Structure and strain relaxation mechanisms of ultrathin epitaxial Pr[sub 2]O[sub 3] films on Si(111)

JOURNAL OF APPLIED PHYSICS97, 074906s2005d

Structure and strain relaxation mechanisms of ultrathin epitaxial Pr 2O3films on Si „111…

T. Schroeder,a! T.-L. Lee, L. Libralesso, I. Joumard, and J. ZegenhagenE.S.R.F., 6, Rue Jules Horowitz, 38043 Grenoble, France

P. Zaumseil, C. Wenger, G. Lupina, G. Lippert, J. Dabrowski, and H.-J. MüssigIHP, Im Technologiepark 25, D-15236 Frankfurt (Oder), Germany

sReceived 29 November 2004; accepted 7 February 2005; published online 28 March 2005d

The structure of ultrathin epitaxial Pr2O3 films on Sis111d was studied by synchrotronradiation-grazing incidence x-ray diffraction. The oxide film grows as hexagonal Pr2O3 phase withits s0001d plane attached to the Sis111d substrate. The hexagonals0001d Pr2O3 plane matches the

in-plane symmetry of the hexagonal Sis111d surface unit cell by aligning thek101̄0lPr2O3 along the

k112̄l Si directions. The small lattice mismatch of 0.5% results in the growth of pseudomorphicoxide films of high crystalline quality with an average domain size of about 50 nm. The criticalthicknesstc for pseudomorphic growth amounts to 3.0±0.5 nm. The relaxation of the oxide filmfrom pseudomorphism to bulk behavior beyondtc causes the introduction of misfit dislocations, theformation of an in-plane small angle mosaicity structure, and the occurence of a phase transitiontowards as111d oriented cubic Pr2O3 film structure. The observed phase transition highlights theinfluence of the epitaxial interface energy on the stability of Pr2O3 phases on Sis111d. A mechanismis proposed which transforms the hexagonals0001d into the cubics111d Pr2O3 epilayer structure byrearranging the oxygen network but leaving the Pr sublattice almost unmodified. ©2005 AmericanInstitute of Physics. fDOI: 10.1063/1.1883304g

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I. INTRODUCTION

Dielectric layers on siliconsSid play an important role iintegrated circuits of modern microelectronics devices.1 Thegood microprocessing capability, the high dielectric bredown strength, and the quality of the thermally and elecally stable Si–SiO2 interface made SiO2 films the dielectricmaterial of choice over the last 40 years in microelectroindustry.2–4 However, to manufacture new generations oftralarge scale integrationsù107 transistors on a chipd cir-cuits, it is necessary to replace the conventional SiO2 by analternative high-k dielectric material. Further scaling of tvertical SiO2 gate oxide results in unacceptably high leakcurrents of the transistors. Historically, in the 16 Mbitnamic random access memory cells the dielectric waready hardened by using silicon oxide-nitride-oxmultilayer films.5 For future complementary metal–oxidsemiconductorsCMOSd logic circuits the next step on thInternational Technology Roadmap for SemiconductorsITRS2003d is the processing of field effect transistors with a chnel length of 65 nm in about 3 years from now which willthe CMOS devices with a replaced gate dielectric.6 In con-sequence, the need for an alternative gate dielectric ofstatic permittivityk has become urgent and many candidare actively studied.7 Among these, crystalline oxide onsCOSd systems are particularly promising due to the pobility of obtaining a sharp oxide/Si interface with wedefined structural and electronic properties. Moreover,systems have the big advantage to be thermally stable

adAuthor to whom correspondence should be adressed; electronic
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the technologically relevant process temperatures. Basitwo groups of oxide systems with close structural relationthe cubic Si lattice have been identified in the past for Capplications, namely the perovskite related structsSrTiO3, etc.d8–12 and the oxides of thea-Mn2O3 typesY2O3,Pr2O3, etc.d.13–15However, it turned out that bulk latice considerations to identify appropriate high-k epitaxialoxide/Si systems with sharp interface structures may beonly as a rudimentary guide. The assumption of genericbehavior in thin films is naive and many examples havegiven in the literature where thin dielectric layers on Si fato reproduce the expected bulk properties.16–19 For examplethe polycrystalline bulk ceramicsBaxSr1−xdTiO3 termed“BST” can display a relative permittivity of 1000–10 00but the all-important value of thin films structures was foto be substantially lower.20,21 The origins of the high dieletric constant in BST are soft phonon modes related to itstemperature ferroelectric phase. These may damp outthe particular strain conditions of epitaxial growth onStrain in epitaxial systems is even known to influestrongly the stability of bulk phases and alter the phtransitions.22 Therefore, before the dielectric function oCOS system can be calculated in a reliable way to setheoretical marks for optimizing the growth process, iimportant to undertake a fundamental structure charactetion of epitaxial dielectrics.

