:49 � 0:02—; 2:596 � 0:007— < rAs�In < 2:61 � 0:01 A and 2:39�


0:06— < rGa�P < 2:45 � 0:05 A. This implies the presence of structural distortions that accommodatestrain at the local level. A good agreement was found between the XAFS results and high-resolutionXRD data that probe the structure in an average way.

Finally, Boscherini et al. [160] used their EXAFS results to discuss the problem of the band offsets atInxGa1�xAs/InP heterojunctions [193,194]. They underline the fact that in all simulations, even themost advanced, the VCA is adopted. Authors ask the question whether the VCA approximation, whichis used in most of the simulations present in the literature and which is false from the structural point ofview, is adequate or not in reproducing the electronic structure of the system and specifically the bandoffsets. They refer to the work of Peressi et al. [203] which, assuming an abrupt interface, neglect thepresence of interface layers. Deviations from the VCA are taken to be a perturbation from the averagestructure. The conclusion is that deviations from the VCA have a negligible effect on the valence-bandoffsets to linear order in the perturbation; that is, within linear-response theory the VCA is sufficientlyaccurate. Second-order variations have an effect that is estimated to be of the order of 40 meV. Thisvalue is approximately 10% of the total valence-band offsets (350 meV) for this system and is of thesame order of magnitude of the accuracy of the experimental band offsets determination by synchrotronradiation photoemission experiments, see Section 9. In a real heterostructure the situation is morecomplex due to the presence of strained interface layers, as has been demonstrated by the authors. Therelevance of Boscherini’s work [160] in this context is therefore to provide an accurate quantitativedescription of the local structure in a real system with strained interface layers, which can serve as abasis for simulations going beyond the VCA.

4.6. Higher shell data analysis: the necessity of a multiple-scattering approach

When the EXAFS study is extended to coordination shells higher than the first, care must be donebecause the simple EXAFS formula reported in Eq. (26) takes into account only single scatteringcontributions, i.e. the terms where the photoelectron is diffused by a single scattering atom before

Fig. 23. (a) Comparison of first shell fits for the Ga K-edge spectra of a InxGa1�xAs/InP short period superlattice

(period ¼ 37 A) without (bottom) and with (top) Ga–P contribution. The experimental curve is reported as the continuous line

while the fit is the dotted line. The top curves have been offset for graphical purposes. (b) Plot of the difference between the

entities n0(InAsP) and n0(InGaAsP), related to the coordination numbers determined from EXAFS (see Ref. [160] and related

appendix for more details), and the total amount of strain determined from HRXRD (see Section 5) and reported as the product

between the heterostructure period P and the average strain in the out-of-plane direction P Da?/a. Adapted from F. Boscherini,

et al., Phys. Rev. B 58 (1998) 10745, [160], with permission. Copyright (1998) by American Physical Society.


coming back to the absorbing atom. Actually, all possible scattering path where the photoelectron isdiffused by N different neighbors can contribute to the interference phenomenon and thus to theEXAFS signal according that the path is ended into the absorbing atom where it starts. All the pathswhere the number of scattering atoms is higher than two are called multiple-scattering paths. Oftenmultiple-scattering paths have a lower contribution to the overall EXAFS signal with respect to singlescattering ones, since the low free mean path of the photoelectron, l in Eq. (26), penalizes longer paths.However, in some cases the multiple-scattering contributions become important and must be includedwithin the EXAFS data analysis in order to avoid poor, or even misleading results. Limiting thediscussion to a three body path between the absorber A and two neighbor atoms B and C, beside theclassical two bodies SS contributions (A ! B ! A and A ! C ! A) also the MS A ! B ! C ! Ahas to be considered. The intensity of this three body MS contribution is weighted by a factorproportional to cos(g0), g0 being the A–B–C angle [507]. This means that MS contribution will beenhanced in case of collinear arrangements of atoms such as B–A–C or A–B–C, where the so-calledfocusing effect is fully operative. In order to have a serious description of the physics which is behindthe phenomenon of multiple scattering of photoelectrons, the reader should refer to the followingreferences, where he can found information on both theory and applications [510,580–593].

Local atomic investigations on strained semiconductor thin films quoted in the previous subsectionsare mainly limited to first shell structural information, and report both strained and unstrained bondlengths (see Section 4.3). The motivation to extend the comparison to higher coordination shells arisesfrom the answering the question how the distortions of the unit cell in the strained layer influences thelocal atomic structure. In fact, it is now well established that strain due to alloying in bulk pseudo-binary alloys is released mainly through bond-angle distortions, as bond lengths first shell interatomicdistances remain closer to the natural ‘‘unstrained’’ values than to the value predicted by the virtualcrystal approximation [185,187,188]. The tetrahedral building block is therefore distorted in order toaccommodate simultaneously a bimodal distribution of bond lengths and long-range order.

A detailed study of Pascarelli et al. on a set of different InAsxP1�x/InP strained superlattices(0:05 � x � 0:59) and InAsxP1�x (unstrained) alloys (0:21 � x � 1:00) has faced this problem [301]. Itis worth recalling that the InAsxP1�x/InP strained superlattices are grown by just exposing periodicallythe InP surface to the arsenic precursor (AsH3 or As2 depending whether MOCVD [289] or CBE [158]apparatus are employed), resulting in the formation of very thin InAsxP1�x layers (1–3 MLs) byAs $ P substitution effects, as extensively detailed elsewhere by combined high-resolution XRD, TEMand 4 K photoluminescence studies [159,161,163,164,166]. Differences in the local structure betweenthe thin InAsxP1�x strained layers in the superlattices and the bulk alloys are expected to arise only fromtetragonal strain due to epitaxy with the substrate, as interface strain is absent in this system. In thatwork the authors have modeled the kw(k) function as the sum of all the single scattering contributionsrelative to the first three coordination shells around As and the most important multiple-scatteringcontributions. The former trivially correspond to the zinc blende structure. The latter consist of threetriangular paths involving first shell atoms (the As–In–In triangle, hereafter called T1), and second shellatoms (the As–In–P and As–In–As triangles, hereafter called T2 and T3, respectively). These paths areillustrated in Fig. 24.

The contributions arising from the first three coordination shells around As are clearly visible(Fig. 25), and are fairly well reproduced by the model. For all investigated samples, Pascarelli et al.[301] found that the first peak was well reproduced by the contribution of four In atoms. As for thesecond peak, all samples have been tested for the presence of As–As and As–P second shell


interactions. In some superlattice samples with low As content (x ¼ 0:05), however, the best-fits wereobtained without contribution due to As–As interactions. The third peak was reproduced by an averagesignal due to 12 In atoms bonded to the second shell As (or P) atoms. To illustrate the importance of themultiple-scattering terms in this system, Fig. 25b shows the calculated signals due to the various pathsincluded in the model function. Note that the multiple-scattering terms, and in particular signal g(triangle T3), are important in the r range lying between the second and third shells. Fig. 25c shows thequality of the fitting when the model contains single scattering terms only. By comparing parts (a) and(c) of Fig. 25, it was concluded that multiple-scattering terms improve the quality of the fitting, inparticular in the r-space region between the second and the third peaks. Moreover, a correctreproduction of the position and amplitude of the second peak, as well as of the small peak lyingbetween the second and third peaks is possible only when multiple-scattering terms are considered,allowing one to obtain a more reliable set of parameters for the second and third shells. In fact, theabsence of multiple-scattering terms in the model function leads to an overestimation of the secondshell distance rAs–As of up to 0.1 A, a result that is not physically explainable [301].

As far as the unstrained InAsxP1�x bulk alloys are concerned, Pascarelli et al. [301] found that alsothis system follows the general behavior of pseudo-binary semiconductor alloys [531,532,539]: (i) thefirst shell distance rAs–In decreases very slightly as x ! 0, remaining much closer to the value in pureInAs than to the VCA prediction; (ii) the second shell splits into two As–P and As–As sub-shells. Theywere also able to observe, for the first time, a splitting of the third shell into two sub-shells, relative toIn atoms bonded to second shell P and As atoms, respectively. These two sub-shells lie at distinctdistances, rAs�InP

and rAs�InAs, respectively, as the In sublattice is distorted in order to accommodate the

almost constant In–P and In–As bond lengths. Second shell coordination numbers obtained are

Fig. 24. Atomic configurations relative to all the calculated signals included in the model kw(k) function, relative to single

((a)–(d)) and multiple ((e)–(g)) scattering paths from the central As atom in InAsxP1�x. An average signal has been used to

account for the two third shell As–In interactions, relative to a third shell In atom bonded to second shell P (d0) or As (d00)atoms, respectively. Adapted from S. Pascarelli, et al., Phys. Rev. B 56 (1997) 1936, [301], with permission. Copyright (1997)

by American Physical Society.


consistent with a random distribution of As and P atoms on the chemically disordered lattice for all theinvestigated bulk samples, in agreement with the known complete miscibility of pseudo-binary solidsolutions [540,543,594]. Fig. 26 summarizes the results on first, second and third shell distances foundby Pascarelli et al. [301] on the unstrained InAsxP1�x bulk alloys. Bond-angle fluctuations sy are foundto be relatively constant and equal to 28 throughout the composition range.

Fig. 25. (a) Amplitudes of the Fourier transforms, in the 3–20 A�1 k-range, of experimental k2w(k) in the InAsxP1�x system

(solid line) and of its best-fit model function (dotted line), performed with a model including both single and multiple

scattering contributions. (b) Fourier transforms of the k2w(k) calculated signals relative to all the scattering paths included in

the model function shown in part (a), the associated atomic configurations being shown in Fig. 24. (c) Same as part (a) where

the fit is performed with a model function that does not include multiple scattering contributions. Adapted from S. Pascarelli,



As far as the InAsxP1�x/InP strained superlattices are concerned, two effects influence the values ofthe measured structural parameters in strained layer superlattices, and must be taken into account tomake a comparison with bulk samples. The first effect is related to the loss of cubic symmetry of thecrystalline structure induced by tetragonal distortion; the second is due to the limited thickness (about3 MLs [159,161,163,164,166]) of the ternary layers in the samples. In a tetragonally distorted zincblende structure, shell splitting may occur: atoms in the same coordination shell in an undistorted cubicsystem are found to lie at two slightly different average distances with respect to a central atom. In astrained layer of InAs epitaxially grown on an InP substrate, if pseudomorphic growth is assumed,second shell rAs–As distances relative to atoms lying on the growth plane (rAs–Ask) are expected to beequal to second shell rP–P distances in the InP substrate, while distances relative to second shell Asatoms lying on the growth direction (rAs–As?) are a function of tetragonal distortion. The ratio betweenthe number of atoms seen using EXAFS at distance rAs–As? and rAs–Ask, respectively (N?/Nk), is afunction of beam polarization direction.6 In the polarization-averaged situation, typical of polycrystal-line samples, N? ¼ 8 and Nk 4, resulting in N?=Nk ¼ 2. Conversely, in the geometry adopted by

Fig. 26. (a) comparison between first shell As–In interatomic distances determined by EXAFS data analysis (circles),

theoretical prediction valid for bulk alloys from Refs. [535,536], and the virtual crystal approximation [529,530] (solid and

dashed line respectively) for the bulk unstrained InAsxP1�x alloy vs. x. (b) same as part (a) for the As–P second shell. (c) same

as part (a) for the As–As second shell. (d) same as part (a) for the As–In average third shell. Adapted from S. Pascarelli, et al.,

Phys. Rev. B 56 (1997) 1936, [301], with permission. Copyright (1997) by American Physical Society.

6 The radiation emitted by a synchrotron is polarized in the plane of the electrons orbit. As a consequence EXAFS spectra

performed on a single crystal (or on an epitaxial film) measure a fraction of in plane and out of plane distances which depends

on the angle between the single crystal growth direction and the Pointing vector of the synchrotron radiation beam, vide infra

Section 4.7 for a detailed discussion.


Pascarelli et al. [301] for the superlattices N? 9 and Nk 3, resulting in N?=Nk 3. The samearguments have been extended to the third shell, even though here the two sub-shell distances (namedas r0 and r00) are both a functions of tetragonal distortion, as third shell atoms lie in all cases out of thegrowth plane (see Fig. 24). In a polarization-averaged situation (polycrystalline alloys) the number ofatoms lying at distance r00 (further from the growth plane) is N 00 ¼ 4, and those at distance r0 (closer tothe growth plane) is N 0 ¼ 8, with N 00=N 0 ¼ 0:5. For superlattices, in the geometry adopted by Pascarelliet al. [301], they have N 00 5:5, N 0 6:5, resulting in N 00=N 0 0:85.

The second effect, related to the limited extension of the InAsxP1�x layers in the growth direction,changes the relative number of second shell P and As atoms, and therefore also the relative number ofthird shell InP and InAs, with respect to the situation in a bulk sample of InAsxP1�x. In fact, the thinnerthe InAsxP1�x layer embedded in InP, the higher the number of second shell P atoms with respect to Asatoms. In the limiting case of x ¼ 1 (pure InAs), the ratios N?(As–P)/N?(As–As), N0(As–InP)/N’(As–InAs), N00(As–InP)/N00(As–InAs), increase from zero (in bulk InAs) to 1/3, 1/6 and 1/3, respectively, for a3 ML InAs film embedded in InP.

The results relative to the interatomic distances in InAsxP1�x/InP strained superlattices are shown inFig. 27 (squares). There is evidence of deviations from the behavior of bulk alloys described above andsummarized in Fig. 26. The interatomic distances in the strained layers are on the average shorter thanthe corresponding ones in the unstrained alloys. In order to understand the origin of these discrepancies,

Fig. 27. Comparison between the interatomic distances for strained InAsxP1�x/InP superlattices determined by EXAFS data

analysis (squares), theoretical prediction valid for bulk alloys from Refs. [535,536] (solid line), and the theoretical prediction

of the strained layer model described by Pascarelli et al. [301]: (a) first shell As–In; (b) second shell As–P; (c) second shell

As–As; (d) third shell As–In, where the measured values of the third shell As–In distances are compared to two differently

weighted averages of rAs�InPand rAs�InAs

: assuming a random distribution of As and P atoms on the mixed lattice (dashed line),

and based on measured second shell coordination numbers (dotted line). Adapted from S. Pascarelli, et al., Phys. Rev. B 56

(1997) 1936, [301], with permission. Copyright (1997) by American Physical Society.


Pascarelli et al. [301] calculated first, second, and third shell interatomic distances in a tetragonallystrained semiconductor alloy thin film, based on a model that combines the macroscopic theory ofelasticity with the known structure of bulk pseudo-binary alloys. The model, able to satisfactory matchwith the experimental data (dashed lines in Fig. 27), is based on two assumptions: (i) the growth of thestrained ternary layers is pseudomorphic at all compositions and (ii) in the x ! 0 limit, which impliesnegligible tetragonal distortion, the behavior of the ternary layer out of the plane of growth is identicalto that of a bulk alloy.

Coming to the bond-angle distortions, authors of Ref. [301] concluded that they are quite differentfrom the well-known bond-angle distortions found in amorphous tetrahedral semiconductors, such asamorphous Si, Ge, GaAs, and GeN [511–513]. In fact, in these systems the bond-angle distributionremains centered at 109.478, and acquires a mean-square deviation of 6–98. In the case of InAsxP1�x/InP strained superlattices the average value of bond angles shifts with increasing tetragonal strain,while the disorder remains virtually unchanged. In contrast to the first and second shells, third shellmean-square relative displacement values are much larger than those found for the unstrainedInAsxP1�x bulk alloys, indicating a general increase in static disorder with increasing distance from thecentral atom, to be attributed to the combined effect of alloying and tetragonal distortion.

Coming to other higher shell studies, Tormen et al. [578,595] have investigated the lattice distortionof pseudomorphic epitaxial InxGa1�xAs/InP thin films by polarization-dependent EXAFS. Five sampleswith 0:25 < x < 0:75 have been investigated so covering both from tensile to compressive-strainedlayers. The measured second and third shell distances exhibit a clear dependence on the angle betweenthe photon beam and the sample normal, in agreement with the expected tetragonal distortion of theunit cell. A method is proposed to extract from the polarization-dependent measurements the values ofthe strain-induced split of second and third shell interatomic distances. The values obtained by thismethod are in excellent agreement with the predictions of a model that calculates the variations ofinteratomic distances due to strain by applying the macroscopic strain tensor at local scale and linearlysumming the known alloying effect. A more detailed description of these works is reported in Section4.7.2, especially devoted to polarization-dependent EXAFS.

Yu et al. [596] reported and EXAFS study on two shells surrounding Ga atoms in free standingAlxGa1�xN alloy films in the 0–0.6 x range. The first shell rGa–N bond length had only a weakcomposition dependence, roughly one-quarter of that predicted by Vegard’s law. As far as the secondshell distances are concerned, the rGa–Ga bond length was found to be 0.04–0.065 A longer than therGa–Al one. A bond-type specific composition dependence was observed for the second shell cation–cation distances. While the composition dependence of the rGa–Ga bond length is similar to 70%of that predicted by Vegard’s law, the rGa–Al bond length was essentially composition independent.Yu et al. concluded that the local strain in AlxGa1�xN was also accommodated by lattice distortionin the Al cation sublattice.

The microstructure of InxGa1�xN samples grown on sapphire substrates by electron cyclotronresonance plasma assisted MBE has been studied, as a function of the indium concentration, usingEXAFS, TEM and XRD by Katsikini et al. [597]. Authors used the electron and XRD patterns todetermine the correct composition of the samples. Phase separation phenomena are observed in theXRD pattern of the sample with the In content higher than 17%. The EXAFS analysis reveals that forIn concentrations up to 20%, the cation–N distances do not vary with the sample composition.Contrary to that, the cation–cation distances depend on the In concentration, and more specificallyrGa�Ga < rGa�In < rIn�In.


Let us now come to the discussion of short-range ordering in a quaternary alloy, a problem that arisesfrom the fact that the relative number of bonds is not simply determined by the composition. Let us usethe InxGa1�xAs1�yNy system as case study. The bond distribution in this quaternary can have two limits,in which the material can be thought of, for x ¼ y ¼ 0:5, either as InAs þ GaN (no In–N bonds) orInN þ GaAs (no Ga–N bonds); for arbitrary compositions it is possible to introduce an order parameterto describe the relative atomic short-range order [598,599]. Kim and Zunger discussed the oppositeroles of bond and strain energy in determining the degree of short-range order [598]. They studied thedistribution of bonds using Monte Carlo simulation and find that the number of In–N and Ga–As bondsincreases relative to random alloys. They also defined a short-range order parameter which is positivefor InN þ GaAs and in fact predicted a positive value in thermodynamical equilibrium. Short-rangeorder is predicted to have an important effect on the physical properties of the alloy, since its positivevalue is expected to increase the band gap [598]. The short-range order induced blue shift of the bandgap could therefore represent an intrinsic materials limitation since it would hinder access to the longestwavelengths (see Section 1). Clearly, an experimental quantification of the degree of short-range orderin InxGa1�xAs1�yNy is of fundamental importance.

From the experimental point of view the local structure and ordering in dilute nitrides has beenrecently investigated using EXAFS by three groups [599–602]. In the first published paper, Soo et al.[600], did not detect an In–N signal. Lordi et al. [601] concluded that, while the as-deposited alloy has arandom atomic distribution, annealing favors an increase of the relative number of In–N bonds.According to these authors annealing brings the system towards a thermodynamically more stable state,characterized by a ‘‘not quantified’’ degree of short-range order. Ordering was detected by Ciatto et al.in hydrogenated InxGa1�xAs1�yNy/GaAs single QWs [602] and in the dilute nitride InxGa1�xAs1�yNy

quaternary alloys an in Ga1�xAs1�yNy and InxGa1�xAs ternary alloys ad hoc grown to address theproblem of short-range order [599]. The two works of Ciatto et al. [599,602] will now be discussed insome more detail.

In [602] authors reported an In K-edge EXAFS study up to the second coordination shell on threeInxGa1�xAs1�yNy/GaAs single QWs (0:32 � x � 0:38, 0:027 � y � 0:052), grown by MBE on (1 0 0)-oriented GaAs substrates, with a well width w ranging from 60 to 80 A. Also samples subjected to apost-growth treatment at room temperature by atomic hydrogen irradiation at 100 eV (hydrogen dose of3:0 � 1018 ions/cm2) were investigated. Authors demonstrated the presence of a local N enrichmentaround indium for y > 0:04 bonds with respect to the random atomic distribution case. For thehydrogenated samples this tendency was enhanced. A local ordering was detect starting from lower Nconcentration (y ¼ 0:027). EXAFS results reported by Ciatto et al. [602] are in agreement with thetheoretical prediction by Kim and Zunger of an excess of In–N over In–As bonds [598]. Parallel PLmeasurements show that in hydrogenated InGa–AsN the band gap returns to the value of the non-hydrogenated alloy. The modification of electronic structure of the alloy following hydrogenation is dueto the strong interaction between H and the very electronegative N atom. Even if the introduction of Hin the alloy can break traditional bonds and induce the formation of new bonds, the results reported in[602] suggest that this is accompanied by an atomic rearrangement that increases the relative number ofIn–N bonds over the number of In–As bonds. Since the In enrichment around N causes a blue shift ofthe band gap [598] this can provide a further mechanism that drives the H-induced band gap opening. In[599], Ciatto et al. reported and In K-edge EXAFS study providing a quantitative determination of theeffect of annealing on the short-range ordering in InxGa1�xAs1�yNy alloys. In conclusion, authorsprovided the first quantitative determination of short-range ordering in as-deposited and annealed


InxGa1�xAs1�yNy samples using state-of-the-art EXAFS analysis tools. Measurable ordering has beenobserved, as the obtained probability for a N atom to occupy an In first neighbor site has been found tobe up to three times the random one. Notwithstanding this fact, the agreement between theexperimental data and the predictions based on Monte Carlo simulations of Kim and Zunger [598] isonly qualitative: even if ordering has the same sign of the predictions the measured order parametersare about one order of magnitude smaller than the predicted one. This weak ordering could explain theblue shift of the band gap observed in annealed InxGa1�xAs1�yNy. Parallel N K-edge NEXAFS studyand relative simulations supports the In K-edge EXAFS investigation (vide infra Section 4.9).

Also the recent work of De Salvador et al. [548] is worth noticing. The authors used Ga K-edgeEXAFS spectroscopy to determine the interatomic distances and the Debye–Waller factors up to thethird coordination shell in Si1�x�yGexCy alloy as a function of the carbon concentration. An increase ofstatic disorder with increasing the C concentration the Si1�xGex matrix has been observed, being theeffect larger for higher coordination shells. A parallel molecular dynamics study allowed De Salvadoret al. [548] to conclude that the static disorder is due to the strong deformations induced by the small Catoms in the Si1�xGex matrix.

4.7. Polarization-dependent EXAFS studies

As the synchrotron radiation is linearly polarized in the plane of the electron orbit, the single crystalcan be oriented in the electric field (E) of the photon beam in order to modulate the angle y0 betweenthe growth axis and E ideally in the 0–908 range. Each two-body atomic correlation contributes to thetotal EXAFS signal with a weight equal to 3 cos2(a), where a is the angle between the interatomicvector r, connecting the absorbing and the scattering atom, and the electric vector E (which isperpendicular to the X-ray beam). This sentence holds in the plane wave approximation and in thesmall atom limit only [603], however, it does provide the major polarization dependence and is thususeful for the sake of a qualitative discussion. The polarization dependence of the EXAFS cross-sectionallows structural determination with directional sensitivity; in fact, by exploiting the linear polarizationof the synchrotron beam and by orienting the sample with the surface normal either parallel orperpendicular to the electric vector of the impinging radiation it is possible to preferentially probe out-of-plane or in-plane atomic correlations [588,603,604]. As a consequence a modulation in the angle y0,between electric vector E and the growth axis [0 0 1] of the monocrystalline sample, implies amodulation in cos2(a) i.e. in the relative weight between in-plane and out-of-plane distances of thepseudomorphic film. In the ideal cases of y0 ¼ 0� (beam in grazing angle with respect to the surface) ory0 ¼ 90� (beam perpendicular to the surface), only out-of-plane or in-plane contributions are present,see Fig. 28a and b, where the y0 angle tuning is performed by rotating the sample around the verticalaxis perpendicular to the beam direction k.

Along this review strained layers play a primary role (see Sections 1.2 and 2 and the relevant list ofexamples along the whole review), it is thus evident that a technique able to discriminate between in-plane and out-of-plane bond lengths will be extremely powerful since it potentially allows to measureexperimentally both Dak and Da?, and thus to obtain ek, e? and g, see Eqs. (1)–(4). The independentmeasurement of Dak and Da?, represents the great power that polarization-dependent EXAFS has in thecharacterization of the strain of thin epitaxial films with respect to electron diffraction-based techniquesmeasuring either the in-plane lattice constant (LEED) or the in-plane to out-of-plane lattice constantratio (photoelectron diffraction and related techniques). In a practical case, however, the situation is far


to be as simple as the last sentence of the previous paragraph seems to tell us. In most of the cases, thevector r, connecting the absorbing and the scattering atom does not lie on the (0 0 1) plane nor isparallel to the [0 0 1] direction. This means that when performing a y0 ¼ 0� or 908 EXAFSmeasurement, the contribution of that scattering atom will be present in both cases but with differentweights. In this regard, the discussion of polarization-dependent EXAFS spectra collected on III–V andIV–IV semiconductor films or SL with zinc blende structure is particularly complex. The complexitycomes from the Td-like local symmetry of the absorbing atom, resulting in four r vectors relative tothe four nearest neighbors, located along the tetrahedral directions, which are r1 ¼ a=4 ½1 1 1�;r2 ¼ a=4 ½�1 �1 1�; r3 ¼ a=4 ½�1 1 �1�; r4 ¼ a=4 ½1 �1 �1�. None of these directions is parallel or perpendicularto the growth axis [0 0 1], but the sum over the four r contributions is almost independent from thepolarization. As a consequence, a rotation in y0 will leave almost unaffected the global first shellcontribution, and the analysis of higher shells must be done in order to appreciate significantpolarization effects and thus to be able to extract important information on the parallel andperpendicular strain via the determination of in-plane and out-of-plane bond lengths.

Due to these complexities the case of III–V and IV–IV semiconductor films with zinc blendestructure will be treated in Section 4.7.2 only. Section 4.7.1 concerns Ni, O and Mg K-edgepolarization-dependent EXAFS studies of NiO and MgO thin films (3–50 ML) pseudomorphicallygrown on metallic Ag(0 0 1) substrate. In these two case studies, for any K-edge, the absorbing atomlies in a Oh-like (octahedral) local symmetry. This means that among the six nearest neighbors

Fig. 28. Pictorial representation of the grazing (y0 0�) (a) and normal (y0 90�) (b) incidence geometries. k and Erepresent the wavenumber and the electric field vectors of the incoming X-ray beam, while y0 represents the angle between Eand [0 0 1] vector, normal to the sample surface. Substrate and film have been represented using gray and white rectangles,

respectively. Using the MgO/Ag(0 0 1) or the NiO/Ag(0 0 1) as case studies (where the six-fold coordinated cation has four in-

plane and two out-of-plane first shell O neighbors), parts (c) and (e) depict the sensitivity to the direction of the bond length of

the EXAFS technique as a function of y0. (c) y0 08 out-of-plane neighbors; (d) y0 45� in- and out-of plane neighbors; (e)

y0 90� in-plane neighbors. Due to the structure of NiO and MgO crystals, this scheme also holds when oxygen is the

absorbing atom.


(Fig. 28d) four lie in the (0 0 1) plane, and can be selectively detected in the y0 ¼ 90� geometry(Fig. 28c), while the remaining two are parallel to the [0 0 1] vector, and can be selectively detected inthe y0 ¼ 0� geometry (Fig. 28e). No intermixing between in-plane and out-of-plane first shell bondlengths is expected in these favorable cases (for the y0 ¼ 90� and 08 geometries).

Before entering in the discussion on the selected examples from the literature, some technicalconstraints that must be fulfilled in order to be able to collect good quality and meaningful data in apolarization-dependent EXAFS study have to be defined. In some beamlines, due to limitations in thesolid angle viewed by the fluorescence detector, the y0 ¼ 90� limit case cannot be reached (X-ray beamnormal to the surface). This limitation does not hold when the electron yield detection mode is applied,vide infra Footnote 7. For practical reasons the y0 ¼ 0� limit case can never be reached (X-ray beamparallel to the surface). The lower limit of the y0 angle is fixed by the simple geometric rule defining theprojection of the beam size on the sample. Being bh the horizontal size of the beam, its projection onthe sample will be bh cos�1(y0), which may not exceed the size S of the sample. Thereforeymin

0 ¼ arcsinðbh=SÞ. This means that bigger samples, at least in one direction, allow to reach lower y0

values and thus a better resolution between in-plane and out-of-plane contributions. Of course, the bh

can also be reduced by cutting the beam using the horizontal slits with consequent lost of photons onthe sample and thus of statistic in the fluorescence counts. Practically speaking, in order to be able tofully benefit of the polarization dependence of SR, it is very important to be able to prepare high qualityepitaxial growth on pretty long substrates (2–3 cm). Of course, the samples must also guarantee anexcellent spatial homogeneity, otherwise only averaged values will be extracted.

4.7.1. Polarization-dependent EXAFS studies on NiO and MgO films on Ag(0 0 1) substrate

In the last years, the physical properties of two-dimensional metal oxide epilayers on metal substrateshave become a topic of great interest [605–610]. Films of few ML can be deposited epitaxially on metalsubstrates by ultra-high vacuum techniques, yielding reproducible and well-characterized systems.

Due to the relatively large Eg, bulk NiO and MgO are usually classified within the insulating class ofsolids. However, it has been claimed by some authors that the Eg of the oxide, in the oxide/metalsystem, can be modulated by the film thickness T [607,611–613]. The ability to control T couldrepresents therefore a new technological opportunity for band-gap engineering: this makes such films ofpotential interest for main topic treated in this review. For highly ionic solids such as NiO and MgO, theEg basically corresponds to the energy required to perform oxygen to metal charge transfer. Now,quoted authors explain that the Eg reduction, observed for few ML-thick NiO or MgO layers on metalsubstrate, is due to the presence of charges images localized in the metal at the metal/oxide interfacehaving an opposite sign with respect to those present on the ionic oxide on top, which results in adecrease of the energy needed to perform the charge transfer from an oxygen atom to a Ni (or a Mg)atom [613]. Muller et al. have even inferred the presence of metal-induced states within the band gap ofMgO, at the MgO/Cu interfaces [607]. Conversely, Schintke et al. [609] reports that even a 3 ML-thickMgO film epitaxially grown on Ag(0 0 1) exhibits a band gap of about 6 eV, corresponding to that ofthe MgO(0 0 1) single crystal surface. It is therefore clear that the matter is already under debate.Before entering in the discussion of the polarization-dependent EXAFS studies, a brief overview on thecharacterization obtained with classical surface science and/or theoretical methods on both NiO/Ag(0 0 1) and MgO/Ag(0 0 1) are reported. In this regard, note that the choice of Ag(0 0 1) as substrateis related to the fact that its lattice parameter as ¼ 2:045 A is relatively close to half that of NiO(a=2 ¼ 2:088 A) and of MgO (a=2 ¼ 2:110 A), resulting in lattice strains compatible with the


pseudomorphic growth of few ML: ek ¼ �0:0206 and �0.0308 for NiO and MgO, respectively. We areso dealing with biaxial compressive-strained films, see Fig. 3a.

The structure of ultra-thin NiO films grown on Ag(0 0 1) has been studied with different techniques,such as Auger electron diffraction (AED) [614], photoelectron diffraction [615], primary beamdiffraction modulated electron emission (PDMEE) [616], LEED [616–618], electron energy loss [617]and direct [619,620] and inverse [620] electron photoemission spectroscopies. The films are found to bepseudomorphic to Ag up to a thickness of �5 ML. For higher coverages the strain is suggested to bereleased by the introduction of misfit dislocations [618]. XPS has been used by Luches et al. [615] andReissner et al. [621,622], the latter group having also reported an ultraviolet photoelectron spectroscopystudy. The film morphology has been investigated by means of scanning tunneling microscopy (STM)[623,624], which suggested a rather complex interface with NiO island formation and the presence ofvacancy islands in the Ag substrate after NiO deposition. Ultra-thin NiO films present also interestingmagnetic properties [625,626] different from the bulk [627]. Coming to the MgO/Ag(0 0 1) system,Wollschlager et al. have shown that the growth of the first few ML induces the formation of mosaicgrains [628] and Kiguchi et al. have given evidence for layer-by-layer growth [629]. Two STM studieshave shown a complex morphology of the first three MgO layers involving substrate disruption and theformation of small islands [609,630]. The epitaxial strain of the films has been found to be graduallyreleased as the film thickness is increased [628,629,631]. The comparison of the films obtained bymeans of different growth procedures in terms of morphology and structure has proved that reactivegrowth is the best method to obtain low defectivity films [628,632].

A complete polarization-dependent X-ray absorption study, at the Ni K-edge, has been reported byGroppo et al. [431,633–635] on the NiO/Ag(0 0 1) system performing experiments with three differentsample orientations: y0 ¼ 15�, 458 and 758. The effect of the sample thickness has also beeninvestigated measuring two samples with T ¼ 3 and 10 ML. Both samples have been capped by 5 MLof MgO to avoid surface hydroxylation.

The structure of NiO (Fig. 29a) exhibits an high number of aligned atoms. As a consequence the roleplayed in the overall EXAFS signal by collinear MS paths is important, see first paragraph of Section4.6. Fig. 29b reports the results of the comparison between experiment (shot dots) and fit (bold line) forthe NiO bulk, which acts as reference of an unstrained sample. Vertically shifted in the lower part of thefigure are also reported the resolved components of the different SS (continuous lines) and MS (dashedand dotted lines) paths contributing to the fit [634]. In the 1.5–3.0 A region the signal is dominated bythe first Ni–O and second Ni–Ni SS contributions, being the contribution of the third Ni–O shellnegligible. As expected, in the region between 3.0 and 6.0 A, the MS contributions are as strong as theSS ones. In the figure caption all these paths are described in details, referring to the cluster reported inFig. 29a. Note that a negative shell number (e.g. Ni(�2a)) refers to the atom obtained from thatreported in Fig. 29a with positive shell number (e.g. Ni(2a)) by axis reflection.

Fig. 29c and d reports the comparison between experiment (shot dots) and fit (bold line) for the 3 and10 ML-thick NiO layers as a function of the X-ray polarization (the y0 ¼ 15� and 758). From a simpleinspection to the shape of the experimental data a strong influence of the sample orientation is evident.Groppo et al. [431,633,634] have simulated the data of the 10 ML in normal and grazing geometriesand of the 3 ML in normal incidence (Fig. 29c) using as unique structural optimized parameters thevariations (with respect to the bulk 2.088 A) of the in- and out-of-plane Ni–O distances, defined as DRkand DR? in [634] which, in this case, simply correspond to (1/2)Dak and (1/2)Da? as defined in Eqs. (1)and (2). All higher shells distances (corresponding to half the SS path lengths) and all MS path lengths


Fig. 29. (a) Representation of the portion of the NiO cluster adopted in Ref. [634] for the MS calculations lying in the

positive region of the x-, y-, and z-axes. Small spheres represent the Ni, whereas the big ones refer to O. Number 0 identifies

the absorbing Ni atom, whereas the progressive 1–7 numbers refer to the first to seventh coordination shell around Ni(0). All

atoms belonging to the same shell are degenerate in the cubic symmetry of the bulk case and so do the scattering paths. The

letters following the numbers are used to distinguish atoms of the same shell once the degeneration is removed by tetragonal

distortion. (b) Reference sample: NiO bulk. Vertically shifted for clarity, from top to bottom the k3-weighted, phase


have then been fixed to the values obtained on the hypothesis of an ideal tetragonal distortion, i.e. allthe in-plane and out-of-plane distances are contracted/extended in the same proportion. On these basesthe authors have expressed all the changes in interatomic distances with respect to the bulk case interms of DRk and DR?. See Table 2 for the [0 0 1] polarization (grazing incidence, see Fig. 28a), whilefor the in-plane polarization a similar table has been reported in the appendix of [634]. For the strainedfilms, the polarization removes the degeneration of several scattering paths listed in the caption ofFig. 29b for the bulk unstrained case. As an example, the SS contribution from the first coordinationshell is split in two different contributions when a polarization along the [0 0 1] direction is taken intoaccount: the first path has a component along the polarization direction and involves two firstneighboring atoms (O(1c) and O(�1c), see Fig. 29a) while the second one has a null component alongthe polarization direction and involves four first neighboring atoms (O(1a), O(�1a), O(1b) andO(�1b)). The intensity of this last contribution is negligible with respect to the previous one. The samephilosophy applies for the successive SS and MS paths, so that 23 different paths have to be consideredin the data analysis, as reported in detail in the first column of Table 2 for SS and MS paths. All these 23different paths are characterized by different path lengths. Table 2 (third column) reports the analyticalexpressions for the variation in scattering path lengths, caused by pseudomorphism, defined as thedifference between the scattering path lengths in the bulk and in the film cases, respectively. All pathlength variations are functions of DRk and DR?. All these 23 paths have to be weighted by thecorresponding degeneration factors (second column in Table 2).

