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Analysis of thermal-treatment-induced dislocation bundles in GaAswafers by means of X-ray transmission topography and complementarymethodsP. Mock
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J. Appl. Cryst. (2001). 34, 65–75 P. Mock � Dislocation bundles
J. Appl. Cryst. (2001). 34, 65±75 P. MoÈck � Dislocation bundles 65
research papers
Journal of
AppliedCrystallography
ISSN 0021-8898
Received 2 March 2000
Accepted 3 November 2000
# 2001 International Union of Crystallography
Printed in Great Britain ± all rights reserved
Analysis of thermal-treatment-induced dislocationbundles in GaAs wafers by means of X-raytransmission topography and complementarymethods
P. MoÈck²
Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, England.
Correspondence e-mail: [email protected]
By means of a heat treatment that was part of a molecular beam epitaxy (MBE)
growth procedure, dislocation bundles have been induced in two-inch-diameter
undoped (001) GaAs substrates. On the basis of contrast variations in
synchrotron-based single-crystal X-ray transmission topograms that were
recorded under conditions of high anomalous transmission, these dislocation
bundles have been classi®ed into three different types. Dislocation bundles of
the majority type start at the sample edges in regions around the four h100iperipheral areas, glide typically up to about 1.5 cm into the bulk of the wafer
following perpendicular h110i line directions, and form a pseudo-symmetric
fourfold set. There are dislocations with two different Burgers vectors in each
majority-type dislocation bundle and the extended segments of all of these
dislocations are of the 60� type. In order to explain complementary experimental
results, it is suggested that dislocation pairs are formed in the majority-type
dislocation bundles. Theoretical support for this hypothesis is derived from a
model of plastic deformation of GaAs wafers during typical MBE growth.
Dislocation bundles of two minority types, on the other hand, are not part of the
fourfold set and originate in peripheral areas at and around h110i.
1. Introduction
It has been demonstrated in a recent X-ray topography survey
that a quite common, radiatively heated, non-indium-bonded
sample-holder design can cause severe plastic deformation in
two-inch-diameter GaAs (001) substrates when the sample is
heated to about 923 K in a molecular beam epitaxy (MBE)
machine and subsequently cooled to room temperature
(MoÈ ck, 2000a). In addition, it is known that heat-treatment-
induced plastic deformation of GaAs substrates is a key factor
that reduces the yield of electronic devices in manufacturing
processes on an industrial scale (Tatsumi et al., 1994; Kiyama et
al., 1997; Sawada et al., 1996).
It is expected that the current market for four-inch-
diameter GaAs wafers will, in the near future, be overtaken by
demand for six-inch-diameter GaAs substrates for industrial
applications (Sawada et al., 1995). Since the thermal-treat-
ment-induced residual strain and plastic deformation is more
dif®cult to avoid in the latter case (Flade et al., 1999) and
because further thermal processing of already dislocated
wafers that possess residual strain leads to more plastic
deformation (Tatsumi et al., 1994; Kawase et al., 1993), it will
be bene®cial to identify the key features of the plastic defor-
mation process.
In our case (MoÈ ck & Smith, 2000), the technical problem of
plastic deformation could be overcome by modi®cations to the
sample holder of a custom-built MBE machine. The science
concerning the nature of the dislocation bundles and the
mechanisms involved in the plastic deformation of two-inch-
diameter substrates, however, remains of interest and it is
likely that the same mechanisms operate more readily in
larger-diameter III±V semiconductor wafers.
The main aim of this paper is to perform a complete Burgers
vector analysis on dislocation bundles of the so-called majority
type for one sample that was part of the earlier X-ray
diffraction topography survey (MoÈ ck, 2000a). For the discus-
sion of the X-ray topography data, results of complementary
analyses that employed scanning infrared polariscopy, visible-
light interferometry, Nomarski microscopy, high-resolution X-
ray diffractometry and transmission electron microscopy will
be drawn upon (MoÈ ck et al., 1999, 2001; MoÈck & Smith, 2000).
In addition to the Burgers vector analysis and in order to
verify its results, the point symmetry group of the crystal-
lographic parameters of the plastic deformation that is
realised by the majority-type dislocation bundles will be
elucidated.² Present address: Department of Physics (MC 273), University of Illinois atChicago, 845 West Taylor Street, Chicago, IL 60607-7059, USA.
