700

J. Appl. Cryst. (1995). 28, 700--706

X-ray Triple-Crystal Diffractometry and Transmission Electron Microscopy Characterization of Defects in Lattice-Mismatched Epitaxic Structures

B¥ R. N. KYUTT, S. S. RUVlMOV* AND T. S. ARGUN()VA

loffe Physical-Technical Institute of the Russian Academy of Sciences, Politechnikheskaya 26, St Petersburg 194021, Russia

(Received 25 March 1993: accepted 19 August 1994)

Abstract X-ray triple-crystal diffractometry has been applied to heterostructures with a misfit of lattice parameters in the interfaces. Si~_.~Ge,./Si compositions as well as GaSb layers strongly mismatched to GaAs substrates have been studied. By use of various scans in both the Bragg and Lauc geometries, the data are presented either as two-dimensional maps in the scattering plane or as the intensity distribution along the diffraction vector. The structural parameters of the layers were determined from a detailed analysis of the diffraction patterns. The X-ray diffractometry results are supported by a transmission electron microscopy study.

I. Introduction Difl'raction methods arc known to be profitable for studying the structural quality of bulk crystals and epitaxic tilms. In this paper, one of them, X-ray diffractometry, is applied to heterostructures (HSs) with the layers lattice mismatched to the substrates.

Over the last few decades, double-crystal diffrac- tometry (DCD) has proved to be a powerful tool to extract deformations, compositions, thicknesses etc. For nearly perfect HSs, with a simulation of Bragg diffraction curves, one can find the variation of the relative interplanar spacing component (M/d). across the depth (Fukuhara & Takano, 1977: Hill, Tanner, Halliwell & l~yons, 1985, Tapfer & Ploog, 1986). For HSs with a misfit of lattice parameters in thc interfaces, much of the in-plane data can be determined from asymmetric double-axis diffraction measurements. Many authors have competently discussed the dependences of the strain components on the elastic properties, the thicknesses of HSs and the misfit dislocation (MD)densities in their interfaces (Chu, Macrander, Strege & Johnson, 1985).

It is well known that the broadening of 0-scan diffraction peaks obtained in the double-axis setting is due to both a tilt and an expansion of the crystal

* ('urrent address: l,;.iwrel]Ce Berkeley l,aboratorv, University of California, Berkeley. CA 94720, I;SA le-mail r u v , mhl.lbl.gov).

~' 1995 International Union of Crystallography Printed m Great Britain all rights reserved

lattice. We are unable to analyze them separately, because we integrate along the Ewald sphere. In order to overcome the limitations of this scheme, a third crystal or a detector with a slit is used as an analyzer. In this case, the diffracted intensity is measured as a function of the incident and diffraction angles and the scattering data obtained can be plotted as two- dimensional maps in reciprocal space. Utilizing an X-ray detector with a slit, Funtner (1985) detected the tilt of superlattice layers. Various applications of a similar arrangement have been reported by Itoh & Okamoto (1988). A slit anlayzer is resolution limited, so a high-quality crystal is much better suited to this purpose.

Lately, triple-crystal diffractometry [TCD) has been successfully applied to nearly perfect HSs (Lucas et al. 1988; Fewster, 1989) as well as to layers with MD networks in their interfaces (Kyutt & Argunova, 1989). In our previous papers (Kyutt, 1989: Argunova, Kyutt, Ruvimov & Scheglov, 1991) we reported a comparative TCD study of Si~ .,Ge.,/Si HSs made in the Bragg and Laue settings. This paper deals with HSs containing structural defects inside the layers. We illustrate our studies using various scans and both diffraction geometries for investigating the quality of the layers and demonstrating the capabilities of TCD. The results obtained are supported by a TEM study.

2. Experimental procedure A triple-crystal mode (lida & Kohra, 1979) is used to register the diffracted intensity cersus the specimen (~) and analyzer (0 A) deviation angles from the Bragg condition. The arrangement allows the following scans in the scattering plane, in the case of 0-scan, when the specimen is rotated and the analyzer remains tixed, the end point of the difl'racted wave vector moves along the transverse direction to the reciprocal lattice vector H or along the q~ axis. With this scan, we measure the intensity from the scattering regions having equal interplanar spacings. To make the end point of the wave vector mov~ parallel to It, we u ~ the 0-20 scan providing the intensity distribution along the q . axis.