Research efforts in our group focused in the past ongrowth of single crystalline Pr2O3 films on Si surfaces.23–25

The Pr2O3 layers show interesting dieletric propertieshigh-k applications, as recently reviewed in detail by Os

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© 2005 American Institute of Physics6-1

license or copyright, see http://jap.aip.org/jap/copyright.jsp

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structure data for epitaxial Pr2O3 films on Sis001d over thetechnologically important thickness ranges1–10 nmd.26 Here,a similar study is undertaken for the heteroepitaxial sysPr2O3/Sis111d. The SiO2/Sis111d system is not used nowdays in microelectronics due to the higher interfacialdensity with respect to SiO2/Sis001d.27 However, when thSiO2 gate oxide is replaced by an alternative high-k dielectriclayer, this argument of the bad oxidation propertiesSis111d surfaces does not hold anymore. Different Si surorientation might come into play again depending onspecific interface properties of the studied high-k/Si systemIn the case of Pr2O3 films on Si, the close lattice matchingthe hexagonal Pr2O3 phase with the Sis111d surface makethe Pr2O3/Sis111d system the most promising candidatesolving the difficult task of preparing a high-k/Si systemwith an atomically sharp interface structure.

II. EXPERIMENT

Boron-doped Sis111d substrates were cleaned by a sdard procedure and a HF dip removed the native oxideimmediately before the H-passivated wafers were loadedthe UHV chamber.28 The Pr2O3 layers were grown by molecular beam epitaxy according to a procedure repoelsewhere.29 Before exposing to air, the Pr2O3 films werecovered by an amorphous Si capping layer of several nmeters thickness to protect the oxide layers from moistu30

The Pr-oxide layer thickness was determined byex situx-rayreflectivity sXRRd studies and quantitative fluorescence msurements of the PrL lines.31 Samples of 1.1, 1.6, 4.2, 7and 11.7-nm-thick Pr2O3 films were studiedex situby syn-chrotron radiation-grazing incidence x-ray diffractionsSR-GIXRDd at the insertion device beamline ID 32 of the Eupean Synchrotron Radiation Facility using a beam energ11 keV s0.1127 nmd. For grazing incidence diffraction stuies, a Kappa-Six circle diffractometer was used with thecident angle of the beam on the sample surface fixed toThe Bragg reflections of the oxide and the Si substratealways indexed with respect to the corresponding bulktices but the Si substrate crystal truncation rodssCTRsd aremore conveniently denoted by the Si substrate hexagsurface coordinate system.32 Intensities are given in counper second.

III. RESULTS

A. Structure and epitaxial relationship

The vertical stacking of the Pr2O3 epilayer on theSis111d substrate was determined by detecting all oxideflections situated on thes00Ld CTR. Figure 1 shows thspecularu–2u scans of the 1.6 and 4.2-nm-thick oxide filin the 2u angular range from 5° to 75° as representaexamples. The results of thes00Ld CTR measurements cbe summarized as follows: The Si substrates111d, s222d, ands333d Bragg peaks are very sharp with a full width at hmaximumsFWHMd of 0.002°fe.g., sharp spike structuresthe Sis333d Bragg positiong. The positions of these refletions are marked by dotted lines in the top of Fig. 1 andintensity of the forbiddens222d reflection is of course muc
weaker than the signals of the alloweds111d and s333d dif-

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fraction peaks.33 The presence of the oxide modifies thetensity distribution on thes00Ld CTR of the Sis111d surfaceIn case of the 1.6 nm oxide film, broad shoulders aparound the sharp Sis111d, s222d, ands333d reflections. Thesbroad oxide reflections can be either assigned to thes000l;l =2,4,6d reflections of the hexagonalshexd Pr2O3 phasesspace group:P-3m1d or theshkl; h=k= l =2,4,6d diffractionpeaks of the cubicscubd Pr2O3 phasesspace group:I a-3d.The positions of these hex- and cub-Pr2O3 Bragg peaks arlabeled by dashed and solid lines in Fig. 1, respectivelconsequence, the vertical stacking of the 1.6 nm oxidesand also of the 1.1 nm layerd cannot be unambiguously dtermined from specularu–2u measurements. In contrastthis, the hex-Pr2O3 Bragg peaks are clearly evolved ons00Ld CTR for all films thicker than 1.6 nm. These oxreflections are visible in the scan on the 4.2-nm-thick land can be assigned to thes000n; n=1–6d reflections of thehex-Pr2O3 phase. In addition, the high crystalline qualitythe oxide epilayer results in the presence of well-evothickness fringesDL sindicated by the arrows in Fig.dwhich allow to determine the oxide layer thickness. Hever, these fringes complicate the spectra and make thtection of possible contributions froms111d orientedcub-Pr2O3 crystal grains in the mainly hex-Pr2O3 epilayerstructure more difficult. In consequence, as pointed outit was only with the help of in-plane scans that the presof cub oxide crystal grains was confirmed in the thics.1.6 nmd hex-s0001d Pr2O3 epilayers on Sis111d.