Coming to the 3 ML film measured at grazing incidence (Fig. 28a), the contribution of both silversubstrate and MgO cap have been included in order to improve the quality of the fit: compare bottomand top curves in Fig. 29d. From this analysis Groppo et al. determined the NiO–Ag(0 0 1) interfacedistance: dinterface ¼ 2:36 � 0:05 A. This value is expanded if compared to both NiO and Ag half latticeparameters (2.088 and 2.045 A, respectively) [634,635].

Fig. 30b summarizes the in-plane and out-of-plane Ni–O bond length obtained on NiO films ofthickness T ¼ 3 and 10 ML with EXAFS data collected at y0 ¼ 15�, 458 and 758. According to whatnaively schematized in Fig. 28, with y0 ¼ 15� (758) only R? (Rk) parameter is obtained with a highprecision, while for y0 ¼ 45� both Rk and R? parameters are simultaneously obtained but with muchhigher error bars. Within the experimental errors, the 3 ML film has both in- and out-of-plane Ni–Odistances compatible with those expected in the case of perfect pseudomorphism on Ag(0 0 1):Rk ¼ 2:046 � 0:009 and R? ¼ 2:12 � 0:02 A, resulting in ek ¼ �2:0 � 0:4% and e? ¼ þ1:4 � 0:9%.A rough film morphology, possibly including also the presence of NiO islands, is also suggested by theoptimized coordination numbers. Conversely, the 10 ML film is partially relaxed (Rk ¼ 2:052 � 0:006

uncorrected, FT of the w(k) of experimental (points) superimposed with the best-fit up to the seventh coordination shell (solid

line); first shell SS; second shell SS; third shell SS; fourth shell SS; Ni(0)–O(1a)–Ni(4a)–Ni(0) MS path; Ni(0)–O(1a)–Ni(4a)–

O(1a)–Ni(0) MS path; fifth shell SS; Ni(0)–O(1a)–O(5a)–Ni(0); sixth shell SS; seventh shell SS; Ni(0)–Ni(2a)–Ni(�2a)–Ni(0)

MS path; Ni(0)–Ni(2a)–Ni(7a)–Ni(0) MS path; Ni(0)–Ni(2a)–Ni(0)–Ni(�2a)–Ni(0) MS path; Ni(0)–Ni(2a)–Ni(7a)–Ni(2a)–

Ni(0) MS path. See part (a) for the path definition. (c) Same as part (b) for the NiO films. From top to bottom: 10 ML in

normal (y ¼ 75�) and grazing (y ¼ 15�) geometries and 3 ML in normal (y ¼ 75�). Only experimental data and fit are

reported. (d) Same as part (b) for the 3 ML NiO film in grazing (y ¼ 15�) geometry. The upper curves refer to a fit including

the signals from the tetragonally distorted NiO film only (i.e., with the same approach used in the fits reported in (c)). Bottom

curves refer to the fit performed by including the second shell Ni–Mg signal from MgO cap (dotted line) and the second shell

Ni–Ag signal from the Ag substrate (dashed line). White and gray-dashed parts differentiate the R region where the

experimental data have been fitted to those excluded from the fitting procedure. Adapted from E. Groppo, et al., J. Phys.

Chem. B 107 (2003) 4597, [634], with permission. Copyright (2003) by American Chemical Society.


and R? ¼ 2:101 � 0:006 A) without significant deviation from ideal two-dimensional film. TheEXAFS study reported by Groppo et al. ruled out any significant atomic interdiffusion process betweenthe silver substrate and the NiO film [634].

Groppo et al. [634] concluded by hypothesizing a two-step growth mechanism for NiO films on anAg(0 0 1) substrate. The first step is characterized by the nucleation of NiO crystallites perfectly

Table 2

Type, degeneration and length variation, due to tetragonal distortion, of the paths involved in the EXAFS data analysis of the

NiO/Ag(0 0 1) films reported in Ref. [634] in the case of [0 0 1] polarization (grazing incidence, see Fig. 28a)a

Degeneration Path length variation

SS paths

Ni(0)–O(1c)–Ni(0) 2 DR1 ¼ DR?

Ni(0)–Ni(2c)–Ni(0) 8 DR2 out ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2R2

1 þ 2R1ðDRk þ DR?Þ þ DR2k þ DR2

?

q�

ffiffiffi2

pR1

Ni(0)–O(3)–Ni(0) 8 DR3 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3R2

1 þ 2R1ð2DRk þ DR?Þ þ 2DR2k þ DR2

?

q�

ffiffiffi3

pR1

Ni(0)–Ni(4c)–Ni(0) 2 DR4 ¼ 2DR?

Ni(0)–O(5e)–Ni(0) and

Ni(0)–O(5f)–Ni(0)

4–4 DR5 out ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi5R2


?

q�

ffiffiffi5

pR1

Ni(0)–O(5c)–Ni(0) and

Ni(0)–O(5d)–Ni(0)

4–4 DR5 out ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi5R2

1 þ 2R1ðDRk þ 4DR?Þ þ DR2k þ 4DR2

?

q�

ffiffiffi5

pR1

Ni(0)–Ni(6c)–Ni(0) 8 DR6 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi6R2


?

q�

ffiffiffi6

pR1

Ni(0)–Ni(6a)–Ni(0) 16 DR6 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi6R2

1 þ 4R1ðDRk þ 2DR?Þ þ 2DR2k þ 4DR2

?

q�

ffiffiffi6

pR1

Ni(0)–Ni(7b)–Ni(0) and

Ni(0)–Ni(7c)–Ni(0)

4–4 DR7 out ¼ 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2R2


?

q� 2

ffiffiffi2

pR1

MS paths

Ni(0)–O(1c)–O(�1c)–Ni(0)

and Ni(0)–O(1c)–

Ni(0)–O(�1c)–Ni(0)

2–2 DR ¼ 2DRk

Ni(0)–O(1c)–Ni(4c)–Ni(0)

and Ni(0)–O(1c)–Ni(4c)–

O(1c)–Ni(0)

4–2 DR ¼ 2DR?

Ni(0)–Ni(2c)–Ni(�2c)–Ni(0)

and Ni(0)–Ni(2c)–

Ni(0)–Ni(�2c)–Ni(0)

8–4 DR ¼ 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2R2


?

q� 2

ffiffiffi2

pR1

Ni(0)–Ni(2c)–Ni(7c)–Ni(0)

and Ni(0)–Ni(2c)–

Ni(7c)–Ni(2c)–Ni(0)

16–8 DR ¼ 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2R2


?

q� 2

ffiffiffi2

pR1

Ni(0)–O(1a)–O(5c)–Ni(0)

and Ni(0)–O(1c)–O(5c)–Ni(0)

8–8 DR ¼ 1

2DRk þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2R2


?

qhþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi5R2


?

q� ð

ffiffiffi2

pþ

ffiffiffi5

pÞR1

iNi(0)–O(1a)–Ni(2b)–Ni(0) 16 DR ¼ 1

2DRk þ DR?�þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2R2


?

q�

ffiffiffi2

pR1

ia Atomic labels refer to Fig. 29a. See Appendix A of the original work for the same information in the case of the in-plane

polarization (normal incidence, see Fig. 28b).


matched with the substrate, starting from islands: this phase is characterized by a great surface roughnessso that the second shell coordination numbers, N2 in Eq. (26), obtained in both [0 0 1] and [1 0 0]polarizations, and even the first coordination number obtained with the out-of-plane polarization, arelower than the expected in the case of a perfect bidimensional layer. In the second step, occurring around4–6 ML the elastic energy stored during the distortion increases until it is partially released through thecreation of dislocations. At the same time, the NiO islands grow and begin to connect together until thefilm grows in a completely relaxed manner showing, within the experimental errors, coordinationnumbers in agreement with the hypothesis of a perfect bidimensional film.

To validate the picture emerging from EXAFS experimental data the same authors, in collaborationwith Pisani’s group [635], have successively also performed periodic ab initio calculations withCRYSTAL code [636]. The supported film was simulated by a two-dimensionally periodic slab of fivelayers of silver atoms parallel to the (0 0 1) face, epitaxially covered on both sides with 2 ML of NiO(Fig. 30a). A hybrid-exchange Hamiltonian was adopted because of its satisfactory performance indescribing the bulk properties of both silver and nickel oxide [626], and a basis set of triple-zeta qualitywas used for all atoms. The equilibrium geometry of the substrate, and that of an epitaxial NiOmonolayer was there determined. In particular, the O-on-top configuration was found more stable thanthe Ni-on-top one by 0.25 eV/NiO unit. The z coordinates of all atoms of the oxide have beenoptimized. The energetic and geometric features of the optimized structure are as follows: interactionenergy per NiO unit 0.21 eV; distance between O and Ag surface 2.46 A; dinterface 2.40 A; Rk has been

Fig. 30. (a) Representation of the optimized bi-dimensional slab used in the ab initio simulations reported in Ref. [635] for

the modeling of the NiO/Ag(0 0 1) system. Silver atoms in gray, oxygen atoms in red and nickel atoms in blue. The bottom

NiO bi-layer has been added to increase the symmetry of the system, which reduce the computational cost of the simulation.

(b) Summary of the in- and out-of-plane distances obtained from the EXAFS results reported in Refs. [634,635] using different

polarization geometries and comparison with ab initio simulations. The solid line represents the values calculated assuming

NiO bulk elastic constants [637] and a value for bulk NiO a/2 of 2.088 A.


constrained to that of the silver substrate (pseudomorphism model) while R? has been optimized. Thetheoretical value R? ¼ 2:10 A is in excellent agreement with the Ni K-edge EXAFS value:2:118 � 0:02 A. The same holds for dinterface ¼ 2:40 A, to be compared with dinterface ¼2:37 � 0:05 A. Fig. 30b summarizes both experimental and theoretical data reported in [634,635].

The parent MgO/Ag(0 0 1) system has been investigated in the polarization-dependent EXAFSstudies of Luches et al. [638,639]. In these studies combined Mg and O K-edge data are reported, bothcolleted in total electron yield mode. As for the Mg K-edge, the T ¼ 3, 10 and 20 ML-thick films havebeen capped with 5 ML of NiO to avoid surface hydroxylation. T ¼ 3, 10, 20 and 50 ML-thick filmshave been in situ grown (thus without cap) for the O K-edge measurements. The T ¼ 50 ML-thick filmhas been used as reference for a totally unstrained crystal.

The quality of the raw experimental data collected at the Mg and O K-edges can be appreciated inFig. 31 top and bottom parts, respectively. The quality of the w(k) function for the T ¼ 10 and 20 ML-thick films is comparable with that obtained for the standard samples and only the T ¼ 3 ML filmsexhibit a lower signal to noise ratio. This is rather impressive by considering that we are dealing withlow energy EXAFS measurements and that 1 ML of MgO corresponds to 1:15 � 1015 Mg and O atomscm�2.

Due to the important ek (�0.0308), the difference in ak between the T ¼ 3, 10 ML films (measured innormal geometry) film and the unstrained MgO polycrystalline sample can be qualitatively appreciated

Fig. 31. Mg (top) and O (bottom) K-edge w(k) of the 3, 10 and 20 ML MgO films grown on Ag(0 0 1) substrate, measured at

normal (?) and grazing (k) incidences. Reference for unstrained lattices have been a MgO single crystal and a MgO

polycrystalline sample for Mg K-edge and a 50 ML MgO film for the O K-edge. Adapted from P. Luches, et al., Phys. Rev. B

69 (2004) 045412, [638], with permission. Copyright (2004) by American Physical Society.


just by a simple inspection to the imaginary part of the Fourier transform of the corresponding w(k)functions, as reported in Fig. 32a. The summary of all the EXAFS data analysis is reported in part (b) ofFig. 32. Luches et al. [638] have found that, in analogy with the NiO/Ag(0 0 1) system [634], the 3 MLfilms are pseudomorphically strained, matching the Ag(0 0 1) in-plane lattice parameter. The out-of-plane lattice parameter of this phase is expanded to the value calculated by using the bulk MgO elasticconstants [640]. The compressive in-plane strain and the expansive out-of-plane strain are graduallyreleased with increasing film thickness and the bulk-relaxed structure is reached at 20 ML. Theintermixing between the MgO films and the Ag substrate is negligible at the atomic scale. Finally, the OK-edge spectrum collected in grazing geometry on the T ¼ 3 ML film has allowed Luches et al. todetect the MgO–Ag(0 0 1) interface distance: dinterface ¼ 2:51 � 0:03 A. This value is in goodagreement with the calculated value of 2.45 A [641], obtained by an ab initio periodical approach basedon the CRYSTAL code [636]. The value measured by polarization-dependent EXAFS improves theprecision of the one obtained by joint LEED and primary beam diffraction modulated electron emissiontechniques, 2:39 � 0:06 A [641]. This significant interfacial expansion, 20 � 1% with respect to bulkAg or MgO interlayer spacing, may have interesting implications on the electronic properties of thevery thin layers, reducing the influence of the metallic substrate in hybridization and charge screening.On the opposite system, Ag/MgO(0 0 1), a similar expansion has been measured by EXAFS andGIXRD [642]. As discussed above, also the similar NiO/Ag(0 0 1) system exhibits a comparableelongation of the interface distance: 2:37 � 0:05 A [634,635]. A comparison between the EXAFSresults obtained on the NiO/Ag(0 0 1) and the MgO/Ag(0 0 1) systems is given in [639].

An other open point on thin oxide layers grown on metal substrates concerns the enhancement of thechemical reactivity as experimentally observed by some authors [612,643,644]. It has also been argued

Fig. 32. (a) Imaginary part of the k2-weighted FT of the Mg K-edge w(k) function of the 3 (dotted line) and 10 (dashed line)

ML-thick MgO films grown on Ag(0 0 1) measured at normal incidence (y ¼ 90�) compared with that of MgO polycrystalline

sample (full line). (b) Out-of-plane and in-plane Mg–O distance obtained by the analysis of Mg (full markers) and O K-edge

(open markers) EXAFS data for the different film thickness and for the measured MgO reference samples, with the relative

uncertainties. The in-plane and out-of-plane values for a bulk (gray square) and in the case of perfect pseudomorphism with

Ag(0 0 1) (gray circle) are also indicated. The solid line represents the values calculated assuming MgO bulk elastic constants

[640] and a value for bulk MgO a/2 of 2.1055 A. (a) Unpublished, (b) reprinted from P. Luches, et al., Phys. Rev. B 69 (2004)

045412, [638], with permission. Copyright (2004) by American Physical Society.


that the presence of the metal substrate can alter significantly the electronic structure of the oxide andinfluence its chemical properties, with a prospective range of important applications [612]. In the latterrespect, ab initio simulations of perfect oxide/metal epilayers [626,645] have given so far a differentindication, namely, the electronic structure of the oxide is modified only in a strict vicinity of theinterface. The question has therefore been raised whether residual film defectivity could be responsiblefor the observed enhancement of chemical activity [643,644,646,647] and other evidence of modifiedelectronic structure, such as the shift of oxygen core levels, in which case a perfectly epitaxial overlayerwould be a poor model of the real systems. In this regard, the comprehensive works of Groppo et al.[431,634,635] and Luches et al. [633,638,639], here reviewed, have demonstrated that the experimentalstructural values obtained with polarization-dependent EXAFS are in excellent agreement with thoseobtained with an ab initio calculation [626,635,645] performed on idealized bidimensional oxide films.Therefore the high reactivity of oxide films experimentally observed and never reproduced theoreticallycannot be ascribed to significant difference in the structure of real systems and their theoretical models[635].

4.7.2. Polarization-dependent EXAFS studies on conventional IV–IV, III–V and II–VI semiconductorsComing back to more classical semiconductor systems, for the IV–IV semiconductor alloys Aebi

et al. [648] have performed Ge K-edge EXAFS studies on nominally pure Ge layers buried in singlecrystal Si(0 0 1). The dependence on thickness, number of Ge layers and growth temperature isexplored. Authors found that the technique exhibits a considerable sensitivity to the quality of theepitaxial growth. In particular, the degree of mixing of the Si and Ge layers was found to be a functionof the growth temperature. The quantitative analysis provides estimates of intermixing in the thinnestlayers that are compatible with results of complementary Raman measurements. A weak polarizationdependence of the Ge K-edge EXAFS is observed. In this regard a great improvement was made byWoicik et al. [569] who have performed a polarization-dependent EXAFS study on the first shell ofstrained GexSi1�x layers grown on Si(0 0 1). According to the previous literature data (reviewed in thiswork in Sections 4.3 and 4.4), Woicik et al. [569] proposed a model where the strain within theGexSi1�x layer is accommodated primarily through bond-angle rather than bond-length distortions. Thetetrahedron centered on a Ge atom should therefore exhibits four, in first approximation, equivalent firstshell bond lengths (r) but two unequivalent families of bond angles, labeled as j and j0 in the schemereported in Fig. 33a. This tetrahedron is under compressive strain in the growth plane (0 0 1). Thelattice parameters parallel and perpendicular to the interface are given in terms of the bond length r andbond angle j:

ak ¼ ð2ffiffiffi2

pÞr sin

j2

�and a? ¼ 4r cos

j2

�: (33)

By differentiating to the first-order equations (33), Woicik et al. [569] correlated the macroscopicstrains ek and e?, see Eqs. (1) and (2), to the microscopic distortions Dr and Dj:

ek ¼Dak

a¼ Dr

rþ Dj

2ffiffiffi2

p ; (34)

e? ¼ Da?a

¼ Dr

r� Djffiffiffi

2p : (35)


Combining Eqs. (34) and (35) one obtains:

e? ¼ �21 � ð

ffiffiffi2

pðDr=rÞ=DjÞ

1 þ ð2ffiffiffi2

pðDr=rÞ=DjÞ

ek: (36)

Now, recalling Eq. (4): e? ¼ �ð2C12=C11Þek, it is evident from Eq. (36) that the ratio between themicroscopic deformations, ðDr=rÞ=Dj, can be written as a function of the macroscopic elastic stiffnessconstants C11 and C12:

Dr=r

Dj¼ 1ffiffiffi

2p 1 � ðC12=C11Þ

2ðC12=C11Þ þ 1

� �; (37)

which represents the microscopic analogous of Eq. (4). On the basis of the above described model, andby fixing Dak to the value expected by assuming perfect epitaxy with the Si(0 0 1) substrate, Woiciket al. [569] estimated for the Si0.784Ge0.216/Si(0 0 1) system the following microscopic deformations:Dr ¼ �0:008 A, Dj ¼ �0:08� and Dj0 ¼ þ0:04�, see Fig. 33a. The predicted Dr value is borderlinewith EXAFS sensitivity, but these distortions implies a significant increase in the out-of-plane latticeconstant: Da? ¼ 0:035 A. Because the small strain-induced bond-length change is negative, thedistortion of the tetrahedral angles must account for the much larger, 0.035 A, expansion in a?. Thisrelatively large distortion should be evident in a second shell EXAFS analysis, where the in- or out-of-plane second-neighbor distances are expected to be d ¼ 2r sinðj=2Þ and h ¼ 2r sinðj0=2Þ, respectively,see Fig. 33a.

Fig. 33. (a) Schematic representation of a tetrahedron under biaxial compression in the growth plane (0 0 1), with four

equivalent first neighbor bond lengths r and two families of unequivalent bond angles: j and j0. (b) k2-weighted Fourier

transforms of the Ge K-edge EXAFS spectrum collected from a Si0.784Ge0.216/Si(0 0 1) film oriented with the polarization

vector E of the synchrotron radiation aligned parallel (bold line) and perpendicular (line) to the growth axis [0 0 1]. Also

reported are the in- and out-of-plane second neighbor distances d and h, respectively. Adapted from J.C. Woicik, et al., Phys.

Rev. B 55 (1997) 15385, [569], with permission. Copyright (1997) by American Physical Society.


Coming to the experimental results, the k2-weighted FT obtained by Woicik et al. [569] on aSi0.784Ge0.216/Si(0 0 1) film are reported in Fig. 33b in both in- (thin line) and out-of-plane (bold line)polarizations. As expected, the differences in the first shell signal are minimal, but a systematic shifttowards lower radial values is observed for the higher shells when the in-plane polarization is used. Toavoid any risk of systematic error in the EXAFS data analysis, the authors reported, for both first andthe second shell bond lengths, the differences between the values measured in the two polarizations(Dr ¼ Drout � Drin): Dr1 ¼ �0:001 � 0:005 A and Dr2 ¼ �0:02 � 0:01 A. In agreement with thepresented model, the contraction of the first shell bond distance was within the error bars, but Woiciket al. [569] were able to evidence the effect of strain in the second shell signal.

More recently, Demchenko et al. [649] employed Ge K-edge polarization-dependent X-rayabsorption spectroscopy to study the local microstructure of Ge layers buried in silicon. The layers withthickness from 6 to 20 MLs of Ge were grown by MBE on Si substrate and were covered by 20 nm ofSi cap. Authors observed the changes in atomic order around the Ge atoms in buried with respect to thatin crystalline Ge. A substantial increase in intensity, broadening and chemical shift of the X-rayabsorption near-edge structure spectrum for 8 ML buried Ge film was observed and explained in termsof an increase in density of electron states caused by increase in the localization of the states due topotential appearing at the Ge island boundaries and indicated the formation of quantum dots [649]. Ofcourse, the modulations of the in-plane and the out-of-plane radial distribution as a function of the Gefilm thickness has been discussed.

The work of Tormen et al. [578] will now be discussed in detail, first because it represents one of thebest example to show the potentialities of the polarization-dependent EXAFS technique, representing acompletion of the previous work of the Woicik et al. [569], second because the investigated system,InxGa1�xAs/InP (0:25 < x < 0:75, corresponding to þ0:0195 < ek < �0:0142), represents one of themost important system for optoelectronic applications and last, but not least, because it represents theextension to the second and third shells around Ga and As of the first shell study previously reported bythe same group in Ref. [188] and here deeply reviewed in Section 4.4. The data analysis reported byTormen et al. [578] has been performed on the same set of five samples, characterized by x ¼ 0:250,0.316, 0.524, 0.705 and 0.757, which first shell EXAFS analysis was already discussed in previousworks by the same group [188,190]. As already discussed in Section 4.4, the crystallographic andstructural quality of the investigated films has been checked by parallel XRD and RBS-channelingcharacterization. This allows to have an independent check on the chemical composition of the film andto prove that the five films were pseudomorphic. Moreover, AFM investigations of tensile samples haveshown that the surface is free from cracks and atomically flat.

Since the unit cell of epitaxial InxGa1�xAs films, grown on InP, is tetragonally distorted (x > 0:53), itis natural to expect that the interatomic distances oriented close to the surface normal are increased andthose close to the surface plane are contracted in the case of compressive strain. The opposite willhappen in the case of tensile strain (x < 0:53). On the basis of what discussed in the introduction of thissubsection, it is evident that polarization-dependent EXAFS is the technique of choice in thedetermination of in-plane versus out-of-plane interatomic distances and in the study of their evolutionunder the effect of strain in the þ0:0195 < ek < �0:0142 interval.

When the crystal of a III–V compound is tetragonally distorted, the second and third shell sitesare split in two subsets of equivalent sites. Considering for instance, a compressive strain (x > 0:53for the InxGa1�xAs alloy), the length of the vector r connecting the photoabsorber to an arbitraryatom is increased if oriented along the normal to the growth plane. The contrary will happen for


vectors parallel to the growth plane. In general, in tetragonal strained samples, the lengthening orshortening of interatomic distances depends essentially on the angle between the growth vector[0 0 1] and r.

In agreement with the previous results of Woicik et al. [569], no distance splitting for the atoms of thefirst shell is expected, see Fig. 33a. In fact, owing to the local Td symmetry, the sum over the four firstshell contributions is, in first approximation, independent to the polarization direction. As aconsequence, no distance splitting occurs for the atoms of the first shell. Conversely, the atoms of thesecond shell can be divided into two subsets: (i) four atoms lie in the (0 0 1) plane at distance r

ðinÞ2nd , (ii)

the other eight atoms lie out of the (0 0 1) plane, at distance rðoutÞ2nd , with r that forming an angle of 458

with the [0 0 1] axis (see Fig. 34). It results that each of the second shell distances obtained from the fitprocedure, i.e., Ga–Ga, Ga–In, As–(Ga)–As, As–(In)–As, is split in two subsets of interatomic distances(r

ðinÞ2nd and r

ðoutÞ2nd ). A similar split occurs also for the 12 atoms of the third shell: there are eight atoms at

distance rðinÞ3nd and four at distance r

ðoutÞ3nd forming, with the [0 0 1] axis, an angle of 72.458 and 25.248,

respectively. After a complex and refined data analysis on the whole set of films measured in bothgrazing and normal geometries Tormen et al. [578] were able to give an exhaustive description of howtetragonal strain (of both compressive and tensile nature) modifies the local environment on both anionand cation sites, which is here summarized in the data reported in Fig. 35.

Polarization-dependent EXAFS study of Tormen et al. [578] have shown that the second and thirdshell interatomic distances of InxGa1�xAs epitaxial layers under tetragonal distortion split into twosubset distributions. The experimental results are reproduced very well by a model proposed by theauthors that applies the macroscopic strain tensor to the interatomic distances independently of theatoms and bonds involved. This fact suggests that the matrix in which each single bond or bond angle isactually embedded introduces a smoothing of the local fluctuations of the lattice structure response toan external strain field.

Fig. 34. Schematic representation of atomic sites in the zinc blende structure subject to a tetragonal strain. In second and

third shells we distinguish the two subsets of non-equivalent sites by the indexes in and out. In the InxGa1�xAs case, when the

absorber is Ga, the first and third shell atom must be As, while the second shell one may be either In or Ga. When the absorber

is As, the first and third shell atom may be either In or Ga, while the second shell must be As. Adapted from M. Tormen, et al.,

Phys. Rev. B 63 (2001) 115326, [578], with permission. Copyright (2001) by American Physical Society.


Fig. 35. (a) Ga cations second shell distances vs. In atomic fraction for pseudomorphic InxGa1�xAs/InP(0 0 1) films: squares

refer to rGa–Ga, circles to rGa–In. Solid and open symbols indicate, respectively, measurement collected at two polarization

incidence angles: y ¼ 25� (grazing incidence) and y ¼ 70� (normal incidence). Linear fits of the different data set are

represented by continuous lines. Dashed lines show the linear dependence calculated for in- and out-of plane components. (b)

Same as part (a) for the As–(cation)–As second shell distances. Squares refer to rAs–(Ga)–As, circles to rAs–(In)–As. (c) Same as

part (a) for the Ga–As third shell distances. (d) Same as part (a) for the As cations third shell distances. Adapted from M.

Tormen, et al., Phys. Rev. B 63 (2001) 115326, [578], with permission. Copyright (2001) by American Physical Society.


The next examples of this subsection are devoted to summarize EXAFS experiments used todirectionally probe distortions of local structure induced by heteroepitaxial growth in III–V-nitridessemiconductor alloys, most of them exhibiting hexagonal unit cells. By using polarization-dependentX-ray absorption spectroscopy at the Ga K-edge, Boscherini et al. [650,651] studied the growth of GaNon SiC(0 0 0 1) in the thickness range 0.7–150 nm. They find that the growth is always relaxed (i.e.,non-pseudomorphic) even for the thinnest epilayers, i.e., below the expected critical thickness. Noevidence was found for a mixed Ga/Si interface plane, while a C/N mixed interface plane cannot beruled out. The results have been discussed with reference to the electronic structure of the SiC/GaNheterojunction and in particular to band offsets and strain-induced piezoelectric polarization [650].D’Acapito et al. [652,653] have probed by polarization-dependent EXAFS the local structure of 7–8 nm thick GaN epilayers deposited on AlN as a function of the growth temperature (ranging between620 and 790 8C). From the interatomic distances in the second coordination shell around Ga the authorsobtained values of the in- and out-of-plane strain due to heteroepitaxial growth and compare theirrelation to published values of the elastic constants.

On this system also the Lawniczak-Jablonska group has made an impressive work [654–656]. In Ref.[654] they reported a combined Ga and N K-edge polarization-dependent EXAFS study the samewurtzite GaN system. The layers were grown by MBE and MOCVD on different substrates such as(0 0 0 1)-oriented 6H–SiC, sapphire (Al2O3), and GaN itself. From the observed XANES of the Ga K-edges, it was found that MOCVD introduces a stronger disorder around Ga atoms than MBE.Comparing the Ga and N K-edges of the epilayers and the bulk crystal, a prevailing contribution of Nvacancies in the layers and dominance of Ga vacancies in the bulk crystal were found. The bonds alongthe c-axis are less perfect than the bonds in the ab-plane for all investigated epilayers. The EXAFS dataanalysis performed on spectra collected with different polarization vector E resulted in a direct estimateof the bond lengths in the ab-plane and along the c-axis. The same group, in a successive workhighlights the anisotropy of atomic bonds formed by Mg and Zn acceptor dopants with nitrogen in bulkwurtzite GaN crystals [655]. K-edge of Mg and Zn polarized EXAFS spectroscopy was used in thiscase. Authors found a single acceptor N bond along the c-axis and three bonds realized with N atomsoccupying the ab-plane perpendicular to the c-axis. The Zn dopant formed resonant spectra similar tothat characteristic for Ga cations. In the case of the Mg dopant, similarity to Ga cations was observedfor triple bonds in the ab-plane, only. Practically no resonant structure for spectra detected along the c-axis was observed. The absorption spectra were compared with ab initio calculations using the full-potential linear muffin-tin-orbital method. These calculations were also used for determination of thebond length for Mg–N and Zn–N in wurtzite GaN crystals and show that introducing dopants causes anincrease of the lengths of the bonds formed by both dopants. EXAFS measurements performed for bulkGaN:Zn confirmed the prediction of the theory in the case of the Zn–N bond. Lawniczak-Jablonskaet al. [655] concluded by suggesting that the anisotropy in the length of the Mg–N bonds, related totheir larger strength in the case of bonds in the ab-plane, can explain preferential formation of asuperlattice consisting of Mg-rich layers arranged in ab-planes of several bulk GaN:Mg crystalsobserved by transmission electron microscopy. Finally, no parasitic metallic clusters or oxidecompounds formed by the considered acceptors in GaN crystals were found. The last paper quoted inthis subsection for the group III nitrides systems, is probably the most relevant one, since it reports acomprehensive study of the electronic structure of the AlN, GaN, InN, and BN binary systems,crystallizing in the wurtzite, zinc blende, and graphite-like hexagonal (BN) structures [656]. A large setof the X-ray emission and absorption spectra collected at the several synchrotron radiation facilities at


installations is presented. By taking advantage of the linear polarization of the synchrotron radiationand making careful crystallographic orientation of the samples, the bonds along c-axis p and ‘‘in-plane’’ s in the wurtzite structure have been separately examined. Particularly for AlN the authorsfound pronounced anisotropy of the studied bonds. Of particular interest is the fact that experimentalEXAFS data have been directly compared with ab initio calculations of the partial density of statesprojected on the cation and anion atomic sites. For the GaN, AlN, and InN the agreement betweenstructures observed in the calculated density of states and structures observed in the experimentalspectra was impressive. In the case of hexagonal BN an important influence of insufficient corescreening in the X-ray spectra that influences the DOS distribution has been found [656]. All theseworks complement previous angular-dependent EXAFS measurements at the N K-edge of undopedGaN and AlN by Katsikini et al. [657–659].

We conclude this paragraph reporting an example of polarization-dependent EXAFS study of II–VIheterostructures [660,661]. The authors have studied the local atomic structure of two different shortperiod ZnTe/CdSe(0 0 1) SLs grown by MBE. The data obtained for the Se edge at room temperatureindicate Zn–Se and Cd–Te coordination numbers greater than those expected for sharp interfaces in theSL. Although strain would appear to suppress interdiffusion, Kemner et al. [661] showed that the resultsare consistent with an interchange of Zn and Cd atoms across the Zn–Se interface, and Se and Te atomsacross the Cd–Te interface. The accommodation of this increased strain through bond bending and bondstretching has also been discussed.

4.8. Surface EXAFS or SEXAFS

Once a defined M atomic species has been selected, by tuning the monochromator to thecorresponding M K-edge (or L-edge), transmission EXAFS spectroscopy will report the localenvironment of all the M absorbing atoms averaged over the whole volume of the sample. Even whenthe experiment is performed in fluorescence mode, the long penetration depth of the in-comingsynchrotron radiation beam and the long mean-free path of the out-coming fluorescence photons makethe investigated volume micron-deep, reflecting the fact that EXAFS is basically a bulk technique.7

This fact can represent a serious problem when the region of interest is a few nanometer thick layerepitaxially grown on a substrate. In the case of InxGa1�xAs/InP thin epitaxial layers (see Section 4.4),fluorescence EXAFS was able to overcome the problem by tuning the energy of the synchrotron beamon the Ga and As K-edges, which atomic species are present on the surface only. It is so the chemicalselectivity of EXAFS that made (in that case) the technique also surface selective. Of course an In K-edge EXAFS study would have no meaning in that case because it would just results in establishing thelocal environment of indium atoms in the InP substrate.

7 Due to the much shorter mean free path of electrons [662] with respect to X-rays, a much higher sensitivity to the

uppermost fraction of a sample is obtained when the electron-yield detection mode is adopted. Since both primary (XPS) and

secondary (Auger) electrons are proportional to the photon absorption (i.e. the physical quantity directly measured in

transmission mode), the electron current measured on the sample as a function of the photon energy is an EXAFS-like

spectrum. In such a case, the absorption coefficient is obtained, in perfect analogy with the formula (27) used for the

fluorescence mode, by: mðEÞx ¼ IeðEÞ=I0ðEÞ, where Ie(E) is the electron yield. For high-Z elements, such as Ge, Ga, As, and

In, this technique is, however, penalized with respect to the fluorescence mode by the low yield of Auger electrons with

respect to the yield of the complementary disexcitation phenomenon.


A way to overcame this problem is to have a diffractomenter on the beamline [663] and to mount thesingle crystal on it in such a way that the synchrotron beam reaches the sample in grazing-anglegeometry. In such a way, we are working in total reflection conditions and the electromagnetic field ofthe radiation is penetrating into the material only as an evanescent wave which intensity is dumped by asevere exponential factor. In these conditions, by carefully selecting the incidence angle ai across thelimit angle once can define the penetration depth of the electromagnetic field and thus the surfacesensitivity of the measurement, starting from few MLs down to the bulk. This peculiar case of EXAFShas been called surface EXAFS or SEXAFS [664–669] whose surface sensitivity can be tuned, in theai ! 0� limit (see Fig. 36) down to less than 10 A [670].

From what we have discussed in Section 4.7, it is evident that SEXAFS can operate in a geometrylike that shown in Fig. 28a, therefore it is intrinsically also a polarization-dependent technique. Themain differences concern the fact that the angle ai between the photon beam k and the single crystalsurface8 in a standard polarization-dependent EXAFS study performed in grazing-angle geometry istypically in the 10–208 range, while in a SEXAFS experiment it is much closer to zero, in the mradrange. In this configuration, schematically described in Fig. 36b, y0 0� and we probe selectively theout-of-plane components, but a 908 rotation of the sample along the axis of the photon beam(represented by the horizontal k vector) allows to rotate the single crystal surface in the E vector(y0 90�) and thus to become selective to the in-plane contributions.

Before entering in the list of reviewed examples, some points of general validity should beunderlined. For the reasons discussed above, most of the here reviewed results have exploited thepolarization-dependent potentialities of the SEXAFS technique. SEXAFS has been often coupled withother typical surface science techniques like, LEED, Auger electron diffraction, XPS, electronmicroscopies, AFM, STM, etc. [671–676], to obtain a complete characterization of the investigatedsemiconductor surface by complementary techniques. Moreover, the experimental set-up needed toperform SEXAFS is almost that needed to perform X-ray standing waves (XSW) measurements,therefore some papers report a combined use of these two synchrotron radiation techniques. In thesecases combined results will be discussed here, while the reader is remanded to Section 7 for adescription of the XSW technique. Two main families of SEXAFS experiments have been reviewedhere, where the technique has been used either (i) to determine the adsorption site of an atom or amolecule on a well-characterized semiconductor surface or (ii) to determine the structure of a few ML-thick film deposited onto a substrate. In both cases we are dealing with typical surface scienceexperiments requiring in situ sample preparation and thus UHV conditions. Such conditions are alsoideal for soft X-ray spectroscopies. This is the reason why in the literature we found often studiescombining SEXAFS and NEXAFS (see Section 4.9) spectroscopies, two techniques that can take greatbenefit from the exploitation of the polarization properties of synchrotron radiation beams.