Jourmd ~?/ ,4pplied ()'.l.walk~.qral~h 3" ISSN OO21-8898 ~ 1995

R. N. KYUTT. S. S. RUVIMOV AND T. S. ARGUNOVA 701

When a specimen contains a tilt of the reflecting planes relative to the surface, the latter scan is insufticient to present the data along H. In order to obtain a correct intensity distribution, one has to integrate the scattered intensity normal to the diffraction vector and plot the curve J(q,) according to the following expression (Lucas et al., 1988: Kyutt & Argunova, 1989):

.l{q.,) = ~" l(z{) dz{. { I )

The angle interval should be chosen in such a way thai, beyond the limits, no more than I% of the integrated intensity is left.

In the present work, the triple-crystal arrange ment of the ( + n, - m, + n) setting was utilized. Silicon and germanium crystals of high purity and free from dislocations were used as the monochromator and the analyzer. In order to prevent the appearance of pseudo-peaks due to the slowly decreasing tails of the beams reflected from the monochromator and the analyzer, a tail-less beam was obtained by successive (threefold for Me K~ and fivefold for Cu K~ radiation) reflections from the grooved silicon monochromator. Although the analyzer analyzed a single reflection, the pseudo-peak was easily discerned only for the substraie reflection; the latter was marked as the reference point q, = 0.

Two types of structure were studied: vapour-phase- epitaxy grown Si~_xGex/Si HSs with x either fixed or increasing upwards from the interface to the surface and molecular-beam-epitaxy-grown GaSb layers largely mismatched to GaAs substrates. For Si~ _.,.- G%/Si HSs, the obtained misfit values were ~$a,"a < 4 x 10 3; for GaSb,iGaAs HSs, the value was 7 x I0 2. The thickness of the layers was 10 pm for Si~_,Ge,/Si and 21,tin for GaSb/GaAs HSs. The structures had (001)-oriented substrates 0.4 mm thick.

When studying Si~ .~Gex/Si HSs with a silicon monochromator and silicon anlayzer, we completely excluded the dispersion broadening. But for GaSb/'- GaAs HSs, flat germanium crystals served as the monochromator and the analyzer. In an attempt to obtain a series of reflections, two wavelengths (Me K:z and Cu K~) were applied, and two effects were taken into account before the monochromator and analyzer diffraction conditions were chosen, namely, the reduction of the dispersion broadening and the possible appearance of strong reflections at ,,;,/n wavelengths, where n is the reflecting order. To satisfy

. both conditions, we used the 111 reflection for the monochromator and the analyzer, when the 200 sample reflection was measured, and the 400 reflection for the 400 and 800 sample reflections. The dispersion broadening was calculated according to

W = a)./').(tan O~ t - tan 0s), (2}

where D2 is the spectral line width and 0~ ~ and 0~

are the Bragg angles for the monochromator and specimen, respectively.

For the ( + n , - m , + n) setting, the dispersion broadens the peaks in the direction parallel to H but they remain unchanged in the transverse direction.

We utilized the Bragg and Laue settings when studying the silicon-based HSs and used the symmetric Bragg settings for GaSb layers grown on GaAs substrates. TEM plan view and cross-section images were obtained to characterize the defects and to reveal their distribution across the layers. JEOL JEM-7A and 100C (100 kV) microscopes were used.

3. Experimental results

3.1. X-ray di[]'raction .li'om Si t xGe.,./Si HSs

When measured in a double-axis mode with use of both geometries, Sit .,G%/Si HSs with a fixed value of x (x = 0.07) showed two peaks from the substrate and the layer, with the latter remarkably broader than the former. By using the third crystal as an analyzer, we made a series of 0 scans and found that the full widths at half-maxima (FWHMs} of the obtained curves l(x) were much larger than those expected for a high-quality crystal. This means that the experi- mental curves were broader than the convolution of the monochromator reflecting curve with that of the analyzer. Integration of the scattered intensity normal to the reciprocal-lattice vector provided the plot of J(qn) according to (1)(Fig. 1). The J(qn) plots contained two peaks belonging to the substrate and the layer: the latter being noticeably narrower than in the double-crystal rocking curve. Thus, we quantified the scattering in such a way that we obviously improved the resolution of the curves obtained in the double-axis mode.

Comparing the Bragg and Laue diffraction data presented in Fig. 1, one can see that, tirstly, the layer

4 i[ k \\ 10

, I / / t 2 / / ~ \ \ \ \ 5 , 20" ,

L/Y " ' --- . . . .