In-plane scanssL=0.1d were applied to determine tazimuthal orientation of the oxide layeron the Sis111d sur-face. The inset in Fig. 2 shows the reciprocal in-plane smap of the hexagonal system. Two high-symmetry in-pdirections can be identified in this system. First, the indic

FIG. 1. Specularu–2u scans of 1.6 and 4.2-nm-thick Pr2O3 epilayers onSis111d. Dotted, dashed, and solid lines indicate the positions of Si subshex-Pr2O3 and cub-Pr2O3 reflections, respectively. Arrows are appliedshow the periodicityDL of the thickness fringes.

Si surface unit cell vectorsf100g sH directiond andf010g sK


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directiond point along bulk Sik112̄l directions and blacpoints denote reflections along these directions. Secofurther high-symmetry direction alongH=K exists whichcorresponds in Si bulk as well as in Si surface coordinat

k11̄0l directions. Gray points denote the diffraction pealong the latter direction. Both high-symmetry directiwere studied in the present case and gray panels underlchosen directions.

The in-plane scans alongH are summarized for all stuied film thicknesses on the left of Fig. 2. The Si surfdiffraction peakss100d ands200d correspond to CTRs but th

origin of the s300d substrate reflection is the bulks224̄dBragg peak. All these substrate peaks are again verysFWHM=0.002°d and appear as intense spikes in the ssbut are missed at some positions due the comparablstep width of the in-plane scansd. In contrast to the substrapeaks, the oxide reflections are much broadersFWHM=1°d and are therefore easily distinguished. It is clearly sthat such broad oxide peaks are superimposed on thestrate reflections for all studied samples. These oxide p

can be assigned to hexagonal Pr2O3 s101̄0d, s202̄0d, and

s303̄0d reflections which overlap with the Si surface pes100d, s200d, ands300d, respectively. However, the growththe thicker oxide layerss4.2, 7.6, and 11.7 nmd is compli-cated by the appearance of new oxide reflections. Tpeaks are very tiny in case of the 4.2-nm-thick overlayerjust enhance the background but are clearly visible forthicker layers. These reflections occur at positions whichvery close to the values expected for the second, third

fourth orders112̄d diffraction peaks of the cub-Pr2O3 phaseThe in-plane scans alongH=K of all samples are show

FIG. 2. In-plane scanssL=0.1d along the two high symmetry Si surfadirectionsf100g sleftd andf110g srightd to measure the azimuthal oxide laorientation on the Sis111d substrate surface.

on the right of Fig. 2. Here, the sharp Si surface diffraction


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peakss110d and s220d correspond to the allowed Si bu

reflection s022̄d and s044̄d, respectively. Again, it is foun

that the broad oxide reflectionss112̄0d and s224̄0d of thehex-Pr2O3 phase are superimposed on the sharp sub

peaks. However, also the allowed cubic Pr2O3s044̄d and

s088̄d reflections are situated along this direction close tosubstrate peaks. In this way, these peaks are only dete

in form of shoulder structures close to the dominants112̄0dand s224̄0d hex-Pr2O3 peaks.

To complete the structure determination of the Pr2O3

layer on Sis111d, off-plane measurements were performedstudying the Sis11Ld CTR. The pictogram in Fig. 3 explaithe two different measurements performed on the Sis11LdCTR.

The measurement 1 consists of a scan along thes11LdCTR from L=0 to L=2.1 by keeping the incoming wavectorK i constant and varying the outgoing wave vectorK f.Theses11Ld CTR scans are summarized for all studiedthicknesses in Fig. 4. Again, oxide reflections become clevisible on the rods when the Pr2O3 layer thickness excee1.6 nm. The indexing of these oxide diffraction peakgiven in Fig. 4. Filled and open circles are used to deallowed and forbidden reflections, respectively. As thdspacing of hexs0001d oxide planess0.6013 nmd is about thesame as that of cubs111d oxide planess0.6438 nmd, hex andcub oxide reflections always overlap on thes11Ld CTR.

However, structure factor calculation show that thes153̄d and

s371̄d cub oxide diffraction peaks are forbiddensh+k+ l=2n+1d. In consequence, the oxide peaks on thes11Ld CTRwith L=0.5 andL=1.5 can result only from the hex-Pr2O3

phase.In order to demonstrate the hexagonal symmetry o

Pr2O3 epilayer on Sis111d, we performedf scanssmeasure

ment 2 of Fig. 3d at L=1.5 to record the family ofs112̄3d hexoxide reflections. Thef scan consists of turning the samaround its surface normal while keepingK i andK f constantSuch af scan is shown in Fig. 5 for a 4.2-nm-thick Pr2O3

epilayer on Sis111d as a representative example. The dete

60° spacings between the variouss112̄3d hex oxide reflections confirms the hexagonal film symmetry.

