Thin Solid Films, 189 (1990) 329-338

PREPARATION AND CHARACTERIZATION 329

STRUCTURAL CHARACTERIZATION OF AN (InAs),(AlAs), SUPERLATTICE ON GaAs(OO1) WITH A FOUR-CIRCLE X-RAY DIFFRACTOMETER

JOSE FAYOS

Instituto Rocasolano, Departamento de Cristalograja. CSIC, Serrano 119,28006 Madrid (Spain)

MERCEDES PEREZ MENDEZ

Centro National de Microelectronica. CSIC, Serrano 144,28006 Madrid (Spain)

(Received July 24,1989; revised January 24,199O; accepted February 27,199O)

An (InAs),(AlAs), superlattice (SL) 0.3 urn thick grown on a GaAs(OO1) substrate by alternate layer molecular beam epitaxy, has been structurally characterized with a conventional four-circle X-ray diffractometer. Alternative structural models for any (InAl),,(AlAs),, SL are established. The SL Laue group mmm was selected on the basis of the 2468 reflections measured in the half Ewald sphere of the sample. The structural model best matching the observed 200 SL independent reflections can be described by the space group Pmm2, where a considerable improvement in the fit is reached by introducing some InAs-AlAs diffusion through the interface, modulating the interplanar spacings, which is here indistinguishable from interface roughness.

1. INTRODUCTION

Epitaxial superlattices (SLs) of isomorphic semiconductors with different compositions and lattice parameters have received renewed attention. It has been shown that the lattice mismatch in a strained-layer SL is accommodated by the tetragonal distortion of the successive layers of the SL1. Moreover, strained-layer heteroepitaxy gives a further degree of freedom for band gap engineering, allowing the growth oflayers even if they do not match the substrate with respect to the lattice constant. The strain in turn modifies the electrical and optical properties of the materials in a manner which can be of benefit for device performance293.

Standard powder diffractometry and high resolution double-crystal X-ray diffractometry are non-destructive techniques which are routinely used in the study of SL structural parameters such as cell constants and interplanar spacings4, tetragonal expansion and compression of the lattice5, strain profiles6 and lattice defects’. The X-ray precession camera has also been used to determine the a and b cell parameters in the interface plane of short period strained-layer SLs together with those of the substrate*.

In the present work, the characterization and the crystal structure of an [(InAs),,(AlAs),,]. SL are determined using a conventional four-circle single-crystal X-ray diffractometer.

004~6090/90/%3.50 0 Elsevier Sequoia/Printed in The Netherlands

330 J. FAYOS, M. PEREZ MENDEZ

2. SUPERLATTICEGROWTH MODEL

We assume a periodic growth [(InAs),,(AlAs),,], on the GaAs(OO1) substrate

plane where the approximately 79; lattice mismatch between InAs and AlAs would cause the zinc-blende-type coherent growth to be located at crystalline domains interrupted by breaking surfaces. As lattice defects produced during molecular beam epitaxy (MBE) crystal growth or afterwards, we also include in the model the possibility of some In-Al diffusion through interfaces (or interface roughness, as they are equivalent in this experiment). In fact a Raman study’ of these samples

suggested the presence of this defect, which could, moreover, be introduced in the structure factor calculation as a variable diffusion in the growth model

The level of diffusion would be related to the quality of the epilayer, as a large degree of diffusion would accommodate the lattice mismatch, increasing the size of the domains. We also consider two kinds of diffusion: symmetrical, which does not distinguish the growing direction, and asymmetrical, along the growing z direction.

The SL structure so built is a modification of that of the GaAs, InAs or AlAs

C-centred zinc blende type with a z 6 A along the growth direction. When n, + n, is even, the SL structure can be described in terms of a C-centred cell with orthogonal axes a = b z 6 8, and c including n, + n2 layers, or in a P-primitive cell with

a’ = b’ = a/$ and c’ = c axes. For n, + n2 odd, an F-centred lattice instead of the C-centred lattice or an I-centred lattice instead of the P-centred lattice, with a double c parameter in both cases, should be considered in order to preserve the cell orthogonality.