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66 P. MoÈck � Dislocation bundles J. Appl. Cryst. (2001). 34, 65±75
The results of the X-ray transmission topography study [and
the results of the complementary studies (MoÈ ck et al., 1999,
2001)] reported herein have been used for the development of
a new model for the plastic deformation of GaAs wafers under
conditions that are typical for MBE growth (MoÈ ck, 2000b).
Since this model accounts for the core of the experimental
observations in a semi-quantitative manner, it lends theore-
tical support to the dislocation-pair formation hypothesis
presented in this paper.
2. Experimental details
The sample that was selected for the X-ray transmission
topography, scanning infrared polariscopy and Makyoh
topography analyses of this study is a double heterostructure
which consists of an undoped vertical-gradient freeze-
Bridgman-grown two-inch-diameter GaAs wafer, with (001)
orientation and 450 mm thickness, a GaAs buffer layer of
thickness 500 nm, an In0.06Ga0.94As epilayer of thickness
60 nm, and a GaAs capping layer of thickness 10 nm. The
epitaxic structure was grown by MBE in a Varian Gen II
machine at a rate of one monolayer per second. While the
GaAs buffer layer was grown at 873 K, both of the hetero-
epitaxial layers where grown at 793 K. Prior to the epitaxial
growth, the surface oxide was desorbed at a temperature of
923 K.
This sample was analysed by means of synchrotron-based
single-crystal X-ray transmission topography under conditions
of high anomalous transmission, employing the experimental
facilities at Daresbury Laboratory (UK). A complete set of
symmetry-related 111, �111, 202, 313 and �313 topograms was
recorded on double-sided Agfa-Gevaert Structurix D4 X-ray
®lm. While topograms of the 111 and �111 re¯ections and two
of the 202 re¯ections were taken at more or less optimized
azimuths at � = 0.13 nm [i.e. just above the Ga K-absorption
edge at 0.1195 nm (International Tables for X-ray Crystal-
lography, 1985)], deliberate azimuthal offsets of about 10�
resulted in the simultaneous diffraction of pairs of 202 and 313
or �313 re¯ections at �1 = 0.073 nm and �2 = 0.053 nm [i.e. just
above the In K-absorption edge at 0.0444 nm (International
Tables for X-ray Crystallography, 1985)]. The optimized
azimuth is de®ned by the condition that the normal of the
diffraction plane, the incident and the diffracted beam are
coplanar. Experimental details on the complementary scan-
ning infrared polariscopy and Makyoh topography studies of
this and other samples of the same sample series (MoÈ ck,
2000a) have been presented by MoÈck et al. (1999).
For comparison purposes only, a 1�11 topogram was
recorded at � = 0.13 nm from a second sample of the same
sample series (MoÈ ck, 2000a) on an Ilford L4 nuclear plate. The
growth conditions of this second sample were identical to
those of the ®rst sample and it differs from the ®rst sample
only in so far as its heteroepitaxial layers are twice as thick as
the heteroepitaxial layers of the ®rst sample. As an 0�22topogram of this second sample shows (MoÈck & Smith, 2000),
its In0.06Ga0.94As layer, of thickness 120 nm, is partly relaxed
by mis®t dislocations at the interface between this layer and
the underlying GaAs buffer layer.
Different kinds of X-ray transmission topography are
distinguished in Appendix A on the basis of the prevalent
absorption conditions. Brief comments on the Burgers vector
determinations by means of X-ray diffraction topography
under conditions of high anomalous transmission are given in
Appendix B.
Epitaxial samples were used for this study because they
were, on the one hand, readily available, and on the other
hand, as shown by Tatsumi et al. (1994) and Kawase et al.
(1993), perfectly adequate for this purpose. This is because the
defects in the GaAs substrates are not caused by the epitaxial
growth process itself, but by the thermal treatment associated
with it (Tatsumi et al., 1994; Kawase et al., 1993).
3. Results of the X-ray transmission topography study
3.1. Distinction between majority- and minority-typedislocation bundles on the basis of their respective spatialarrangements
As Figs. 1, 2 and 3 show, the plastic deformation is mainly
(i.e. typically up to about 98%) realised by bundles of dislo-
cations which start at the sample edges around the four h100iperipheral areas, glide into the bulk of the substrate following
h110i and h1�10i line directions, and form a pseudo-symmetric
fourfold set in undoped GaAs. These dislocation bundles are
called majority-type dislocation bundles and typically extend
up to about �25� around h100i poles (see also MoÈ ck, 2000a).