As far as clean surfaces are concerned, SEXAFS is certainly one of the techniques of choice in thestudy of the surface reconstruction. As an example, Woicik et al. [677] have determined the near-neighbor bond lengths at the clean InP(1 1 0) surface. They find no change in the first neighbor P–Inbond length and a small but measurable (0.1 A) expansion of the average P–P second-neighbor

8 Note that the ai angle has the same value than the y0 angle between the E and the [0 0 1] vectors in the two geometries

reported in Fig. 28a and b, where the sample rotation occurs along the vertical axis perpendicular to the beam direction k.

Conversely, by rotating the sample along the horizontal k direction (Fig. 36), we are able to tune y0 in the 0–908 range without

changing the ai value, i.e. being always in SEXAFS conditions.


distance. Together with surface-sensitive XSW results, published by the same group the same year[678,679], these data establish the bond-length conserving rotation model for the non-polar III–Vsemiconductor cleavage surfaces.

Coming to the examples where SEXAFS has been used to study the adsorption sites of atoms onclean surfaces, Cl K-edge SEXAFS and NEXAFS spectroscopies have been used by Purdie et al. [680]to investigate the structure of Sið1 0 0Þð2 � 1Þ-Cl. The experiment was performed by exposing a single-domain Sið1 0 0Þð2 � 1Þ substrate to Cl2 at about 500 K to yield a coverage of about 0.25 MLs. Theroom temperature SEXAFS data indicates that Cl sits atop the upper Si atom of a buckled dimer at abond distance of 2:00 � 0:02 A. Analysis of the polarization-dependent NEXAFS data, which relies onthe pseudo-intramolecular behavior of a s� resonance, is consistent with this geometry. The same groupalso investigated the Sið1 1 1Þð7 � 7Þ–Cl surface [681]. A combined XPS and SEXAFS study of Naadsorbed on c(2 � 8)-Ge(1 1 1) surface at different coverage regimes has been reported by Aminpiroozet al. [682]. The c(2 � 8) LEED pattern of the clean Ge(1 1 1) surface changes to a (1 � 1) with higherbackground after Na adsorption. A plasmon feature appears on the low energy side of Na(2p) core levelthat indicates metallization of the Na overlayer. SEXAFS data showed that Na atoms are adsorbed onthree-fold-coordinated hollow sites with a Na–Ge bond length of 2.9 A and a second nearest-neighbordistance of 3.4 A to the Ge atoms in the second layer. Maeyama et al. instigated S on GaAs(1 1 1)[683].

The epitaxial growth of a cubic Fe silicide phase on Si(1 1 1) has been confirmed by the combineduse of SEXAFS and X-ray photoelectron diffraction (XPD) experiments [684]. XPD experiments showthat a 5 ML Fe film deposited on Si(1 1 1) and subsequently annealed at approximately 500 8C has acubic structure. Fe K-edge SEXAFS reveals that Fe atoms are coordinated with eight Si atoms withbond length of 2:38 � 0:04 A and with six Fe atoms with bond length of 2:71 � 0:04 A. Authorsconcluded that the iron silicide has a CsCl-type structure.

The Te/Si(1 0 0) system, of particular interest due to its use in the surfactant aided growth ofCdHgTe–CdTe–Si(1 0 0) based infrared detectors, has been studied by Burgess et al. [685] using

Fig. 36. Two extreme conditions of a SEXAFS experiment: E? [0 0 1] (a) and Ek [0 0 1] (b). The former case allows to

selectively detect in-plane components, the latter out-of-plane components. Of course all intermediate acquisition geometries

are possible. k and ai represent the photon wavevector and its angle formed with the (0 0 1) surface of the sample, respectively.


combined Te L3-edge SEXAFS and XSW methods. The SEXAFS results indicated that the Te atomssat in two-fold bridge sites directly above a fourth layer Si atom located at 2:52 � 0:05 A. The XSWmeasurements of the (4 0 0) reflection gave a coherent position of 1:63 � 0:03 A and a coherentfraction of 0.65. This is consistent with the breaking of the Si–Si dimers and thus could be an exampleof the phenomena of adsorbate-induced dereconstruction of the surface.

Sb L3-edge SEXAFS has been combined with scanning tunneling microscopy by Richter et al. [686]to determine both the local and long-range bonding properties of the Sið0 0 1Þð2 � 1Þ-Sb interface. SbL3-edge SEXAFS shows that Sb dimers occupy a modified bridge site on the Si(0 0 1) surface with aSb–Sb near-neighbor distance of 2:88 � 0:03 A, which is almost identical to the bulk Sb–Sb bondlength of 2.90 A. Each Sb atom of the dimer is bonded to two Si atoms with a Sb–Si bond length of2:63 � 0:04 A. STM resolves the dimer structure and provides the long-range periodicity of the surface.LEED of vicinal Si(0 0 1) shows that the Sb dimer chains run perpendicular to the original Si dimerchains. Successive work by the same group [687] demonstrates that the Sb atoms lie 1:74 � 0:06 Aabove the Si(0 0 1) surface. Successively, Jenkins and Srivastava [688] report an ab initio densityfunctional calculations (DFT) study on the Si(0 0 1)(2 � 1)-Sb surface. DFT results showed that thesurface reconstruction is due to dimerization of the Sb atoms in the direction perpendicular to the dimerrows of the clean Si(0 0 1) surface, in agreement with previous SEXAFS results. The nature of thebonding and band structure of the relaxed Sb-capped surface was also investigated and it has beenfound that the normal energy ordering of ungerade and gerade p orbitals localized on the Sb dimer isreversed [688]. Woicik et al. also investigated the Sb–Si(1 1 1) interface by combined high-resolutionXPS and SEXAFS [689]. Authors found that Sb atoms are coordinated to 2:1 � 0:3 Sb atoms at2:86 � 0:02 A and to 2:0 � 0:4 Si atoms at 2:66 � 0:03 A. XPS spectra indicates that one Sb MLcompletely eliminates the surface components of the Si(2p) core level and that the Sb-induced Si(2p)interfacial core level is shifted 0:20 � 0:02 eV toward higher binding energy with an intensity thatcorresponds to the top 1 ML of surface atoms. XPS and SEXAFS results indicate that Sb trimersoccupy the three-fold atop sites of the Si(1 1 1) surface where each Sb atom is bonded to two Si atomsin a modified bridge configuration rotated by 608 relative to the atop ‘‘milk stool’’ geometry proposedby Abukawa et al. [690]. Reported models predict perpendicular distances of 1.76 and 2.60 A betweenthe top Si atoms and the Sb layer, respectively. Successively polarization-dependent SEXAFS data,combined with back-reflection XSW measurements (see Section 7), by Woicik et al. [691] are in clearsupport of the milk stool geometry.

Successively the same group deposited antimony on GaP(1 1 0) [692] and on germanium [693,694]substrates. XPS, XSW, and SEXAFS have been used in [693] to characterize the atomic structure of anannealed ML of Sb on the Ge(1 1 1)(2 � 1) surface. Sb L3-edge SEXAFS data determines the bondlengths within the first Sb shell to be 2:87 � 0:03 and 2:67 � 0:03 A for the Sb–Sb and Sb–Ge bonds,respectively. The XSW data for (1 1 1) planes, taken in the back-reflection diffraction geometry, locatethe Sb layer 2:60 � 0:05 A above the Ge(1 1 1) surface. A relatively high coherent fraction (0.85)indicates small disorder or buckling in the Sb overlayer. The Sb overlayer is found to quench the cleansurface shifted components of the Ge(3d) core-level spectrum, which indicates an ideal termination ofthe Ge(1 1 1) surface with all dangling bonds saturated by the Sb adatoms. Lack of chemically shiftedcomponents in both the Ge(3d) and the Sb(4d) core-level spectra indicates a single bonding site for theSb atoms [693].

The Ge(0 0 1)(2 � 1)-S overlayer formed by dosing H2S at room temperature on a clean Ge(0 0 1)(and subsequent annealing to remove H) has been studied using both SEXAFS and NEXAFS


spectroscopies by Newstead et al. [695]. Authors showed that the S atoms sit in bridge sites on thesurface with a bond length of 2:36 � 0:05 A. Being this result consistent with the breaking of the Ge–Ge surface dimers, we are in presence of an other example of the adsorbate-induced dereconstructionphenomenon.

Auger electron diffraction and SEXAFS have been used by Tuilier et al. [696] to obtain a completedescription of the atomic structure of a two-dimensional epitaxial Er silicide layer on Si(1 1 1). AEDreveals that a ML of Er is located underneath a buckled Si double layer. The relevant Er–Si interlayerspacings are determined to be 1:92 � 0:05 and 2:70 � 0:05 A to the first and the second Si top layer,respectively. Er near-neighbor bond lengths and coordination numbers are obtained independently frompolarization-dependent SEXAFS. The SEXAFS data, when combined with the Si top-layer geometryinferred from AED, permit the determination of the atomic positions at the silicide/Si(1 1 1) interface.Batchelor and King [697] reported on the adsorption of Cs on the Si(1 1 1)(7 � 7) surface. SEXAFSrevealed a contraction in the Cs–Si bond length from 3:79 � 0:04 A at low coverage to 3:50 � 0:04 A atsaturation coverage. Authors interpreted the longer bond length observed at lower coverage on the basisof an important degree of ionicity in the Cs–Si surface bond, due to charge transfer from Cs to Si.Conversely, the Cs–Si bond length present at saturation coverage is consistent with a covalent bonding.At saturation a second site is also populated which has Cs–Si bond length of 4:68 � 0:06 A.

Polarization-dependent SEXAFS has been used on the Si/GaAs(1 1 0) system by the Flank and co-workers [698,699] in order to characterize the adsorption sites of Si as a function of the Si coverage ofthe surface. In the first paper [698], up to 14 A thick films have been investigated, while the first stagesof the adsorption process (up to 1.5 ML) have been addressed in the second one. They found that at acoverage of 0.8 ML, silicon atoms sit just above the middle of the As–As and Ga–Ga bond along the[0 1 1] direction while above 1.0 ML, Si atoms begin to be ordered with a silicon-like structure [699].

Proietti et al. [559,700], performed a SEXAFS study on six InAs ML grown on InP. This experimentis interesting since it represents the x ! 1 limit of the data reported by Lamberti et al. [164–167,301]on InAsxP1�x/InP strained superlattices and largely debated in Section 4.6. In [559,701] also a sampleobtained by growing six MLs of GaAs on InP has been treated. The same group reports also SEXAFSresults on three nominal MLs of GaAs grown on InP [304] and on an uncapped 20 A thick InGaAssample grown on GaAs(0 0 1) substrate [560]. Finally, Oyanagi et al. report SEXAFS results on 1, 2and 4 Ge MLs epitaxially deposited on Si(0 0 1) [567,568].

SEXAFS has been used to study the local environment of Ga and As at the interface between thin(300 A) oxidized Al0.06Ga0.94As film on GaAs substrate [702]. Bulk Al0.06Ga0.94As oxide has beenused as reference. Parallel X-ray reflectivity experiments have also been employed to investigate thedensity profile of the oxide film on a GaAs substrate revealing the density profile as a function of depth.Authors made an attempt to correlate the As incorporation at the interface, the interfacial strain, and therelated local structure.

D’Acapito et al. [703] reports an In K-edge SEXAFS study on InxGa1�xAs quantum dots prepared byself-organized epitaxial Stranski–Krastanov growth on a GaAs(0 0 1) substrate and capped by a GaAsfilm. This technique for the preparation of 0D structures starts with the formation of a pseudomorphicstrained layer, referred to as the wetting layer (WL), and proceeds with the spontaneous formation ofdots above the critical thickness (Tc) of the film. The strain energy accumulated in the wetting layer ispartially released by the formation of coherent, dislocation-free, QDs. The critical thickness Tc at whichthe formation of coherent 3D islands onto the initial 2D WL occurs, is determined by the interplaybetween the energy gain due to the partial relaxation of the strain and the increase in free energy


because of the augmented surface. In agreement with previous theoretical and experimental works[285,704–707], D’Acapito et al. [703] have verified by SEXAFS that the growth of InAs onGaAs(0 0 1), for which the lattice mismatch is 0.072 and Tc ¼ 1:7 ML, does not proceed following apure Stranski–Krastanov mode. In fact, the chemical composition of the WL and the 3D islands isdifferent from the deposited InAs material with significant Ga/In interdiffusion between 3D island andWL and substrate, resulting in the formation of InxGa1�xAs film or quantum dots for T < Tc andT > Tc, respectively. This effect determines the strain fields in the islands and the WL that has animportant role in QDs self-aggregation. The variation of the strain field in the films has been realized bychanging the InAs film thickness from below (WL data in Fig. 37) to above (dots data in Fig. 37) Tc.The analysis of the SEXAFS data reported in Fig. 37a resulted in first shell In–As values reported inpart (b) of the same figure. Such values never reaches the rInAs ¼ 2:570 A value expected for achemically pure InAs layer strained on GaAs(0 0 1) substrate [708] and are more similar to thoseobserved in intermixed InxGa1�xAs systems [187,188,707]. As reported in Fig. 37b, authors determinedthe indium composition x of the samples from the first shell bond lengths measured by SEXAFS. Fromcalculations based on the valence force field method and assuming the validity of macroscopic elastictheory for strained epilayers [187,188,578,579,595], D’Acapito et al. [703] have predicted that for theInxGa1�xAs/GaAs(0 0 1) the variation of first shell bond length rInAs with the alloy composition x

(dotted line labeled as strained alloy in Fig. 37b). In Fig. 37b also other rInAs(x) relationships for bothrelaxed and strained alloys have been reported according to models derived from [185,536,542]. Allmodels evidence quite clearly a markedly different behavior between strained and relaxed alloys. TherInAs bond length tends to elongate with growing the indium content in the relaxed samples whereas itcontracts in case of strained systems. The difference between the two types of curves is such (about0.03 A) to permit the distinction between a strained or relaxed system by EXAFS-based techniques.The two calculations agree quite well and demonstrate that by considering the first shell bond lengthsvalues it is possible to determine the status of the samples even with moderately accurate data. On onehand, the sample grown with T < Tc (WL) is a strained In0.15Ga0.85As film compatible with the modelfrom [536]. On the other hand, the sample grown with T < Tc (dots) exhibit an In–As bond length thatis compatible only with a relaxed In0.40Ga0.60As alloy. This is in agreement with a dot growthmechanism based on the release of the strain energy accumulated in the lower lying layers. From the studyreported in [703] it emerges that the determination of quantitative experimental data of interdiffusion isparticularly important to understand the microscopic mechanisms of QDs self-aggregation.

Similar systems have been investigated also by Proietti’s group [709], who has used conventionalfluorescence EXAFS and SEXAFS to study the strain and the local composition of encapsulated self-assembled InAs/InP quantum wires and InAs/GaAs quantum dots. Bond distances up to the thirdcoordination shell have been obtained. Authors concluded that, contrary to what expected due todiffusion and intermixing of the Group V species, the wires are made essentially of InAs. Conversely, inthe dots a strong In diffusion is observed, in agreement with the well known In tendency to diffuse andsegregate towards the surface, in strained InGaAs systems. DAFS investigation of these low 1D and 0Dheterostructures has also been performed by the same group [710–712], see Section 6.

4.9. The near-edge structure: NEXAFS spectroscopy

From Section 4.1 up to now we have focused the attention on the energy range 50–1500 eV above theabsorption edge, which is called extended XAFS (EXAFS) and provides information about the


Fig. 37. (a) The k2-weighted FT of the EXAFS spectra (inset) performed in the 3–10 A�1 range (dotted curves) and corresponding best-fits done in R space in

the 1.5–2.7 A range. Results refer to an unstrained InAs bulk reference sample measured in transmission mode (InAs), to two InAs/GaAs(0 0 1) films with a T

value below (WL) and above (dots) Tc. (b) rIn–As bond lengths determined from the SEXAFS study compared with theoretical predictions in relaxed and

strained, upon epitaxy on GaAs(0 0 1), InxGa1�xAs alloys. Continuous lines are obtained from Ref. [536] (relaxed) and from Ref. [185] (strained); dotted lines

are obtained from the model presented in Ref. [542] (relaxed) and from the same model adapted to the strained layer case. Adapted from F. D’Acapito, et al.,

Nucl. Instrum. Meth. B 200 (2003) 85, [703], with permission. Copyright (2003) by Elsevier.

84

C.

La

mb

erti/Su

rface

Scien

ceR

epo

rts5

3(2

00

4)

1–

19

7

microstructure (nearest-neighbor distances, coordination numbers and Debye–Waller factors) aroundthe absorbing atom. Now we will concentrate on the portion of the spectrum close to the absorptionedge, which is called near-edge XAFS (NEXAFS9) [668,713]. NEXAFS provides information aboutthe partial density of empty states, the local symmetry around the absorbing atom and the presence ofdefects that introduce empty states in the gap [714]. Due to the dependence that some of the mentionedfeatures have on the crystallographic directions, most of the reviewed studies exploit the polarizationpeculiarities of synchrotron radiation.

Hexagonal, cubic, and mixed phase GaN samples grown by MBE have been investigated by Katsikiniet al. [715] using polarization-dependent N K-edge NEXAFS spectroscopy. It is shown that the N K-edge NEXAFS spectra, which are proportional to the p-partial density of states in the conduction band,are characteristic of the cubic or hexagonal structure of the examined crystal. The spectra of the cubicsample do not depend on the angle of incidence (ai), contrary to the spectra of the hexagonal sample inwhich the areas under the NEXAFS resonances depend linearly on cos2(ai). From the fitting of the linesAðiÞ ¼ A þ B cos2ðaiÞ, where A(i) are the areas under the resonances and A and B are constants, thedirections of maximum electron charge density with respect to the normal to the surface are determinedfor the hexagonal sample. The energy positions of the absorption edge and the NEXAFS resonances inthe spectra from the cubic sample are different from those of the hexagonal sample and in either caseare independent of theta. Contrary to that, the energy positions of the NEXAFS resonances in a mixedphase sample have a characteristic angular dependence and shift between the energies corresponding tothe cubic and hexagonal polytypes. Based on this observation, Katsikini et al. [715] proposed that thespectrum of the mixed phase sample can be approximated as the weighted average of the spectra fromthe pure cubic and hexagonal samples. From this approximation the coexisting fractions of a- and b-GaN in a mixed phase sample are determined and they are found in good agreement with results fromhigh-resolution transmission electron microscopy and XRD.

Katsikini et al. [549,716] have demonstrated that the NEXAFS spectra are a fingerprint of thesymmetry and the composition of the binary nitrides GaN, AlN and InN, as well as of three ternaryalloys: In0.16Ga0.84N, Al0.25Ga0.75N and Al0.5Ga0.5N. From the polarization dependence of the N K-edge NEXAFS spectra, the hexagonal symmetry of the under study compounds is deduced and the px�y

or pz character of the final state is identified. The energy position of the absorption edge E0, vide supraEq. (24), of the binary compounds GaN, AlN and InN is found to red shift linearly with the atomicnumber of the cation (see Fig. 38). The E0 of the AlxGa1�xN alloys takes values in between thosecorresponding to the parent compounds AlN and GaN. Conversely, the E0 of In0.16Ga0.84N is red-shifted relative to that of GaN and InN (see Fig. 38), probably due to ordering and/or phase separationphenomena. The EXAFS analysis results reveal that the first nearest-neighbor shell around the N atom,which consists of Ga atoms, is distorted in both GaN and AlxGa1�xN for x < 0:5. Discussed referencescomplement previous angular-dependent NEXAFS studies at the N K-edge of undoped GaN and AlNby the same group [658,659].

Polarization-dependent N and Al K-edges NEXAFS experiments have been performed by Fukui et al.[717] on wurtzite AlN, GaN and InN binary compounds, and their AlxGa1�xN, InxGa1�xN andInxAl1�xN ternary alloys. The spectral distribution of the N K-edge NEXAFS spectra clearly dependson both the incident light angles and the molar fractions x of the samples. Also Al K-edge NEXAFS

9 For light elements (having the K-edge below ca. 3 keV), the near-edge structure of the X-ray absorption spectra is usually

named NEXAFS while, for the heavy ones it is usually named XANES (X-ray near-edge spectroscopy).


spectra show the clear angle dependence, but a strong dependence on x has not been observed. Asalready discussed in Section 4.7.2, in [654] Lawniczak-Jablonska et al. reported a combined Ga and NK-edge polarization-dependent NEXAFS study the same wurtzite GaN system. The layers were grownby MBE and MOCVD on 6H–SiC(0 0 0 1), Al2O3, and GaN substrates. From the observed XANES ofthe Ga K-edges, it was found that MOCVD introduces a stronger disorder around Ga atoms than MBE.

0

2

AlN

0

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Al0.5

Ga0.5

N

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2Al

0.25Ga

0.75N

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nsity

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. uni

ts)

0

2

In0.16

Ga0.84

N

400 410 420 430 440

0

2

InN

Energy (eV)

Fig. 38. NEXAFS spectra recorded at three different angles of incidence: normal (dashed line), grazing (thin solid line) and

at the magic angle (thick solid line) of the under study binary and ternary nitrides. The difference spectra (normal incidence

minus grazing incidence) are also shown at the lower part of each figure. Adapted from M. Katsikini, et al., J. Electron

Spectrosc. Related Phenom. 101–103 (1999) 695, [716], with permission. Copyright (1999) by Elsevier.


D’Acapito et al. [652] have probed by polarization-dependent Ga K-edge NEXAFS (XANES) the localstructure of 7–8 nm thick GaN epilayers deposited on AlN as a function of the growth temperature(ranging between 620 and 790 8C).

As for the EXAFS part of the X-ray absorption spectrum, also the near-edge part can be simulatedaccording to a structural model of the local environment of the absorbing atom. The main differencebetween EXAFS and NEXAFS (XANES) simulations concerns the much longer mean-free path l, seeEq. (26), of the photoelectron when its kinetic energy is of only few eV. As a consequence, NEXAFSspectra are dominated by multiple-scattering contributions [593] and much larger clusters (with respectto those used for EXAFS simulations) must be constructed to reproduce a NEXAFS spectrum. A goodexample for showing the utility of near-edge simulation is given by the work of Ciatto et al. [599] whoinvestigated, by means of N K-edge NEXAFS spectroscopy, the dilute nitride InxGa1�xAs1�yNy

quaternary alloys an in Ga1�xAs1�yNy ternary alloys (Fig. 39a) ad hoc grown to address the problem ofshort-range order (vide supra Section 4.6 where the problem of short-range order in quaternarysemiconductor alloys has been addressed and the parallel In K-edge EXAFS study has been discussed).The NEXAFS spectra were simulated in the full multiple-scattering approach using self-consistency forthe potential [593]. The cluster for simulating InxGa1�xAs1�yNy was created by introducing an Nimpurity in the GaAs structure (GaAs:N) and relaxing the first and second shell distances throughnumerical minimization of the total energy, using a valence force field potential [209] with appropriateforce constants [718,719]. Authors reported that relaxation beyond the second shell have negligibleeffects on the simulations. The same procedure was adopted for a N impurity in InAs. These clustersconsist of 20 atomic shells around the central N, i.e., of 381 atoms; linear combinations of the simulatedNEXAFS spectra for GaAs:N and InAs:N were made in order to simulate the quaternary alloys withdifferent In contents. Fig. 39b reports the effect of increasing the indium content (decreasing from topto bottom) of the clusters used to create the simulated spectra. It is apparent in Fig. 39a that all the

Fig. 39. (a) Experimental N K-edge NEXAFS spectra of InxGa1�xAs1�yNy quaternary and GaAs1�yNy ternary samples

subjected to different annealing processes: 633 V (as-deposited quaternary); 633 A1 (700 8C, 90 s); 633 A2 (700 8C, 300 s);

632 V (as-deposited quaternary); 711 V (as-deposited ternary); 712 V (as-deposited ternary); 712 A2 (700 8C, 300 s). (b)

Simulated N K-edge NEXAFS (dotted line spectra). The In content of the clusters used to simulate the spectra decreases from

top to bottom; two experimental spectra (bold lines at the bottom) are also reported for a comparison. Adapted from G. Ciatto,



spectra, including those relative to the most ordered samples, are quite similar to each other andexcellently simulated starting from a simple GaAs:N structure. The fact that the N–In coordination isnot visible here is not surprising as the In-edge EXAFS data showed that the N–In relative coordinationis at most 12% (vide supra Section 4.6) and in Fig. 39b it is evident how simulations for quaternaryalloys below 20% are not significantly modified with respect to the simulation for GaAs:N. Thesesimulations confirm that the preferential In–N bonding is weak, since a stronger ordering would resultin one of the upper line shapes in Fig. 39b.

In conclusion, the EXAFS and NEXAFS data of Ciatto et al. [599] provided the first quantification ofshort-range order in as-deposited and annealed InxGa1�xAs1�yNy quaternary alloys using state-of-the-artEXAFS and NEXAFS analysis tools. The so obtained results strongly disagree from a quantitativeviewpoint with the recent predictions based on Monte Carlo simulations by Kim and Zunger [598]. Evenif ordering has the same sign of the predictions and even if Ciatto et al. [599] estimated the probabilityfor a N atom to occupy an In-first-neighbor site to be up to three times the random one, the measuredorder parameters are about one order of magnitude smaller than the predicted [598]. This weak orderingcould explain the blue shift of the band gap observed in annealed InxGa1�xAs1�yNy quaternary alloys.

Paloura [714] reports a NEXAFS study at the N K-edge on the microstructure and the annealingbehavior of N-rich SiNx, films fabricated with ion implantation of 35 keV Nþ ions into Si substrates, inthe dose range 2 � 1017 to 2 � 1018 ions/cm2. The near-edge X-ray absorption fine structure (NEXAFS)spectra of the N-rich films are characterized by a strong resonance line at 403:3 � 0:1 eV, whoseintensity increases with the implantation dose. This XANES feature has been attributed to dipoleelectron transitions, from 1s to unoccupied p orbitals at a defect site containing a N dangling bonddefect. A parallel EXAFS study on the as-implanted and annealed films reveals that subnitrides areformed upon implantation. These nitrides are characterized by a Si–N nearest-neighbor distance that iscomparable to that of the reference nitride, while the coordination number in the first nearest-neighborshell depends on the implantation dose. The stoichiometry deviation, as measured from the value ofcoordination numbers that takes values between 1.7 and 2.5 for the limiting doses of range 2 � 1018 to2 � 1017, respectively, shows the correlation between the 403.3 eV NEXAFS feature and the presenceof N dangling bonds in the as-implanted films. The same group [720] has extended the N K-edgeNEXAFS investigation to Nþ and Oþ implanted GaN. They demonstrated that implantation increasesthe surface microhardness, explaining the phenomenon on the basis of the formation of N interstitialsthat pin the dislocations and prohibit the plastic deformation. In addition to the hardening effect, theimplantation induced N interstitials introduce a characteristic resonance in the NEXAFS spectra, at1.4 eV below the absorption edge. This works complements a previous one [523] where N K-edgeEXAFS data on the same samples has been reported. It has been found that in the as-grown sampleGaN, the central N atom is four-fold coordinated with 3.35 Ga atoms at the expected distance of1.93 A, and 0.65 Ga atoms at 2.26 A. Authors attributed this distortion of the first coordination shellaround N to thermal strain and/or to the presence of second shell N vacancies. Implantation with eitherNþ or Oþ ions enhances the distortion and the number of the displaced Ga atoms increases from 0.65 to1. In addition to that, implantation causes a reduction in the nearest-neighbor distances by about 2%and an increase in the Debye–Waller factors. In the same year, Paloura’s group reports thecomplementary EXAFS study performed at the Ga K-edge [721]. They found that the localenvironment around the Ga atom is distorted due to a splitting of the second nearest-neighbor Ga shell.This splitting results in an additional Ga path at a distance longer than expected by 0:8 � 0:05 A and isattributed to local lattice relaxation around nitrogen vacancies.


N–K-edge NEXAFS measurements by Katsikini et al. [722] investigated the effect of 100 keV Si ionimplantation in GaN samples grown by ECR-MBE. Authors demonstrated that the implantation-induced increase of the static disorder is detectable in the NEXAFS spectra as a broadening of theNEXAFS resonances. In addition to that, implantation introduces two new resonance lines in theNEXAFS spectra, labeled as RL1 and RL2 lines. The RL1, which appears at 1.7 eV below theabsorption edge, is observed in all the implanted samples and is due to nitrogen interstitials and/or Nantisite defects. The RL2 appears at about 1.0 eV above the absorption edge, when the implantationdose exceeds 1:0 � 1016 ions cm�2, and has been attributed to nitrogen dangling bonds created by theimplantation. Parallel AFM study shows that the surface roughness decreases with increasingimplantation dose while the overall surface morphology changes significantly after implantation with adose that causes amorphization [722].

The nitridation of GaAs, InAs, and InSb by low-energy N2þ ion bombardment at room temperature

was investigated by combined NEXAFS and XPS measurements [723]. The formation of thin surfacenitride layers, consisting mostly of GaN or InN but also containing minor amounts of mixed nitrides,was observed. Besides the nitride-related features, sharp peaks in the NEXAFS due to p� resonance at401.0 eV and correlated peaks at 403.8 eV in N 1s core-level spectra have been detected. Both spectralfeatures could be assigned to the presence of interstitial nitrogen, most likely molecular nitrogen. It wasfound that the amount of interstitial nitrogen in the surface layer strongly depends on the III–Vsemiconductor system and may be affected by modification of the conditions during low energy ionbombardment.

The phase composition and microcrystalline structure of thin GaN grown by nitridation ofGaAs(0 0 1) was investigated by Lubbe et al. [724]. Using surface-sensitive NEXAFS at the nitrogenK-edge, the partial nitrogen p density of states was determined. Comparing the data to reference spectraof hexagonal and cubic GaN, the amount of cubic GaN in the nitrided film was estimated to be20–25%. Varying the angle of polarization of the synchrotron radiation with respect to the samplesurface, the geometric anisotropy of the GaN film, and thus its crystalline structure, was probed,providing information on the orientation of the GaN microcrystallites. The results from thepolarization-dependent measurements suggest that the c axes of the hexagonal GaN crystallites inthe film are mainly oriented parallel to the [0 0 1] direction of the GaAs substrate. The c axes of roughly45% of the crystallites are tilted by 908 and lie parallel to the surface plane.

The ordered molecular orientation of CH3Cl, CH3Br and CH3I on GaAs(1 1 0) has been studied by acombined NEXAFS and angle-resolved time-of-flight spectra of methyl fragments ejected bydissociation due to photoinduced electron transfer processes [725]. The molecular orientation, probedby NEXAFS, indicates that the tilted orientation of adsorbed molecules accounts for the angulardistribution of methyl fragments ejected from hot-electron transfer reactions in these systems.

As an example taken from the II–VI literature, we mention the polarization-dependent C K- andS L-edges NEXAFS studies of Han et al. [288,295,726] on CdS films grown on ZnSe(1 0 0) by atomiclayer epitaxy using a binary reaction sequence of (CH3)2Cd and H2S as precursors. The interest of thisstudy is related to the fact that it is an in situ study, made during the growth of the CdS film, at both CK- and S L-edges. Authors have found that the growth model is based on self-limiting surface reactionswith a mechanism based on sequential surface ligand displacement [295]. This evidence, combinedwith a temperature programmed desorption TPD study, shows the presence of alternating methyl- andhydride-terminated surfaces, which are passivated to further uptake of Cd or S, respectively, asschematized in Fig. 40. These articles [288,295,726] represent a detailed study of the fundamental


surface chemistry of the growth process. Epitaxial growth was also characterized in the growth chamberusing electron and ion surface probes, resulting in a layer-by-layer growth of good quality.

Hitchcock et al. [727,728] performed a polarization-dependent Si K-edge EXAFS and NEXAFSstudy on several [(Si)m(Ge)n]p atomic layer superlattices and on a range of SixGe1�x alloy thin filmsgrown epitaxially on both Si(1 0 0) and Ge(1 0 0). The near-edge spectral features of atomic layer SLand alloy samples with similar (average) chemical composition were found to be remarkably similar.The spectra of both the strained atomic layer SL and alloy samples contain features at the SiK-threshold that exhibit a small but characteristic polarization dependence. The polarizationdependence is reduced or absent in strain-relaxed materials such as annealed atomic layer SL,annealed alloys, or thick alloy films. The polarization-dependent components of the signal areattributed to anisotropic states associated with strain-induced tetragonal distortions [727]. The senseof the polarization is inverted between samples grown on Si and those grown on Ge, consistent withthe expected inversion in the spatial orientation of the strain field. An explanation is proposed for thedependence of the magnitudes of the Si 1s polarization effect on the composition of alloys and atomiclayer SL. Castrucci et al. [570] reported Ge L3-edge NEXAFS spectra on thin strained layer (GenSin)p

SL grown on Si(0 0 1). In particular, authors have succeeded in reproducing the experimentalNEXAFS spectra (Ge2Si2)15/Si(0 0 1) SL by accounting for a single phase, fully strained, Ge0.5Si0.5

Fig. 40. Mechanism for the ALE growth of CdS on a ZnSe(1 0 0)-cð2 � 2Þ surface proposed by Han et al. [295]. When

(CH3)2Cd is first supplied to the freshly prepared surface, Cd uptake occurs until a full monolayer of methyl groups cap the

surface. Next, H2S is supplied and methane is displaced and the sulfur uptake occurs until a complete hydrogen-terminated

layer is obtained. Layer-by-layer growth is attained by continuing this dosing sequence. Adapted from M. Han, et al., Surf. Sci.

415 (1998) 251, [295], with permission. Copyright (1998) by Elsevier.


alloy consisting of four chemically ordered domains with the same atom type occupying widelyspaced (1 1 1) planes.

Purdie et al. [729] performed a polarization-dependent NEXAFS study of the Si(1 1 1)ð7 � 7Þ-Cl andSi(1 0 0)ð2 � 1Þ-Cl systems. The modulation of the Cl K-edge white-line10 has exhibits the trendexpected on the basis of a pseudo-intramolecular s�-resonance model. Authors argued that NEXAFSprovides a simple but incisive monitor of the surface structure for atomic adsorbates onsemiconductors. Using also the parallel SEXAFS data (see Section 4.8), authors concluded that, inthe Si(1 0 0)ð2 � 1Þ-Cl system, Cl atoms bonds atop a buckled dimer with a Cl–Si bond length of2:00 � 0:02 A.

5. Application of high-resolution XRD

XRD is the most widely employed and the most informative characterization technique in thestructural studies of crystalline materials and thus does not need any basic introduction, which isreferred to text books [433,730–732]. In Section 5.1 the attention will so immediately focused on theapplication of XRD on SL and heterostructures. What disused in Section 5.1 holds already forexperiments performed using conventional laboratory X-ray sources: the improvements performedexploiting the unique characteristics of synchrotron beams is then discussed in the next subsection.Section 5.3 deals with XRD studies performed in situ during sample growth. Section 5.4 reportsexamples of XRD reciprocal maps and finally, Section 5.5 reports some selected examples on surfacediffraction.

5.1. Basic concepts of XRD applied to SL

High-resolution XRD provides critically important structural and chemical information ofheterostructures and consequently of their interfaces [308,733,734]. The simulation of angularposition, relative intensity and lineshape of all satellite peaks (the zero-order peak included) present inthe experimental high-resolution XRD pattern allows to determine separately the well and barrierwidths and to infer the interface composition [147,158,159,161,162,164,166,308,733–735], as shownhereafter.

A typical MQW X-ray rocking curve (Figs. 41 and 42) is composed of a prominent substrate peakand several equally spaced satellite peaks (0, �1, �2, etc.) attributed to the heterostructure; usually, thezero-order peak has the highest intensity among all satellite peaks. The angular separation among thesatellite peaks is directly related to the period of the heterostructure P (i.e. the sum of the well andbarrier thickness), while the number of observed satellite peaks is related to the X-ray source intensity,the number of grown periods and the reproducibility of the structure. The relative intensity of thesatellite peaks is also determined by the interface composition and roughness. High-resolutionXRD and the related simulation have thus been widely used as a powerful technique in characteriz-ing semiconductor heterostructures [36,50,53,92,147,148,158,159,161,162,164,166,280,282,284,306–308,352,403,457,469–473,733–757]. The presence of chemical gradient at the interfaces implies

10 By white-line the most intense resonance of a NEXAFS (XANES) spectrum is denoted.


a gradient in the interplanar distance (in the direction of the growth axis), giving rise to an angularspacing of the diffracted X-rays observable in the experimental patterns.

Coming to the details of high-resolution XRD analysis, the period P of the SL structure isimmediately determined from the angular SL peak spacing Dy0 through the relationship [750]:

P ¼ l2Dy0 cosðyþ Dy0Þ

; (38)

Fig. 41. (a) (0 0 4) HRXRD spectra of In0.51Ga0.49As/InP SL with P ¼ 146 A and a nominal well width of 73 A. (The upper

curve is the measured data, and the lower curve, vertically shifted for graphical reasons, is the simulation result.) The large

number of observed satellite peaks and their sharpness are indicative of the good reproducibility of the heterostructure along

the 40 periods. (b) An expanded view of the spectra around the zeroth-order SL peak. Adapted from C. Lamberti, Comput.