Table I contains the Laue groups and space groups consistent with this SL growth model. Except for the triclinic case where each atom would have three degrees of freedom, atoms are always in special positions of the space group. In the Pm group, atoms would lie on symmetry planes perpendicular to the b axis. For the remainder of the space groups, most of the atoms would be placed at 2 or mm, both with only one degree of freedom, z. Some space groups also containing fixed atoms at 222, 4 or 32rn do not include the asymmetrical diffusion possibility. The last column in Table I lists the groups allowing asymmetrical diffusion and those only allowing symmetrical diffusion.

3. EXPERIMENTAL (InAs),(AlAs),/GaAs(OOl) SUPERLATTICEX-RAY SPECTRUM

The sample studied was a plate of size 0.55 mm x 0.55 mm of the (InAs),(AlAs), SL grown 0.3 urn thick on a GaAs(001) substrate by alternate layer MBE”. The substrate was lapped to a thickness of 160 urn for the X-ray study in order to decrease the contribution from the substrate lattice. The plate was fixed to a capillary at the substrate side with the SL growth direction parallel to the goniometer head rotation axis, as shown in Fig. 1.

A preliminary Cu Ka X-ray analysis of the sample with a precession camera gave a first estimate of the SL cell constants: all = b,, = 6.05 A and cI = 29.11 A.

STRUCTURE OF (InAs),(AlAs), SUPERLATTICE ON GaAs(001) 331

TABLE I POSSIBLE SPECTRUM AND CRYSTAL SYMMETRIES FOR THE SUPERLATTICE

Laue class Space group Special positions Growth type”

i Pl AD

2lm Pm m AD lm m AD P2 2 AD 12 2 AD

mmm Pmm2 mm AD lmm2 mm AD c222 2,222 SD F222 2,222 SD

4/m P4 2,4 SD 14 2,3 SD

4/mmm P4m2 mm,42m SD 14m2 mm, 32m SD

a AD includes the possibility of asymmetric diffusion, while SD means that only symmerical diffusion is allowed.

Fig. 1. A schematic drawing showing the sample assembly on the four-circle diffractometer. The goniometer head rotation axis C$ is almost parallel to the (001) SL direction.

Then the sample was mounted on a Philips PWllOO four-circle diffractometer equipped with a copper fine focus X-ray tube, a graphite monochromator and a 0.8 mm collimator. During the experiment, the X-ray beam was always incident on the SL side, i.e. only (HKL) planes with L 3 0 were recorded. In spite of the strong absorption of the X-rays, the SL was thin enough to let the GaAs substrate diffract, its reciprocal lattice overlapping that of the SL with an intensity 10 times as strong and with narrower peak profiles. This allowed the SL cell constants to be determined accurately, using the GaAs substrate (reported” a = 5.653 25(5) A) as an internal standard. Several slow and fine Q-29 scans around each of the SL reflections (400),(~00),(040),(0~0),(00 lo), (00 20) and (00 30), using a detector window of l”, gave precise 26, values. The SL cell parameters obtained were a = 5.972(4) A, b = 5.971(4) A and c = 30.00(5) A, the standard deviations being given in paren- theses. The a and b values lay between the cell parameters of unstrained AlAs and InAs, 5.66 A and 6.05 A respectively, and the translation along the growth direction c was about 5a, which confirms the assumed ten layers for the SL with an average thickness of 3.00 8, per layer.

While the SL and substrate peaks were being centred, a systematic angle of about 0.25” was observed between the (001) directions of the two lattices, which

332 J. FAYOS, M. PEREZ MENDEZ

would not affect the SL measurements, as a suitable SL orientation matrix was chosen. Intensities for 2468 SL reflections, corresponding to one-half of the Ewald sphere with L 3 0 and 0 < 70”, were registered using a detector aperture of I”, Q-20

scans at 1 S“ min ‘, and a variable scan amplitude AU = 1” + 0.6 tan 8, which was appropriate for resolving the SL peaks, although a few substrate peaks overlapped.