In addition, the high crystalline quality of the Pr2O3 ep-ilayers is demonstrated in Fig. 4 by the thickness fringesDLon the Sis11Ld CTRs which, for the wavelength appliedour diffraction study, are clearly observed for the Pr2O3 lay-

FIG. 3. The pictogram illustrates theL scansmeasurements 1d and theFscansmeasurement 2d performed on thes11Ld CTR.

ers of 1.6, 4.2, 7.6, and 11.7 nm thickness. TheseDL oscil-


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lations are indicated by arrows in Fig. 4 and the determfilm thicknesses fit well with the values derived fromx-ray reflectivity measurements discussed earlier.

B. From pseudomorphism to bulk behavior

Thecritical thickness tc and the thickness-dependentdo-

FIG. 4. Measurement 1 of Fig. 3 consists of scanning thes11Ld rod fromL=0.1 toL=2.15. Thes11Ld scans of all studied film thicknesses are shoThickness fringesDL are indicated by arrows. The indexing of the peakthe s11Ld rod according to the different lattice systems is given onFilled and open circles are used to denote allowed and forbidden reflecrespectively.

main size Dof the hex-Pr2O3 epilayer on Sis111d were de-


termined by monitoring the evolution of the h

-Pr2O3s101̄0d in-plane reflection at the position of tSis100d surface diffraction peak. This study was performby recording in-planehkl mesh scanssL=0.1d which aredisplayed on the left of Fig. 6. The Sis100d peak is situated ithe center of all thehkl mesh scanssH=1; K=0d but canonly be distinguished in form of an intensive and sharpin case of the 1.1-nm-thick Pr2O3 overlayer where the su

rounding hexagonal Pr2O3 s101̄0d diffraction peak is verweak. With increasing the oxide film thickness from 1.111.7 nm, the oxide reflection gains intensity and becomedominant signal in thehkl mesh scans. It is clearly seen tthe oxide reflections exhibit an isotropic peak shape fostudied film thicknesses. It is noted for completeness t

weak superstructure around the hex-Pr2O3 s101̄0d in-planereflections appears in Fig. 6 in case of the thicker filmss7.6and 11.7 nmd. The symmetry of the observed satellite pesuggests a sixfold overstructure in case of the 7.6-nm-film, but only a threefold symmetry seems to exist for11.7-nm-thick Pr2O3 overlayer. Further studies are unway to elucidate the details of this satellite structure andisclose its origin.

The value of the critical thickness tc is evaluated by accurately determining the positions of the in-pla

Pr2O3 s101̄0d diffraction peaks. In order to do this, line scawere applied to thehkl mesh scans along the Si surfacef100gdirection. These line scans are plotted on the right of Fon different logarithmic scales to highlight their positio

and shapes. It is seen that the hex oxides101̄0d reflectionsare exactly situated at the substrate Sis100d position in casof the thin oxide layerss1.1 and 1.6 nmd. Therefore, thesultrathin layers grow pseudomorphic adopting in-planeunit cell length of 0.384 nm of the Sis111d surface. In contrast to this, the position of the oxide reflection of thenm-thick Pr2O3 overlayer deviates from the pseudomorpposition towards smaller reciprocal space values. An in-punit cell length of 0.3846±0.0004 nm is deduced fromoxide peak position. This value is situated between theSi substrate unit cell dimensions0.384 nmd and the bulkhex-Pr2O3 unit cell lengths0.3859 nmd showing that the ac

,

FIG. 5. Measurement 2 of Fig. 3 is aF scan over the family o

hexs112̄3d Pr2O3 reflectionssL=1.5d to confirm the hexagonal film symmtry. The representative example is given for theF scan of a 4.2-nm-thicPr2O3 layer on Sis111d. A well-evolved 60° spacing between t

hexs112̄3dPr2O3 peaks is observed.

cumulated compressive strain energy, acting on the hex


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-Pr2O3 epilayer on Sis111d, exceeds the epitaxial interfaenergy and the relaxation process towards bulk behstarts.34 The value oftc for pseudomorphic hex-Pr2O3 growthon Sis111d is therefore in the range between 1.6 and 4.2The relaxation process towards the bigger oxide bulk valmore advanced in case of the 7.6-nm-thick epilayer. Incase, the in-plane oxide unit cell lattice spacing amoun0.385±0.0004 nm. When the film thickness is increase11.7 nm a further change in the position of the oxide retion occurs and an in-plane lattice constant0.3856±0.0004 nm is calculated. Within the limits of erthis agrees with the bulk hex-Pr2O3 unit cell length and it cabe concluded that the transition from pseudomorphismbulk values reaches its end at a Pr2O3 epilayer thickness oabout 11.7 nm thickness. This relaxation process of thplane hex-Pr2O3 unit cell lengthsa axesd is summarized othe right of Fig. 6. For completeness, the thickness dedence of the vertical unit cell lengthsc axesd of the