-2.0 -I.5 qn [ l@cm-I]

Fig. 1. Tile ,l(qn) intensity distribution along H plotted fl}r Si I . .,Ge, Si HS {x = 0.07) with use of the l,auc setting {solid linel ;.ind the Bragg one {dashed line}. 400 Me Kz~ radiation. The qu-axis reference point is the position of the substratc peak.

702 DEFECTS IN LATTICE-MISMATCHED EPITAXIC STRUCTURES

peak in the reflection geometry is wider than in the transmission and, secondly, the distances between the layer peaks and the substrate ones are identical. Since these are the interplanar spacing components, namely, (6d/d)± and (6d/d)l I, which are responsible for the peak positions, we must conclude that (6d/d)± = (6d/dll). Stress relief implies the presence of MDs and, in our case, as the tetragonal distortion was found to be totally absent, MDs arranged in the networks completely accommodate the lattice misfit in the interfaces. In support of this point, X-ray topography and T E M have been applied to the studied structures. The topography revealed the M D networks and TEM showed them to be flat and to be localized actually in the interfaces.

The results of 0 scans for the structures with x growing from 0 at the interface to 0.15 at the layer surface are demonstrated in Fig. 2. The curves obtained in the two geometries have similar features that may be characterized as follows:

(a) the width of the peaks varies along the qH axis; (b) the height of the maxima slowly changes in the

same direction; (c) the tops of the peaks are displaced from the qH

axis (Table 1). The diffraction data have also been presented as

maps in reciprocal space (Fig. 3). it is obvious that the conclusions drawn from these maps are exactly the same as those derived from the characterization of the 0 scans.

The J(qH) curves are shown in Fig. 4. It can be seen that the plots have an oscillating shape and that the number of oscillations in the Bragg case is larger. Considering the reasons for this phenomenon, we have to suggest the depth variation of the interplanar spacing components. In the transmission setting, the vector H is parallel to the specimen surface; thus, it is the parallel component (6d/d)l, that should be

j

50 / "" 100" 80"

180"

0 , , 0 -

Fig. 2. Laue 0-scan curves I(~) obtained from the Si~ _~Gex/Si HSs with different analyzer positions (x increases within the layer depth). The narrower peaks are pseudo-peaks appearing at the substrate reflection conditions. The arrows indicate the shift 6~ of the I(~) peaks from the qH axis.

Table 1. The structural parameters o f the sublayers in the Sil_xGex/Si HS with varyinq x value (Laue

settin,q)

Sublayer* I 2 3 Ri x 10- 7 4.5 10.4 9.9 t (p.m) 1.4 (1) 3.1 (2) 3.0 (2) W ± ~") 110 (5) 140 15) 145 (51 6~ (") 62 (5) 120 (5) 140 (5)

(6d/d) ( × 10 -4) 4.5 (3) 10.7 (3) 14.5 (3)

* Sublayer 1 is closest to the substrate.

assumed to change within the layer depth. Good resolution of the peaks is convincing evidence for a steplike variation. Therefore, we could treat the peaks as corresponding to the sublayers separated by the networks of M Ds. Since x increased upwards, the

(a)

(} ? ~ k , , ) ~ ' 4 , x 10"(cm-~l)

q~

~ HH

(h)

Fig. 3. The intensity contours around the 400 reciprocal-lattice point (Mo K~, Si~ ~Gex/Si HS with changing x value). (a) Bragg geometry. (h) Laue geometry.

R. N. KYUTT, S. S. RUVIMOV AND T. S. A R G U N O V A 703

sublayers with larger (6d/d)± values were closer to the surface. When revealed, the networks could be characterized as follows" their location depths derive from the sublayer thicknesses and their densities are evaluated from the peak positions.

To determine the thickness of a sublayer, we integrated its reflectivity Ri and used the well known expression of the kinematical theory (James, 1948):

Ri = I(~) de dO/Io R.a,

= [rcZz 2 e x p ( - 2 M ) / 2 sin 20B]

x P(t/cos On) exp (- /~T/cos 0,), (3)

where I o is the intensity of the beam incident on the sample, R a is the integral reflectivity of the analyzer, T is the substrate thickness, t is the sublayer thickness, M is the Debye-Waller factor, gn is the Fourier component of the polarizability, P is the polarization factor, # is the absorption coefficient and 0E is the Bragg angle.