Phys. Commun. 93 (1996) 82, [163], with permission. Copyright (1996) by Elsevier.


where l is the selected X-ray beam wavelength,11 y the Bragg angle, and Dy0 the angular differencebetween the substrate and the zeroth-order peak. Dy0 is directly connected to the average mismatchalong the growth axis Da?ð�xÞ=as, where as is the lattice parameter of the substrate and whereDa?ð�xÞ ¼ a?ð�xÞ � as (vide supra Section 2.2). Since simulations are aimed to identify a chemicalgradient in the heterostructure along the z-direction, a unique lattice parameter a? that is valid along thewhole w width does not exist. We are thus forced to use an averaged a?ð�xÞ that takes into account thethree different a? values of interface 1, the well layer, and interface 2, properly weighted by theircorresponding widths. From the example shown in Fig. 10b, i.e. winterface1, wwell and winterface2 ¼ 10, 80and 10 A, respectively, we have a?ð�xÞ ¼ 0:1ainterface1 þ 0:8awell þ 0:1ainterface2. If the well is a ternarylayer AxB1�xC, then the average difference in lattice parameter along the growth axis of the epitaxiallystrained SL (Da? and thus Dy0) is related to the fraction �x averaged over the whole period P of the SLstructure. Quantitatively the angular separation Dy0ð�xÞ from the substrate peak and the zeroth-order SLpeak is given by [749]

�Dy0ð�xÞ ¼ tanðyÞDa?ð�xÞas

: (39)

As already discussed in Section 2.2, assuming a pseudomorphic growth, the SL cell undergoes atetragonal deformation in which the average perpendicular lattice parameter mismatch ½Da?ð�xÞ�=as is

Fig. 42. (a) (0 0 4) HRXRD spectra of a 50-period InAsxP1�x/InP SL with P ¼ 90 A (lower curve), relative best-fit

performed with n ¼ 4 (middle curve) and relative best-fit in the ideal SL approximation (n ¼ 2, upper curve). (b) An expanded

view of the spectra around the zeroth- and �first-order diffraction peaks. Adapted from C. Lamberti, et al. J. Appl. Phys. 83

(1998) 1058, [164], with permission. Copyright (1998) by American Institute of Physics.

11 When the conventional laboratory Cu Ka1 source is used, l ¼ 1:54051 A, and for the InP substrate y0 0 4 ¼ 31:67� and

y0 0 2 ¼ 15:22�.


related to the free lattice parameter mismatch through the relationship given by the linear elasticitytheory

Da?ð�xÞas

¼ 1 þ g1 � g

� �Dað�xÞ

as

; (40)

where g is the Poisson’s ratio and a?ð�xÞ the free standing lattice parameter of AxB1�xC as deduced fromVegard’s law [529,530]. From the experimental Dy0ð�xÞ value, �x is thus analytically determined throughEqs. (39) and (40) and Vegard’s law [164,166].

If the well layer is a ternary AxB1�xC, then the entire SL structure can be considered as equivalent toa stack of n thin crystal lamellae of thickness wi and constant lattice parameter with a uniform Acontent xi; the stack is then repeated NSL times, NSL being the number of wells of the SL, Fig. 43b. Foreach layer of defined xi composition, the unstrained lattice parameter ai and Poisson’s ratio gi’s arecomputed as a function of the local A concentration xi by linear interpolation from correspondingvalues in binary alloys (vide supra Table 1), the same holds for the atomic-scattering factors fi. Thethickness wi and local A content xi are related to the period P and to the average value �x by

�x ¼ 1

P

Xn

i¼1

wixi withXn

i¼1

wi ¼ P: (41)

Note how in this formalism, the nth layer represents the barrier (note that xn ¼ 0 for both InAsxP1�x/InPand In1�xGaxAs/InP [163,164,166]). The simulation of high-resolution XRD pattern of MQWs havingnon-abrupt interfaces is performed using the dynamical theory of diffraction [758], which is a first-order approximation of Maxwell’s equations describing an X-ray wave propagating in a distortedcrystal. The Takagi–Taupin equations [746–748,759] describe the spatial variation of the complexamplitudes of both incident and diffracted beams, whose solutions gives rise, at any depth in the SL, toa recursion relation of diffracted and incident amplitudes. Computer software have been developed

Fig. 43. (a) Schematic representation of the simulated heterostructure, in the ideal SL approximation (where the well layer is

approximated as a single layer of uniform average chemical composition): right, corresponding Da/a. (b) Same as part (a) for

the full-interface approximation (where the compositional gradient has been taken into account). Adapted from C. Lamberti,

et al. J. Appl. Phys. 83 (1998) 1058, [164], with permission. Copyright (1998) by American Institute of Physics.


according to this theory, capable of simulating the XRD pattern diffracted from an arbitrary layersequence with a discrete step of 1 ML, taking into account the effects of interface non-planarity androughness [158,159,161,162,164,166]. Once an initial guess on the number of layers n and on thecorresponding 2n variables wi and xi is performed (i.e. once a distribution of the A atoms in the SLstructures for a given SL period P and average A content �x has been inferred), the simulation is able togenerate a theoretical XRD pattern Dfitðy; xi;wiÞ to be compared with the experimental Dexp(yj), whereyj is a discrete set of y values for which Dexp is sampled. The exact A distribution at the interface canthus be determined by changing the A content profiles xi and the corresponding thickness wi until asatisfactory match between experimental and simulated profiles is obtained. This means that thesimulation runs by minimizing, in a 2n � 2 dimensioned space,12 the w2-like function

Fðxi;wiÞ ¼1

Npoints

XNpoints

j¼1

log10

Dfitðyj; xi;wiÞDexpðyjÞ

� �� 2

; (42)

where the logarithmic-weighted fit is adopted to avoid an underestimation of the high-order satellitepeaks. This formulism can be extended to cases where a quaternary AxB1�xCyD1�y acts as a well layer,with the evident modifications of Eqs. (39)–(42), where Da? and thus Dy0 becomes depending on both�x and �y, defined as

�y ¼ 1

P

Xn

i¼1

wiyi: (43)

In this case, the number of optimized parameters increases to 3n � 2, depending the simulated patternDfit and the minimized function F from the (wi, xi, yi) set of variables.

A critical point in such simulation is the choice of a reasonable value for the number of layers n.n ¼ 2 is the minimal choice and represents an ideal abrupt interface with only two different chemicalcompositions, one for the well (of width w) and the other for the barrier (of width P � w) and nochemical gradient at the interfaces [164]. The n ¼ 2 simulation will be hereafter referred to as the idealSL approximation. In the case of a AxB1�xC ternary alloy, this approximation leads to the followingsimple relationship among x;w;�x and P:

xw ¼ �xP: (44)

The ideal SL approximation should be a starting point for any XRD pattern refinement. If theagreement between Dexp(yj) and Dfit(y, xi, yi, wi) is satisfactory, then it can be concluded that theheterostructure has abrupt and well-defined interfaces. Otherwise, n has to be set to n þ 1 in a recursiveway and a new simulation is started with a more complex structural model. This procedure will bestopped once a satisfactory agreement with the experimental pattern is obtained.

As a first example, let us consider the InGaAs/InP system. According to what is briefly mentioned atthe beginning of Section 3 and schematically depicted in Fig. 10b, the high-resolution XRD pattern hasbeen reproduced using the following n ¼ 4 scheme: layer 1 (first interface) InAsyP1�y; layer 2 (well)In0.51Ga0.49As; layer 3 (second interface) InxGa1�xAsyP1�y; layer 4 (barrier) InP [163]. Fig. 41compares the experimental high-resolution XRD spectrum (upper curve) and the simulated pattern

12 The number of free parameters is reduced from 2n to 2n � 2 due to the two relations given in Eq. (41).


(lower curve) for an In0.51Ga0.49As/InP SL with P ¼ 146 and w ¼ 73 A. In this case the presence of athin InGaAs contact layer, on top of the heterostructure, has been simulated as well. As shown inFig. 41a, the view over the whole collected pattern allows us to observe the agreement of both angularposition and relative intensity of the experimental and simulated SL peaks. An expanded view aroundthe zeroth- and �first-order peaks (Fig. 41b) demonstrates the high quality of the fit even in fine details.Moreover, the Pendellosung fringes generated by the presence of an InP cap are clearly visible betweenthe �first- and zeroth-order peaks. The closeness of the nominal composition with the lattice-matchedone (vide supra Section 2.4) results in a low Da?/as value and thus in the closeness between theInP(0 0 4) reflection and the zeroth-order peak.

A second example concerns an InAsP/InP system SL that is grown by exploiting the As $ Psubstitution occurring by just periodically exposing the as-grown InP surface to AsH3 [152,155,159,161,163–167,301,457]. Fig. 42 reports for a 50-period InAsxP1�x/InP SL with P ¼ 90 A, theexperimental high-resolution XRD pattern (lower curve) together with the fit in the frame of the idealSL approximation (n ¼ 2, upper curve) and of full-interface fit (n ¼ 4, middle curve). The ideal SLapproximation simulates an InAs0.33P0.67/InP system with w ¼ 10 A, while the full-interface simulationrefers to a chemically gradiented structure with three different InAsxP1�x layers with decreasing x. Theschematic representation of both approaches is displayed in Fig. 43. A good fit of the fundamentalfeatures of the experimental profile can be obtained using the simplified approach ðn ¼ 2Þ. In fact, onlyafter a more careful inspection of Fig. 42a, it can be noted a less sensitive evaluation of the relativeintensity of the satellite peaks. However, no relevant difference can be appreciated in the zoom-in viewaround the �1 SL peaks (Fig. 42b), since the details of the arsenic distribution profile (the typical Asdiffusion distance being given by the length w [164]) are able to appreciably affect only the highestorder SL peak intensities.

Simulation of high-resolution XRD patterns allows the prediction of the chemical spread occurring atthe interfaces of real non-abrupt SLs. Moreover, the output of high-resolution XRD simulations (wi xi

and yi) can be used as input for the 4 K PL simulations, which represents thus a self-consistent cross-check for the high-resolution XRD simulation [36,163,164,739]. This parallel 4 K PL simulationrepresent thus the key to distinguish among the different local minima of F. Such high-resolution XRDstudies are well supported by parallel high-resolution TEM investigations, which allow an independentand direct measurement of w and P values (vide supra Fig. 14a) as well as the identification of theinterface layers, when a sufficient contrast is present (Fig. 14b).

5.2. Few selected examples

The use of SR sources will considerably increase the ability to collect high order SL peaks, whoseintensity is several order of magnitudes below that of the substrate peak (note that the ordinate axis ofFigs. 41 and 42 has a logarithmic scale). The collection of such high order satellite peaks with a goodstatistic is very important for XRD simulation of the heterostructure described in the previoussubsection.

The execution of a standard XRD experiment on a semiconductor SL at the synchrotron has to face atrivial but imperative problem: the high quality of the semiconductor lattices and the high photon fluxof the source results in a saturation of the detector when the substrate and the lower order SL peaks aresampled. This means that a (0 0 l) scan, like those shown in Figs. 41 and 42 cannot be performed in anunique acquisition at a SR source. Filters of different thickness have to be inserted in front of the


detector to reduce the photon flux on it. Filters are calibrated, chemically pure, metal foils of preciseand uniform thickness. The nature of the metal is chosen on the basis of the adopted l. The substratepeak has so to be acquired using a thick filter while SL peaks will be acquired using filters withprogressive decreasing (down to zero) thickness. For each couple of adjacent scans, performed withdifferent filter thickness, an as large as possible overlap region (between SL peaks) must be acquired inorder to allow the overall rescaling of the diffracted intensities of the several scans resulting in anunique (0 0 l) diffraction pattern. This long procedure is depicted in Fig. 44, using an InGaAs/InP shortperiod SL as example, adapted from Ref. [160]. Using this approach, it has been possible to collect the(0 0 l) diffraction pattern over the (0 0 2), (0 0 4) and (0 0 6) reflections as reported in Fig. 45 for50-period InAs0.30P0.70/InP SL. In the region between the (0 0 2) and (0 0 4) the high positive highorder SL peaks of the (0 0 2) reflection overlap with the negative ones of the (0 0 4) reflection. A muchless important overlap occurs between (0 0 4) and (0 0 6) reflections. Note that odd l (0 0 l) reflectionsare forbidden for the cubic InP (or GaAs) lattice. Let now come to discuss few selected examples. Asimilar figure has been reported by Schuster et al. (Fig. 1 in Ref. [760]) for the (0 0 2) and (0 0 4)reflections of an (AlAs)m/(GaAs)n short period SL.

In this review the problem of interface mixing in InGaAs/InP short period SL has already faced byEXAFS spectroscopy (Section 4.5). From Sections 3.1 and 5.1, it is evident that the intermixing cangive rise to different compositions but the macroscopic effect on the XRD patterns is a consequence ofthe mismatch induced from these interface layers and depends on the combination of the thickness andcomposition of each of the four constituent layers. Aruta et al. [303] report SR high-resolution XRD ona set of In1�xGaxAs/InP short period SL with nominal x ¼ 0:47 value. The simulation of theexperimental pattern has been performed by assuming that each SL is composed by four layers ofdefined chemical composition (barrier (InP), first interface (InAs0.7P0.3), well (In0.53Ga0.47As) andsecond interface (In0.53Ga0.47As0.7P0.3)), and of variable length, xb, xI1, xw, and xI2 respectively, beingxb þ xI1 þ xw þ xI2 ¼ P. To further reduce the number of free parameters period P of the SL was fixedto the value experimentally obtained by the separation of the SL satellite peaks (38). The experimentaldiffraction patterns (Fig. 46a) exhibit the InP(0 0 4) substrate peak, sharp and intense (located aty ¼ ysub), together with the broader and less intense zero-order SL peak. In Fig. 46a, patterns have beenordered as a function of the corresponding hDa?/ai value which decreases from top to bottom astestified by the convergence between the substrate and the zero-order SL peak. Aruta et al. [303] haveremarked that the relative fraction of the interface layers ðxI1 þ xI2Þ=P correlates well with the hDa?/ai(see squares in Fig. 46b), i.e. a low SL mismatch value is accompanied by a low relative fraction of theinterface layers with respect to the overall period. Since the two interface layers (InAs0.7P0.3 andIn0.53Ga0.47As0.7P0.3) have an opposite effect on the average mismatch, the correlation of ðxI1 þ xI2Þ=Pwith hDa?/ai (squares) reflects the dominant role played by the first interface [158,161,163–166],which is further confirmed by the improvement of the correlation obtained by reporting the relativefraction of the first interface versus the average mismatch (Fig. 46b, triangles). An XSW study on thesame set of samples is reviewed in Section 7.3.

Some other examples will now be briefly itemized. Among them, multiple diffraction study ofAl0.304Ga0.172In0.524As quaternary alloy grown by MOVPE on InP(0 0 1) substrate [762]. Examinationof the multiple diffraction peak profiles allows Sasaki et al. to reveal how the epitaxial layers have ahigher mosaic spread than the underlying substrate materials.

A remarkably complete diffraction study has recently been reported by Li et al. [763] on short period(InAs)n/(GaAs)m SL. The lateral composition modulation in (InAs)n/(GaAs)m heterostructures was


Fig. 44. High-resolution XRD patterns (l ¼ 1 A) in the neighborhood of the InP(0 0 4) reflection for In1�xGaxAs/InP SLs

(with nominal x ¼ 0:47). Parts (a) and (b) refer to a SL with P ¼ 31 A, while part (c) refers to a different SL with P ¼ 59 A. In

(a) the central region has been omitted (due to saturation of the detector) and the �1 and �2 SL peaks are evident. In (b),

collected with a thicker filter before the detector, the substrate and zero-order SL peak are detected. In (c) a full diffraction

pattern is reported in an extended l range, obtained by joining several scans (performed with different filter thickness) and

appropriately renormalizing. The reflections are labeled with the reciprocal lattice indices (0 0 l) of the InP substrate. Adapted

from F. Boscherini, et al., Phys. Rev. B 58 (1998) 10745, [160], with permission. Copyright (1998) by American Physical

Society.


Fig. 45. High-resolution XRD pattern collected on BM2 beamline at the ESRF on a 50-period InAs0.30P0.70/InP SL. To allow

a better observation of the high order satellite peaks, data have been truncated at 100 in arbitrary units. Adapted from

S. Pascarelli, Ph.D. Thesis in Physics, University Joseph Fourier, Grenoble, 1997, [761], with permission.

Fig. 46. (a) Experimental XRD curves of five of In1�xGaxAs/InP SL, with increasing the average mismatch hDa?/ai from

bottom to top, across the (0 0 4) reflection. y ¼ ysub corresponds to the Bragg angle of the (0 0 4) reflection of the InP

substrate. At lower y, for all samples, the zero-order SL peak of the (0 0 4) reflection is observed. The curves related to the

different samples have been vertically translated for graphical reasons. Around the Bragg reflections the frequency of the data

is increased (lower angular step) to obtain a better resolution in the interesting angular region. (b) Relative fraction of the

interface layers ðxI1 þ xI2Þ=P and of the first interface layers xI1/P vs. hDa?/ai (squares and triangles, respectively). Full and

dotted lines represent the linear fits of the reported data. Since the two interface layers (InAs0.7P0.3 and In0.53Ga0.47As0.7P0.3)

have an opposite effect on the average mismatch, the correlation of ðxI1 þ xI2Þ=P with hDa?/ai (squares) reflects the dominant

role played by the first interface [158,161,163–166], which is further confirmed by the improvement of the correlation

obtained by reporting xI1/P vs. hDa?/ai (triangles). Adapted from C. Aruta, et al., J. Appl. Phys. 93 (2003) 5307, [303], with

permission. Copyright (2003) by American Institute of Physics.


investigated by means of grazing-incidence small angle X-ray scattering (GISAXS) and grazing-incidence diffraction (GID) and coplanar X-ray diffraction. From GISAXS measurements the authorsdetermined the interface profile of a vertical superlattice, which then was used as the basis for thediffraction analysis of the lateral composition profile. Li et al. [763] found that the interfaces in thevertical superlattice have an asymmetric profile with an average undulation wavelength of about 280 Aand an average amplitude of about 1 A. For the analysis of the lateral composition profile, a structuralmodel based on the measured interface profile was proposed. The model also assumes that thecomposition is uniform in the growth direction but modulated laterally, because authors consider onlythe zero-order vertical X-ray SL peak. This model, combined with strain analysis, was employed toextract the composition information from the X-ray GID and coplanar diffraction data. For theparticular sample studied, both the GID and the coplanar diffraction measurements yielded a lateralcompositional wavelength of about 280 A (which is the same as the morphological undulationwavelength of the interfaces) and a composition amplitude of about 15–16%. The upper limit of theamplitude of composition modulation has been determined to be 18% for this particular sample. Liet al. [763] concluded that the observed composition modulation is predominantly caused bymorphological undulation driven by the misfit strain.

The crystalline quality and the interface roughness of a set of unintentionally-doped InAs/AlSbstrained MQW grown on GaSb substrates by MBE using different cell shutter sequences at thearsenide/antimonide interfaces has been determined by Prevot et al. [458] using combined high-resolution XRD and small angle X-ray reflectivity measurements.

The direct evidence of ordered SiO2, which is epitaxially related to the underlying Si(0 0 1) substrate,has been reported by Munkholm et al. [764]. This evidence consists of diffraction peaks at the[h ¼ 1; k ¼ 1; l ¼ 0:45] positions. For films with thickness in the range 80–160 A the integratedintensity of these diffraction peaks increases roughly linearly and the ordered oxide grain size parallelto the surface is constant at 130 A.

X-ray microbeam ð203 mm � 29mmÞ with a narrow energy bandwidth and a small angular divergenceð185 mrad � 11 mradÞ has been used by Matsui et al. [765] to measure by high-resolution XRD the locallattice strain map in silicon materials after several wafer preparation processes or device fabricationprocesses. Local strain in an Si crystal around the SiO2/Si film edge and strain at silicon-on-insulatorinterface have also been measured.

5.3. In situ XRD studies during growth

All the diffraction studies described so far in this review have been done at room temperature afterthe growth of the complete device structure, while the actual growth process takes place at elevatedtemperatures. Hence, room temperature measurement of rocking curves of such structures cannotprovide the actual information about the growing epilayers, because significant strain is incorporatedinto the various interfacial layers of the device structure when it is cooled down to room temperature,due to the different thermal expansion coefficients of the individual layers. Ideally, in order tounderstand the growth mechanisms, rocking curves should be measured in real-time during the growthprocess itself. Moreover, since simulation of rocking curve of the entire device structure involves ahuge number of parameters (see Section 5.1), it can be useful to evaluate each layer separately after it isgrown and subsequently observe the evolution of the entire rocking curve. When room temperaturerocking curve is then compared to that collected in situ at high temperature, the effect of cooling on the


structure due to strain redistribution could easily be realized. The experimental difficulties related tosuch in situ studies have been overcome by Kawamura et al. [296] attaching a special MOVPE growthchamber directly on to the four-axis X-ray goniometer placed in one of the beam lines of Spring-8synchrotron radiation facility. This experimental set-up allows to follow in real-time, under in situconditions, the different surface phenomena occurring during the epitaxial growth of semiconductorfilms and heterostructures. It is evident that this is a welcome improvement in the investigation ofgrowth processes since measurement of real-time rocking curves of semiconductor heterostructures atvarious stages of epitaxial growth provides useful information about the composition, thickness and in-built strain in the growing epilayer.

Kawamura et al. [296] reported X-ray reflectivity measurements on the InP surface during in situgrown with MOVPE technique as a function of the different growth temperatures. At the lowestinvestigated temperature (450 8C) the formation of significant indium islands was evidenced by a largedecrease of the observed reflectivity value. At 550 8C, only small changes were observed at high growthrate, indicating the step-flow growth mode. Oscillations longer than monolayer growth were alsoobserved at 500 and 550 8C, and roughness changes obtained from these oscillations were less than0.01 nm suggesting small islands formation on the terrace or step-edge fluctuation during the growth.The same group, with the same experimental set-up [279], has studied the growth of GaxIn1�xPepilayers of different composition and thickness, on previously grown lattice-matched GaInP/GaAsheterostructure. Strain redistribution at the interface of the GaInP/GaAs substrate due to the differentlinear thermal expansion coefficients of GaInP and GaAs was determined from rocking curve of theheterostructure measured at 570 8C. The change in rocking curve due to the growth of as thin as 16 nmof In-rich Ga0.42In0.58P epilayer at the initial stage of growth was detected. Data from the simulation ofeach intermediate rocking curve during growth was systematically used to grow a lattice-matchedGaInP epilayer (Fig. 47).

Fig. 47. (a) XRD rocking curve collected in situ on a 16 nm thick Ga0.42In0.58P epilayer grown by MOVPE on a lattice-

matched GaInP/GaAs substrate at 570 8C. Photon energy ¼ 20 keV. (b) Same as part (a) for new epilayers of Ga0.48In0.52P

with a thickness of 25 and 35 nm grown with a growth interruption time of 5 min in between on the previous surface of

Ga0.53In0.47P/Ga0.42In0.58P/GaInP/GaAs. Adapted from S. Bhunia, et al., Appl. Surf. Sci. 216 (2003) 382, [279], with

permission. Copyright (2003) by Elsevier.


Semiconductor InN films epitaxially grown by the radio frequency magnetron sputtering depositionmethod were studied by Hur et al. [766] in terms of the strain evolution as a function of the filmthickness and growth temperature. The structure and surface morphology of the InN films wereanalyzed using synchrotron X-ray scattering and supported by successive AFM experiments. Thefollowing main conclusions have been reached: (i) the lattice strain of the InN films grown at 300 8Cwas larger than that of the films grown at 490 8C; (ii) as the film thickness increases, the lattice strain isreduced and completely relaxes when the thickness is larger than 350 8C; (iii) the average roughness onthe surface of the InN film increased with the growth temperature.

5.4. XRD reciprocal space maps

Instead of collecting high-resolution XRD patterns by scanning only one reciprocal lattice parameter(as was the case of all the examples discussed up to now in Section 5.1), the much higher photon fluxavailable using SR sources allow to collect in reasonable time high quality XRD reciprocal space maps(RSMs) by scanning simultaneously two different reciprocal lattice parameters, which are moreinformative than the conventional one-dimensional scans [767]. In fact, the distribution of the scatteredintensity around the reciprocal lattice peaks is directly correlated to the presence of lattice distortionand/or defects, misfit dislocations and mosaicity [767–771].

De Padova et al. [772] report a combined XRD reciprocal space maps and polarization-dependentEXAFS study on two Si1�xGex films grown on a Si(0 0 1) substrate (x ¼ 0:05 and 0.70). High-resolution RSMs were collected around the Si(1 1 3) reflection to determine the elementary celldimensions of the alloy film along the three crystallographic directions. The distribution of the scatteredintensity in the reciprocal space is illustrated by the RSMs shown in Fig. 48a and b for Si0.95Ge0.05 and

Fig. 48. Reciprocal space maps near the Si(1 1 3) reflection for Si0.95Ge0.05/Si(0 0 1) (a) and Si0.30Ge0.70/Si(0 0 1) (b) films.

Adapted from P. De Padova, et al., Thin Solid Films 319 (1998) 20, [772], with permission. Copyright (1998) by Elsevier.


Si0.30Ge0.70 films, respectively. The Si substrate has coordinates h ¼ 1, l ¼ 3, while the vertical andsloping lines mark the reciprocal lattice positions of fully compressive-strained and completely relaxedSi1�xGex films, respectively. In the case of the Si0.95Ge0.05 films sample (Fig. 48a) the isointensitycontours are symmetric around the [0 0 1] direction through the position of the substrate, proving an in-plane lattice constant equal to bulk silicon (5.43 A) and a tetragonal distorted cell. The fully strainedcondition is confirmed by the absence of any alloy peak broadening in the l-scan direction. Thus, theposition of the RSM maximum (h ¼ k ¼ 1, l ¼ 2:982) indicates a tetragonal structure with a equal tothe bulk silicon value and c equal to 5.46 A, which gives a Ge concentration of 0:048 � 0:003.Conversely, the RSM of the Si0.30Ge0.70 film (Fig. 48b) shows a maximum at h ¼ 0:973, l ¼ 2:92indicating a cubic structure fully relaxed with a lattice parameter of 5.58 A and an x value of0:66 � 0:04, in good agreement with the nominal x ¼ 0:70 value. Moreover, the maxima lies along the[113] direction indicating that the epilayer has the lattice vectors parallel to the substrate vectors [772].

On the same films, De Padova et al. [772], have also performed the EXAFS experiments at the GeK-edge in fluorescence mode. In order to correlate the rGe–Ge and rGe–Si bonds to the lattice parametersobtained by X-ray diffraction maps, the EXAFS data were collected putting the (0 0 1) surface of thesamples parallel and perpendicular to the polarization direction of the beam (vide supra Section 4.7).The Ge coordination ratio NGe/4, where NGe is the average number of Ge nearest atoms around a Geatom and 4 is the number of nearest neighbors in the perfect diamond structure, was derived by theRSM extracted concentration values. For the Si0.30Ge0.70/Si(0 0 1) system, the same rGe�Ge ¼2:44 � 0:02 A and rGe�Si ¼ 2:40 � 0:02 A first shell distances where obtained independently to theorientation of the sample in the SR beam, vide supra Section 4.7. The EXAFS analysis confirms that weare dealing with a fully relaxed Si0.30Ge0.70 film, being the optimized rGe–Ge and rGe–Si bond lengthssimilar to the ones of pure crystalline germanium, rGe�Ge ¼ 2:45 A [564], and amorphous Si1�xGex

alloys ð0:2 < x < 0:8Þ, rGe�Ge ¼ 2:38 A [513]. In this respect, previous studies on amorphouscrystalline Si1�xGex alloys ð0:2 < x < 0:8Þ [513,545–547] showed that the bond lengths wereindependent on the Ge concentration and were the sum of the alloy constituent element atomic radii,vide supra Section 4.3. For the Si0.95Ge0.05/Si(0 0 1) system, however, the data measured by De Padovaet al. [772] with the sample surface parallel to the incident wave polarization give smaller values forboth rGe–Ge and rGe–Si bond lengths (rGe�Gek ¼ 2:40 � 0:02 A; rGe�Sik ¼ 2:50 � 0:02 A; rGe�Ge? ¼2:44 � 0:02 A and rGe�Si? ¼ 2:37 � 0:02 A), indicating that with an x value as low as 0.048, thechemical environment seen by the scattering Ge atom is effectively modified with respect to a Ge richerðx � 0:20Þ Si1�xGex alloy. Conversely, the spectrum measured with the sample surface perpendicular tothe incident wave polarization gives larger rGe–Ge and rGe–Si distances, consistent with a lattice cellelongated along the [0 0 1] surface normal as measured by RSMs. De Padova et al. [772] concluded byunderlying the satisfactory correlation found between the Ge coordination ratio and the rGe–Ge andrGe–Si distances, derived by best-fitting the EXAFS curves, and the X-ray diffraction structural parametersindicates that the combination of the two techniques is a unique approach to achieve a thoroughcharacterization of the structural and chemical properties of lattice mismatched heterostructures.

Giannini et al. [471] have investigated the morphological transition from a step-like interfacemodulation to a highly periodic lateral thickness modulation that occurs on symmetrically strained(GaIn)As/GaAs/Ga(PAs)/GaAs superlattices grown by metal-organic vapor phase epitaxy on miscutGaAs(0 0 1) substrate. The combination of X-ray reciprocal space mapping, around the (0 0 4), (2 0 0)and (0 2 0) reflections, and TEM resulted in an accurate analysis of the structural periodicities andordering of heterointerfaces and to relate them to the elastic strain. The laterally ordered macrosteps on


the growth surface have been investigated and discussed as a function of the strain misfit betweenepitaxial layer and substrate. Within this purpose, authors also employed the complementaryinformation obtained by grazing-incidence X-ray diffraction to gain further information on the effectsof strain and morphological modulation of the interfaces in the process of macrostep formation [471].

The InP/GaAs(0 0 1) heterostructures has been analyzed using three-beam Bragg surface diffractionof the X-ray multiple diffraction phenomenon by Avanci et al. [773]. The angular multiple diffractioncondition is scanned by varying both the O incidence angle and the j rotation angle around [0 0 1] inorder to provide the mapping of this condition. From the two-dimensional mapping O/j scan, thecrystalline perfection (mosaic spread) parallel and perpendicular to the growth direction have beeninvestigated along the layer surface and the substrate interface. The O/j scan has been used to analyzethe growth processing and post-growth annealing of InP/GaAs samples. The effect of various defect-reduction tools on layer and substrate crystal quality has also been reported.

Korakakis et al. [774] report an XRD on a 15-period GaN/Al0.20Ga0.80N (50 A/50 A) MQW whichwere grown on (0 0 0 1) sapphire substrate by MBE. The crystal structure of this system wasinvestigated by studying the reciprocal lattice map of off-axis diffraction peaks as well as the y–2ypattern around the (0 0 0 2) reflection. Authors demonstrated that the MQW is coherent and has a latticeparameter of the underlying Al0.25Ga0.75N phase. The good agreement between experimental andtheoretical data in the relative intensity of up to third-order satellite peaks suggests the presence ofrather abrupt MQW interfaces and thus are of negligible interdiffusion of Ga and Al atoms.

5.5. Surface diffraction

Diffraction represents the most important tools for structural analysis in condensed matter. Asdiscussed in Section 4.8, when SEXAFS spectroscopy was introduced, by choosing grazing incidencesangles between the photon beam and the single crystal surface, XRD becomes surface sensitive. As aconsequence, surface XRD becomes an important structural characterization technique for surfaces andthin films which is complementary to the traditional electron-based diffraction techniques, such asLEED, RHEED, Auger, X-ray photoelectron diffraction, etc. [672–674,676], which surface selectivityis determined by the low mean-free path of electrons in the condensed matter [662]. Being theintensities of the diffracted beams proportional to the volume of the sample contributing to thescattering process, surface diffraction is reasonably feasible only using the high X-ray flux available atsynchrotron radiation facilities. Surface X-ray scattering has seen a rapid development in recent years[775–784], parallel to the development of new and more performing SR facilities.13 X-ray diffractionhas the important advantage of being sufficiently sensitive to detect a single layer of atoms, but at thesame time being sufficiently penetrating to reach buried interfaces [786]. It can therefore be usedequally with surfaces and interfaces.

The basic concepts of surface diffraction can be summarized following the simple and cleardescription proposed by Ferrer and Petroff [776]. The diffraction of the X-rays by crystals is describedby the Bragg law that establishes the conditions for such interferences to occur. In the left part of Fig. 49an infinite set of crystal planes is represented. If we consider the direction perpendicular to these planes

13 The development of surface neutron scattering has been much slower, in part because of the lower neutron flux available

from nuclear reactors as compared to the photon flux from synchrotron sources. Notwithstanding this handicap, the feasibility

of neutron surface diffraction has been demonstrated in the 1990s [775,785].


(L-axis in the figure), then for specific scattering conditions that satisfy Bragg law, one finds veryintense diffracted beams that resemble delta functions as schematized in the top of the figure. Theintensity of these Bragg reflections arises from the constructive interference of many (typically severalthousand) crystal planes. The information contained in the Bragg reflections concerns averageproperties of these diffracting planes that constitute the crystal.

Let us consider now the mid-point in the L-axis between the two Bragg reflections (circles) of thefigure. At this precise location, the scattering conditions are such that a destructive interference occursbetween the X-ray waves scattered from two consecutive crystal planes. This causes a very strongcancellation that reduces the diffracted intensity to almost zero. It is precisely this ‘‘almost zero’’ whichis the object of surface diffraction. It may be shown that the remaining intensity under destructiveinterference conditions arises from the topmost atomic planes of the crystal. Thus, by measuring at thedestructive interference conditions, one does not sense the bulk of the crystal but only the surface.

In a slightly more precise manner, Ferrer and Petroff [776] describe a crystal terminated by a surfaceby multiplying by a step-shaped function the response of an infinite set of crystal planes as schematizedin the right part of Fig. 49. In Fourier space (i.e. in the space where the scattering geometry isdescribed) the simple product transforms in a convolution product. As the Fourier transform of the stepfunction is proportional to q�1, where q is the amplitude of the scattering vector q (difference ofwavevectors of the scattered and incident X-ray beams q ¼ kf�ki), the result is that the distribution ofthe intensity of the scattered X-rays does not look as a set of sharply peaked delta functions as in the leftpart of the figure. These continuous intensity distributions are usually designated as crystal truncation

Fig. 49. Principle of surface diffraction. Left: the diffracted intensity from an infinite set of crystal planes in a direction L

perpendicular to the planes is very concentrated around the reciprocal space points which satisfy Bragg conditions (circles).

The intensity distribution along L consists of very sharp peaks as indicated in the I vs. L plot reported on the top. Right: a

crystal terminated on a surface may be visualized as the result of multiplying an infinite set of planes by a step function

(middle of the figure) equal to zero outside the surface and to 1 from the surface to interior of the crystal. In reciprocal space,

the above multiplication results in a convolution product which has the effect of transforming the sharply peaked diffracted

intensities to continuous intensity distributions which vary slowly with L as indicated in the top of the figure. Adapted from

S. Ferrer, Y. Petroff, Surf. Sci. 500 (2002) 605, [776], with permission. Copyright (2002) by Elsevier.


rods (CTR). They are curves that connect the Bragg reflections. At the minima of the CTR the surfacesensitivity is highest as discussed above. In practice however, the intensities of the CTR are sensitive tothe surface structure everywhere except at the immediate vicinity of the Bragg reflections. Surface X-ray diffraction basically consists of measuring the intensities of the CTRs that contain information onthe structure of the topmost atomic planes of the crystal (the surface). The structure is normallydetermined by fitting to the measured CTRs, calculated CTRs obtained from aprioristic surface models.Selected examples follow now to illustrate some applications of the technique.

Torrelles et al. [778–780] report some real examples of surface reconstructions determined by directmethods. Authors determine the reconstructed surfaces using a two-stage approach: (i) the (x, y)projection of the reconstruction is determined by direct interpretation of the two-dimensional partialPatterson map computed with the intensities of the reconstruction in-plane reflections only; and (ii) thisprojection is subsequently expanded to three dimensions by fitting the full data set (in-plane plus out-of-plane data) [779]. Selected examples have been arranged according to the interpretation complexityof the respective two-dimensional Patterson maps and correspond to the most common types of surfacereconstructions. The Ge(0 0 1)-cð4 � 2Þ and GaAs(0 0 1)-pð2 � 4Þ reconstructed surfaces as deter-mined by the surface XRD study of Torrelles et al. [779] have been reported in Fig. 50. In a successivework, the In0.04Ga0.96As(0 0 1)-pð4 � 2Þ reconstructed surface has been chosen by the authors as anexample of a shift of the surface atoms from their ideal positions, a phenomenon which is often foundon (0 0 1) semiconductor surfaces and its most characteristic structural feature is the pairing ofneighboring surface atoms forming dimers. Torrelles et al. show how different atom types occupyingthe surface sites can be induced by the adsorption of deposited atoms onto the surface, e.g. Sb/Ge(1 1 3)-cð2 � 2Þ [780]. Adsorption of Sb on the Ge(1 1 1) surface has been previously investigatedby Ferrer [787].