FIG. 6. Left : hkl mesh scanssL=0.1d around the Sis100d CTR reflection to

monitor peak shape and position of the hex-Pr2O3 s101̄0d diffraction peak

Right: Line scans across the hex-Pr2O3 s101̄0d peak along the Sif100g sur-face directionstopd. Thickness dependence of the oxide unit cell latparameters and of the domain size of the hex-Pr2O3 layer on Sis111dsbottomd.

hex-Pr2O3 epilayer is also included. These values were ex-


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tracted from the positions of thes0006d hex-Pr2O3 reflectionsin the specularu–2u scans of the various film thicknessstudied. As pointed out earlier, from the epilayers of 1.11.6 nm thickness, no oxide diffraction peaks on thes00Ld rodcould be detected so that thec-axes length of pseudomorphfilms could not be determined. Surprisingly, thec-axeslength of all the thicker hex-Pr2O3 epilayerss4.2, 7.6, and11.7 nmd is not bulk-like s0.6013 nmd but always increaseby about 0.6% to a value of about 0.605 nm. These increc-axes values are probably caused by a combination oeffects. First, increasedc-axis lengthes are expected duethe compressive strain field acting on the hex-Pr2O3 epilayeron Sis111d. Second, a further contribution could result frthe reported big thermal expansion coefficient ofhex-Pr2O3 lattice along thec axis so that the expanded lattparameters were frozen in during the cooling processfilm growth was performed at elevated temperature.35

The thickness-dependent domain size Dof the oxidelayer was extracted from the FWHM values of the line sc

of the Pr2O3 s101̄0d diffraction peaks shown in Fig. 6. Tpseudomorphic oxide films of 1.1 and 1.6 nm result in v

narrow Pr2O3 s101̄0d reflections whose FWHM values agiven by 0.006 and 0.007 reciprocal lattice unitssr.l.u.d, re-spectively. A lateral domain sizeD of about 50 nm is deduced which reflects the considerable long-range ordpseudomorphic Pr2O3 epilayers on Sis111d. In contrast tothis, oxide layers whose thickness exceeds the earliermined value oftc are characterized by a broadening of

Pr2O3 s101̄0d reflections. The transition to bulk behaviorobserved in the 4.2-nm-thick overlayer and results in astantially increased FWHM values0.016 r.l.u.d of the

Pr2O3 s101̄0d diffraction peak. From this, a reduced averdomain sizeD of 21 nm is deduced. This result shows tthe relaxation process from pseudomorphism to bulk beior reduces the long-range order of the oxide film. Thelated relaxation mechanism is probably a plastic deformin the oxide layer, resulting in the creation of misfit dislotions which limit the coherence length of the film. The snario of an elastic deformation by the growth of relaxedide islands beyondtc, i.e., a roughening transition, is nsupported by XRR and reflection high-energy electronfraction studies which indicate a smooth film growth inthickness regime beyondtc.

36 Increasing the film thickness

7.6 nm broadens the Pr2O3 s101̄0d reflection further towidth of 0.021 r.l.u., resulting in a reduction of the latedomain sizeD to 16 nm. This process saturates in this thness range because the 11.7-nm-thick overlayer is char

ized by a Pr2O3 s101̄0d diffraction peak with a very similaFWHM value s0.019 r.l.u.d. A lateral domain sizeD of 17.5nm is deduced which, in consequence, can be considethe characteristic dimension of crystalline domains whenthickness of the Pr2O3 layers on Sis111d reaches the bulkdetermined range.

The influence of strain effectsis responsible for the fathat, in case of the oxide films thicker thantc, the domainsizesD given earlier are low limit values of the actual crysgrain sizes. This is true because the values were ded
from radial scans which are influenced by shape and strain