The kinematical approximation is justified by the fact that the sublayer thicknesses are small compared to the extinction depths corresponding to the diffraction conditions.

The J(qn) peak positions provide the steps of the abruptly varying in-plane component. The MD density can be estimated from these steps:

N = (6d/d),/bll, (4)

where bll is the Burgers vector component parallel to the interface• The results are presented in Table 2.

When processed, the data were displayed as the (6d/d)l 2 depth profile (Fig. 5). Using Bragg's law, we evaluated the step heights from the distances between the sublayer peaks and the substrate position (the reference point). The step widths were calculated according to (3). The TEM cross section is placed alongside the diagram in Fig. 5. The agreement is

?

t,\ I f \ l

2 I

/ / /

-3.0 -2.0

.<._

r ~.JA~ I l.o

a / \ l I ,'? \,, ,.,/

•

I I . -1.0 0 qH [l~crn-tl

Fig. 4. The Bragg (dashed line) and the Laue (solid line) J(qn) curves for the graded Sil _ xGG/Si HS. The dashed-dotted line represent the DCD rocking curve R(~); the specimen angle ~ is expressed as ~ = qn/2k cos 0B, where k = 1/2.

Table 2. The M D densities between sublayers in Sil_xGex/Si (X = 0-0.15) HSs obtained from TCD

and T E M data

Interfaces 0-1 1-2 2-3

Dis locat ionon densities N ( 1 0 - 4 c m -x)

TCD 2.3 3.2 2.0 TEM 1.0 3.0 2.0

good enough; the distances between the networks de- termined from the TEM data are equal to the thicknesses of the sublayers responsible for the peaks in Fig. 4. From comparison of the MD densities, we found that the TEM plane view and TCD results fitted each other (Table 2). Before this evaluation, MDs were identified by TEM diffraction analysis (Hirsch, Howie, Nicholson, Pashley & Whelan, 1965). They were found to be primarily of the 60 ° type with the Burgers vector b of a/2(110).

3.2. Strongly mismatched GaSb/GaAs HSs 9rown by MBE

It was shown that strongly mismatched GaSb/- GaAs HSs, compared to nearly perfect epitaxic structures, exhibited a remarkable broadening of the diffraction peaks in both 0 and 0-20 scans. In order to check whether these structures were mosaic to some degree or not, we treated the diffraction data in the following way. We assumed that the disorder comes

1.5

N" 1.0

0.5

I \%

N'~'N %. [

! 5

t [gml

%INNNNNd • 10

Fig. 5. Sil_xGeffSi HS (6d/d)ll depth profile obtained from the Laue-geometry measurements and its TEM cross-section image. The dashed line shows how x increases with the layer depth.

704 I)EFI:'('TS IN 1.ATT1CE-MISMATCHEI) EPITAX1C STRUCTURES

from three sources, such as the finite size of the scattering regions, the misorientation between them and the strain inside each region. In an attempt to support or to reject the treatment, we plotted the dependence of the full width at half-maximum (FWHM) values obtained by both scans on the Bragg angle. Cu K:~ and Mo K~ wavelengths and 200, 400 and 800 sample reflections were used. We found that

(a) the reflections were broadened in the directions parallel and perpendicular to the reciprocal-lattice vector H;

(h) the broadening in the transverse direction to H was always larger than in the parallel one;

(c) F W H M values W± measured normal to H were independent of the wavelength and the reflecting order (Fig. 6);

(d) F W H M values W I parallel to H rose linearly with tan 0 R (Fig. 6).

The results obtained forced us to correct the initial consideration. Assuming the finite size of the coherent scattering regions, one should expect the I4<, and W~ values to increase with s in0 B and cos0 R according to,

W = ) , / 2 t 1 cos 0 H, W± =) . /2 t 2 sin 0 u,

where t I and t2 are the average sizes of the scattering regions in the directions parallel and perpendicular to H, respectively.

Since we found no dependence of this type, we had no means of making a judgement about the presence of small grains inside the layers. Consequently, we had to conclude that either we dealt with large blocks and their size contribution was small compared to their strain and tilt, or we were unable to treat the diffraction from the layers like that of a mosaic crystal. Having chosen the latter conclusion, we interpreted the large parallel W values as being due to the high density of threadingdislocations inside the layers. As to the dependence of these values on the Bragg angle, it is known from the theoretical considerations

(Ryaboshapka, 1981 ) that, when distributed randomly inside a crystal, dislocations cause W, to vary linearly with tan0B. So, the dislocations were concluded to be arranged in a rather disordered manner. But their density is high, and if they should gather in groups and form low-angle boundaries, this will prove to be the reason for the large perpendicular W± values.