Ferrer et al. [788] have highlighted the cð4 � 2Þ reconstruction of Ge(0 0 1) by X-ray diffraction of150 K measuring in-plane reflections and out-of-plane intensities of fractional order rods. The structureconsists of an alternate arrangement of buckled dimers exhibiting a tilt angle of 19� � 1�, along the

Fig. 50. Upper and side views of the Ge(0 0 1)-cð4 � 2Þ (a) and of the GaAs(0 0 1)-pð2 � 4Þ (b) reconstructions. Adapted

from X. Torrelles, et al., Surf. Sci. 423 (1999) 338, [779], with permission. Copyright (1999) by Elsevier.


[1 1 0] and ½1 �1 0� surface directions. The dimer rows are not straight along the [1 1 0] direction butshow a slight zig-zag with an amplitude of 0:340 � 0:005 A [788]. The Ge(0 0 1)ð2 � 1Þ reconstructionhas been successively reported in Ref. [789].

Self-assembled SiGe wires in a SiGe/Si multilayer, have been investigated by Roch et al. usinggrazing-incidence X-ray diffraction [790]. In the measured reciprocal space maps, satellite intensitymaxima indicate a good lateral and vertical correlation of the wire positions. Grazing-incidencediffraction, supported by PL investigation resulted in an average Ge content in the wires of 20% [791].In Ref. [790], the same authors report grazing-incidence X-ray diffraction measurements on Ge-richislands grown by molecular beam epitaxy on Si(0 0 1) vicinal substrates with a miscut 28 along the[1 0 0] direction. By varying the angle of incidence, data sets were obtained for different informationdepths. These data were analyzed quantitatively using a model based on the distorted wave Bornapproximation. The authors report the shape modifications undergone by the islands in a 20-period Si/SiGe island multilayer sample upon annealing (80 min at 750 8C). For the top island layer a comparisonwith atomic force microscopy topographs was made [790].

A grazing incidence XRD study on the CdTe(0 0 1) surface has been published by the same group[777] reporting a cð2 � 2Þ reconstruction. The surface arrangement is accompanied by a significantrelaxation of the underlying substrate down to the sixth atomic layer. A strong anisotropy of thereconstructed domain dimensions has been also observed. This finding has been able to explain theanisotropic behavior observed during homoepitaxial and heteroepitaxial growth on CdTe. Successively,the evolution of the CdTe(0 0 1) surface during ion bombardment was studied by grazing incidenceXRD supported by Monte Carlo simulation [293]. A layer-by-layer removal was observed at 270 8Cwhich evolves to a step-flow mode above 300 8C. An anisotropic relaxation of the surface latticeparameter and a long-distance correlation between islands along the ½1 �1 0� direction were observedduring sputtering [293].

Emoto et al. [792] studied by means of grazing-angle XRD the strain induced on the InGaP surfaceby the sputtering procedure usually adopted during surface-cleaning treatment. Authors found thepresence of two broad subpeaks near the (1 1 3) reflection due to a compositional fluctuation near thesubsurface. Changes in the main peak versus sputtering bias voltage indicate that bias sputteringintroduces a tensile strain to the InGaP surface. Furthermore, changes in the subpeak versus suppliedbias voltage curves indicate that excessive sputtering generates a heavy compositional fluctuation nearthe InGaP subsurface.

Chamard et al. [793] have recently reported an anomalous GID study on GaN quantum dots stackedin AlN multilayer. Samples have been prepared as follows in a MBE growth chamber: a thick AlNbuffer layer (5000 A) is first grown on a 6H–SiC(0 0 0 1) wafer, prior to the GaN quantum dots. DuringGaN deposition, a two MLs wetting layer first forms before the strain relaxation leads to the self-organized growth of quantum dots. Each quantum dot layer is covered by an AlN spacer, withequivalent thickness of 100 A. At the end, the multilayer consists of 80 bilayers and a final uncappedQD plane deposited on the top. A scheme of the QD multilayer is presented in Fig. 51a. The GIDmeasurements have been performed at ID01 beamline at the ESRF [783], according to the experimentalset-up reported in Fig. 51b. The surface is illuminated with a monochromatic beam of energy E

(corresponding wavevector ki and jjkijj ¼ 2p=l) under grazing incidence angle ai. The intensity iscollected with a position sensitive detector oriented vertically with respect to the sample surface, alsoshown in Fig. 51b. Its angular position is given by the exit angle af defined in regard to the samplesurface and the out-of-plane angle 2y measured from the plane of incidence. The 2y value is set to the


in-plane Bragg angle of the material. In this geometry, the scattered intensity I(q, E) is proportional to[793]

Iðq;EÞ / TðaiÞSðq;EÞTðafÞ; (45)

where q is the wavevector transfer (¼kf � kiÞ, S(q, E) the scattering power of the sample for a givenphoton energy and wavevector transfer and T the transmission factor for the incidence and exit beam[775].

A typical GID measurement curve on GaN quantum dots stacked in AlN is presented in Fig. 52a(triangles) [793]. This strain sensitive scan is measured at the ð1 1 �2 0Þ Bragg reflection withE ¼ 10:263 keV and ai ¼ 0:174�. Note that for this sample at the critical angle ai ¼ ac ¼ 0:18�, theincidence configuration allows a penetration depth of about the two topmost bilayers. The intense peak,observed at the relaxed AlN bulk lattice parameter position (close to 4.04 A�1), corresponds to thediffracted signal from AlN in the spacer layers. A second peak, less intense and broader, is observed atsmaller wavevector values, between the values of relaxed AlN and relaxed GaN (close to 3.95 A�1). Itresults from the scattering by the nanostructures, mostly GaN QDs. However, as the technique is notchemically sensitive, it is not possible with this single measurement to identify this second peak as adiffraction from pure GaN because some of the AlN spacer layer material, strained coherently to thequantum dots also contribute at signal.

Chamard et al. [793] overcome this lack of element sensitivity by exploiting anomalous scatteringeffects [794]. At the ð1 1 �2 0Þ Bragg reflection the scattering power of bulk GaN is given by

Sð1 1 �2 0ÞðEÞ / jfGaðEÞ þ fNðEÞj2; (46)

where fGa(E) and fN(E) are the atomic-scattering factor of gallium and nitrogen at the used photonenergy E. Far away from an absorption edge, f varies slowly with E. Conversely, near the Ga K-edgeboth real and imaginary parts of fGa(E) vary strongly, vide infra Section 6. For Ga, the real part of theatomic-scattering factor f1 decreases from around 27 to 19.443 electron units at the absorption K-edge(E ¼ 10:367 keV), as reported in Fig. 52b. By changing the energy of the incident beam, the relativecontribution of Ga to the diffracted signal can therefore be significantly varied. A simultaneous increaseof the absorption coefficient m(E) is observed in the fluorescence spectrum (Fig. 52c), which is basicallya Ga K-edge XANES (NEXAFS) spectrum, see Section 4.9. Chamard et al. [793] performed then a

Fig. 51. (a) Schematic representation of the GaN/AlN QD multilayered sample; (b) geometry used for the GID

measurements. ai and af represent the angles formed with the sample surface by the incident (with wavevector ki) and the

diffused (with wavevector kf) X-ray beam, respectively. The position sensitive detector used to collect the diffused photons is

also represented. Adapted from V. Chamard, et al., Nucl. Instrum. Meth. B 200 (2003) 95, [793], with permission. Copyright

(2003) by Elsevier.


second GID measurement by choosing the photon energy exactly in the minimum of the f1 curvereported in Fig. 52b (solid circles in Fig. 52a). After normalization, the difference between the twocurves (shadowed curve in Fig. 52a) allows to enhance the maximum of the Ga contribution, indicatedby an arrow at 3.975 A�1, corresponding to Da=a ¼ 0:017. The comparison with the theoreticaldifference shows that the contribution of Ga is about two times less intense than the expectedcontribution in case of diffracted intensity from pure GaN. Chamard et al. [793] repeated the anomalousGID experiment for ai ¼ 0:224�, which corresponds to a penetration depth of the entire multilayer. Inthis second case, the maximum of contribution of Ga is slightly shifted 3.985 A�1, which correspondsto Da=a ¼ 0:015 and which basically confirms the results of the first experiment.

Fig. 52. (a) GID patterns at the (1 1 �2 0) Bragg reflection measured on the GaN/AlN quantum dot multilayer sample, for the

two energies indicated on the graph (ai ¼ 0:174�). The two energies used for the measurements are indicated by symbols (*)

on the Ga K-edge) and (~) just before the Ga K-edge. The maximum of Ga contribution is indicated on the difference pattern

(gray filled curve) by the arrow. (b) Real part of the atomic-scattering factor f1 at the Ga absorption K-edge (symbols as in (a)).

(c) Experimental fluorescence signal measured on the GaN/AlN QD multilayer sample at the Ga K-edge, used for the edge

calibration and for the selection of the two energies used for the anomalous GID experiment reported in part (a). (d) Model for

the strain distribution in the GaN/AlN quantum dots multilayer sample derived from the anomalous GID study performed with

different penetration depths: ai ¼ 0:174� (see part (a)) and ai ¼ 0:224� (not reported). The gray scale stands for the in-plane

lattice mismatch in regard to relaxed AlN. Adapted from V. Chamard, et al., Nucl. Instrum. Meth. B 200 (2003) 95, [793], with

permission. Copyright (2003) by Elsevier.


The following considerations and conclusions have been discussed by the authors [793]. (i) Thestrain in the nanostructures between the value of relaxed AlN and relaxed GaN has been observed.(ii) Using the anomalous behavior of the Ga atomic-scattering factor, at the resonance edge, the strainin the quantum dots has been separated from the strain in the surrounding matrix. (iii) The missingintensity in the maximum of Ga contribution (at 3.98 A�1, corresponding to Da=a 0:015)indicates that another part of the multilayer is strained to the GaN quantum dot lattice mismatch, mostprobably the surrounding matrix around the quantum dots, contributing at the same values oftransferred momentum. It can either be pure AlN or an AlxGa1�xN alloy, resulting from interdiffusionof Ga, from the quantum dots to the matrix. The second hypothesis has to be rejected by Chamard et al.[793] as parallel high-resolution TEM and Raman investigation have demonstrated the absence ofsignificant interdiffusion in the GaN/AlN quantum dot system. Finally, (iv) the anomalous GIDmeasurements, repeated for two different penetration depths, allow the authors to draw a model ofstrain distribution in the entire multilayer, which is consistent with the strain-induced vertical dotordering, see Fig. 52d.

As for point (iii), it is worth noticing that the conclusions draft by Chamard et al. [793] mean that theGaN/AlN quantum dot system behaves in an opposite way to the InAs on GaAs(0 0 1) one, for which asignificant Ga/In interdiffusion, actually resulting in the formation of InxGa1�xAs/GaAs(0 0 1) quantumdots, was highlighted by D’Acapito et al. [703], using SEXAFS technique, see Section 4.8.

Tomographic nanometer-scale images of self-assembled InAs/GaAs quantum dots have beenobtained from surface-sensitive X-ray diffraction by Kegel et al. [706]. Based on the three-dimensionalintensity mapping of selected regions in reciprocal space, the method yields the shape of the dots alongwith the lattice parameter distribution and the vertical interdiffusion profile on a subnanometer scale.The material composition is found to vary continuously from GaAs at the base of the dot to InAs at thetop [706].

The features of surface and interface roughness in crystalline AlAs/GaAs SL grown by MBE onGaAs(0 0 1) substrates have been studied using GIXS by Kondrashkina et al. [784]. The effects ofdifferent growth modes (step-flow or two-dimensional (2D) nucleation), different substratepreparations, and growth interruption times on the interface roughness have been investigated. Theresults of GIXS are compared with AFM images of sample surfaces. For samples grown in the step-flow mode, both of the methods display a distinct anisotropy in the lateral size of roughness along thesubstrate miscut direction and perpendicular to it. The lateral correlation lengths given by GIXScorrespond to the size of step bunches observed by AFM, while individual steps are resolved by AFMonly. GIXS reveals also a strong interface–interface correlation or inheritance of roughness for all thesamples which is not accessible by AFM [784]. Moreover, the angle of inclination of the direction ofthis inheritance from the surface normal is found to be dependent on the growth conditions. Two effectsin the skew inheritance have been observed by means of 2D mapping of GIXS in the reciprocal space:(i) in the direction of substrate miscut the angle of skew inheritance inverted its sign and (ii) in thedirection perpendicular to the miscut a strongly skew inheritance appeared as an effect of GITs [784].Four years later, the same group reported an improved version of the experiment, performing resonantdiffuse scattering on the same system [795]. Inclined inheritance leads to corresponding shearing of theRDS sheets. A simple model for the evaluation of inclined roughness inheritance in three dimensions ispresented, where the sheared resonant diffuse scattering sheets are modeled by anisotropic shearedellipsoids. From measurements at different azimuthal sample orientations the two angles characterizingthe inclined inheritance of interface roughness has been determined accurately. It has been shown that


the inheritance of interface roughness approximately follows the direction of step-flow during growth.The results show that a three-dimensional analysis of diffuse scattering is necessary for a correctevaluation and interpretation [795].

A study of X-ray resonant diffuse scattering was performed by Chernov et al. [796] to investigate aW/Si multilayer. The dependence of the of X-ray resonant diffuse scattering on the momentum transfernormally to the specular diffraction plane has been deeply discussed.

The influences of the Si caplayer or spacer layer on the microstructures of the Ge/Si(0 0 1) quantumdots (underneath or on the top of the Si thin layer) have been studied by Jiang et al. combining alaboratory AFM technique with several synchrotron radiation X-ray techniques: reflection, XRD andGID [797]. It is found that the Ge composition varies with the dot size in the freestanding Ge dotssample with a bi-modal size distribution. When a Si caplayer is deposited on the Ge dots, the Gequantum dots are laterally compressed by the surrounding Si lattice. The strain of the Ge dots spreadsinto the caplayer and reaches to the surface even if the caplayer is as thick as 70 nm. It is confirmed thatthis residual strain induced by the buried Ge dots improves the size uniformity of Ge dots grown on theSi caplayer surface, so that a uniform size distribution of the Ge dots is observed by AFM and thecorresponding strain is measured by GID. However, for a Si caplayer with a thickness larger than90 nm, no residual strain from the buried quantum dots was observed near the sample’s surface. In thiscase, the dots grown on the surface show the same features as that grown on a Si substrate wafer (i.e. bi-modal size distribution), so that no strain-mediated influence of the buried dots takes place [797]. X-rayreflectivity curves are commented in Section 8.

Sztucki et al. [798] have studied the depth distribution and structure of defects in boron implanted(6 � 1015 ions/cm2 at 32 keV) Si(0 0 1) as a function of different annealing treatments. Using diffuseX-ray scattering at grazing incidence and exit angles (GIXDS, see the acquisition geometry defined inFig. 51b) authors singled out the presence of point defect clusters and of extrinsic stacking faults on{1 1 1} planes and determined their depth distribution as a function of the thermal budget. Reciprocalspace mappings in transversal ½1 �1 0� direction around the (2 2 0) surface Bragg reflection are sensitiveto scattering induced from defect clusters (see Fig. 53a), whereas the diffuse scattering measured inlongitudinal [1 1 0] direction is dominated by diffuse intensity streaks in [1 1 1] directions (seeFig. 53b). These streaks are induced by extrinsic stacking faults on {1 1 1} planes. Hence, for the depthinvestigation the defect cluster induced scattering has been measured at the reciprocal lattice pointðh ¼ 2:05; k ¼ 1:95; l ¼ 0Þ as indicated in Fig. 53a, the stacking fault induced scattering at ðh ¼ 2:1;k ¼ 2:1; l ¼ 0Þ, see Fig. 53b. Parallel cross-section TEM study was used to gain complementaryinformation. Authors determined the strain distribution caused by the boron implantation as a functionof depth from rocking curve measurements [798]. Fig. 53c–e reports the experimental rocking curvesmeasured at the (0 0 4) reflection of the sample subjected to different annealing treatments, togetherwith the corresponding best-fits. The fitting parameters varying with depth are the exponent of the staticDebye–Waller factor and the lattice strain. This strain information can be correlated with the depthdistribution of the different kinds of defects as determined by diffuse X-ray scattering at grazingincidence and exit angles (GIXDS) and TEM. The best-fit of the rocking curve of the sample withoutRTA shows positive tensile strain (see the inset of Fig. 53c). A first layer with a maximum strain ofabout Da=a ¼ þ2:2 � 10�3 extends from 50 to 130 nm in depth, a second from 140 to 240 nm with amaximum tensile strain of Da?=a ¼ þ5:0 � 10�3. This positive strain has been explained by latticeexpansion due to the presence of a large number of silicon or boron interstitials and defect clusterscontaining Si self-interstitials and B. The strain value in between the two above described layers can be


Fig. 53. Left: reciprocal space mappings in the vicinity of the (2 2 0) surface Bragg reflection of B implanted (6 � 1015 ions/

cm2 at 32 keV) Si(0 0 1) crystal, collated at the ESRF BM01 with a 9 keV X-ray beam using the geometry reported in Fig. 51b.

In part (a) the defect cluster induced diffuse scattering in transversal direction is shown while the mapping in longitudinal

direction is reported in part (b). The gray bar in parts (a) and (b) marks the integration interval of the position sensitive detector

during the ai scans (see Fig. 51b). Right: rocking curves measured at the (0 0 4) reflection as a function of different annealing

treatments. (c) Without rapid thermal annealing (RTA); (d) after a RTA at 1060 8C for 20 s; (e) after a RTA at 1060 8C for

120 s. For each measurement the best-fit of the rocking curves and the corresponding lattice strain as a function of depth

(inset) is shown. In each graph the scattering of original unimplanted silicon is indicated by the dotted line, for comparison.

Adapted from M. Sztucki, et al., Nucl. Instrum. Meth. B 200 (2003) 52, [798], with permission. Copyright (2003) by Elsevier.


interpreted as a strongly disordered layer. These results are consistent with the results determined byGIXDS and TEM [798]. The fit of the rocking curves of the sample after 20 s of RTA (see Fig. 53d)shows a surface near layer of positive strain ðDa?=a ¼ þ0:7 � 10�3Þ induced by residual defectclusters and a layer with negative compressive strain ðDa?=a ¼ �1:8 � 10�3Þ between 120 and 230 nmfrom the surface due to both Si vacancies and B on substitutional lattice sites. After a RTA of 120 s alldefect clusters have dissolved, as shown by the rocking curve reported in Fig. 53e which best-fitevidenced a negatively strained layer ðDa?=a ¼ �0:9 � 10�3Þ between 120 and 270 nm from thesurface. The broadening of this strain distribution, compared to the sample subjected to a RTAtreatment of 20 s is the proof of B diffusion into deeper layers during the annealing process. No positivestrain due to defect clusters is observed any more [798].

The evolution of surface structure and morphology during deposition of Ge on Ge(1 1 1) has beeninvestigated by Vansilfhout et al. [292]. At 300 K the growth proceeds through two-dimensionalnucleation. The analysis of the diffracted intensities along the integer-order rods of Bragg scatteringperpendicular to the surface plane resulted in the determination of the sites on the cð2 � 8Þreconstructed Ge(1 1 1) surface to which the first deposited Ge atoms bond. For higher coveragesislands of bilayer height have been observed. Torrelles et al. [799] observed the ð2 � 1Þ reconstructionof Ge(0 0 1) occurring at room temperature. The resulted structural model consists of a buckled array ofdisordered dimers: there is a 0.5 probability of finding one of the two dimer orientations (positive andnegative tilt angles) in any unit cell. The dimer tilt angle is found to be 15:6� � 0:6�, with a Ge–Gebond length which is expanded by 4% compared to the rGe–Ge bulk value. The reconstruction is found toextend to eight atomic layers and the maximum distortion of the bonds has been found to be less than6%. The model is compared with similar models, and the dynamical and ordered models and thedynamics of the dimer flipping are discussed. The same group reported about the cð4 � 2Þ structure ofthe Ge(0 0 1) structure at lower temperature [800].

Epitaxial growth of germanium on boron-terminated Si(1 1 1) results in the formation of partiallyrelaxed triangular pyramidal Ge islands, which residual strain has been determined by X-ray crystaltruncation rod scattering [801]. It has been found that the Ge lateral lattice parameter changes linearlyfrom the bottom to the top of the islands. In a parallel work, the same group used atomic forcemicroscopy to prove that that Ge islands are strongly ordered in the direction perpendicular to themiscut induced terrace steps of the substrate [802]. They also showed how grazing incidence smallangle X-ray scattering is able to assess the island shape and size distribution. Nakatani et al. [803]have reported a combined grazing-angle XRD and XSW study on Ge layers buried on a GaAs/Ge/GaAs(0 0 1) heterostructures designed for prototypes of non-linear optical devices. The intensitydistribution of the CTR scattering has been used to prove the quality of GaAs epitaxial layers. Theauthors first measured the intensity distribution of CTR scattering, around the GaAs(0 0 4) reflectionpoint. The measurement of the period in the intensity oscillation of the CTR scattering allowed theauthor to evaluate the thickness of the GaAs epilayer, which was almost equal to the designed value of500 A. This is adequate evidence that the epitaxial growth was performed fairly well. The authors havealso estimated the thickness of the intermediate Ge layer by the analysis of the asymmetric shape of thecurve.

The grazing incidence X-ray diffraction technique has been applied to monitor the anodic dissolutionprocess of GaAs(0 0 1) in 0.1 M HCl solution [294]. It was found that the surface diffraction intensityfor the [11] direction of GaAs(0 0 1) decreased with time when the positive potential was applied to theelectrode.


The elastic strain relaxation in a series of dry-etched periodic multilayer Si/SiGe quantum wire withdifferent etching depths was investigated systematically by means of GID by Hesse et al. [804]. Thesamples were patterned by holographic lithography and reactive ion etching from a Si/SiGe superlatticegrown by MBE. SEM and SFM were employed to obtain information on the shape of the wires. Theinhomogeneous strain distribution in the etched wires and in the non-etched part of the multilayers wasderived by means of finite element calculations which were used as an input for simulations of thescattered X-ray intensities in depth dependent GID. The theoretical calculations for the scatteredintensities are based on distorted wave Born approximation. The unperturbed scattering potential waschosen by the authors with a reduced optical density corresponding to the ratio of wire width and wireperiod, in order to reflect the main interaction between the incident X-rays and the patterned samples.The calculations are in good agreement with the experimental data demonstrating the variation of strainrelaxation with depth [804].

Being a surface diffraction-based study, the glancing angle DAFS experiments of Proietti’s group onInAs/InP(001) quantum wires [711,712,805] and InAs/GaAs(0 0 1) quantum wires quantum dots [712]have to be mentioned here (see the end of Section 6 for more details). For the discussion on theSEXAFS study of these heterostructures [709], see Section 4.8.

6. Application of DAFS

Diffraction anomalous fine structure (DAFS) is a diffraction technique, thus involving materialscharacterized by long-range order that results in an EXAFS-like signal. It thus reports information onthe local environment of a selected atomic species. This section is divided into two sections only. Theformer deals with the introduction of the basic concepts of the technique, while in the latter someselected examples have been reported.

6.1. Basic concepts of DAFS applied to SL

The intensity of a diffraction peak of a crystalline material normally varies smoothly with the l(i.e. with the photon energy hn) used to perform the diffraction experiment. This statement does nothold if the l variation goes across absorption edge of an element present in the material. This fact isthe basis of resonant diffraction experiments [794,806]. Now, if one measures the intensity of sucha diffraction peak as a function of l(hn), across the absorption edge of an element present in thematerial, he will found an EXAFS-like signal, see Figs. 54 and 55a, from which structuralinformation around the selected atomic species can be extracted. This is the field of the diffractionanomalous fine structure method, which combines in the same experiment X-ray diffraction andX-ray absorption [794,807,808]. In this way, the long-range structural information contained indiffraction peaks can be combined with the chemical and local structure selectivity of X-rayabsorption spectroscopy. Thus, it can provide site-selective and chemical-selective structuralinformation.

Following the simple and brief arguments reported by Woicik et al. [186], we can affirm that theDAFS technique is based on the premise that information contained in absorption spectra can also beextracted from resonant, energy-dependent diffraction measurements through the causal relationshipbetween the real and imaginary parts of the atomic-scattering amplitude f [732]. The integrated


intensity Ih k l of the X-ray Bragg reflection (h k l) from a weakly scattering crystal is proportional to thesquare of the crystallographic structure factor [731]

Ih k lðEÞaXN

j¼1

fjðEÞ expðiqh k lrjÞ��

��2

; (47)

where the sum run over the N atoms of the unit cell. The crystallographic structure factor accounts forscattering at photon wavevector transfer qh k l ¼ kf � ki from each of the j atoms in the unit cellaccording to their positions rj and their atomic-scattering amplitudes fj. The atomic-scatteringamplitude f(E) from a single atom is, in turn, the sum of the Thomson scattering amplitude f0, which isindependent of the photon energy E, and an energy-dependent resonant correction Df(E), whichchanges dramatically in the vicinity of a core-level excitation energy. Df(E) is the sum of a real partf 0(E), and an imaginary part f 00(E) [730]. In the standard EXAFS description of the absorptioncoefficient m(E) is given by mðEÞ ¼ m0ðEÞ½1 þ wðEÞ�, see Eq. (25), where m0(E) is the bare-atom,background absorption, and w(E) is the oscillatory part of the X-ray absorption coefficient that arisesfrom the local backscattering from nearby atoms. Analogously, the real and imaginary parts of Df(E)are also separable into their atomic and oscillatory terms,

Df ðEÞ ¼ fa0ðEÞ þ if 00a ðEÞ þ f 000 ðEÞ½w0ðEÞ þ iwðEÞ�: (48)

The subscript a denotes the smooth, atomic-like contribution to the response function, and½w0ðEÞ þ iwðEÞ� is the generalized, energy-dependent fine structure function. Because fa

0ðEÞ andf 00a ðEÞ are linked by causality, the latter may be determined either directly by measuring the totalabsorption cross-section stotðEÞ : f 00ðEÞ ¼ E=ð2hcÞstotðEÞ, or by measuring the photon-energy-dependent intensity of a Bragg reflection and then applying the Kramers–Kronig (principal value)dispersion relations to iteratively solve Eq. (47) for fa

0ðEÞ [186,808].

Fig. 54. (a) DAFS spectra collected at the Ga K-edge on the (0 0 6) reflection of strained GaAs1�xPx (x ¼ 0:20 and 0.23 for

full and dotted lines, respectively) films grown on GaAs(0 0 1) substrate with a residual strain of ek ¼ 0:004 (full line) and

0.007 (dotted line). (b) DAFS spectra collected at the Ga K-edge on the (0 0 1 5) and (0 0 1 0) reflections (open and full

circles, respectively) on (GaP)2(InP)3 strained SL grown on GaAs(0 0 1) substrate. Adapted from M.G. Proietti, et al., Phys.

Rev. B 59 (1999) 5479, [305], with permission. Copyright (1999) by American Physical Society.


Fig. 55. (a) Normalized intensity of the (0 0 4) strained-layer Bragg peak from the pseudomorphic Ga1�xInxAs alloy grown

on GaAs(0 0 1) substrate as a function of photon energy around the Ga and As K-edges. The data have been corrected for the

background fluorescence from the substrate. (b) The k-weighted w(k) function deduced from the Ga K-edge DAFS data shown

in part (a), top curve. The data are compared to their Fourier-filtered first shell contributions which contain only Ga–As bonds.

Also shown is the Ga K-edge EXAFS of the GaAs and InAs standards (middle curves). The bottom curves report the first shell

data compared with its best-fit. (c) Same as part (b) for the As K-edge. (d) Comparison between experimental In–As and Ga–

As bond lengths determined by Woicik et al. from DAFS data, parts (a)–(c), and from EXAFS data [185] with the theoretical

results of random-cluster calculation [197]. The dashed lines are the calculated cubic (bulk) bond lengths, and the solid lines

are the calculated tetragonal (strained) bond lengths. The separation between the bulk and strained bond lengths is the same for

In–As and Ga–As bonds, reflecting that they are uniformly distorted. Adapted from J.C. Woicik, et al., Phys. Rev. B 58 (1998)

R4215, [186], with permission. Copyright (1998) by American Physical Society.



Due to space limitations only few examples on the application of DAFS technique to semiconductorthin films and heterostructures will be briefly presented. The advantage of DAFS for studying epilayersor multilayers is to give selective structural information by choosing the Bragg peaks (spatial-selectiveBragg peak) of the strained phase and the heterostructure is probed through the entire thickness[186,305,710–712,805,809,810].

As briefly mentioned at the end of Section 4.4, Woicik et al. [186] have performed a DAFSstudy at both the Ga and As K-edges in a buried, 213 A thick In0.215Ga0.785As layer growncoherently on GaAs. Fig. 55a reports the raw DAFS data collected by measuring the normalizedintensity of the (0 0 4) strained layer Bragg peak across both Ga and As K-edges (compare withFig. 16a reporting the raw data collected with classical EXAFS technique on a GaAs bulk sample).The top curves in parts (b) and (c) report the EXAFS-like signal extracted from the DAFS data atGa and As K-edges, respectively. The analysis of DAFS oscillations at the Ga K-edge resulted inrGa�As ¼ 2:440 � 0:007 A while rAs�Ga ¼ 2:444 � 0:006 A and rAs�In ¼ 2:529 � 0:024 A valueshave been obtained from the As K-edge data (bottom curves in Fig. 55b and c). The first shell Ga–As bond length, determined from DAFS, resulted then to a strain-induced contraction of0:013 � 0:005 A relative to the rGa–As in bulk InxGa1�xAs of the same composition. Excellentagreement was found with the uniform bond-length distortion model for strained layer previouslyproposed by the same group to explain the In K-edge EXAFS study on the same sample [185],resulting in a contraction of the In–As first shell bond length of 0:015 � 0:004 A relative to the rIn–

As bond length in bulk InxGa1�xAs of the same composition (Fig. 16d). This is a further evidenceof what highlighted in Refs. [185,187,188,190], i.e. that ek imposed by pseudomorphic growthopposes the natural bond-length distortion due to alloying [531,532] and here reviewed inSection 4.4.1.

The effect of built-in strain on III–V epitaxial semiconductors has been further investigated byProietti et al. [305] with DAFS technique at the Ga and As K-edges. Authors provide a generalformalism for analyzing the diffraction DAFS oscillations, valid for any type of crystallographicstructure, proving that the DAFS spatial selectivity provides a unique tool for studying systems thatare out of the reach of other X-ray techniques. They studied two different systems grown on aGaAs(0 0 1) substrate: a strained layer superlattice of (GaP)2(InP)3 and three single epilayers ofGaAs1�xPx partially relaxed, with a different amount of residual strain in the 0:004 � ek � 0:007range, see Fig. 54. The first shell rGa–P bond distance in the superlattice was stretched by about0.04 A in agreement with the predictions of the elastic theory. The rGa–As and rGa–P bond lengths inGaAs1�xPx films (rGa�As ¼ 2:44 � 0:01 A and rGa�P ¼ 2:37 � 0:02 A) remain very close to theirrespective values in the bulk binary compounds independent of the residual strain. The next-nearest-neighbor distances obtained by a multishell analysis of the raw DAFS data compare well with thevalues predicted for the relaxed and pseudomorphic alloy. The GaAs1�xPx epilayers have also beenmeasured by switching the light polarization vector from the [1 1 0] to the ½1 �1 0� crystallographicdirection, see Fig. 56. These directions are not equivalent for the zinc blende structure and the shapeof the DAFS spectrum changes appreciably for the most strained ðek ¼ 0:007Þ film, see bottom partsof Fig. 56. The difference is particularly relevant in the low-k region of the spectrum, which is moresensitive to the contribution of the light P atoms, see the discussion in Section 4.5. The multishell fitanalysis indicates that for the ½1 �1 0� direction, the number of P atoms seen by the Ga absorber is


much lower, as deduced qualitatively by comparing the two spectra with the GaP and GaAs bulkmeasurements. This result has been explained by the authors in terms of a partial P orderingmechanism along the [0 0 1] growth direction. Proietti et al. [305] also pointed out the interest of theDAFS spectra analysis for obtaining further information about the average crystallographicstructure.

The same group has successively extended the application of DAFS from 2D to 1D and 0D systemsby investigating InAs/InP(0 0 1) quantum wires [711,712,805] and InAs/GaAs(0 0 1) quantum wiresand quantum dots [710] by working in glancing angle geometry. Authors reported, for the first time,DAFS spectra of such low coverage epitaxial layers, and showed that important information aboutcomposition and strain of the nanostructures can be obtained. For the discussion on the SEXAFS studyof these heterostructures [709], see Section 4.8.

Fig. 56. Left: kw(k) curves extracted from DAFS data collected on different light polarization directions (full lines) and

corresponding best-fits (open circles) for GaAs1�xPx/GaAs(0 0 1) films. Right: corresponding Fourier transforms. The residual

strain of the films and the adopted light polarization is also reported in the right parts. Adapted from M.G. Proietti, et al., Phys.

Rev. B. 59 (1999) 5479, [305], with permission. Copyright (1999) by American Physical Society.


7. Application of XSW

In a periodic structure, a standing-wave field is formed through the interface of the incident and of thereflected wave fields which can be described in the framework of the dynamical theory of diffraction[758]. In Bragg diffraction, the position of the nodal and anti-nodal planes of the standing-wave fieldchanges drastically as a function of the angle of incidence in the region of total reflection (see Fig. 57).Therefore anomalous changes are observed in the yield of secondary emissions or scattered X-raysproduced by interaction of the X-ray standing-wave field with the constituent atoms in the crystal [811–814]. The X-ray standing-wave technique consists in measuring the fluorescence or electron yieldemitted by a specific atomic species during the scan of a (h k l) Bragg reflection, done either at lconstant by tuning the Bragg angle y or vice versa [813,814]. XSW measurements gives the averageposition of the selected atomic species within the crystal unit cell along the selected [h k l] direction,see Fig. 57 for the ð1 �1 5Þ and ð�1 �1 5Þ reflections of the GaAs lattice. The measurement of the XSWsignal generated by scanning three crystallographic independent [h k l] reflections allows to locate theselected atom in the unit cell. This location do not reach the typical spatial precision of XRD but, unlikeXRD, XSW is sensitive to the phase of diffracted wave. In this regard, Bocchi et al. [815] have reporteda paper showing how, in the study of InP implanted with Oþ ions close to the amorphization threshold,the combined use of XRD and XSW data sets has been extremely informative. They used XSW data toselect the most appropriate strain and damage depth profiles among those that were virtually equivalentfor the phase insensitive XRD data.

Fig. 57. Schematic view that illustrates how the XSW field moves with the change in the incidence angle of X-rays. The

picture illustrate the GaAs crystal where the (1 �1 5) and (�1 �1 5) reflections are under Bragg conditions: upper and lower parts,

respectively. The parameter Z indicates the deviation angle from the exact Bragg angle. Adapted from S. Nakatani, et al., Appl.

Surf. Sci. 159 (2000) 256, [803], with permission. Copyright (2000) by Elsevier.


As far as the technique is concerned, XSW is certainly a bulk technique, since it needs a 3D orderedlattice, well oriented with respect to the X-ray beam to generate the standing wave, which exists insidethe whole crystal. Therefore XSW has been widely used in the localization of doping atoms inside bulksemiconductors [813,816,817]. Notwithstanding this fact, XSW is also an useful tool in the field ofsurface science. In fact, at the surface of the crystal, the standing-wave generated in the bulk will notlose its intensity abruptly but smoothly exhibiting so, within few A from the surface, a sufficientstrength to be used in the structural characterization of molecules adsorbed on the surface[813,814,818]. Some examples, showing the importance of XSW in the characterizations of atomsor of ML-thick films deposited on semiconductor surfaces, have already been discussed in Section 4.8because performed in parallel with SEXAFS measurements, in particular: the Te–Si(1 0 0) system[685]; Sb–Si(1 1 1) system [691]; and the Sb–Ge(1 1 1)ð2 � 1Þ system [693,694]. As a further example,Comin and co-workers [819], using XSW, have directly measured the asymmetry of Ge dimers on theSi(0 0 1) surface as 0:55 � 0:02 A. They showed that the dimer asymmetry decreases upon increasingthe temperature, raising the possibility of a high temperature asymmetric to symmetric phase transitionof Ge dimers on the Si(0 0 1) surfaces. The same phenomenon allows to study thin ML films depositedon semiconductor surfaces. Semiconductor films will be treated successively (Section 7.2), while twoexamples of metal films on semiconductor surfaces, both from the Lagomarsino group, are mentionedhere: Cs and Rb on Si(1 1 1) [820] and Rb on Si(0 0 1) [821]. Bedzyk and Materlik [822] investigated asubmonolayer of Br atoms adsorbed on Ge(1 1 1) surface, by collecting XSW signals from the substrate(1 1 1) and (3 3 3) diffraction planes. The results from both the (1 1 1) and (3 3 3) measurements areconsistent with the one-fold-atop-site surface model. The increase in local sensitivity from using the(3 3 3) diffraction planes highlighted the potentialities of the technique for determining the vibrationalamplitude of an adsorbate.