In order to assign the most probable space group from all those proposed in Table I, some tests of the spectrum were performed for the possible symmetry planes (100) (010) (110) and (ITO), and for the 2-fold or 4-fold axes along the (001) direction. Table II shows the internal consistency Z 1 r- Ii l/C17 for some symmetry options, where ris the average intensity among those li related by these symmetries.

The results suggest that the last group, i.e. mmm, is the most probable Laue group. Using Table I, we select the space group Pmm2, as n, + n, = even, in which an asymmetrical diffusion model is possible in the SL. Hence the P elementary cell used is given by c( = 4.223(3) A, b = 4.222(3) A and c = 30.00(5) A. Among the 664

averaged r values for mmm, 206 observed reflections were selected, those with T> 30(1) being considered (where a(r) is the mean quadratic deviation of I), and excluding four reflections which overlapped with some of the reflections of the substrate. The SL density of 5.372 g cm 3 and the strong mass absorption with

respect to copper radiation yielded a linear absorption coefficient of 900 cm- ‘. However, because of difficulties in correcting intensities for absorption in this thin layer, only (HKO) reflections were assumed to be affected. Six of the observed (HKO) reflections were also excluded, so finally only 200 reflections were retained for the structure calculations. Intensities were reduced to structure factors by Lorentz and polarization effect corrections. A Wilson plot gave an overall thermal factor B = 2 A’. which was used to calculate the structure factors.

TABLE II

SUPERLATTI(‘E LAUE SYMMETRY TESI

Symmrrry 5IT-IJfi N

2 0.043 1035

4 0.078 538

4mm 0.078 394

mm(100)+(010) 0.077 623

mm(llO)+(liO) 0.048 664

Terms with 11-1,I > 5a(I,) are excluded from the summation when the mean IS taken between two

supposed equivalent reflections, and terms with 1 r-1, / > 2u(fi) are excluded when the mean is obtained

from more than two (where g(I<) c ,‘y).

The SL spectrum is assembled around the substrate peaks, i.e. around the (213)

GaAs I-lattice reflection, the SL “zero-order” peal< (2 1 15) and its satellite peaks (2 1 15k i) for i = 1,2, are observed, their intensities being higher when the corresponding substrate reflection is higher. On the contrary, as the SL is a modification of the zinc blende structure (which can be described in an I-centred cell

with dimensions a/$, ~13, a), it is not surprising that SL pseudo-extinctions are observed when H + K + L/5 # 2n; the extinction would be total if indium and aluminium positions were occupied by the same atomic species.

STRUCTURE OF (InAs),(AlAs), SUPERLATTICE ON GaAs(OO1) 333

In the space group Pmm2, atoms should be in special positions: (a) O,O,z; (b) 0.1/2,2;(c) 1/2,0,2;(d) l/2,1/2,2. We place n, arsenic atoms at a and nd arsenic atoms at d. Above each of these atom layers, the nb b positions and n, c positions would be populated by indium and aluminium atoms, which in a growth with In-Al diffusion would distribute their populations in each layer. The general formula is As,In,Al,_.,wheren=n,+n,(alson=n,+n,),n,=n,,n,=n,and

x = 2 pJIn,b) + 2 pj(In,c) L j

pi(In,b) and pj(In,c) are respectively the indium populations in the b and c positions. In this model, let ci = 4 COs(2XLzi) and si = 4 sin(2nLzi), the structure factor

being Fcal = A’ + iB’, where the real part A’ is

A’(HKL) = fAs~Ci+(-l)H+KfAs~Ci+ 1 1

(-l)K~CiCfinPi(In,b)+fA~{l-Pi(In,b)}l+ 1

(1)

the imaginary part B’ being given by the same formula but with si instead of ci. Apart from the zi coordinates and the scattering factors fAs, fi, and iA,, the