The interpretation of the X-ray data was checked by applying the TEM technique. The threading dislocation density was found to decrease from 10 '° cm 2 at the interface to 10 a c m 2 at the layer surface. In most cases, the overall dislocation density was reduced for distances of about 200-400 nm from the interface. The majority of threading dislocations had Burgers vectors of the type a / 2 ( l 1 0 ) and they lay on their respective [111] glide planes. Those dislocations located near the surface were found to be mainly of the screw type. The plane-view images showed the dislocations to be arranged randomly. Nevertheless, groups of parallel dislocations with identical Burgers vectors were also observed and may be characteristic of fragments of low-angle bound- aries. The parallel dislocations in the groups were primarily of the screw type. The effective tilt associated with such an array can be evaluated as follows:

6¢b = n h / n L = h/L ,

where n is the number of dislocations in the group, L is the distance between the dislocations and h is the dislocation-Burgers-vector modulus.

If L is taken as 0.5 1.01Jm and h is equal to 4 × 10 4" tam, the roughly estimated tilt is 80-160". From the X-ray diffraction data, it follows that F W H M values of the 0-scan peaks are equal to W~ = 150" (Fig. 6). A good agreement of the results confirms that it is the tilt provided by the groups of dislocations that broadens the diffract,ion peaks in a direction normal to H.

200

150

100 ~ (h)

0 ; 110 1; 2'0 3'0 OB[°]

Fig. 6. The dependence of the FWH M values obtained by (a) 0 20 and (h) 0 scans on the Bragg angle fin: GaSb GaAs IIS.

4. Discussion

While processing the data, we used widely the J(qll) intensity distribution along the diffraction vector obtained from 0-scanning measurements.

Summarizing the advantages of this pattern, we want to emphasize the following points. When layers are nearly perfect and their lattices match the substrates, all the J(qll) characteristics are quite the same as those of the double-axis rocking curves. But the appearance of MD networks strongly worsens the resolution of the latter. The low resolution could also be caused by a high density of threading dislocations inside the layers. Plotting the J(qll) curve, one can observe a good separation of the peaks, because the influence of MDs is entirely eliminated: as for

R. N. KYUTT, S. S. RUVIMOV AND T. S. ARGtJN()VA 705

threading dislocations, most of the broadening, namely, that in the transverse direction to H, is kept out. When the peaks are fairly well discerned, the lattice-spacing variation as well as the thickness of the layers can be obtained. 0-20 scanning is also known to provide the intensity distribution along H. Utilizing this scan, one should be aware of the fact that the J(q,) and 0-20 scanning patterns completely tit each other only when the lattice tilt is absolutely absent and the ()-scan FWHM values are identical at every point. In this case, the tops of the 0-scan peaks are aligned strictly parallel to H.

Now, we discuss the problems associated with interpretation of the patterns from HSs with structural defects inside the layers. Dealing with a multilayer structure or a graded layer, we obtain rocking curves of a complicated shape. When layers are nearly perfect and the dynamic theory or semikinematical approx- imation may be employed, one finds the (6d/d)± depth protile by using a simulation of the curve. In an attempt to analyze the curves from the lattice- mismatched HSs with defects in their interfaces, we immediately face some difficulties. A few peaks observed in the Bragg reflection curve are certainly due to the depth variation of the (M/d)± component, but whether the character of the distribution is step-like or smooth cannot be established without a simulation; and it is also hard to say how the observed peaks correlate with the scattering layer depth. The basic principles of the simulation in this case still remain unclear. So, we have to consider each peak in the curve as corresponding to a definite sublayer. The sublayer depth can be estimated by utilizing different X-ray wavelengths and by comparing the peak intensities in different absorption conditions. Besides, the change in the lattice spacing is already known from the growth conditions. When the corre- spondence between the sublayers and the peaks is found, we can ewfluate the thickness of the sublayers. For nearly perfect layers, the thickness is obtained from either the integral reflectivity or the relative intensity measurements. The integral reflectivity is measured with respect to the intensity of the incident beam, otherwise, the intensity reflected from the layer should be evaluated relative to that of the substrate. For HSs with MDs, not only the layer peaks but also the substrate peak are broadened. Since the intensity of the latter peak does not comply with the dynamic theory, the only way to lind the correct thicknesses of the sublayers is to determine them from the integral reflectivity of the corresponding peak.