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effects.33 To describe the influence of strain broadeningthe oxide reflections,hkl mesh scanssL=0.1d of the first,

second, and third orders101̄0d Pr2O3 diffraction peaks situated along the Si surfacef100g direction were detected for astudied film thicknesses. As an example, the results o4.2-nm-thick oxide layer are displayed in Fig. 7sad. The ox-ide reflections are observed around the sharp Si subpeaksfnot visible in the intensity maps of Fig. 7sadg and arecharacterized by a substantial broadening with increadiffraction order. The dashed arrow on the bottomhkl meshscan in Fig. 7sad indicates the direction of radial scans alothe H direction atK=0 which were performed to quantithis broadening behavior. Figure 7sbd displays the result anthe strain induced broadening can be seen. While

s101̄0d Pr2O3 diffraction peak is almost symmetric,

strongly asymmetrics303̄0d oxide peak shape is observCertainly, the asymmetric shoulder structure of the latteride reflection towards smaller reciprocal space values isto the relaxation of the film lattice parameter fromsmaller substrate induced values0.384 nmd towards the bigger bulk oxide parameters0.3859 nmd. In this way, the highindexed reflections allow for a better discrimination oflaxed and unrelaxed lattice parameters in a given epistructure. This is the case because the broadening of areflection due to the finite sizeR is to a good approximatioequal to 2p /R and remains constant in reciprocal spawhereas the strain-induced broadeningDa/a sa: substratespacing;Da=aFilm−aSubstrated results in a practical consta

FIG. 7. sad hkl mesh scanssL=0.1d of the first to third order he

-s101̄0d Pr2O3 diffraction peaks.sbd Radial scans of the respectivehkl meshscans across the Sif100g surface direction highlight the strain induced broening. scd Plot of the angular widthDQ/2 of the first to third order he

-s101̄0d Pr2O3 diffraction peaks against the momentum transferQ to deter-mine the in-plane mosaicity of oxide films thicker thantc.

DQ/Q ratio and thus increases with the reciprocal space vec


te

e

rg

tor Q. Therefore, if the condition 2p /R, sDa/adQ is ful-filled, we can directly extract the percentage of the filmtensity due to the relaxed film parametersDa. This allows togive a more accurate estimate oftc: As the film lattice parameter varies during the transition from pseudomorphisbulk behavior monotonously across the layer thicknessmay think of the spread out intensity as attributed to thethickness intervalDt beyondtc which is characterized by thpresence of partially or totally relaxed lattice parameDa.37–39 Thus, applying a peak fit analysis to

s303̄0d Pr2O3 diffraction peaks of the 4.2, 7.6, and 11.7epilayers shows that 37%, 56%, and 70% of the totaltering intensity are related to relaxed film parametersDa,respectively. In this way, atc value of 3.0±0.5 nm can bestablished for the heteroepitaxial system-Pr2O3/Sis111d.

It is important to note in Fig. 7sad that, despite the straiinduced broadening along the radial direction, the peak s

of the family of s101̄0d Pr2O3 diffraction peaks remains istropic. Therefore, a further broadening mechanism muactive along the angular direction. The angular widthDQ ofa diffraction peak, indicated on the bottom scan in Fig.sadby the dotted arc, is not sensitive to strain but dependsize and mosaicity effects.33 Again, size effect broadeningconstant in reciprocal space but a linear relationship ebetween the momentum transferQ and the angular widthDQof the diffraction peaks in case of mosaicity. To discriminbetween size and mosaicity effects, the angular widthDQ/2

values of the first to third orders101̄0d Pr2O3 peaks are ploted in Fig. 7scd as a function of the respective momenttransferQ for all studied Pr2O3 films thicker thantc. TheDQ/2−Q relationship is found to be roughly linear, as incated by the dotted line in Fig. 7scd. In this way, an in-planmosaicity structure is detected in Pr2O3 epilayers thickethantc, resulting in crystal grains with surface normals dating by 0.5° ±0.2° from the pseudomorphic Si surfacef100gdirection.

IV. DISCUSSION

Based on the results of the presented SR-GIXRD sthe characteristics of the real space structure of the hetetaxial system Pr2O3/Sis111d can be described as follows.

The Pr2O3 epilayers on Sis111d are mainly composedthe hex-Pr2O3 phasesspace group:P-3m1d over the studiethickness range. The specularu–2u scans in Fig. 1 prove ththe hex-Pr2O3 lattice grows with itss0001d orientation on th

Sis111d substrate surface. A side view along thef112̄0g di-rection of the bulk lattice structure of this oxide is showith the s0001d oxide axes pointing upwards in Fig. 8sad. Itis seen that thes0001d oriented hex-Pr2O3 lattice can bviewed as an alternating sequence of vertically stackedand PrO2 layers. These layers are indicated on the lefparentheses in form of solid lines. The bulk unit cellsdashedparentheses on the rightd contains alongf0001g one PrO anone PrO2 layer so that the Pr2O3 stoichiometry results. Thstructure representation is correct because thes0001d hex-Pr2O3 structure can be derived from thes111d oriented fluo
-rite PrO2 phase in the following way. Thes111d PrO2 struc-