F,,,(HKL) value only depends on L and the parity group of (H,K). Hence, for a structural model that can be described by the group Pmm2, all the SL reciprocal lattice rows parallel to (OOl), with say indices (EEL), possess the same structural information, and this is the same for (OOL), (EOL) and (OEL), where E = even and 0 = odd. Thus all the structural information is contained within the rows (OOL), (1 lL), (01 L) and (1OL). In fact, an analysis of the observed Fobs spectrum confirms this hypothesis. As a consequence, a test for possible tetragonal4/mmm symmetry could only be performed using (EOL) reflections and their symmetric reflections (OEL). In our spectrum, systematically F,,,(EOL) > F,,,(OEL) for L = 5 or 25, and F,,,(EOL) < F,,,(OEL) for L = 15 or 35, which clearly shows a break from the 4/mmm tetragonality, according to the overall test results in Table II, and confirms the chosen Pmm2 space group.

4. PROFILEANALYSISOFTHE(OOL)SUPERLATTICEPEAKS

We now consider some profile analysis from our data, in order to reveal the possible defects which could be involved in the real SL crystal, which could modify both the position and the intensity of the observed peaks7. Although a conventional four-circle diffractometer may not be the most adequate tool for analysing peak profiles, the following observations, using the Cu Kcl radiation, could be significant.

(a) There is a systematic displacement of the (0 0 L f 1) satellites, moving away about 0.05” from the (OOL) zero-order reflection with respect to their theoretical positions for c = 30.00 A. This indicates some interface roughness’ or In-Al interface diffusion as included in our model.

334 J. FAYOS, M. PEREZ MENDEZ

(b) The full widths at half-maximum (FWHM) for the substrate peaks (002)

(004) and (006) (at 8 = 16”, 33” and 55”) were 0.15”,0.20” and 0.25” respectively (in e), including the Ku, + Ka, overlap, which we assumed to result from the instrumental broadening. The zero-order SL peaks (0 0 lo), (0 0 20) and (0 0 30) were, nevertheless, 0.40”, 0.50” and 0.60” (in 0) broad. The differences suggest lateral variation of the composition in the SL’ or crystal size broadening. As we expected some domain distribution due to the large InAs-AlAs lattice mismatch, we assigned the observed

peak broadening to the average size of those domains. From Scherrer’s formula’* D = KA/p cos 8, where D is the domain size, p is the FWHM crystal broadening (20) K = 1 for (OOL) reflections and i. is the wavelength, we estimate the SL domain average thickness along the growth direction to be about 200 A. This result is also supported by the Raman spectrum of this sample’, which evidences zones with different degrees of stress. Conversely, if the SL had grown coherently within the entire volume of the sample, the unique domain 0.3 urn thick would have only produced l/10 of the observed broadening.

(c) The FWHM of the first-order satellites are about 157; greater than those of the corresponding zero-order reflections, which could include effects from some other SL growth defects. Nevertheless, this fact was not considered in correcting the observed SL intensities.

5. FITTING BETWEEN THE SUPERLATTICE GROWTH MODEL AND THE OBSERVED

SPECTRUM

Agreement factors R = CHKL( Fobs - 1 Fca, ~(/CF,,, have been calculated for different growth models of atoms As,@-Al), . . . As,,(InAl),, in Pmm2, where the indium population distribution p,(In) (pi(Al = 1 --p,(In)) in the ten layers and the zi coordinates for the As and In/Al layers, have been taken as variables. Three

hypotheses have been considered: (a) a unique (30.00 A/20 = 1.5 A) interplanar spacing for the entire (As,In-Al),, period: (b) two interplanar spacings, one for the zone supposed to be occupied by InAs of 1.53818, and other for the AlAs zone of 1.3475 A; (c) spacings modulated according to the indium population in each layer.

Spacings in hypothesis(b) were worked out by taking into account the InAs and AlAs elasticity coefficients, through 4d, = ao( I+ EJ, where cI = - r-:,,(2c, */cl i) and

sll = (u,, -a,)/~~, where 2c,,/c,, = 1.313 for InAs” and 0.865 for AlAs13, u0 is the unstrained lattice parameter of InAs or AlAs, d is the strained interplanar spacing and ali = 5.97 8, is the strained parameter on the interface surface. Finally, d, values are normalized so that 4d,(Al) x 0.2 +Id,(In) x 0.8 = 30.00/5 A.