This section is organized into three subsections. In Section 7.1 the basic formulae used to define themain parameters of the XSW study are concisely recalled. Section 7.2 is devoted to briefly overview onfew selected examples of the technique applied to heterostructures and thin films, while Section 7.3 willdeal with the InGaAs/InP SL system, considered a case study.

7.1. Basic concepts of XSW applied to SL

Fig. 58 depicts the basic experimental set-up needed to perform a typical XSW experiment. Theincoming white beam is first monochromatized with a double crystal device to yield the desiredenergy, above one of the edges of the atomic species selected for the experiment (e.g. Ga and Asin an InGaAs/InP SL). The intensity of the monochromatized beam is then measured, typically withan ionization chamber (flux monitor in the figure), to have a reference signal for correction of thedrift caused by the decay of the synchrotron current during the measurements. Successively theX-ray beam reaches the sample, positioned on a diffractometer which allows to achieve the desired(h k l) Bragg reflections. As done in any XRD experiment, a conventional X-ray detector isused to collect the diffracted beam, usually named reflected beam in XSW papers. The yield ofsecondary emissions (electrons and/or fluorescence photons, representing the actual XSW signal)is simultaneously collected with and independent energy resolved detector, which allows thediscrimination among the signals coming from different atomic species. This detector is usuallypositioned in front of the sample in a glancing-exit geometry to reduce the secondary emission signalfrom the substrate.


We will now consider the InGaAs/InP heterostructure as a representative example for XSWmeasurements on SLs [303]. Raw XSW data can be collected with a multichannel analyzer set to acceptthe As Ka, and Ga Ka fluorescence yields. The In Ka fluorescence cannot be used to collect the XSWfrom the In atoms present in the heterostructure, since the signal would be overshadowed by the Inatoms of the substrate. In such a case, the In XSW signal can be measured by collecting Inphotoelectrons, a solution that implies a strong increase of the experiment complexity, owing to thenecessity to operate in UHV conditions.

For each (h k l) reflections of the substrate there is a corresponding zero-order SL peak occurring atDy0 apart from it, see Eq. (39), Figs. 41b and 42b. As an example, Fig. 59a reports the typical XSWsignal emitted by the atomic species present in the InGaAs/InP SL: in this case the As Ka fluorescenceyield is collected around the (0 0 4) reflection of the InP substrate [303]. For this example,d0 0 4 ¼ 1:4674 A for the substrate peak and equal to the average (0 0 4) lattice spacing of the SL for thezero-order SL peak (see Section 5.1). Note how the experimental curve has been normalized to unit faraway from any Bragg reflection.

By rocking the crystal, the antinodal planes of the standing-wave field move from being directly onthe atomic planes to midway between them. Therefore, if one measures the fluorescence of the atoms ofthe SL as a function of the angle through the standing-wave range, it is possible to determine theaverage location of the X-ray absorbing atoms relative to the scatterer planes. A coherent XSW signalfrom the atomic species present in the SL (Ga and As) is observed around the SL peak only(y � �0:002 rad in the example report in Fig. 59a), having the SL a slightly different average dh k l,with respect to the substrate, vide supra Section 5.1. At the substrate reflection (at y � ysub in Fig. 59a)the fluorescence yield of SL atoms exhibits a symmetric peak which mimics the reflectivity curvewithout containing any structural information not already available from XRD [191]. Conversely, at the

Fig. 58. Schematic representation of the experimental set-up devoted for a XSW experiment. Adapted from S. Nakatani,

et al., Appl. Surf. Sci. 159 (2000) 256, [803], with permission. Copyright (2000) by Elsevier.


zero-order SL peak the standing wave has the periodicity of the average SL plane and the atoms presentin the SL have a non-negligible coherent fraction, resulting in the typical derivative-like modulation ofthe fluorescence yield (y � �0:002 rad). Part (b) of Fig. 59 reports the X-ray standing-wave fieldintensity distribution within the superlattice as a function of depth and angle.

From the raw XSW data reported in Fig. 59 it is possible, in principle, to determine the averagelocation of the X-ray absorbing atoms relative to the scatterer planes. In the dipole approximation thenormalized XSW field intensity of the ith layer is given by [813]

YðyÞ ¼ 1 þ RðyÞ þ 2ffiffiffiffiffiffiffiffiffiffiRðyÞ

pF cosðnðyÞ � 2pP0Þ; (49)

Fig. 59. (a) Experimental normalized arsenic fluorescence yield (open circles) and best simulation (continuous line) obtained

after normalization of the sum of curves reported in part (b). (b) X-ray standing-wave field intensity distribution within the 60-

period InGaAs/InP superlattice as a function of depth and angle, calculated according to Eq. (49) with the coherent fraction

and the coherent position values F ¼ 0:5 and P ¼ 0:98. Adapted from C. Aruta, et al., J. Appl. Phys. 93 (2003) 5307, [303],

with permission. Copyright (2003) by American Institute of Physics.


in which F is the coherent fraction and describes the static and the thermal displacements of the atomsfrom the mean positions and P0 is called coherent position and is equal to z/d, where d is the periodicityof the standing-wave field and z the atomic displacement parallel to the diffraction vector. R(y) and n(y)are, respectively, the reflectivity and the phase between the incident and diffracted X-ray waves.

In the case of a static distribution of atoms the coherent fraction and the coherent position can beexpressed as [813]

F ¼ AS ¼ ðGC2 þ GS2Þ1=2and P0 ¼ 1

2parctan

GS

GC

� �: (50)

For a diffraction vector H the coefficients GC and GS are

GC ¼ N�1XN

i¼1

cosð2pH � riÞ and GS ¼ N�1XN

i¼1

sinð2pH � riÞ; (51)

where N is the number of atomic layers and ri the position of the fluorescent atoms with respect to thestanding waves phase. Taking into account the thermal vibrations and the random or incoherent part ofthe atomic distribution, the coherent fraction F becomes the product of three terms:

F ¼ ASDwð1 � UÞ; (52)

where AS is the static term or occupation factor calculated in (50) for the case of ideal order, Dw theDebye–Waller factor and U is usually called incoherent fraction. In the case of SLs the fluorescenceyield profiles depend on the structural parameters of all the layers. For each constituent layer thereflectivity Ri and the phase ni are given by

Ri ¼jEij2

jE0j2and ni ¼ arctan

ImðEi=E0ÞReðEi=E0Þ

� �: (53)

The ratio of the electric field amplitudes Ei/E0 to be used in formula (53) can be calculated with therecursive formula based on Takagi–Taupin equations with the approach introduced by Wie [308].


The first XSW study on semiconductor heterostructures has been reported in 1995 by the Brennanand co-workers [760] reporting a combined high-resolution XRD and XSW study on (AlAs)m/(GaAs)n

short period SL. Successively a paper of Lagomarsino and co-workers appeared on a GeSi/Si(0 0 1) SL[823]. Boscherini et al. have presented an XSW study on a set of InAsxP1�x/InP superlattices in the0:05 < x < 0:40 composition range [191]. More recently, the Brennan and co-workers [824,825] havereported a deeper investigation of the (AlAs)m(GaAs)n system. Related studies on InAs layers buried inGaAs have been reported by Woicik and co-workers [708,826–828].

As already mentioned in Section 5.2, Nakatani et al. [803] have reported a combined grazing-angleXRD and XSW study on Ge layers buried on GaAs. The results of XSW measurements clearlyindicated that the 908 rotation of the epitaxial layers, which is a necessary condition for the phasematching, occurs in the GaAs/Ge/GaAs(0 0 1) heterostructure. Being the XSW field generated by the


interference of incident and reflected X-rays perpendicular to the net planes of the Bragg reflection,information on atomic sites parallel to the surface can be obtained by using an asymmetric reflection(vide supra Fig. 57). Therefore, Nakatani et al. [803] used the ð1�15Þ and the ð�1�15Þ reflections whose netplanes are inclined from the [0 0 1] direction to the [1 1 0] direction and the [1 1 0] direction, which areat right angles, respectively. Fig. 60 reports the intensity of reflected X-rays and the intensities of bothAs Ka, and Ga Ka fluorescence yields for the ð1�15Þ and the ð�1�15Þ reflections, parts (a) and (b),respectively. Together with the experimental XSW curves (dots) also the simulations performedadopting both the sublattice-inversion (continuous line) and the sublattice-inversion free models (dot

Fig. 60. (a) Experimental XSW curve collected on a GaAs/Ge/GaAs(0 0 1) heterostructure under (1 �1 5) Bragg reflection

(dots), compared with corresponding simulations performed adopting both the sublattice-inversion (continuous line) and the

sublattice-inversion free models (dot-dashed line). (b) Same as part (a) for the (1 �1 5) Bragg reflection. Adapted from

S. Nakatani, et al., Appl. Surf. Sci. 159 (2000) 256, [803], with permission. Copyright (2000) by Elsevier.


dashed line) are reported. It is clear that the former theoretical curves that agree with the experimentalresults, which is clear evidence of sublattice inversion, which is the requirement needed to exploit thelarge optical non-linearity of the heterostructure [829], see Section 1.

Hartmann et al. [830] report a XSW study of 1 ML of MnTe sandwiched between CdTe thick layersepitaxially grown on CdTe(0 0 1), either by conventional molecular beam epitaxy or by atomic layerepitaxy. Also supported by parallel reflection high-energy electron diffraction and scanning tunnelingmicroscopy data, the authors comes to the conclusion that a significant differences concerning the ratioof Mn atoms involved in MnTe clusters to those incorporated as part of a CdMnTe alloy are observedbetween the samples. Those differences have been ascribed to a different surface roughness of theepitaxial CdTe surface on top of which the MnTe ML is grown.

Of great interest is the very recent work of Drakopoulos et al. [831] reporting the first microprobetechnique based on the XSW. They demonstrated that structural analysis of an epitaxially grown GaAs/Al0.1Ga0.9As/GaAs(0 0 1) heterostructure (mounted in cross-section) can be achieved with chemicalsensitivity on a microscopic scale. The synchrotron beam was focused by a refractive lens onto thecleaved sample and analyzed the constituent elements within the Al0.1Ga0.9As layer resolving thesubstitutional location of Al. The authors claim that the new micro-XSW technique will permitmicroscopic examinations of the structure of integrated semiconductor devices or microscopiccrystalline grains with chemical sensitivity and structural resolution on the atomic scale.

Coming to the studies of XSW on thin semiconductor films, Lee et al. [832] have reported an XSWstudy on one InxGa1�xAs ML of pseudo-binary alloy buried in GaAs(0 0 1). The measured In positionalong the [0 0 1] direction exhibited a nearly linear dependence on the In concentration x, thussupporting the validity of macroscopic continuum elasticity theory at the 1 ML limit. A random-clustercalculation using a valence force field was performed to explain microscopically the origin of thevertical expansion of the strained monolayer observed by the experiment. The calculated As–In–Asbond angle and the positions of the first nearest-neighbor As atoms of In suggest that the nearly lineardependence of the In height on the alloy composition is a combined result of the As–In–As bondbending and the local lattice distortion at the GaAs/InxGa1�xAs interface. The calculated rIn–As andrGa–As bond lengths were found to depend weakly on the In concentration. Sakata et al. [833] report agrazing-angle XSW study characterizing the in-plane structure of an arsenic-deposited Si(0 0 1)surface. Kawamura et al. [834] reported an XSW investigation on the initial domain structure of GaAsfilm grown on Si(0 0 1).

One ML of Sb on GaP(1 1 0) substrate has been investigated by Miyano et al. [692]. The authors,using the XSW signal collected in the back-reflection geometry from (2 0 0) and (2 2 0) planes,determined that the buckling of the Sb chains is 0:04 � 0:10 A and that the perpendicular displacementof these chains from the extrapolated bulk (2 2 0) plane is 2:31 � 0:10 A. These measurements favor astructure such that Sb adatoms occupy sites analogous to those of the next extrapolated substrate layer.The same group also investigated the Sb–Si(1 1 1) [691] and the Sb–Ge(1 1 1)ð2 � 1Þ [693,694]interfaces. Structural XSW studies of a ML of Sb on GaAs(1 1 0) [835,836], Sb on InP(1 1 0) [837,838]and Bi on InP(1 1 0) [838] indicate a tendency of ML of group V elements on III–V semiconductor(1 1 0) surfaces to form ordered, ideally terminated surfaces. The adatoms form ‘‘zig-zag’’ chains onthe (1 1 0) direction, with the chain geometry described by epitaxial continued layer structure model[835–838]. The Bi/GaP(1 1 0) interface has been investigated by Herrera-Gomez et al. [839] as a casestudy of XSW application to a non-ideal system. This case differs from the previously enumerated onesdue to the much higher mismatch between the covalent radius of the adatom and the value computed by


averaging the covalent radii of the substrate anion cation. This large difference induces the formation ofsurface vacancies to allow relaxation.

Kohn has recently described a computer code where the theory for the dynamical X-ray diffractionand the yield of the secondary radiation scattered via incoherent channels under Bragg conditions of X-ray diffraction (XSW signal) is developed for the crystal systems composed from many layers [840].The formulae are derived in a form suitable for a computer simulation of the experimental angular orenergy spectra as well as for a determination of unknown parameters via fitting. The Bragg case(reflection) and the Laue case (transmission) are considered within the same approach. The case of anIn0.5Ga0.5P epitaxial film grown on the GaAs substrate is discussed.

Finally, an original application of XSW has recently been proposed by Woicik et al. [841], who haveexamined the valence-electron emission from Cu, Ge, GaAs, InP, and NiO single crystals under thecondition of strong X-ray Bragg reflection; i.e., in the presence of the spatially modulated X-raystanding-wave interference field that is produced by the superposition of the incident and reflected X-ray beams. Single crystals have been ad hoc selected in order to span the entire metallic, covalent, andionic range of solid-state bonding. It has been demonstrated that the valence-electron emission isclosely coupled to the atomic cores, even for electron states close to a metallic Fermi edge. Moreover,using the bond-orbital approximation, the authors have demonstrated that the X-ray standing-wavestructure factor for valence-electron emission is derived in terms of the bond polarities andphotoionization cross-sections of the atoms within the crystalline unit cell and compared to experiment.Moreover, Woicik et al. [841] have demonstrated for GaAs and NiO that, by exploiting the spatialdependence of the electric field intensity under Bragg condition, site specific valence electronicstructure may be obtained.

7.3. InxGa1�xAs/InP short period SL: a case study

In this review the problem of interface mixing in InxGa1�xAs/InP short period SL has already facedby EXAFS spectroscopy (Section 4.5) and XRD (Section 5.2), where the results from Boscherini et al.[160] have been discussed. Here we will briefly summarize the XSW results obtained by Aruta et al.[303] on the same set of samples.

The best fit of the high-resolution XRD pattern described in Section 5.2 has given to the authors theSL composition in terms of a barrier (InP), a first interface (InAs0.7P0.3), a well (In0.53Ga0.47As) andsecond interface (In0.53Ga0.47As0.7P0.3), whose widths have been optimized resulting in xb, xI1, xw, andxI2 values, respectively, being xb þ xI1 þ xw þ xI2 ¼ P. On these basis, Aruta et al. [303] have computedthe fluorescence yield using the thickness and the chemical composition for each layer obtained by theprevious simulations of the reflectivity curves according to the equations reported in Section 7.1. Fig. 61reports for all set of samples investigated in Ref. [303] the reflectivity curve and both Ga and Asfluorescence yields, measured across the zero-order SL peak of the (0 0 4) reflection (open circles),together with the corresponding best-fit (full lines) performed by optimizing the coherent fraction F andthe coherent position P0. From the fitting procedure the two parameters P0 and F are so determined forboth Ga and As elements, and summarized in Fig. 62 versus the mismatch of the SL. The authors showedhow the experimental P0 and F values cannot be explained on the basis of the linear elasticity theorycoupled with the VCA model. As was the case for EXAFS data, a more complex model has to be used.

By observing the optimized P0 values (Fig. 62a), Aruta et al. [303] underlined how the coherentpositions decrease from approximately 1.1 for low mismatch samples to approximately 1 for the high


mismatch samples, correlating remarkably with the hDa?/ai value determined by XRD. The highestvalues imply rather high displacements of the atoms from the average superlattice periodicity, of theorder of 0.5 A. Rather large atomic displacements were also found in previous XSW study on SL[824,825], and thus this might be a general feature.

Aruta et al. [303] also observed how the coherent fractions F, are always significantly lower thanunity (but with considerable variations among samples, see Fig. 62b). In this regard, it is worth noticingthat low values for the coherent fraction in semiconductor SL were also found by Schuster et al. [760]and by Lessmann et al. [824,825]. In this regard, Schuster et al. [760] suggested that the deviation of the

Fig. 61. As and Ga Ka fluorescence yields together with the rocking curve (reflectivity) across the zero-order SL peak of the

(0 0 4) reflection for five In0.53Ga0.47As/InP short period SL. Open circles (experimental data), continuous lines

(corresponding best simulations). All the experimental data were normalized to unity far from the Bragg peak, see

Fig. 59a. For the sake of clarity the fluorescence curves are shifted and the reflectivity is scaled. The three figures on the top

refer to three samples grown by MOCVD, the two on the bottom by CBE. Adapted from C. Aruta, et al., J. Appl. Phys. 93



coherent fraction from unit is caused by atoms in non-substitutional lattice positions. A low coherentfraction could be due, in principle, either to a peculiar distribution of the atoms on the lattice planes(through the GC and GS coefficients, see Eqs. (50) and (51) above) or to the presence of a considerablenumber of atoms in random or disordered sites (which contribute to the incoherent fraction, U, seeEq. (52)). Supported by the parallel TEM study, Aruta et al. [303] hypothesized that the low values of Fare due to a significant number of atoms in random or disordered sites. The authors also remarked howsamples grown by CBE (#411 and #411) exhibits the highest coherent fraction F for both As and Gaatoms, with respect to those grown by MOCVD technique (#161, #162, and #164). This experimentalevidence reflects the fact that the CBE technique is more suitable for heterostructures requiring a veryrapid switching time between barrier and well growth, as is the case for short period SL. Note that thereis a factor close to 3 in the growth rate of the two growth methods: as an example, for the InP layers, thegrowth rate for MOCVD is close to 1 mm/h, being 0.3 mm/h for CBE. So, the difference in F valuesbetween CBE and MOCVD grown samples illustrates how XSW can provide important information onthe quality of semiconductor superlattices.

8. Application of X-ray reflectivity: basic concepts

X-ray reflectivity (XRR) measurements across the critical angle are very informative in thecharacterization of thin films and SL structures, reporting important information concerning the

Fig. 62. Coherent positions P0 and coherent fraction F, parts (a) and (b) respectively obtained for As (full squares) and Ga

(open triangles) from the best simulations of the experimental XSW data (reported in Fig. 61) of five In0.53Ga0.47As/InP short

period SL. Adapted from C. Aruta, et al., J. Appl. Phys. 93 (2003) 5307, [303], with permission. Copyright (2003) by

American Institute of Physics.


interface roughness. In fact, in contrast to specularly reflected beam, the non-specular diffuse intensityis sensitive to the lateral structure of rough interfaces.

The reflectivity coefficient r1,2(n1, n2) of an ideally perfectly smooth interface between mediums 1and 2 (characterized by refractive indexes of n1 and n2, respectively) can be calculated with Maxwelltheory (Fresnel equation, for small scattering angles) [842,843]:

r1;2ðn1; n2Þ ¼q1 � q2

q1 þ q2

being qj ¼ nj

4pl

� �sinðyjÞ and j ¼ 1; 2; (54)

where yj is the angle between the interface and the X-ray beam direction in medium j and l the X-raywavelength in vacuum. The experimentally measured reflectivity R1,2 is simply given by

R1;2 ¼ jr1;2ðn1; n2Þj2: (55)

Interface roughness can be incorporated into Fresnel reflectivity by multiplying the reflected amplitudeof the ideally planar interface, Eq. (54), with the Fourier transform of a Gaussian to a roughnessparameter s [843]:

R1;2 ¼ jr1;2ðn1; n2Þj2 ¼ q1 � q2

q1 þ q2

exp �q1q2s2

2

� ��2

: (56)

In the cases of interest for this review, mediums 1 and 2 can be: (i) air and semiconductor surface; (ii)film and substrate surfaces; (iii) well and barrier surfaces in a SL. In the case of a SL structure, arecursive approach is needed since, beside the air–cap interface, we are dealing with several buriedinterfaces between well and barrier and between barrier and substrate where different nj and yj (and thusqj) are present. We can so naively rewrite Eq. (56) by considering the total reflectivity R as the sum ofthe contributions of all interfaces [843]

R ¼ jrðn1; n2; . . . ; nNÞj2 ¼XN

j¼1

qj � qj�1

qj þ qj�1

exp �ðqjsjÞ2

2

" #exp½iqfilmzj�

��2

: (57)

The strong approximation done by writing Eq. (57) is related to the fact that it does not take intoaccount multiple reflections between the surfaces, which must to be included in order to be able toreproduce quantitatively the experimental data. Moreover, in Eqs. (56) and (57), the reflectivitycoefficient r is related to qj in a non-linear way. The calculation of reflectivity of stacked slabs withdifferent qj is therefore a complex matter, that will not be treated here. The reader is referred to Refs.[756,843–846] for a detailed discussion of the topic.

Asmussen and Riegler [843] reported an efficient numerical analysis procedure of X-ray reflectivitydata from ultra-thin films at interfaces. It allows virtually exact modeling of reflectivity data in theentire q-vector range including the critical angle and below with minimum fit parameters andcalculation effort. The electron density profile is interpreted as a linear superposition of the air/filminterface, the internal film structure, and the film/substrate interface, see Fig. 63. The reflectivities at theinterfaces are calculated from the accurate Fresnel reflectivities. Authors parameterized the internalfilm structure in a Fourier series; its reflectivity contribution is then calculated from refraction-corrected, approximated (linearized) Fresnel reflectivities. The delicate problem of determining the


degree of correlation between the fit parameters and of obtaining absolute errors for the fit parametershas been addressed [843].

De Caro and Tapfer [845,846] presented a detailed description of the dynamical theory of X-raydiffraction within the Laue formalism for the two-beam case, which is valid for X-ray Bragg and Lanediffraction on ideal crystals of finite thickness. With the equations derived it is possible to describe theinteraction of the X-ray beam with the crystal in a dynamical way in the whole angular range from 0 top/2. The theory can be applied for describing: (i) symmetric and asymmetric reflections both near theBragg condition and at the far tails of the Bragg peaks; (ii) Bragg diffraction of X-rays at very smallglancing angles of the order of the critical angle; (iii) Bragg and Laue diffractions in which thediffracted beam travels almost parallel to the crystal surface [845,846]. In a successive work the authors[756], generalized the theory for strained multilayers. The following cases have been described indetail: coplanar diffraction (i) very far from the Bragg condition, (ii) near to the Bragg condition forstrong asymmetric reflections, and (iii) for highly mismatched heterostructures.

After this brief introduction to the technique few selected examples are discussed in the followingsubsection.


Dura et al. [19] reported an X-ray reflectivity study aimed to characterize the interface roughness inAlGaAs/GaAs high electron mobility devices. X-ray reflectivity experiments have been employed toinvestigate the density profile of the oxide film on a GaAs substrate revealing the density profile as a

Fig. 63. Separation of the overall reflected amplitudes into contributions from the interfaces: (a) air/film; (c) film/substrate

and (b) the internal film structure. Adapted from A. Asmussen, H. Riegler, J. Chem. Phys. 104 (1996) 8159, [843], with

permission. Copyright (2000) by American Institute of Physics.


function of depth [702]. Various X-ray techniques have been applied by Ming et al. [847] to study someInxGa1�xAs/GaAs 100-period SLs grown on GaAs(1 0 0) substrates by MBE. Structural parameterspertaining to the morphology of interfaces and thickness variations were obtained. The interfaces inthese SLs are found to be highly correlated, and the layers all show a high degree of crystallinity.Splitting in the X-ray reflectivity and diffraction patterns in one of the samples provide clear evidencefor pronounced thickness modulation, and direct comparison of the diffraction satellite peaks withresults of high-resolution TEM indicates that there exists a lateral structural ordering in the [1 1 0]direction during epitaxial growth [847]. Sanyal et al. [848] reported an X-ray reflectivity study of thickAlAs–AlGaAs and thin GeSi–Ge multilayers grown using MOVPE and ion-beam sputtering depositiontechniques, respectively. Asymmetry in interfaces is observed in both systems. It is also observed thatalthough the Si-on-Ge interface is sharp, an Si0.4Ge0.6 alloy is formed at the Ge-on-Si interface. In thecase of the III–V semiconductor, the AlAs-on-AlGaAs interface shows much greater roughness thanthat observed in the AlGaAs-on-AlAs interface. Authors demonstrate how, for thin multilayers, thecompositional profile can be obtained as a function of depth directly from the X-ray reflectivity data[848].

The Si1�xGex/Si ðx < 0:50Þ system has been investigated also by Fernandez et al. [849] reporting acombined XRD, X-ray reflectivity and TEM approach. Silicon–germanium/silicon MQWs have beengrown on Si(0 0 1) substrates by MBE using disilane (Si2H6) and germane (GeH4) as source gases inthe 450–520 8C temperature range. Authors observed that, in the adopted conditions, the Si growth rateis limited by hydrogen desorption kinetics, whereas the growth of SiGe is limited primarily by thearrival rate of the source gases onto the Si substrate. XRD analysis of the structures indicates asignificant well plus barrier period variation of approximately 5–10%, attributed to fluctuations in thesubstrate temperature during growth, causing a significant variations in the growth rate of the Si barriers[849]. Also the work of Menon et al. [850] on the SiGe/Si system merits consideration. High-resolutionreciprocal lattice mapping and X-ray reflectivity measurements have been used to characterize theepitaxial quality and the interfacial defects, respectively. The surface morphology of the structures wasstudied by AFM. Authors have shown that the generation of defects in non-selective SiGe layers isstrongly dependent oil the thickness of the buffer layer. Moreover, the selective growth of a Si bufferlayer requires a growth temperature above 770 8C in order to obtain a smooth layer surface, which isbeneficial for the succeeding growth of the SiGe layer. The surface can also be smoothed by anannealing treatment at 900 8C for 40 s. This annealing step is crucial to remove the interfacial defects inthe case of Si/SiGe structures grown with different Si sources [850].

As already discussed in Section 5.5 the influences of the Si caplayer or spacer layer on themicrostructures of the Ge/Si(0 0 1) quantum dots (underneath or on the top of the Si thin layer) havebeen studied by combining a laboratory AFM technique with several synchrotron radiation X-raytechniques: reflection, XRD and GID [797]. Strong intensity oscillations caused by the interference ofX-rays scattered from the surface and the buried Ge dots layer have been observed in the X-rayreflectivity measurements of the different samples reported in Fig. 64. Samples labeled by the authorsas B–D have been grown as follows. For sample B, after the deposition of the Ge film, a Si caplayerwith nominal thickness of about 90 nm was deposited at the temperature of 700 8C. For sample C,another 8.5 ML Ge film was deposited on the Si caplayer (acting as spacer layer) to form new layer ofGe dots on the top. Sample D has the same structure as sample C, but with thinner spacer layer of about70 nm. From the periodicity of the oscillations in the reflectivity curves, the thickness T of the Sicaplayer/spacer layer has been obtained for the three heterostructures according to equation:


T ¼ 2p=ðDqÞ, where Dq is the difference, in the reciprocal space, between two adjacent oscillations.Values of T ¼ 97, 93 and 74 nm have been obtained for samples B, C and D, respectively.

X-ray reflectivity studies of Al0.46Ga0.54As/GaAs QWs structures have been undertaken by Brownet al. [851] to establish, by means of a non-destructive technique the investigating interdiffusionbetween layers in these structures. Layer thickness were obtained from the reflectivity data bothdirectly and by the application of modeling techniques. In addition to the layers expected from thefabrication of the samples, the reflectivity data showed that a surface layer was present on the as-produced samples which was consistent with a native oxide. Anodic oxidation and annealing ofthe samples gave rise to marked changes in the reflectivity profiles consistent with interdiffusion at theinterfaces. The feasibility of using anomalous dispersion to highlight the gallium distribution in thesamples was demonstrated. It has been demonstrated that X-ray reflectivity can give information aboutthe layers and the interdiffusion between layers of significant value to scientists interested insemiconductor device fabrication.

Prevot et al. [458] investigated the crystalline quality and the interface roughness of twounintentionally-doped InAs/AlSb strained 20 periods MQW grown on GaSb substrates by MBE usingdifferent cell shutter sequences at the arsenide/antimonide interfaces using combined high resolutionXRD and small angle X-ray reflectivity measurements. For sample A (B) the width (w) of InAs barrierwas 76 A (101 A) while the width of the AlSb barrier was 206 A (188 A). Samples A and B were grownusing the same GIT shutter sequence at the antimonide on arsenide interface (Sb/As), but a differentshutter sequence at the reverse interface (As/Sb) has been used. Experimentally, the interface andsurface roughness decreases the contrast of high order fringes of XRR curves (see Fig. 65). As the GaSbcap layer thickness is similar for samples A and B, it is appropriate to compare qualitatively theirexperimental reflectivity patterns. For sample A, a faster decay of peak intensity is observed at higherangles (2y > 5�, Fig. 65). It means that the interface roughness is higher for sample A than for sampleB. A good ft between experimental and simulated patterns is obtained for 0:1� < 2y < 5:0� for eachsample. For 2y > 5:0� the fit is not as good because simulations do not take into account the diffuse

Fig. 64. X-ray reflectivity patterns of three different Ge/Si(0 0 1) quantum dots samples, see text for sample description.

Adapted from X. Jiang, et al., Nucl. Instrum. Meth. B 200 (2003) 40, [797], with permission. Copyright (2003) by Elsevier.


diffusion that occurs at these high angles [458]. The best-fits are obtained for a roughness of the As/Sbinterface between 1 and 2 ML for sample B and between 2 and 3 ML for sample A. The roughness ofthe reverse interface (Sb/As) is found to be the same for both samples and less relevant than that foundfor the As/Sb interface. Experimental and simulated XRR patterns reveal a higher quality for sample B.As the only difference in the growth procedure is the shutter sequence used at the arsenide onantimonide surface, authors concluded that the GIT under As flux at the beginning of the InAs growthare effective to improve the interface roughness and the crystalline quality of the samples. These growthinterruptions should increase the diffusion length of surface adatoms and thus reduce the roughness inthe growth plane [458], see Section 3.

Coming to II–VI semiconductors, Bunker et al. [852] have investigated the ZnTe/CdSe system bymeans of EXAFS, XRD, and X-ray reflectivity.

X-ray reflectivity has been very informative in the characterization of the oxide films formed onsemiconductor surfaces [851,853–857]. Pincik et al. [855] have characterized the oxide layers formedon the semi-insulating GaAs surfaces, while Awaji et al. [853,854] have investigated native oxides andultra-thin thermal oxides on Si(1 0 0). The SiO2/Si system has been investigated by Eymery et al. also[857]. X-ray reflectivity has been used by Hong et al. [856] to investigate the Ga2O3(Gd2O3)/GaNmetal-oxide–semiconductor interfaces.

Takeda and Tabuchi [858] reported a combined X-ray CTR scattering and X-ray reflectivity study ofGaN-based heterostructures, emphasizing the effect on the topmost layers of the sapphire substrates ofsevere thermal activation in reactive atmospheres. They investigated the surface amorphization processoccurring by heated the samples at 1150 8C in H2 and NH3 atmospheres, the latter resulting in theformation amorphous-like AlN layers. Effects of nitridation process and AlN buffer layer (the low-temperature-deposited amorphous-like AlN layer) on the quality of GaN and GaInN overlayers weredescribed [858].

Fig. 65. X-ray reflectivity curves and corresponding simulations for two unintentionally-doped InAs/AlSb strained 20-period

MQW grown on GaSb substrates by MBE. Sample A: 76 A of InAs barrier alternated with 206 A of AlSb barriers. Sample B:

101 A of InAs barrier alternated with 188 A of AlSb barriers. Adapted from I. Prevot, et al., J. Cryst. Growth 227 (2001) 566,

[458], with permission. Copyright (2001) by Elsevier.


The low-temperature Si(1 1 1)ð7 � 7Þ-Pb interface has been investigated using X-ray reflectivity byEdwards et al. [859] to investigate the atomic reconstruction of the Pb/Si interface which is a keyparameter in the determination of the height of the corresponding Schottky barrier. Authors havestudied the structure of the evolving interface by monitoring (at ai ¼ af) the intensity of the X-rayreflected beam as a function of the growth of the metal layer for different l values. At any l values theintensity of the X-ray specular reflectivity versus the growth evolution exhibits an oscillatory behavioranalogous to the classical RHEED growth oscillations, as clearly shown in Fig. 66. It is immediatelyapparent from Fig. 66 that the Pb growth shows a strong layer-by-layer character with oscillations in the

Fig. 66. X-ray reflectivity growth oscillations measured at various l values: (a) l ¼ 1:64; (b) l ¼ 1:38; (c) l ¼ 1:25; (d)

l ¼ 1:08; (e) l ¼ 0:82; (f) l ¼ 0:59 (dotted lines). Experimental data have been collected with l ¼ 1:00 A, corresponding to

12398 eV (i.e. below the Pb LIII adsorption edge: 13041 eV). Superimposed on (a) and (e) are the theoretical growth curves

(full lines) calculated according to the model of Finney et al. for ideal layer-by-layer growth [860], which intensity has been

scaled by matching the starting intensity to that from the clean Si(1 1 1) substrate. Adapted from K.A. Edwards, et al., Surf.

Sci. 424 (1999) 169, [859], with permission. Copyright (1999) by Elsevier.


intensity at all l values. It is evident that the frequency of the oscillations decreases with decreasing the lvalue used to collect the data (top to bottom trend in Fig. 66). This fact is due to the inverse relationshipexisting between l and the number of layers required before the phase results in destructive interference.Authors compared some experimental curves (dotted lines) with theoretical growth curves (full lines)calculated using the model of Finney et al. for perfect layer-by-layer growth [860] resulting in sharpparabolic cusps. The first maximum occurs when the first Pb layer is complete (T ¼ 1:2 ML).14 Thesecond layer scatters out-of-phase with the first, and when this layer is complete (T ¼ 2:4 ML), there isdestructive interference, and the intensity returns to the value due to clean Si(1 1 1) surface. Thisprocess continues with successive layers so that the odd-numbered cusps are intense, and the even-numbered cusps are weak. The peaks are rounded due to imperfect, multilayer growth. Also, theamplitude of the oscillations decays, indicating that the surface roughness increases with increasing T.A significant feature in the growth curves is observed at T � 6 ML, corresponding to five completePb(1 1 1) layers, see the vertical dotted line in Fig. 66. This is most easily seen in the data collected atl ¼ 1:64 (curve a). For T < 6 ML, the peaks are irregularly spaced and the intensity appears to beanomalously small. The minima, where destructive interference are expected are relatively intense.These features indicate a significant degree of disorder in the early stages of growth. The irregularperiod of the oscillations at low coverages cannot be explained by a simple layer-by-layer growthmodel. For T > 6 ML, the oscillations have a regular period and decay uniformly. This is consistentwith the layer-by-layer growth of a Pb(1 1 1) crystal layer with increasing surface roughness. Theregular periodicity of the growth oscillations at coverages above 6 ML has been used by Edwards et al.[859] to calibrate the growth rate of the film, which resulted to be 0:46 � 0:02 ML min�1. Detailedmodels of the mature interface are consistent with the preservation, after burial, of the Si(1 1 1)ð7 � 7Þ-Pb reconstruction originally formed during growth of the first monolayer [859].

In the topic of metal films on silicon, also the work of Kellerman et al. [297] merits consideration.Authors used in situ X-ray reflectivity to investigate the kinetics and structural evolution in the earlystages of Fe deposition on Si(0 0 1) performed from the thermal decomposition of Fe(CO)5 in the 90–220 8C temperature range. The polycrystalline Fe film thickness T, the Fe surface roughness and Fe/Siinterface width have been simultaneously measured. From the thickness measurements, authors wereable to separate the nucleation and growth regimes and found direct evidence for an autocatalyticgrowth effect: an induction period indicative of the rate-limiting nucleation of Fe islands on theSi(0 0 1) substrate followed by a linear increase in growth representing Fe deposition on Fe. Theincubation period decreased with increasing growth temperature. Using a modified version of classicalnucleation theory to model the evolution of T for the initial stages of film growth, authors found adifference in the activation energies for the thermal decomposition of the Fe(CO)5 precursor onSi(0 0 1) and Fe, 0:78 ��0:09 and 0:20 � 0:02 eV, respectively. The surface roughness decreased withincreasing temperature due to enhanced nucleation at higher temperatures. The evolution of theroughness is in agreement with a simple model of nucleation and coalescence of three-dimensionalislands. The large difference in activation energies for nucleation and growth is responsible for thebehavior of both the time dependence of the deposition rate and morphology evolution. A relativelynarrow Fe/Si interface width indicates that very little intermixing occurs in this temperature regime[297].