When the MD network is actually located in the interface, the layer thickness is the depth of the MD locations. Throughout our experiments with Si~ .,Gex/Si HS, M Ds were detected by direct Laue setting measurements of (&l/d). But the in-plane data can also be obtained from the asymmetric Bragg

geometry, which is especially convenient for high- absorption substrates.

As mentioned previously, without simulation one cannot establish the character of the (6d/d)~ depth profile as being step-like or smooth. For Sil .~Gex/Si HSs with x increasing upwards, the number of J(q,) peaks in the Bragg case was larger than in the Laue case (Fig. 4). The comparison of these two plots enabled us to conclude that three peaks located far from the substrate were due to the (~d/d), variation in the region below the surface. But from the X-ray diffraction data, we were unable to find whether the three sublayers with the abrupt interfaces or one layer with a smoothly changing interplanar spacing were responsible for the peaks. The examination of the TEM cross sections gave a convincing reason for the smooth character of the upper region (Fig. 5).

When a correlation between the peaks in the rocking curve and the depth of the sublayers is found, it appears possible to assess the structural quality of each sublayer by using the 0 scan. When the analyzer remains fixed, it allows us to choose the lattice spacing of the definite sublayer and to characterize its imperfection from the width, the shape and the position of the corresponding peak. We applied this technique to Sil xGe.USi HS with the changing x value. The tops of the peaks in both the Bragg and I~aue settings were found to be displaced from the q~ axis (Fig. 2), with the displacement abruptly varying along the axis. The effect was obviously due to a large tilt of the sublayer lattice planes relative to that of the substrate. The abrupt character of the variation was caused by the MD networks between the sublayers. Since the displacement increased with distance from the substrate reciprocal-lattice point and the layer lattice spacing was known to grow in the same direction, the tilt of each upper layer was larger than that of the lower one. In our case, TEM diffraction analysis showed the MDs to be of the 6 0 type. It was shown by Nagai (1974) that, when the substrate surface was inclined with respect to (001) plane, such a network made the layer planes slope from the substrate ones. We found that the tilt rose upwards.

The widths of the curves increased in the same direction. Because of the far-reaching strain fields of the networks (Argunova, Kusov, Petrashen & Shul'pina, 1987), we were, unfortunately, unable to detect the localization of each network by 0 scanning. But if the layer contains other types of structural defects, for example, Coulomb-type ones, their strain lields do not reach far from their location. The difl'use scattering is located near the layer reciprocal-lattice point, so the () scan in the triple-axis mode is a reliable technique for extraction of the depth distribution of these defects.

in this paper, the results have been displayed either as a series of 0-scan curves (Fig. 2) or as

706 DEFECTS IN LATTICE-MISMATCHED EPITAXIC STRUCTURES

two-dimensional maps in the scattering plane (Fig. 3). These two representations are identical but the curves seem to be more evident, because one can simultan- eously observe the shape and estimate the broadening in two directions; the latter is important, when comparing structures with different arrangements of dislocations. Two-dimensional mapping is preferable for studying diffuse scattering; hence, the shape of the contours is primarily due to the structure of the defects.

5. Concluding remarks

We have presented X-ray triple-crystal diffractometry investigation of the structural defects inside the layers lattice mismatched to the substrates. Using various scans, we have analyzed the diffracted intensity in two directions in the scattering plane. The Bragg and Laue diffraction patterns have been compared.

Two types of dislocation arrangements were studied, namely, the misfit dislocation networks in Si~_xGex/Si HSs and the threading dislocations of high density inside the GaSb layers strongly mismatched to GaAs substrates. It has been shown that MD networks cause reflections to broaden in the direction normal to the reciprocal-lattice vector H. As to the threading dislocations, they were responsible for the broadening in both directions, which indicated a disorder coming from two sources. One results from the high density of randomly distributed disloca- tions. The second source is associated with the dislocation arrays or the fragments of low-angle boundaries.

From the Laue diffraction paterns obtained from Si~ _xGex/Si HSs we have detected

(i) the localization of MD networks; (ii) the tilt of the layers with respect to the

substrates;

(iii) the depth of the layers with respect to the substrates;

(iv) the depth variation of this tilt, with x increasing from the interface to the surface.

The structural parameters determined from the X-ray data are in agreement with direct TEM observations.

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