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ture is characterized by two O–Pr–O stacks per unitalong the f111g axes and is reduced to thes0001d hex-Pr2O3 lattice by a crystallographic shear operation wheliminates one oxygen plane per unit cell.40 To highlight thedifferent layer stoichiometry of thes0001d hex-Pr2O3 struc-ture, sketches of the bulk determined hexagonals0001d PrOand PrO2 layers are shown in Fig. 8sbd. It is easily seen thathe Pr sublattices are identical in the two layers but, in cparison to the PrO2 slab, only half the amount of oxygenpresent in the PrO layer. As the Pr valence is fixed to 3positive and a negative ionic charge state can be assignthe vertically stacked PrO and PrO2 layers, respectively. Ths0001d orientation of the hex-Pr2O3 epilayer is thereforepolar oxide surface which creates with increasing film thness a diverging electrostatic surface energy term.41,42 In thisway, adsorption of charged ionssH+; OH−, etc.d or nonbulk-determined interface and surface structures are requircancel the resulting dipole moment and stabilize thes0001dhex-Pr2O3 epilayer structure.43

The in-plane diffraction study in Fig. 2 determinedazimuthal orientation of the hex-Pr2O3 epilayer on theSis111d substrate. It was found that the hexagonals0001dbasal plane grows with itsf101̄0g andf011̄0g in-plane directions oriented along the Si surface vectorsf100g and f010g,respectively. In this way, the hexagonal surface unit celmensions of thes0001d oxide planes0.3859 nmd and theSis111d substrate s0.384 nmd match within 0.5%. Thpseudomorphic oxide layer is thus under compressive sand forms as131d superstructure on the substrate. Tvalue of tc of the system hex-Pr2O3/Sis111d amounts to

FIG. 8. sad Side view sketch of thes0001d oriented hex-Pr2O3 structureshows the alternating sequence of vertically stacked PrO and PrO2 layers.sbd Top view sketches of the bulk determined hex-s0001d PrOstopd and PrO2

sbottomd layers.scd Side view sketch of thes111d oriented cub-Pr2O3 struc-ture shows the vertically stacked Pr2O3 layers.sdd Top view sketch of thbulk determined cub-s111d Pr2O3 layer. Dotted and dashed lines depict sface unit cells of hex-s0001d and cub-s111d layers, respectively. Bulk uncells are sketched by solid lines. Gray and black spheres represent Pratoms, respectively.

3±0.5 nm. Beyondtc, the Pr2O3 layer on Sis111d relaxes


l

to

o

n

towards its bulk structure and different mechanisms arvolved. Besides the creation of misfit dislocation andformation of an in-plane small angle mosaicity in the fiparts of the oxide film are found to undergo a phase trtion. Crystal grains of the cubic oxide phase withs111d ori-entation are detected in thicker Pr2O3 epilayerss4.2, 7.6, and11.7 nmd. Here, the hexagonals111d plane of the cub-Pr2O3

phase is oriented in-plane in such a way that thes111d sur-face unit cell vectors of the oxide and Si point along

same directions, i.e., the bulkf112̄g directions of the twcubic lattices coincide. The resulting lattice mismatchtween the Sis111d substrate and the cub-s111d Pr2O3 plane isabout 2.7% and therefore five times bigger than in casthe hex-s0001d Pr2O3 crystal face. It is most likely this diference in epitaxial strain energy which favors the formaof a hex-Pr2O3 layer on Sis111d. Similar cases of epitaxialstabilized thin film structures have been reported in casrare-earth manganite films.44,45 However, as the epitaxistrain energy is relaxed beyondtc, this stabilization mechanism of the hex-Pr2O3 structure on Sis111d becomes less efective with increasing film thickness. As the hex-Pr2O3

structure is the high-temperature phase of the Pr–O pdiagram, it is beyond tc only metastable at rootemperature.46,47 It is therefore not surprising that oxide laers thicker thantc are found to undergo a phase transitowards the cubic low temperature Pr2O3 phase. This phastransition is incomplete in as-grown samples but it is knthat hex-s0001d Pr2O3 layers on Sis111d can be completetransformed into a cub-s111d Pr2O3 epilayer by annealingnitrogen.48 A side view of the cub-Pr2O3 structure with thef111g axes pointing upward is shown in Fig. 8scd. As theparentheses indicate, thes111d oriented cub-Pr2O3 phase cabe viewed as a vertical stack of stoichiometric Pr2O3 layersIn contrast to the hex-s0001d Pr2O3 structure, the cub-s111dPr2O3 epilayer presents therefore a nonpolar oxide suorientation so that a stable bulk-determined structure spossible. A cub-s111d Pr2O3 layer is depicted in the bottopart of Fig. 8sdd. The hexagonal surface unit cell of the cs111d-Pr2O3 plane is indicated by dashed lines and its dimsion of 1.577 nm results approximately in the formations434d overstructure with respect to the Sis111d surface unicell fthe s131d hex-s0001d Pr2O3 unit cell is indicated inFig. 8sdd by dotted linesg. It is interesting to note in Fig.that the Pr sublattices of the hex-s0001d Pr2O3 planes and thcub-s111d Pr2O3 crystal face are almost identical. The diffence of the two Pr2O3 phases is mainly related to a structurearrangement of the oxygen network. A possible mechaof the relaxation of the hex-s0001d into a cub-s111d Pr2O3