In hypothesis (c), the zi coordinates of arsenic, In-Al,. . ., are calculated from the formula

zi+l = pj(InM, + { l- pjOn)}d,, + zi i=l . ...20 (2)

where z,(As) = 0,j = i+ 1 for In-Al layers and j = i for arsenic layers, and d,, and d,, are the interplanar spacings of hypothesis (b) in the 8:2 SL. For other possible 1n:Al ratios such as 7:3 or 9:1, these spacings were modified proportionally in order to obtain the c parameter exactly by addition over ten layers.

Table III shows the Fobs-Fca, fit for different growth models, where the

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336

STRUCTURE OF (InAs),(AlAs), SUPERLATTICE ON GaAs(OO1) 337

agreement factors R have been calculated with the 200 observed reflectionsI and

scattering factors for neutral atoms . I5 The fit drastically improves when In-Al diffusion is considered for the 8:2 formula (Table III, model c). Even a modulation of the interplanar spacings as a function of pi(In) together with asymmetrical diffusion improves the agreement factor by up to 10.7% (model g). Models f, g and h include increasing amounts of asymmetrical diffusion. Fobs and Fcal for model g appear in Table IV for the representative reflections (2OL), (11 L), (2 1~5) and (124 of each parity group (selected instead of (OOL), (OlL) and (lOL), which overlapped to some extent with the substrate).

In general, as observed in Table IV, Fca, > Fobs for small Fobs values. This could be related to observation (c) above from the profile analysis, but we did not know how to correct the observed intensities for this effect. In order to assume it in the model, the In-Al diffusion was drastically increased in model e with respect to that in model d; however, as a result, the zero-order Fca, values increase too much with respect to their nearer satellites, the agreement factor becoming worse.

We also considered the case in which no chemical diffusion occurs (model i) but

in which the interplanar spacing constantly varies along the growth direction according to model g; the considerable increase in R shows again that a diffusion model fits the observed X-ray intensities better. Finally, models j and k show the fits for different 1n:Al lattice contents. Figure 2 shows the proposed In-Al population distribution of model g.

1

P;Un

0.5

Fig. 2. The proposed growth model g of Table III: the indium population in each layer is shown US. its z

coordinate and layer order, along the growth direction. The aluminium population is I-p(In). The vertical

lines represent the interfaces.

No model from those in Table III could be refined by the least-squares method, whether populations p,(In), atomic coordinates zi or thermal factors were used as variables.

6. CONCLUSIONS

In the present work alternative structural models for any (InAs),,(AlAs),, SL grown by MBE on a GaAs(OO1) substrate are proposed. In particular, the crystal structure for n, = 8, n, = 2, is solved using four-circle diffractometer X-ray data. It is found that the approximately 7% lattice mismatch between its components produces coherent growth in domains about 200 A thick. With mmm as the Laue symmetry of the SL, the space group Pmm2 is chosen to describe the crystal

338 J. FAYOS, M. PEREZ MENDEZ

structure, which is fitted to the X-ray data by the best distribution of both interplanar spacings and In-Al interdiffusion (or interface roughness) along the growth direction, the latter improving the Fobs-F_, fit drastically. Finally, the asymmetrical In-Al diffusion shown in Fig. 2, modulating the interlayer spacings, provides the model with the best fit.

We are not able to understand the reasons for the success of this In-Al model including diffusion, produced both during growth or afterwards, which seems to be unrealistic from the MBE growth point of view. In this respect, it is worth considering that some crystal defects, revealed in the peak profile analysis, could modify the X-ray intensities so that less diffusion would need to be introduced in the model, However, the peak profile analysis also reveals a systematic satellite shift, which suggests the presence of some interface roughness or In-Al diffusion’.

ACKNOWLEDGMENTS

We thank the Centro National de Microelectronica MBE laboratory in Madrid for growing the sample. We also thank Juan Melendez for his help during

the model calculations.

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