14 Since the lattice spacing of Pb is smaller than Si, a fully occupied Pb(1 1 1) layer has a coverage of 1.20 ML Si(1 1 1),

which is the unit used for the absciss axis in Fig. 66.


Remarkable is also the in situ study of Lee and Tseng [287] reporting X-ray reflectivity data acquiredduring the growth of a thin Al film on a Si(0 0 1) substrate. Authors found that the surface roughnessincreased as the film became thicker. The data were compared with die scaling behavior of the surfaceinterfacial width that was theoretically predicted and experimentally verified for non-equilibriumgrowth conditions. Press et al. [844] investigated the interface roughness of an aperiodic CoSi2/Simultilayer grown by MBE using X-ray reflectivity.

9. Application of photoemission spectroscopies

As was the case for XRD, photoelectron spectroscopy (PES), using both UV (UPS) and X-ray (XPS)photons, is a so widely used technique to make useless any basic introduction. It is just recalled that it isbased on the Einstein photoelectric effect, where a monochromatic photon beam of energy hn extractsan electron from a solid with a kinetic energy T 0. The energy conservation implies that hn ¼ T 0 þ f,where f is the work function of the system, i.e. the minimum energy required to extract the electronfrom the solid. This means that by measuring, at fixed hn, the kinetic energy T 0 of the outcomingelectron one can obtain directly f ¼ hn� T 0. As a consequence, a plot of the number of measuredelectrons per energy interval (@N/@T 0) reflects the density of occupied electron states in the solid(DOS).

As the photon source is a major ingredient in all photoemission techniques [318], synchrotron lighthas played an important role in improving the type and the quality of PES experiments. The progress insynchrotron sources marked by three subsequent generations and a fourth generation already appearson the horizon [311,317,318]. Each generation of synchrotron sources opened the way to new PEStechniques relevant to surface and interface research. Among them the following improvements areworth noticing: the possibility of collecting the PES spectra at different photon energies, constant initialstate and constant final state spectroscopies, partial-yield spectroscopy, photon-polarization techniques,angle-resolved photoemission and band mapping, photoemission resonances, photoelectron diffraction,ultra-high-resolution spectroscopy and photoemission spectromicroscopy, laterally resolved studies ofthe fluctuations of interface parameters [311,318,326,329,861,862].

Due to its surface sensitivity and to its ability of studying interface electronic states and interfacechemical properties, PES is, by far, the most widely used class of electron spectroscopy technique forsemiconductor surface and interface research [15,208,286,300,309–312,321,341,368,369,371–381,863,864].

As summarized by Margaritondo [311] in a synthetic clear and simple way, a photoelectronspectrum, also defined as energy distribution curve (EDC), typically contains six types of features asdetailed in the following and which can be appreciated in Fig. 67a. (i) A vacuum-level low-electron-energy cut-off reflecting the work function f of the analyzed system. (ii) A low-energy peak due tosecondary photoelectrons. (iii) Core-level peaks, whose presence reflects that of the correspondingelements. The corresponding energies depend on the atomic core-level energy of the relevant element,corrected for the interaction with the valence electronic charge distribution reflecting the formation ofchemical bonds. Thus, core-level peaks provide information on the qualitative chemical compositionand on the chemical binding status of each component [318]. (iv) Valence-electron peaks which providedirect information on the chemical bonds that determine them [318]. (v) A high-energy cut-off whichreflects either the Fermi edge (for metals) or the valence band edge (for semiconductors and insulators).


(vi) Features due to localized states such as the clean-surface or interface states. The results of Fig. 67show a nice example of weak but clearly visible surface-state features near the Fermi level [311].

In the case of a semiconductor or an insulator (Fig. 67b), there might be a band bending between thebulk and the surface (or the interface with another material). The band bending occurs over a distanceof the order of the Debye length. Because of the high surface sensitivity of photoemission, themeasured photoelectron energies reflect the electronic energies at the surface rather than in the bulk.

Consider now the results for a semiconductor heterojunction interface, see Fig. 67c. Mostimportantly, the valence-electron features reflect the two valence bands at the two sides of the interface.Two edges are visible, and from their distance one can directly derive the valence band offset15 (DEv),as was observed in the favorable case of the ZnSe/Ge interface by Margaritondo et al. [374].Furthermore, the valence-electron features include those related to localized states, and can be used toanalyze their nature. This approach can be extended to all types of semiconductor interfaces in astraightforward manner.

Fig. 67. (a) Schematic explanation of a photoemission experiment in the case of a metal: the density of (occupied) states,

including core, valence and surface states, is reflected in the photoelectron spectrum, with a superimposed secondary electron

distribution and the two cut-offs caused by the Fermi level and by the vacuum level. (b) An initial study of a clean

semiconductor substrate. (c) Subsequent study of the same substrate, covered with a thin overlayer of another semiconductor.

Note the double edge in the photoemission spectrum, which corresponds to the valence-band discontinuity. Adapted from G.

Margaritondo, Rep. Prog. Phys. 62 (1999) 765, [311], with permission. Copyright (1999) by Institute of Physics.

15 See Section 2.3 and Fig. 5.


In the case of heterojunction, small values of DEv often make it impossible to resolve the twovalence-band edges of the two sides of the junction as shown in Fig. 67c. Even then, DEv can be derivedfrom PES spectra by applying the so-called core-level method, which consists in measuring separatelythe energy difference between each edge and a reference core level and the core-level energies, andthen combining these values after correcting them for possible band-bending changes during theinterface formation [208,371–373,381,865,866]. In other words, the valence band offset at the interfacebetween two semiconductors A and B can be determined by PES measuring the energy of the core-levelof two elements (EA

core and EBcore) exclusively present in only one side of the heterojunction. The energy

separation (DECL) between two measured core levels corresponds to the known energy differencebetween the respective core-level binding energies x0 shifted by the valence-band offset DEv of theheterojunction, which can therefore be obtained as

DEv ¼ DECL � x0; (58)

where

DEv ¼ EBV � EA

V; DECL ¼ EBcore � EA

core; x0 ¼ ðEBcore � EB

VÞ � ðEAcore � EA

VÞ; (59)

see also Eqs. (15)–(17) and related discussion in Section 2.3. The core-level method is described inFig. 68 for the GaAs/AlAs(1 0 0) and GaAs/Si/AlAs(1 0 0) heterojunctions [865,866]. In this casealuminum (present only in the AlAs part of the interface) and gallium (present only in the GaAs part ofthe interface) are the selected atomic species, see the inset in Fig. 68. The chosen core levels are Al(2p)and Ga(3d), characterized by known binding energies of 72.86 and 18.86 eV, respectively, values whichdefine x0 ¼ 54:00 eV. On an historical ground, the core-level method was highlighted in 1980 by Kraut

Fig. 68. Al(2p) and Ga(3d) EDC spectra recorded with 95 eV photons on GaAs/AlAs(1 0 0) and GaAs/Si/AlAs(1 0 0)

heterojunctions (GaAs on top), full and open circles, respectively. The gold Fermi-edge spectrum is also displayed for

reference. The nominal concentration of the Si intralayer is 2:23 � 1014 atoms/cm2. The core-level spectra are shown after

peak-area normalization. The origins of the recorded Al(2p) and Ga(3d) signals within the sample are schematically depicted

as shaded regions in the inset. Reproduced from M. Moreno, et al., Phys. Rev. B 58 (1998) 13767, [866], with permission.

Copyright (1998) by American Physical Society.


et al. [371], who applied it to the Ge/GaAs(1 1 0) interface. By measuring the Ge(3d), Ga(3d), andAs(3d) core levels authors obtained a valence band discontinuity at an abrupt Ge/GaAs(1 1 0)heterojunction of DEv ¼ 0:53 � 0:03 eV. This method is very simple; however, it is accurate only ifcertain conditions are fulfilled: the energy levels along the photoemission probing depth must be well-defined levels. If chemical reactions or band-bending effects are present, the analysis should be madevery carefully, since these effects may broaden and/or shift the recorded core-level peaks, and lead toinaccuracy.

The work of Kraut et al. [371] represented a breakthrough in a the field of heterojunction banddiscontinuities, even if the accuracy of the measurement was slightly overestimated, as one can be seeby comparing the DEv values reported in the literature data. In the review work published byMargaritondo in 1993 [310], it clearly emerges that the typical error associated in the DEv

determination by such core PES experiments is around 0.1 eV.The physics which is behind the experiment of Kraut et al. [371] and of Moreno et al. [865,866],

quoted here to introduce the core-level method (Fig. 68), will be discussed hereafter in Section 9.1.Photoelectron spectroscopy with synchrotron radiation employing high-energy and angular

resolutions is a very efficient tool for experimental investigations of the electronic structure of solidsand their surfaces [867]. In addition to standard band-mapping applications, photoemission intensityand line-shape analyses provide valuable information about wave functions, bonds and interactions of amany-electron system. The spatial origin of photoelectrons can thus be assessed and the three-dimensional shape of Fermi surfaces determined.

9.1. Few selected examples using XPS and UPS synchrotron radiation sources

Some interesting application of XPS spectroscopy to thin films deposited on semiconductorsubstrates have already been mentioned in Section 4.8, because combined with SEXAFS measure-ments, in particular: Na adsorbed on cð2 � 8Þ-Ge(1 1 1) [682]; the Sb–Si(1 1 1) interface [689]; and theSb–Ge(1 1 1) interface [693].

Dehaese et al. [868] studied by angle resolved XPS the interface abruptness and band offset of theGa0.5In0.5P/GaAs system grown by gas source MBE. For cations, authors showed that the interface isabrupt for a growth temperature of 400 8C and that indium segregation is effective at 500 8C but lessthan that in GaInAs system at the same temperature. For anions, growth of the two layers in rapidsuccession results in the incorporation of an excess of arsenic in the GaInP epilayers and a diffuseinterface. As soon as these predominant experimental effects are suppressed, the abruptness of theinterface is limited by a weak arsenic surface segregation. For this quasi-abrupt interface, authors reporta valence band offset of approximate to 0.3 eV as determined by XPS [868].

XPS has been used by Waldrop et al. [331] to measure the valence-band offset for the lattice-matchedIn0.53Ga0.47As/InP and In0.52Al0.48As/In0.53Ga0.47As heterojunction interfaces prepared by MBE. Theobtained values are DEv ¼ 0:34 eV, and thus DEc ¼ 0:26 eV, for the In0.53Ga0.47As/InP system, andDEv ¼ 0:22 eV and thus DEc ¼ 0:47 eV, for the In0.52Al0.48As/In0.53Ga0.47As system. By combiningthese measurements with previous literature data on the In0.52Al0.48As/InP system authors concludedthat the band offset transitivity rule is satisfied. Accordingly to this conclusion, authors deduced that theband offsets for heterojunction pairs formed from InP, In0.53Ga0.47As, and In0.52Al0.48As should not beinfluenced by interface-specific effects [331]. As for the In0.53Ga0.47As/InP system it is worth noticingthat the experimental values observed by Waldrop et al. [331] are in excellent agreement with the


theoretical ones (DEv ¼ 0:337 eV, and thus DEc ¼ 0:266 eV) computed according to the ‘‘model solid’’theory developed by Van de Walle et al. [194,204–207,327], Lamberti [162], and here reviewed inSection 2.4 (see Fig. 6).

A combined XRD, In(4d) and Ga(3d) XPS, and Auger electron spectroscopy study on the interfacesbetween InGaSb and InAs(1 0 0) grown by MBE has been reported by Zborowski et al. [869]. The InAson InGaSb interface has been found to be significantly broader than the reverse one and the asymmetryis the result of mixing between arsenic and antimony. The studies of the growth surfaces have shown apersistent presence of antimony on an InAs surface suggesting a lower, antimony-rich, surface freeenergy. This energy imbalance indicates a driving mechanism behind the mixing of the group Velements as the growth of InAs on InGaSb is commenced. The valence band offset of the InAs onInGaSb has been determined by XPS to be 0:62 � 0:1 eV.

Rioux and Hochst [452] reported the observation of strain-induced splitting of degenerate valencebands at the G point in coherently strained Ge(1 0 0) layers using angle-resolved PES. Strain wassupplied via pseudomorphic epitaxial growth of Ge films on well-ordered InP(1 0 0) substrates: theinherent lattice mismatch between the two semiconductors resulted in a 3.9% tensile biaxial strain inthe Ge epilayers. A surfactant layer was employed to increase the critical layer thickness and filmquality so that measurements could be made on high-quality, fully strained films. A comparison is madebetween experimental results and the theoretical predictions of a heterojunction band-offset theorydeveloped by Van de Walle et al. [194,204–207].

The valence-band offset at the SiC/GaN heterojunction, obtained by depositing thin layers of GaN on6H–SiC(0 0 0 1) by means of plasma enhanced MBE, has been investigated by Lantier et al. [651]using in situ XPS spectra. Differently, thick samples were considered, showing a trend in the shift of theGa(3p) core-level position. This effect is connected to a band bending induced by internal polarizationfields. Parallel EXAFS measurements on the same samples showed a relaxed growth already for thethinnest layer. Authors have inferred that the field in the GaN originates from the spontaneouspolarization, without piezoelectric contributions. The extracted DEv ¼ 0:9 � 0:1 eV is in goodagreement with the theoretical results of Bernardini et al. [870]. The fits of the EXAFS data do notexclude a possible C/N intermixing at the otherwise, when abrupt, unstable GaN/SiC interface, seeSection 4.7.2 for the discussion on the EXAFS results on this system. The electronic structure of thewurtzite AlxGa1�xN alloy system has been studied by Duda et al. [437,871] in the 0 � x � 1 rangeusing synchrotron radiation excited soft X-ray absorption and emission spectroscopies. The occupiedand unoccupied partial density of states have been measured for each alloy. High-resolution X-rayemission spectroscopy allowed the motion of the elementally resolved bulk valence-band maximum tobe measured as a function of Al concentration. Using this technique authors estimate that the value ofthe band gap bowing parameter for AlxGa1�xN is negligible. Furthermore, the X-ray emission spectrarevealed resonant like emission at approximately 19 eV below the GaN valence-band maximum. Bymeasuring the intensity of this feature as a function of Ga content, Duda et al. [437] proved that thisemission arises from hybridization of N(2p) and Ga(3d) states. Finally, the authors evidenced an highorbital anisotropy in AlxGa1�xN system proved by the important polarization dependence of both N K-and Al K-edge NEXAFS spectra (see Sections 4.7.2 and 4.9) strongly on the photon angle of incidencewith respect to the surface normal.

XPS has been used by Kitatani et al. [872] to measure the valence-band offsets of Ga1�xNxAs/AlAs(x ¼ 0, 0.014, 0.034) system by using the Al(2p) energy level as a reference. Authors suggested thatDEv decreases in proportion to the nitrogen content in the Ga1�xNxAs system.


Coming to IV/IV interfaces, Almeida et al. [873] investigated the band offsets at Ge/Si(1 0 0)ð2 � 1Þinterfaces grown by hydrogen and Sb-surfactant mediated epitaxy by XPS. For Ge deposited at 400 8Cin Ge/Si(1 0 0)ð2 � 1Þ, the valence-band discontinuity was of DEv ¼ 0:72 � 0:07 eV. Using atomichydrogen and a Sb-monolayer mediated growth, authors obtained values of DEv ¼ 0:75 � 0:07 eV andof DEv ¼ 0:69 � 0:07 eV, respectively. The so obtained data show that the modification of band offsetsdue to strain-induced effects by the surfactant Ge layer are surprisingly small [873].

Let us now discuss II–VI/IV and III–V/IV heterojunctions. By measuring Ge(3d), Ga(3d), and As(3d)core levels Kraut et al. [371] found, for the Ge/GaAs(1 1 0) heterojunction, DEv ¼ 0:53 � 0:03 eV. In asuccessive work [373] authors resolved the spin–orbit split components of the Ge(3d), Ga(3d), andAs(3d) core lines and reported the binding energies of these components, measured relative to thevalence-band maxima. As already mentioned in the introduction to Section 9, the large value of thevalence-band discontinuity DEv of the ZnSe/Ge heterojunction allowed Margaritondo et al. [374] todirectly measure its value by synchrotron radiation soft X-ray valence-band photoemission spectrawithout needing to analyze the core-level shifts (Fig. 67c). Authors used the ZnSe/Ge interface to showthat the valence-band discontinuity DEv is not affected by the interface ordering or by annealingprocesses in general. Margaritondo et al. [374] concluded by affirming that local contributions to theheterojunction discontinuities have small magnitude on the average. A study of the band offset forZnSe(1 0 0)/GaAs(1 0 0) heterojunctions has been reported by Yang et al. [874].

II–VI/II–VI heterojunctions have played an important role in this field of research, because theapplication of the core-level method to the HgTe/CdTe interface [875–877] lead to the contradiction ofthe common anion rule [212], which states that compound semiconductors with the same anion willform an interface with near zero valence-band discontinuity thus resulting in very small DEv values (seeSection 2.1). The value of DEv ¼ 0:35 � 0:06 eV, reported by Kowalczyk et al. [875] for the CdTe/HgTeð�1 �1 �1Þ heterojunction provided direct experimental evidence in contradiction to the common-anion rule for lattice-matched heterojunction interfaces. Five years later, Becker et al. [876] extendedthe study of the CdTe/HgTe heterojunction to three different orientations: (1 0 0), (1 1 0) and (1 1 1).The so obtained results confirmed the violation of the common anion rule reporting a value ofDEv ¼ 0:37 � 0:07 eV independently from the surface orientation and the surface structureimmediately prior to growth of the uppermost layer. An even higher value (DEv ¼ 0:53 � 0:03 eV)has been, more recently, reported by Eich et al. [877], who have investigated the valence-band offset ofthe HgTe/CdTe(0 0 1) heterostructure, grown by MBE, using k-resolved UPS and XPS experiments.This value is significantly higher than those previously reported [875,876], but agrees well withmagneto-optical investigations (DEv ¼ 0:55) [878]. As a result of all this literature, it emerges that theDEv value for the HgTe/CdTe heterojunction is significantly larger than zero, being in the 0.35–0.55 eVrange. This represents a clear violation of the common anion rule [212]. Much better agreement withthe experimental data have been obtained by the theoretical models of Munoz et al. [271,272] and Vande Walle and Martin [273] results predicting DEv in the 0.27–0.46 eV range. The main differences inthe two theoretical approaches is related to the fact that the self-consistent tight-binding calculations ofMunoz et al. [271,272] predicted a dependence of the DEv value on the surface orientation (DEv ¼ 0:46and 0.37 eV for the (1 0 0) the (1 1 0) surface orientation, respectively), whereas the self-consistentlocal density functional methods of Van de Walle and Martin [273] show nearly no orientationdependence (DEv ¼ 0:27 and 0.28 eV, respectively). Coming back to the work by Eich et al. [877],authors have also determined, by a combination of UV and inverse photoemission, the energy gap ofCdTe(0 0 1) and HgTe(0 0 1): EgðCdTeÞ ¼ 1:57 � 0:06 eV; EgðHgTeÞ ¼ 0:0 � 0:06 eV. Authors


therefore concluded that HgTe is a semi-metal with inverted band structure, which agrees with otherresults [879]. One year later, the same group reported a study on the parent MBE-grown HgSe/CdTe(0 0 1) system [880]. The surface termination and geometric structure of HgSe(0 0 1) has beenstudied combining k-resolved XPS and UPS and high-resolution LEED. The valence-banddiscontinuity was determined as DEv ¼ 0:58 � 0:05 eV. This value compared with the above discussedresults for the HgTe/CdTe heterojunction [877] seems to support the trend expected by Wei and Zungertheory16 [274] predicting a larger DEv for selenides than for tellurides: a further decrease in theassociated error bars is, however, still needed before writing the last word on this topic.

Another violation of the common anion rule has been reported by Worz et al. [881] who measuredDEv for the ZnSe/Zn1�xMgxSe system performing synchrotron radiation PES. Author attributed thisviolation to the filled d-shell of Zn which is lacking in Mg. In the paper the ZnSe/Zn1�xMgxSeheterostructures have been further investigated by parallel absorption, photoreflection, photolumines-cence, photoluminescence-excitation characterization techniques.

Synchrotron radiation XPS and RHEED were used to investigate the structural and electronicproperties at the ZnSe/CdTe(1 0 0) heterojunction interface by Nelson [882]. ZnSe overlayers weresequentially grown in steps on p-type CdTe(1 0 0) single crystals at 200 8C. In situ XPS spectra wereacquired after each growth in order to observe changes in the valence-band electronic structure as wellas changes in the Cd(4d), Zn(3d) and Te(4d) core lines. Nelson used the results to correlate theinterfacial chemistry with the electronic structure and to directly determine the ZnSe/CdTeheterojunction valence-band discontinuity (DEv ¼ 0:20 eV) and the consequent heterojunction banddiagram.

Epitaxial layers of ZnS were grown on cleaved GaP(1 1 0) surfaces by MBE in an ultra-high vacuumphotoelectron spectrometer by Wolfframm et al. [883]. The growth mode and the structure of theoverlayer were studied by means of LEED and core as well as valence level photoemission usingsynchrotron radiation. The attenuation of substrate core-level intensities with ZnS deposition indicateslayerwise growth. LEED demonstrates the growth of the cubic (zinc blende) phase as expected forsubstrate-stabilized growth. A minor interface reaction is evident from changes in the appearance of thesubstrate Ga(3d) and overlayer S(2p) core levels with increasing thickness. S–Ga bonding was observedin a thin interfacial layer. The valence-band offset for this lattice-matched heterojunction interfacesystem was determined, and found to be of the straddling type (type I, see Fig. 2).

Franklin et al. [884] used synchrotron radiation PES to study the high- and low-temperature growthphases of ZnTe on GaSb(1 0 0). The deconvoluted core-level line shapes were used to constructstructural models for the interface between these two compound semiconductors. The movement of thevalence-band and Fermi level was used to examine the heterojunction band offset for the low-temperature phase and the dopant incorporation for the high-temperature phase. The interface betweenZnSe and GaAs(1 0 0) has been studied by Colbow et al. [885] as a function of annealing temperatureby synchrotron radiation PES. From an analysis of chemical shifts and relative intensities of the atomiccore levels, authors revealed the formation of an interfacial Ga2Se3 layer due to the loss of Zn and As at

16 Wei and Zunger [274], using first-principles all-electron band structure method, have systematically calculated the natural

band offsets DEv between all II and VI and separately between III and V semiconductor compounds. Fundamental regularities

have been uncovered: for common cation systems DEv decreases when the cation atomic number increases, while for common

anion systems DEv decreases when the anion atomic number increases. Authors found that coupling between anion p and

cation d states plays a decisive role in determining the absolute position of the valence band maximum and thus the observed

chemical trends.


the interface. The valence-band offset between ZnSe and GaAs was found to be DEv ¼ 1:25 � 0:07 eV,at the top of the valence band.

The valence-band offset for the CdS/CdTe system was measured by Boieriu et al. [886], using XPS,and indicates a type I alignment. Authors investigated wurtzite CdS grown by MBE on bothCdTeð�1 �1 �1Þ and CdTe(1 1 1) substrates. CdTe was then grown on top of the CdS layers. XPS indicatesthe existence of a thin reacted layer at the interface when CdTeð�1 �1 �1Þ was used as a substrate.Conversely no reaction was seen during growth of CdTe on CdS/CdTe(1 1 1) substrate. Yu et al. [339]reported an XPS study aimed to in situ measure the valence-band offset for CdSe/ZnTe(1 0 0)heterojunctions grown by MBE. XPS measurements were performed for films of CdSe(1 0 0) andZnTe(1 0 0), and for heterojunctions consisting either in 25 A of CdSe grown on ZnTe(1 0 0) or in 25 Aof ZnTe grown on CdSe(1 0 0). Observations of reflection high-energy electron diffraction patternsindicated that CdSe films deposited on ZnTe(1 0 0) were grown in cubic zinc blende form, rather thanthe natural wurtzite structure of CdSe. Reported measurements yielded a CdSe/ZnTe valence-bandoffset DEv ¼ �0:64 � 0:07 eV. The corresponding conduction band offset for CdSe/ZnTe isDEc ¼ 1:22 � 0:07 eV for room temperature band gaps for ZnTe and for cubic CdSe of 2.25 and1.67 eV, respectively [339] (we are dealing with a type II band alignment, see Fig. 2d). The XPS studyof the Zn(3d5/2), Hg(5d5/2) and Te(4d5/2) core levels for ZnxHg1�xTe bulk crystals has been carried outin the complete x composition range by Marbeuf et al. [887]. The corresponding binding energiesrelative to the valence-band maximum are measured as a function of x. Authors affirm that because of arelaxation in the lattice of the alloy, neither of the cation levels are affected by alloying on an absoluteenergy scale. By combining their shifts, the natural valence-band offset is deduced: its value(DEv ¼ 0:17 eV) appears smaller than the CdxHg1�xTe value (DEv ¼ 0:35 eV). Between ZnTe andHgTe, the main part of the variation of the valence-band maximum is found for semi-metalliccompositions. The deeper Te(4d5/2) level position varies in the same manner, but with a small bowingresulting from the disorder [887]. The band lineups at Ge/ZnS(1 1 1) interfaces have been studied bysynchrotron radiation PES by Ban et al. [888]. Surface-sensitive core-level spectra show that Ge and Satoms react with each other at the interface. Using both the techniques of core-level and valence-bandspectra, authors determined the valence-band offsets to be DEv ¼ 1:94 � 0:1 and 2:23 � 0:1 eV for theheterojunctions grown at the ZnS(1 1 1) substrate at temperatures of 200 and 30 8C, respectively.

By using synchrotron radiation PES, the band lineup of Ge/CdTe(1 1 1) interfaces grown at differenttemperatures have been measured by Ban et al. [889]. Experimental studies showed that the valence-band offset of Ge/CdTe(1 1 1) interface grown at room temperature is DEv ¼ 0:88 � 0:1 eV, while asfor the interface grown at 280 8C, a reduction of valence-band offsets was observed and attributed bythe authors to the effect of different interface dipole.

In 1990 Munoz et al. [254] and in 1991 Peressi et al. [275] reported two famous theoretical workspredicting that band offsets could be modified at semiconductor heterojunctions or created athomojunctions by depositing thin intralayers of group IV atoms at III–V/III–V polar interfaces. Munozet al. investigated the effect of insertion of group IVatoms in the GaAs–GaAs(1 0 0) homojunction [254].Peressi et al. present a theoretical study of Si and Ge intralayers deposited along at GaAs(0 0 1) andAlAs(0 0 1) homojunctions, and at GaAs/AlAs(0 0 1) heterojunctions. Reported results showed that theband offset is predicted to be very sensitive to the coverage and abruptness of the intralayer [275].

The theoretical predictions so far described [254,275] have been rapidly confirmed by thesynchrotron PES experiments of the Franciosi and co-workers [890–894] and Margaritondo andco-workers [309,895–897].


Sorba et al. [890,891] demonstrated that the presence of thin ordered layers of Si within the interfaceregion of AlAs–GaAs heterostructures is able to tune the valence-band offset throughout the 0.02–0.78 eV range. High-resolution XPS studies of heterostructures prepared in situ by MBE as a functionof substrate temperature, arsenic flux, interface concentration of Si, and growth sequence (AlAs onGaAs versus GaAs-on-AlAs) indicate that this tunability is associated with a Si-related local dipolewhich can be added to or subtracted from the intrinsic AlAs–GaAs valence-band offset ofDEv ¼ 0:40 eV [890,891]. Comparison of high-resolution X-ray photoemission studies of AlAs–Ge–GaAs and AlAs–Si–GaAs heterostructures prepared in situ by MBE as a function of the interfaceconcentration of group IV elements shows qualitative similarities and surprising quantitative differences[892]. The observed dipole per group IV atom is three times as large for Ge as for Si, but the totalmaximum dipole achievable at the interface is identical (0.4 eV), within experimental uncertainty, forthe two group IV elements [892]. In Ref. [893] Sorba et al. discriminated between the charged andneutral character of Ge/III–V semiconductor interfaces by examining the band discontinuities acrosseach interface in AlAs–Ge–GaAs(0 0 1) and GaAs–Ge–AlAs(0 0 1) single quantum well structures as afunction of Ge thickness in the 2–16 ML range and comparing them with those of individual, isolatedGe–GaAs(0 0 1), Ge–AlAs(0 0 1), GaAs–Ge(0 0 1) and AlAs–Ge(0 0 1) heterojunctions. While ideallyabrupt polar heterovalent interfaces are predicted to be charged, authors found that all of the observeddeviations from the commutativity and transitivity rules of heterojunction band offsets are consistentwith the establishment of inequivalent, neutral IV/III–V and III–V/IV interfaces [893]. The same groupachieved a similar result with Ge intralayers for the ZnSe–GaAs interface [894]. The photoemission-determined valence-band offset was DEv ¼ 1:10 � 0:05 eV for ZnSe–GaAs(1 1 0) heterojunctionsand DEv ¼ ð0:78�0:83Þ � 0:07 eV for ZnSe–GaAs(1 0 0) heterojunctions. This germanium layers(4–6 ML thick) fabricated at the interface prior to ZnSe deposition yield a decrease in the overallvalence-band discontinuity for both ZnSe–Ge–GaAs(1 1 0) and ZnSe–Ge–GaAs(1 0 0) heterojunctions.These investigations continued in subsequent years, yielding a series of additional significant results[898,899]. Specifically, in Ref. [899], authors showed the achievement of device-grade ZnSe–Ge–GaAsheterostructures with engineered offsets. Authors reported a large tunability of the band discontinuity atthe ZnSe/GaAs n–p heterojunction in the 0.26–0.75 eV range.

Margaritondo and co-workers [309,895–897] worked on the symmetrically inverted type ofhomojunctions (with respect to those investigated in the theoretical studies [254,275]), obtained byintercalating thin III–V intralayers at IV/IV interfaces. More precisely, the possibility of inducing aband offset in the electronic structure of Ge homojunctions has been demonstrated by intercalatingbetween two Ge films double layers of GaAs [895] or of AlAs [309] using synchrotron radiation PESexperiments. This was the first time that intralayer control of band discontinuities was extended tohomojunctions, thereby expanding the potential domain of band gap engineering. Because these offsetsoccur over just a few atomic spacings, they reveal heterojunction band edge discontinuities in breadth.McKinley et al. [895], using as reference the Ge(1 1 1) substrate used for the preparation of theGe–GaAs–Ge homojunction, have shown that the Ge(3d) photoemission peak is shifted by about0.35–0.45 eV in the Ge layer grown on top of the Ga–As double layers. Similar band offset magnitudesoccur for both ‘‘Ga-first’’ and ‘‘As-first’’ growth sequences, consistent with a truly dipolar effect. Bothcleaved Ge(1 1 1) and thick 50 A Ge films deposited on cleaved Ge(1 1 1) were used as substrates,obtaining consistent results. The sign and magnitude of the effect is in agreement with a ‘‘theoreticalalchemy’’ model [895]. One year later, Marsi et al. [309] presented a PES study in which it is provedthat a similar effect can be induced using Al–As as an intralayer in a n-Ge/p-Ge homojunction, see


Fig. 69a. Specifically, an offset of 0.4 eV has been obtained (Fig. 69b). It is found that the cation–anionintralayer deposition sequence produces the same dipole as the anion–cation sequence. This result issimilar to that found for large overlayer coverages in the case of Ga–As intralayers; but contrary to theGa–As intralayers the present system does not exhibit a reversed discontinuity for small thickness[309]. In a successive work, the same group [896] extended the study by investigating the amount of theinduced DEv and DEc at GaAs(1 0 0) polar homojunctions by means of ultra-thin Si intralayers ofdifferent thickness. The microscopic interface dipole responsible for the creation of such offsets can bevaried by changing the Si intralayer thickness; the consequently variable band discontinuities representa tunable parameter with potential applications in band-gap engineering. Authors found that eventhough the existence and the direction of these discontinuities are in agreement with theoreticalpredictions [254,275], the existing models overestimate the amount of the offset and cannot explain itsdependence on the intralayer thickness. The possible presence of Si out diffusion has been ascribed as apossible explanation for this partial disagreement [896].

Coming back to the AlAs/Si/GaAs heterojunction, Akazawa et al. [900] in 1992 and Hashimoto et al.[901] in 1994 confirmed the experimental results of Sorba et al. [890], however reported a differentinterpretation for observed shifts in the XPS spectra. Quoted authors argued that the XPS resultsobtained on the AlAs–GaAs heterojunctions could be connected with the existence of a sharp overlayerband bending rather than with a real modification of the band offset by Si insertion [900,901]. The new

Fig. 69. (a) Schematic diagram illustrating the creation of artificial band discontinuities at a Ge–Ge homojunction. Top: the

homojunction has no discontinuities. Bottom: the insertion of an As–Al double intralayer creates an interface dipole and

discontinuities in the conduction and valence bands. (b) Application of the method illustrated in part (a) to a Ge–Ge

homojunction. The Ge(3d) XPS level reveal the position of the band structure of the Ge substrate (bottom curve) and that of

the Ge overlayer as a function of the overlayer thickness T. By increasing T, the XPS response of the substrate becomes

progressively negligible and the top curve (T ¼ 64 A) reflects the electronic configuration of the Ge overlayer only. In the

intermediate spectra (T ¼ 4, 8 and 16 A) the deconvolved contributions of the substrate and of the overlayer are also reported.

Before depositing the Ge overlayer, a double intralayer consisting of one monolayer of As and one monolayer of Al was

evaporated on the Ge substrate. Consequently, the spectra reveal a clear shift between the substrate and overlayer electronic

structures. The corresponding artificial conduction and valence-band offsets are 0.4 eV. Adapted from G. Margaritondo,

Rep. Prog. Phys. 62 (1999) 765, [311], with permission. Copyright (1999) by Institute of Physics. Adapted from M. Marsi,

et al., J. Vacuum Sci. Technol. A 10 (1992) 741, [309], with permission. Copyright (1992) by AVC The Science and

Technology Society.


interpretation was based on the fact that, beside the large (apparent for authors of Refs. [900,901])change of DEv, the insertion of Si interlayer also caused an anomalous increase of the separationsbetween the core-level peak and the valence-band edge as well as anomalous increase of the full widthat half maximum of the core-level bands. Akazawa et al. [900] and Hashimoto et al. [901] concludedthat the observed change of DEv is only an apparent one and that the XPS anomalies were explainedquantitatively by a new model based on an introduction of band bending in an overgrown layer. Theproposed band-bending model explains all the experimental observations in the X-ray photoemissionspectra; an Al(2p) line broadening and the dependence of a peak energy shift on the crystallographicorientation and an overgrown-layer thickness. Fig. 70 reports schematically the band diagrams for theAlAs–GaAs heterojunction without Si interlayer (part a) and with the Si interlayer according to the twocompeting models of Sorba et al. [890] (part b) and Akazawa et al. [900] and Hashimoto et al. [901](part c).

The reported experimental data have stimulated further improvements of the theoretical models.Results from linear-response theory indicated that band offset modification is not possible at non-polarinterfaces [902]. The first-principles calculations of Christensen and Brey confirmed that at AlAs–GaAs(1 1 0) interfaces, the insertion of interlayers has little or no effect on the band offsets [903]. Incontrast, the calculations of Munoz and Rodrıguez-Hernandez predicted a significant tuning effect forinsertion of Si or Ge at AlAs–GaAs(1 1 0) interfaces [904].

This debated argument has been more recently extensively faced in deep detail by Moreno et al.[381,865,866,905]. In Ref. [381], the authors investigated the effect of inserting thin Si intralayers atGaAs/AlAs and GaAs/GaAs interfaces using synchrotron radiation PES. Results from polar and non-polar interfaces are compared by analyzing samples grown by MBE on (1 0 0) and (1 1 0) substrates,respectively. The Si intralayers were inserted by an improved d-doping method in a concentration of2:2 � 1014 atoms/cm2 (corresponding to about 1/3 ML of a (1 0 0) or to about 1/4 ML of a (1 1 0)).When Si is introduced at GaAs-on-AlAs interfaces, the Al(2p)-to-Ga(3d) energy distance is observed toincrease for both polar and non-polar interface orientations (vide supra Fig. 68). The insertion of Si atGaAs/GaAs(1 1 0) homojunctions modifies the line shape of the Ga(3d) and As(3d) peaks, resemblingthe changes previously reported for the (1 0 0) orientation. The results on polar junctions previouslyobtained were generally interpreted as band-offset changes [309,890,895–897], which would be relatedaccording to the ‘‘interface microscopic capacitor’’ picture with the polar nature of the interface. Authorsof Ref. [381] concluded that the reported PES results disagree with such a model because of the similarbehavior shown by polar and non-polar interfaces and that they can be understood within the ‘‘overlayerband bending’’ interpretation already proposed by Akazawa et al. [900] and by Hashimoto et al. [901].