epilayer is therefore the diffusion of oxygen atoms fromhex-s0001d PrO2 planes into the hex-s0001d PrO layers, resulting in the ordered oxygen vacancy network structurthe stoichiometric cub-s111d Pr2O3 planes. A phase transitiohex-.cub Pr2O3 based on the migration of oxygen insteof Pr atoms would be characterized by a low activationergy which renders the occurence of this relaxation proin as-grown samples understandable. However, as thesities of the observed cub-Pr2O3 peaks do not completescale according to bulk structure factor calculations of

O

cub-Pr2O3 phase, the phase transformation is probably not


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completed and a certain disorder remains in the microsture of the oxygen network. Further studies are under waelucidate the detailed mechanism of the phase transitiothe heteroepitaxial system Pr2O3 on Sis111d. In this contextit is interesting to note that recent studies were reportethe literature on the structurally very similar heteroepitasystem Y2O3/Si.49–51Gaboriaudet al.detected in Y2O3 filmson Si in dependence of the deposition technique the preof a phase transition from the cubic bixbyitesIa-3d structuretowards a fluorite phasesFm3md and identified the rearangement of the oxygen network microstructure as thlated mechanism.

V. CONCLUSION

In summary, ultrathin Pr2O3 epilayers on Sis111d adoptover the thickness range from 1.1 to 11.7 nm the structuthe hex Pr2O3 phasesP-3m1d. Specularu–2u scans reveathat the vertical stacking of the oxide layer is given bys0001d orientation. The in-plane orientation of the oxide

defined by itsk101̄0l azimuthes pointing along the Sik112̄ldirections. The small lattice mismatch of about 0.5% resin a tc of 3.0±0.5 nm. The pseudomorphic oxide layerhibits a high crystalline quality which is reflected in theerage domain size of about 50 nm. The relaxation fpseudomorphism to bulk behavior compromises the lrange order of Pr2O3 epilayers on Sis111d thicker thantc bythe introduction of misfit dislocations, reducing the averdomain size of Pr2O3 films with bulk-like lattice parameteto about 17.5 nm. Furthermore, the strain relaxation iscompanied by the formation of an in-plane small anglesaicity creating oxide crystal grains with an averagealignment of 0.5° ±0.2° with respect to the Si surfacef100gdirection. Most interesting is the observation of the bening of a phase transformation in as-grown samples betc which converts thes0001d hex-Pr2O3 epilayer into ans111dcub-Pr2O3 film structure. This relaxation behavior highlighthe important influence of the epitaxial interface energythe stability of the Pr2O3 phases on Sis111d. The high-temperature hex-Pr2O3 phase is stabilized by the fact thatlattice mismatch between the Sis111d substrate and the hs0001d Pr2O3 surface unit cell is five times smaller thancase of the cubs111d Pr2O3 surface plane. Beyondtc, theinfluence of the epitaxial interface energy decreases raso that the high temperature hexs0001d Pr2O3 phase becomes metastable. The fact that the relaxation into the slow-temperature cubs111d Pr2O3 structure is observed in agrown samples points to a rather low activitation energthe phase transformation. This is probably due to the facthe hexs0001d Pr2O3 structure can be transformed intocub s111d Pr2O3 film lattice by a process which requiresreordering of the oxygen network but no strong modifitions on the Pr sublattice. As the influence of the oxynetwork structure on materials properties is at the heamodern oxide chemistry,52,53 future work in our group wilfocus on the physics of the detected phase transition tomize the dielectric properties of Pr2O3 epilayers on Sis111dfor high-k applications. Of special interest is thereby
s0001d hex-Pr2O3/Sis111d interface structure. From a bulk

-

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f

-

-

d

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i-

determined point of view, two different interfaces canconstructed, namely the PrO+/Sis111d and the PrO2

−/Sis111dstructure. As polarity discontinuities across the interfacetween two different crystalline materials can result in ntrivial local atomic and electronic structures not presenbulk structures,54,55 a detailed structural and electric charterization of thes0001d hex-Pr2O3/Sis111d heterointerfacecurrently under way.

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Structure and strain relaxation mechanisms of ultrathin epitaxial Pr[sub 2]O[sub 3] films on Si(111)

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Transcript of Structure and strain relaxation mechanisms of ultrathin epitaxial Pr[sub 2]O[sub 3] films on Si(111)