Fig. 70. Schematic representation of band diagrams on GaAs/AlAs heterojunctions: (a) without Si intralayer; (b) with Si

intralayer, according to the ‘‘interface band offset change’’ [890]; (c) with Si intralayer, according to the ‘‘overlayer band-

bending change’’ [900,901]. Reproduced from M. Moreno, et al., Phys. Rev. B 57 (1998) 12314, [865], with permission.

Copyright (1998) by American Physical Society.


Few months later, the same group completed the previous work by comparing Si and Be insertions atGaAs-on-AlAs(1 0 0) interfaces, again investigated by synchrotron radiation XPS. The Ga(3d)-to-Al(2p) core-level energy separation is found to increase upon Si insertion, and to decrease upon Beinsertion, see parts (a) and (b) of Fig. 71, respectively. The surface Fermi level moves closer to thevalence-band maximum in Si-containing samples, while it moves away in Be-containing ones. Theseresults are consistent with the n-type and p-type doping behaviors typically exhibited by Si and Beimpurities in GaAs(1 0 0). Authors again reach the conclusion that the observed core-level offsetvariations support an interpretation based on band-bending arguments, rather than on the commonlyinvoked band-offset changes. A simple ‘‘overlayer-capacitor’’ model is proposed to illustrate thephysical origin of such band-bending effects. Two years later, Moreno et al. [381,905] improved theexperiment by reporting low-temperature XPS spectra.

On the other hand, other papers appeared supporting the interface band offset change model(Fig. 70b) [892,906,907]. Vanzetti et al. [906] investigated the effect of Ge insertion in the ZnSe–GaAs(1 1 0) heterojunctions (in situ prepared by MBE) using synchrotron radiation XPS with photonsat 80–130 eV. The effect of ultra-thin Ge interface layers on the band offsets was examined bymonitoring the energy separation of the Ga(2p) and Zn(2p) core levels at the interface. The resultsindicate that the natural (unmodified) valence-band offset for ZnSe–GaAs(1 1 0) grown at lowtemperature is DEv ¼ 1:10 � 0:05 eV, and that the deposition of a Ge overlayer on GaAs prior to ZnSe

Fig. 71. Al(2p), Ga(3d) and valence-band edge EDC spectra, obtained using 95 eV photons, from GaAs-on-AlAs(1 0 0)

heterojunctions without (solid circles) and with (open circles) an intralayer. The effects of Si (a) and Be (b) insertions are

compared. The nominal concentration of the intralayer is 2:23 � 1014 atoms/cm2. Every set of spectra from every sample has

been rigidly shifted in energy to align the extreme edges of the respective valence-band spectra. The core-level spectra are

shown after peak-area normalization. Reproduced from M. Moreno, et al., Phys. Rev. B 58 (1998) 13767, [866], with

permission. Copyright (1998) by American Physical Society.


growth yields a decrease in the ZnSe–GaAs valence-band offset. The offset decreases monotonicallywith Ge coverage in the 0.3–4 ML range and saturates for Ge thickness of 4–6 ML. The minimummeasured valence-band offset that the authors were able to achieve at the engineered interface isDEv ¼ 0:93 � 0:07 eV. Wilks et al. [907] showed, by synchrotron radiation XPS, that the insertion of1 ML interfacial Si and Be dipoles layers at the GaAs–AlGaAs heterojunction modifies the valence-band discontinuity by þ0.4 eV for Si and by �0.52 eV for Be. It is rather evident that the controversybetween models schematized in parts (b) and (c) of Fig. 70 is still under debate.

Worz et al. [908] have investigated the valence-band offset for several Zn based II–VI semiconductorheterostructures by synchrotron radiation UPS. Valence-band offsets have been determined to be:DEv ¼ 0:85 � 0:05 eV for CuInTe2/CuInSe2; DEv ¼ 0:87 � 0:05 eV for CuInS2/CuInSe2; andDEv ¼ 2:3 � 0:1 eV for ZnS/CuInS2. Synchrotron radiation XPS was used by Nelson [909] toinvestigate the development of the electronic structure at the CdS/Cu2�xSe and CdS/In6Se7

heterojunction interfaces grown on GaAs(1 0 0). CdS overlayers were then deposited in situ, at roomtemperature, in steps on these layers. PES measurements were acquired after each growth to observechanges in the valence-band electronic structure and changes in the In(4d) and Cd(4d) core lines. Theresults were used to correlate the interfacial chemistry with the electronic structure and to directlydetermine the CdS/Cu2�xSe and CdS/In6Se7 heterojunction valence-band discontinuities and theconsequent heterojunction band diagrams.

Synchrotron radiation PES has been used by Yuan et al. [910] to investigate GaP(1 0 0) andInP(1 0 0) surfaces treated with a neutralized (NH4)2S solution (pH 7). Compared to the conventionalbasic (NH4)2S solution treatments (pH @ 7), a thick sulfide layer with P–S bond and strong Ga–S (In–S) bond of high thermal stability is formed on the neutralized (NH4)2S-treated GaP (InP) (1 0 0)surfaces. The possible passivation mechanisms of the two (NH4)2S solutions to III–V phosphidesurfaces are also discussed by the authors [910].

By using high-resolution XPS, Hricovini et al. [911] have investigated the electronic-structure and itsdependence on local order for H/Si(1 1 1)ð1 � 1Þ surfaces. Authors found that the valence and core-level spectra of chemically prepared, ideally H-terminated Si(1 1 1) surfaces are characterized byremarkably sharp features. From the Si(2p) spectra, an upper limit of 35 � 10 meV is derived for thecore hole lifetime broadening. Two years later a more extended and complete work on this topic,reporting also parallel IR and ab initio data, appears by the same group [912].

De Padova et al. [913] investigated the effect of Sb-dimer-induced Si(0 0 1) relaxation on the Si(2p)core level by high-resolution PES. Two surface components were identified in the Si(2p) core-levelmeasured on the Sb/Si(0 0 1)ð2 � 1Þ surface at 1 ML Sb coverage. By using the Sb–Ge site exchangeprocess, a Ge layer was inserted between the Sb dimers and the Si substrate to separate the Si(2p)contribution arising from different atomic layers.

Another interesting application of synchrotron radiation in the near UV region is the spectroscopicellipsometry. As an example, Wethkamp et al. [914] investigated thin epitaxial AlN films with thistechnique.

9.2. Space resolved PES experiments

This section is primarily dedicated to one of the most important new avenues in semiconductorinterface research: the investigation of the lateral variations of interface properties. Until recently, thisproblem was almost ignored, largely because of the lack of experimental results. Even now, the lateral


fluctuations of the interface barriers are not even mentioned in the standard textbooks onmicroelectronic devices and are ignored by most theoretical models of semiconductor interfaces [311].

Space averaging has been for several years one of the major limitations of the experimental studies ofsemiconductor interfaces. The transport techniques and the PES experiments were oblivious tomicroscopic scale properties and were averaged over large portions of the interface. In the case ofphotoemission-based techniques, this limitation was overcome with the recent development ofsynchrotron radiation PES combining high-energy and high lateral resolutions [311,321,369,915–920].In parallel, techniques like ballistic electron emission microscopy (BEEM) also broke the lateral-resolution barrier, providing, for the first time, a picture of the interface properties on a microscopicscale [313,921,922].

There exist [311,312,321,915] two ways to obtain lateral resolution in a photoemission experiment:either by focusing the photon beam which stimulates the emission of photoelectrons or by processingthe photoemitted electrons with an electron optics system similar to an electron microscope. The formeris the most appropriate approach for studying semiconductor interfaces [311,312,916,917]. In fact, thelatter, requiring the use of an electron optics system, can interfere with the PES energy analysis whichis essential for measuring semiconductor interface barriers and their fluctuations [311,312,369,915–917,919,920,923]. On the other hand, the recent addition of electron energy resolution to instrumentsbased on the latter approach may change this conclusion in the future [311]. In the top part of Fig. 72 aschematic diagram of a focusing-scanning spectromicroscope is reported. The photon beam is focusedon the sample (which is mounted on an x–y translation system) by either a multilayer-coatedSchwarzschild objective or a Fresnel zone plate [311,915]. The electron energy analyzer measures thephotoelectron spectra corresponding to the small sample surface area which is illuminated by thefocused X-ray beam. The standard procedure in experiments of this kind [311,915] requires first tocollect maps of PES intensity. To do this, the electron analyzer is set at a fixed energy, corresponding tothe photoelectrons excited from one of the electronic states of the sample, in most cases, a given corelevel of one of its elements. The sample is then scanned in the x–y plane with respect to the photonfocusing spot. The photoelectron intensity plot during the scanning produces an image which reveals, inparticular, the lateral distribution of the photoemitting element [311].

Scanning photoelectron microimages taken for different elements are used to identify the mostinteresting parts of the surface; subsequently, one takes small-spot photoelectron spectra on these areas.As the photoelectron energies reflect the initial state energies on the surface (rather than in the bulk)that are affected by the band bending and for a semiconductor. A scanning photoelectron microimage,therefore, can contain lateral fluctuations not only in the chemical composition but also in the bandbending. In turn, such bandbending fluctuations can reflect lateral variations of the interface barriers[924]. Fig. 72 (bottom parts) shows one of the pioneering examples of photoelectron spectromicroscopyapplied to semiconductor surfaces, where the authors investigated the lateral fluctuations of the bandbending of a cleaved GaAs(1 1 0) substrate [924]. The microimages reported in the left-hand side ofFig. 72 (bottom) show evident lateral intensity variations. In principle, such variations could be due tofluctuations in the local chemical composition (for example, to microprecipitates of a given element) orto variations in the band bending. Margaritondo’s work showed us that we can distinguish betweenthese two factors by collecting PES spectra in microscopic spots on different sample surface areas[311]: right parts of Fig. 72 (bottom). Reported PES spectra reveal clear shifts in energy from place toplace, of equal value for both the Ga(3d) and As(3d) core-level peaks. The message is clear: theelectronic structure shifts rigidly from point to point, and this reflects fluctuations in the band bending.


Fig. 72. Top: schematic diagram illustrating the operation of a focusing-scanning spectromicroscope. Bottom: A scanning-

focusing photoelectron spectromicroscopy study of a clean, freshly cleaved GaAs(1 1 0) surface. Bottom left: photoelectron

intensity micrographs (80 mm � 80mm) taken at three different photoelectron energies (70.3, 70.8 and 71.3 eV), in the spectral

region of the Ga(3d) level (photon energy: 95 eV). Right: Ga(3d) and As(3d) microspot-spectra taken in regions A and B of

the micrographs. The rigid shift of the core level peaks reveals that the micrographs’ intensity fluctuations are primarily due to

band-bending changes from place to place. Adapted from G. Margaritondo, Rep. Prog. Phys. 62 (1999) 765, [311], with

permission. Copyright (1999) by Institute of Physics. Adapted from G. Margaritondo, F. Cerrina, Nucl. Instrum. Methods A

291 (1990) 26, [915], with permission. Copyright (1999) by Elsevier. Adapted from F. Cerrina, et al., Appl. Phys. Lett. 63



A clear warning comes therefore out from Margaritondo’s work: even for a clean cleaved surface, thesurface energy barrier corresponding to the band bending cannot be assumed to be constant from pointto point!

Once it has been established by PES that band-bending changes on a microscopic scale [924], seeFig. 72, a key question needed an answer: do similar fluctuations occur for interface barriers like theSchottky barriers and the heterojunction band discontinuities? The answer was provided by theexperiment of Gozzo et al. [916] for ML-thick Au film deposited on GaSe semiconductor substrate. ThePES microscopy data revealed lateral inhomogeneities of the local overlayer thickness and of the localmetal–semiconductor barrier height. Moreover, authors found that the interface formation processinvolves strong substrate–overlayer interactions, the release of free Ga, and the formation of interfacespecies, and leads to a barrier height in disagreement with the Schottky model. As a consequence, thisPES–spectromicroscopy study requires a revision of established ideas about this interface Au/GaSe,which has long been considered a prototype of Schottky-like systems. Two years later, the same groupextended the study of lateral barrier fluctuations to semiconductor–semiconductor interfaces andconsequently to their band discontinuities [917]. Authors investigated the GaSe/Ge interface, seeFig. 73. Data from the substrate core levels reveal coordinated shifts in energy from point to point,corresponding to fluctuations in the substrate band bending. In contrast, the Ge(3d) peak does not

Fig. 73. A scanning-focusing photoelectron spectromicroscopy study of a cleaved GaSe surface covered by a thin Ge

overlayer. Top left: PES intensity micrographs (50 mm � 50 mm) taken at a photon energy of 95 eV, in the spectral range of the

Ge(3d) states. Top right, bottom left and right: Ga(3d), Ge(3d) and Se(3d) microspot-spectra taken in regions A and B of the

micrograph. There is a rigid shift of the Ga(3d) and Se(3d) core level peaks, and no shift for the Ge(3d) peak. This reveals a

change in the band lineup from point A to point B, and therefore a change in the band discontinuities. Adapted from

G. Margaritondo, Rep. Prog. Phys. 62 (1999) 765, [311], with permission. Copyright (1999) by Institute of Physics. Adapted

from F. Gozzo, et al., Phys. Rev. B 51 (1995) 5024, [917], with permission. Copyright (1995) by American Physical Society.


follow the same shifts. Therefore, the relative position of the electronic structure of the overlayer withrespect to the band-bending changes from point to point. This implies fluctuations in the band lineupand in the corresponding valence and conduction band discontinuities. Similar results were obtained byAlmeida et al. [925,926] reporting a study of the lateral band bending at the GaSe/Ge interface.Spectromicroscopy measurements singled out the following effects: (i) lateral band bending; (ii)chemical reactions; (iii) beam stimulated Ge surface migration. These studies allowed the author toseek on the microscopical equivalent of the semiconductor Debye length and to probe the capabilitiesof scanning-focused spectromicroscopical systems [925]. This finding is in sharp contrast with thenotion that this interface is an ideal Schottky system, whose band discontinuities, for example, aredetermined by the Anderson rule and with the widespread belief that most III–VI-based interfacesbehave like Schottky systems [926]. Results such as those reported by Gozzo et al. [916,917] orAlmeida et al. [925,926] deal a rediscussion of the model describing semiconductor interface barriers asglobal properties of the interfaces, with no changes from place to place fluctuations [311]. In contrast,barrier fluctuations not only occur but are quite common, as shown in the reported examples. Thisallowed Margaritondo to conclude that a re-thinking of device modeling and of the notion ofsemiconductor energy barriers was necessary [311].

Successive works have confirmed the observation of semiconductor interface barrier fluctuations[873,927,928] not only with spectromicroscopic techniques based on photoemission and internalphotoemission, but also with other approaches. Among them the near-field optical microscopy work,again from Almeida et al. [927], is worth noticing. Authors investigated the Au/SiNx/GaAs Schottkybarrier. Photocurrent yield microimages taken at different photon energies reveal non-topographicfeatures. Taking into account their dependence on photon energy and bias, such features are consistentwith lateral variations of the local density of states related to defects. The results, therefore, confirm thatlateral variations must be considered when analyzing semiconductor interfaces and of thecorresponding devices [927]. PES spectromicroscopy data on Si/GaSe with 0.2 mm lateral resolutionrevealed laterally inhomogeneous interface Se–Si chemical reactions, as found by Zacchigna et al.[928]. The local Si(2p) fits agrees with interface Si selenide parameters; the Se(3d) peaks indicate a Si–selenide component; the Ga(3d) peaks exhibit a metallic component whose intensity increases with Sicoverage. Authors concluded that this local interface reaction is related to lateral changes in the bandlineup [928].

Also highly informative is the BEEM technique that has been applied by Fowell et al. [929] to probethe conduction band discontinuity, DEc, and its lateral variation at the heterojunction between relaxedInAs and GaAs. By combining BEEM threshold measurements with appropriate modeling of theinterface a value of 0.72 eV is obtained for DEc. The lateral variation of the BEEM current partlyreflects the topography of the overlayer in this domain we note, for example, the results on theconduction band discontinuity of InAs/GaAs. In 1996 the same group found that the InAs/GaAs(1 0 0)barrier height decreases with the InAs thickness and that the detailed variation is in accordance with thetransition/relaxation of the InAs layer [930]. Also, the transport properties at the interface have beenstudied, and the L valley transmission is not observed due to the requirement of lateral momentumconservation.

The characterization of real semiconductor interface with different techniques such as 4 K PL, TEM,Raman and optical second-harmonic generation and sum-frequency generation, has been discussed inSection 3. From the results summarized therein, combined with the here discussed PES microscopydata, it emerges clearly that real semiconductor interfaces behaves differently with respect to ideal


bidimensional uniform systems ant that such dishomogeneities have to be taken into account when thecharacteristics of a device are modeled.

9.3. Internal photoemission spectroscopy: examples using free electron laser sources

The main limitations of PES spectromicroscopy, in dealing with the problem of interface barrierfluctuations, are: (i) its limited accuracy in measuring such barriers (typically 50–100 meV[310,311,377]) and (ii) its inapplicability to buried interfaces, owing to the surface character of PES.Smaller-scale fluctuations can be detected, since the accuracy in measuring relative changes is typicallybetter than the absolute accuracy. Even then, an accuracy better than 30–50 meV does not appearfeasible. This is unfortunate, since even a barrier change of a few meV can strongly influence thebehavior of an interface and of the corresponding devices. On the other hand, new techniques, based onthe free electron laser (FEL) sources, are capable of providing better accuracy. In fact, FEL sources arebecoming an important tool for producing high-intensity photon beams, especially in the IR region ofthe electromagnetic spectrum. Synchrotron radiation’s primary spectral domains are in the ultravioletand X-ray region. FELs are therefore excellent complimentary facilities to synchrotron radiationsources [310,311,321,365–367,369,370].

Fig. 74a explains the philosophy of one of these new FEL-based techniques, which was baptized byMargaritondo’s group as FELIPE (free electron laser internal photoemission) [931]. The technique isbased on photocurrent measurements. The photocurrent thresholds correspond to different interfacebarriers and, in particular, to the heterojunction conduction band discontinuity. Note that to measure theconduction band discontinuity one must use a suitable IR photon source, with wide enough tunability inthe photon energy range of interest. This is why the technique is implemented with a widely tunableFEL. FELIPE experiments constituted one of the very first materials science research applications ofthe FELs. The technique is quite straightforward and yields discontinuity measurements with very good

Fig. 74. (a) A schematic explanation of the ‘FELIPE’ technique. An IR photon emitted by a tunable FEL excites an electron

over the barrier corresponding to a heterojunction conduction band discontinuity. The electron then contributes to the

photocurrent measured by the picoammeter (pA). A threshold in the photocurrent, as a function of the photon energy, reveals

the value of the discontinuity (see curves reported in (b)). (b) A laterally resolved version of the FELIPE technique. The figure

shows two photocurrent spectra obtained on two different microspots, A and B, of a Pt-covered GaP substrate. The change in

threshold reveals a small but clearly detectable change in the Schottky barriers height between the two sites. Adapted from G.

Margaritondo, Rep. Prog. Phys. 62 (1999) 765, [311], with permission. Copyright (1999) by Institute of Physics. Adapted from

J. Almeida, et al., Appl. Phys. Lett. 69 (1996) 2361, [919], with permission. Copyright (1996) by American Institute of Physics

Society.


accuracy of the order of a few meV. Moreover, the FELIPE approach can be applied to buried interfacesalso, making possible the band offset measurement directly on devices. The same approach wasimplemented [919] in a laterally resolved version to analyze lateral barrier fluctuations. The lateralresolution was achieved using a small-tip optics fiber. Fig. 74b shows [919] one particularly significantresult. The shifts from point to point in the photocurrent threshold reveal very small changes in thecorresponding Schottky barrier height. The accuracy in measuring such barrier fluctuations can reach1 meV or better, thus better matching the needs [311].

Almeida et al. [932] measured by internal photoemission the conduction band discontinuity DEc in p-In0.53Ga0.47As/n-InP heterojunctions with a Si d-layer (1 � 1012 cm�2) inserted in InP at 10 A from theinterface. The n-type Si d-doping induced an inhomogeneous and temperature-dependent DEc reductionas revealed by two onsets in the spectral response. The first one was absent in room temperature dataand was due to the Si intralayer presence. The second correlated with the DEc value for heterojunctionswithout d-doping and its presence served as an indication of the inhomogeneity of the Si d-layer. Themeasured value of the modification was 0:11 � 0:04 eV in good agreement with the calculated one.Current–voltage measurements confirmed that the Si d-layer modified the transport parameters of theheterojunction only at low temperature [932]. Two years later, the same group reported a modificationby thin silicon nitride intralayers of the Au/n-GaAs(1 0 0) Schottky barrier height [933]. Thinintralayers were obtained by nitridation of evaporated Si films on decapped GaAs substrates in an Ar–Nmixture plasma. Gold was deposited to study in situ the Schottky barrier formation process with XPS.Internal photoemission spectroscopy and current–voltage measurements were used to evaluate thebarrier modification on fully formed interfaces. Such a modification was analyzed in terms oftheoretical calculations of the dipole created by the substrate–intralayer bonds [933]. The two-photonabsorption in germanium has been reported in Ref. [370].

9.4. Photoemission extended X-ray absorption fine structure (PEXAFS)

Together with SEXAFS, discussed in Section 4.8, there is another way to make EXAFS spectroscopysurface sensitive. This is photoemission extended X-ray absorption fine structure PEXAFS, which is avariation of electron detection EXAFS using photoemission spectroscopy in the constant initial statemode. Due to the much shorter escape depths of electrons (few A), with respect to X-rays, a muchhigher sensitivity to the uppermost fraction of a sample is obtained when the electron yield detectionmode is adopted in the acquisition of EXAFS spectra. Being both primary electrons (the XPS one’s)and secondary electrons (the Auger one’s) proportional to the photon absorption (i.e. the physicalquantity directly measured in transmission mode) the electron current measured on the sample as afunction of the energy of the synchrotron beam is an EXAFS-like signal. For high Z elements, such asGe, Ga, As, In, etc., this technique is however penalized with respect to the fluorescence mode by thelow yield of Auger electron with respect to the yield of the complementary fluorescence disexcitationphenomenon: in such cases an higher counting time is needed. Other major advantages of PEXAFStechnique include [934]: (i) an improved signal/noise ratio allowing very short data collection times,which is an especially useful feature for short lifetime surfaces, and (ii) double-checking interatomicdistances. Combined with core-level and valence-band photoemission spectroscopies, PEXAFSprovides the exceptional ability to probe the atomic geometry and the electronic structure at the sametime and for the same surface. It thus gives access to important issues, such as: (i) surfacereconstruction and/or relaxation, (ii) bonding nature, (iii) adsorption site and (iv) initial interface


formation. Furthermore, it could be used to clarify photoemission core-level shift origin by allowingone to discriminate structural changes from other causes as initial or final state effects [934]. The firstexample of photoemission extended X-ray absorption fine structure was reported by Rothberg et al.[935] in 1984 and several others followed. Few selected examples on the application of PEXAFS to thestudies of semiconductors surfaces and interfaces follow.

The first example concerns the study of the surface reconstruction of InP(1 1 0) by Mangat et al.[936]. The authors investigated an in situ cleaved InP(1 1 0) surface by means of photoemissionextended X-ray absorption fine structure performed collecting the P(2p) photoemission. For the cleanInP(1 1 0) surface, the average first P–In bond length is 2:44 � 0:04 A, which corresponds to acontraction by approximately 4% in comparison to the bulk P–In interatomic distance of 2.54 A. Thesecond shell (P–P) distance is reduced by 0.1 A as compared to its bulk distance of 4.15 A, while thethird shell (P–In) distance obtained is close to its bulk value. The results, reported by Mangat et al. arein very good agreement with previous theoretical ab initio total-energy pseudopotential calculations[937] and LEED experiments [938]. The same group has investigated the structure of the clean and Na-covered Si(1 0 0)ð2 � 1Þ surface by a combination of the polarization-dependent PEXAFS and ab initiototal-energy molecular method using force calculations [939] (DMOL). Both Na(2p) and Si(2p) core-level lines were detected. The experimental Na–Si and Si–Si bond lengths are found to be in excellentagreement with the distances obtained by ab initio total-energy DMOL calculations. Authors also probethe fine structural changes of the Si(1 0 0)ð2 � 1Þ surface upon Na deposition including the Si–Si dimerrelaxation.

Choudhary et al. [940] studied the Bi/InP(1 1 0) interface for 0.35 and 0.9 ML Bi coverages by P(2p)PEXAFS. For 0.9 ML Bi/InP(1 1 0), Bi grows epitaxially and the P–Bi bond length is 2:42 � 0:05 A.The first P–In nearest-neighbor distance is determined as 2:46 � 0:05 A, which is almost equal to theP–In bond length for the clean InP(1 1 0) surface and the bond length is 3% contracted in comparison toits value for bulk InP. This is an effect of surface relaxation pushing out of the band gap the surfacestates for the clean InP(1 1 0) surface. Hence, the interface states due to the atomic geometries of thesubstrate at the interface may not influence Schottky barrier formation to cause Fermi-level pinning.The P–P and P–Bi bond lengths in the second near-neighbor distance were determined as 4:17 � 0:06and 4:26 � 0:06 A, respectively [940].

Other examples of PEXAFS investigations for model elemental (Si) and compound (InP)semiconductor surfaces and their interfaces with alkali metals can be found in the review of Mangatand Soukiassian [934].

Notes added in Proof

The present section is devoted to briefly discuss the most recent works, appeared between thesubmission of the review (end of 2003) and the proofs editing (February 2004). Also, some less recent(but relevant) works, that have been overlooked by me in the first draft are here mentioned. In thisregard, I am deeply indebted to Till Metzger and Joseph Woicik who have kindly provided me a list ofoverlooked publications.

EXAFS and SEXAFS experimentsGa–K edge EXAFS has been used by Miyano et al. [943] to study the local structure of AlxGal�xN

films grown by MOCVD. Authors found that, with increasing Al content, x, the Ga–N bond length


decreases, but much less than the average bond length. On the other hand, the x dependence of the Ga–Ga and Ga–Al distances does follow the variation of the average cation–cation distance. In agreementwith most of the studies discussed in Sections 4.4–4.8 they conclude that bond angle distortionsaccommodate the differences between the Ga–N and Al–N bond lengths.

Polarization dependent EXAFS technique has been employed by Nelson et al. [944] to investigate thelocal structure around Gd in a 23 A-thick Gd2O3 film epitaxially grown on GaAs(0 0 1). The Gd–Obond length was determined to be 2:390 � 0:013 A, which corresponds to a þ0:063 � 0:013 A increaseor a (þ2:7 � 0:6)% bond-length strain relative to the bulk Gd2O3 powder. Using a simple model for thestrained film that matches the [0 0 1] and [�1 1 0] axes of Gd2O3 with the [1 1 0] and [1 �1 0] axes of theGaAs(0 0 1) surface, the measured bond-length increase of the film determined by EXAFS agrees wellwith the perpendicular lattice distortion of the film determined by diffraction.

SEXAFS has been used by Hricovini et al. [945] to investigate the Mn/InAs(0 0 1) system andcombined with X-ray magnetic circular dichroism measurements to couple magnetic and structuralinformations.

Surface diffraction experimentsDerivaz et al. [946] reported that Ge dots can be directly grown by MBE on a Si(0 0 1) surface

covered by a very thin (15 A thick) silicon nitride layer. Authors described the experimental procedure,which induces the growth of nanometric size, isolated germanium dots. The germanium dots are inepitaxy with the silicon substrate. Using grazing incidence X-ray diffraction Derivaz et al.demonstrated that, for very small dots, the in-plane lattice parameter inside the dots is very close tothe silicon lattice parameter. Conversely a strong lattice relaxation and/or silicon inter-diffusion takeplace with increasing dot size. Schulli et al. [947] performed anomalous X-ray scattering experimentsto obtain quantitative measurements of the Ge composition profile in islands on Si(0 0 1). Comparingthe intensity ratios for X-ray energies below and close to the Ge K-edge, at various Bragg reflections, inthe grazing incidence diffraction setup (see Fig. 51b), the sensitivity for the Ge profile is considerablyenhanced. The method is demonstrated for SiGe dome-shaped islands grown on Si(0 0 1). Authorsfound that the composition inside the island changes rather abruptly, whereas the lattice parameterrelaxes continuously.Three-dimensional composition maps of nominally pure Ge domes grown onSi(0 0 1) at 600 8C have been obtained by Malachias et al. [948] from grazing incidence anomalousX-ray scattering data at the Ge K-edge. The data were analyzed in terms of a stack of layers withlaterally varying concentration. The results demonstrated that the domes contained a Si-rich corecovered by a Ge-rich shell and were independently supported by selective etch experiments. Thecomposition profile resulted from substrate Si alloying into the Ge during growth to partially relax thestress in and under the domes [948].

A GaAs surface layer of 100 A thickness was grown on the cleaved edge of an In0.1Al0.9As/Al0.33Ga0.67As multilayer by Sztucki et al. [949] in order to induce a lateral periodic strain modulation.Authors applied surface sensitive grazing incidence X-ray diffraction to distinguish betweencompositional/morphological and purely strain induced modulations. The experimentally determinedstrain profile was confirmed by finite-element model calculations. The GaAs layer was found to bepurely strain modulated with an average lattice parameter change of (0:8 � 0:1)% with respect torelaxed GaAs.

Chamard et al. [950] have quantified as a function of the spacer layer thickness and the number ofbi-layers, the layer-to-layer vertical alignment of GaN quantum dots in AlN multilayers using grazing


incidence X-ray scattering. Although the density of dots is comparable to the density of (0 0 0 1)threading dislocations, authors observed that the strong vertical ordering is strain induced by the burieddots. Elasticity theory calculations confirm this experimental result and explain the observation of theexceptionally strong vertical alignment in nitride compared to other classical systems. This studycomplements Ref. [793] deeply discussed in Section 5.5 (see also Figs. 51 and 52).

DAFS experimentsRenevier et al. [951] describe the state-of-the-art energy scan diffraction set-up available at the

D2AM beamline of the ESRF for DAFS experiments.

XSW experiments

The surface relaxation of clean CdTe(1 1 0) surface has been investigated by Kendelewicz et al. [952]using XSW. Authors compare their experimental results with theoretical, first principles, calculationsand with previous LEED data. Woicik et al. [953], combining back reflection XSW and SEXAFS havedetermined the atomic coordinates at the In/Si(1 1 1)-H3 � H3 interface. Although the In adatoms arefound to reside at a single position, 2:10 � 0:06 A above the first Si bilayer, dual In–Si near-neighbordistances are found: 2:73 � 0:02 A to the first- and 2:49 � 0:03 A to the second-layer Si atoms,respectively.

Order to disorder phase transitions have been investigated, measuring (1 1 1) and (1 1 �1) XSW signalfrom the Pb on Ge(1 1 1) system by Franklin et al. [954]. The same group, also investigated by XSWthe Bi-dimer orientation, location, and bond length for the Si(0 0 1)–(1 � 2):Bi surface [955]. Theresults for Bi directly scale with the covalent radii and with adsorption characteristics of other group-Velements (As and Sb) on Si(0 0 1). Note that each of them (Bi, As and Sb) adsorb in dimer form andwith a dimer bond direction perpendicular to the Si-dimer bond on the clean Si(0 0 1)–(2 � 1) surface[686–688]. Theoretical, first-principles local-density molecular-cluster calculations support theexperimental data.

Herrera-Gomez et al. [956] used XSW to characterize ion implanted As in silicon. The interest of thisstudy is related to the fact that arsenic impurities in silicon can be electrically activated beyond theirelectrical solubility to as high as 4 � 1021/cm3 by ion implantation and laser melting; further annealingdecreases this activity to its equilibrium saturation level. Authors combine XSW investigation with Halleffect and secondary-ion-mass spectroscopy measurements, concluding that the As impurities remain insubstitutional positions even after 85% of the activation has been lost, so deactivation cannot be due toAs migration to interstitial sites or to large precipitates.

Drakopoulos et al. [957] present an advanced microprobe technique based on the XSW methoddemonstrating that structural analysis can be achieved with chemical sensitivity on a microscopic scale.Authors applied the XSW microscopy technique to study the crystallographic polarity from inversiondomains in GaN-based lateral polarity heterostructures. This new micro-XSW technique is extremelypromising as it should permit microscopic examinations of the crystalline structure of modernsemiconductor devices with chemical sensitivity and high structural resolution.

X-ray photoemission experimentsXPS has been used by Liu et al. [958–960] to systematically study the core and valence band

electronic structure of various chemical treatments (H2SO2/H2O2/H2O followed by thermal heating) ofInP(1 0 0), GaAs(1 0 0), and GaN(0 0 0 1).


Angle-resolved XPS measurements have been performed by De Padova et al. [961,962] onInAs(0 0 1)4 � 2–c(8 � 2) clean surfaces in order to investigate two new electronic surface statesrelated to the In-terminated InAs(0 0 1)4 � 2–c(8 � 2) clean surface. The experiments were carried outat normal emission as a function of photon energy using s- and p-polarized light. Authors found thatthe surface states are strongly resonant at photon energies of 31 and 61 eV, which correspond totransitions from bulk electronic states localized at high symmetry points X6, X7 and G7, G6 of thecalculated InAs band structure. The intensities of the two surface states decrease when passing froms- to p-polarization of the radiation: such behavior directly establishes the orientation of the surfacestate bonds [961].

Yu et al. [963] have studied the symmetry properties of the bands of the layered semiconductor GaSealong the D direction by means of spin-resolved electron spectroscopy using circularly polarizedsynchrotron radiation. Spin resolved spectra measured at Auger electrons following the decay ofGa(3d) core holes confirm that p derived unoccupied states exist below the vacuum level.

The initial oxidation of the 6H–SiC(1 1 �2 0) surface was studied by synchrotron-radiation XPScombined with high-resolution medium energy ion scattering by Hoshino et al. [964,965]. The samegroup also investigated, with the same techniques, the 6H–SiC(0 0 0 l)-H3 � H3 surface, on top ofwhich 0.2–5 nickel ML (1 ML: 1.21 � 1015 atoms/cm2) have been deposited [966].

Finally, the combined XSW and XPS approach, proposed by the Woicik’s group [841], and reviewedat the end of Section 7.2, has been further developed in Refs. [967,968] and applied to crystalline Geand GaAs. By monitoring valence-photoelectron emission under condition of strong X-ray Braggreflection, authors have determined that a majority of GaAs valence charge resides on the anion sites ofthis heteropolar crystal [967], in quantitative agreement with the GaAs bond polarity as calculated fromthe Hartree-Fock term values. In contrast, the valence-charge distribution in Ge is found to besymmetric. In both cases, the valence emission is found to be closely coupled to the atomic cores. Theauthors monitored the angle-resolved XPS yield as a function of photon energy near the Ge(1 1 �1)Bragg back-reflection condition of and measured the contribution of quadruple effects to Ge(3p),Ge(3d), and Ge valence-band (4s and 4p) XSW photoelectron emission [968]. Significant changes dueto nondipole emission are measured in both the apparent amplitude and phase of the Ge structure factorrelative to the true Ge atomic distribution, and compared to theory [968].

Acknowledgements

Particular thanks are due to F. Boscherini and S. Pascarelli, who have shared with me numerousnights on different beamlines and who have strongly contributed to most of the ‘‘internal’’ resultsreviewed here, obtained on MQW and SL grown in the CSELT laboratories in Torino (now AgilentTechnologies) where the author performed his Ph.D. in solid-state physics [941]. The stimulatingcollaboration with S. Mobilio, F. Romanato, A. Drigo, A. Antolini, G. Gastaldi, C. Papuzza, F. Taiariol,C. Rigo, D. Bertone, F. Genova, G.M. Schiavini, L. Aruta, C. Ferrari, L. Lazzaroni and G. Salviati formore than 10 years has been highly fruitful. Thanks are due to E. Groppo for her critical lecture of themanuscript. I am deeply indebted to all the beamline scientists and technicians for keeping thebeamline under optimal conditions, in particular: the PULS group (ADONE, Frascati, Italy), theGILDA BM8, D2AM, and ID32 groups (ESRF, Grenoble, France). The continuous encouragements ofA. Zecchina, S. Bordiga, G. Spoto, D. Scarano and G. Ricchiardi are acknowledged. Dr. Eleni C.


Paloura is acknowledged for having kindly supplied me the original version of Fig. 38. This work hasbeen partially supported by INFM PRA ISADORA and PURS projects. Finally, I want to thank theorganizers and the Professors of the ‘‘Scuola Nazionale di Luce di Sincrotrone’’ [942], periodicallyheld in S. Margherita di Pula (Ca), since my participation (as a Ph.D. student) in the first issue (1990)has engendered my entry into the synchrotron radiation community.

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