As the previous studies (MoÈck, 2000a; MoÈ ck et al., 1999)
showed, there can also be dislocation bundles of another type
with a spatial distribution that is centred at and around h110iperipheral regions; these are called minority-type dislocation
bundles (MoÈck, 2000a). This term is used in a generic manner,
being applied to all dislocation bundles that do not belong to
the majority type. While dislocation bundles of the ®rst
minority type tend to be located at or rather close (i.e.��10�)to h110i poles, dislocation bundles of the second minority type
typically deviate by �10� up to about �35� around h110ipoles. Thus, these minority-type dislocation bundles can exist
in areas that are occupied by the pseudo-symmetric set of
majority-type dislocation bundles (see also MoÈ ck, 2000a).
3.2. Assessments of majority-type dislocation bundles
A comparison of Figs. 1(a) and 1(b) shows that the contrast
of the majority-type dislocation bundles is rather similar in
both topograms, despite the fact that opposite surfaces of the
sample have been exposed ®rst to the incoming X-ray beam.
The Borrmann fans (see Appendix B) of the majority-type
dislocation bundles are, thus, rather similar for both re¯ec-
tions. This indicates that the dislocation bundles are distrib-
uted through the whole thickness of the substrate but are
de®nitively not con®ned to the epitaxial structure±substrate
interface.
A comparison of the widths and contrast of individual
quarter subsets of minority-type dislocation bundles in the 0�22
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(Figs. 1a and 2b), 202 (Fig. 2c) and �20�2 (Fig. 1b) topograms
indicates that there must be dislocations of more than one
Burgers vector (bi) in each bundle that belongs to the pseudo-
symmetric fourfold set since there is reduced contrast and
widths (i.e. reduced Borrmann shadow) when gj � bi = 0 is
ful®lled for parts of the dislocations in a bundle. Thus, at least
three re¯ections are required for a determination of the
Burgers vectors in dislocation bundles of the majority type.
In contrast to the intuitive impression of similar `extinction
of shadow contrast' for one quarter subset (markers `A1' and
`A2' in Fig. 1a) of the dislocation bundles in the 1�11, 1�33 and
3�13 re¯ections (Figs. 2a, 2b and 2c), we consider that there is
only partial extinction of the Borrmann shadow in the 1�33 and3�13 topograms, while there is almost complete extinction in
the 1�11 topogram (since the latter plane is the slip plane of all
the dislocations within these bundles). This can be justi®ed by
the cross product [1�33] � [3�13] = �[�334], which does not lead
to an energetically stable Burgers vector in the sphalerite
structure.
The line directions of the quarter subset (markers `A1' and
`A2' in Fig. 1a) of dislocations with `extinction of shadow
contrast' in the 1�11, 1�33 and 3�13 re¯ections (Figs. 2a, 2b and
2c) are�[110]. Since b1 = [1�11]� [1�33] = [1�11]� [0�22] = [1�33]� [0�22] = �1
2[011] and b2 = [1�11] � [3�13] = [1�11] � [202] =
[3�13] � [202] = �12[10
�1], the dislocation type becomes 60�.Table 1 summarizes the parameters of all of the dislocations
that make up the pseudo-symmetric fourfold set of majority-
type dislocation bundles.
Applying Curie's symmetry principle (Shuvalov, 1988;
Pau¯er, 1986; Curie, 1894) to the problem of plastic defor-
mation of GaAs substrates in a typical MBE growth chamber,
one has to conclude that the dislocation parameters as given in
Table 1 have to be related by the symmetry elements of the
point group �42m, which is the result of the intersection of the
two point groups1mm for the temperature ®eld and �43m for
the crystal. Except for the always present symmetry element 1
and including the inverse symmetry elements, the point group�42m consists of a combination of two parallel fourfold inver-
sion axes (also called inverse tetrads) in [001] orientation, with
two mirror planes (also called mirror re¯ections) in [110] and
[�110] orientation, and three mutual perpendicular twofold
axes (also called diads) in h100i orientation (Pau¯er, 1986).
Employing the respective rotation matrices of these
symmetry elements as given in standard text books on physical
crystallography (e.g. Pau¯er, 1986), the crystallographic
parameters of all of the dislocations in Table 1 can be calcu-
lated solely from the experimentally observed dislocation
parameters of the bundle that is denoted as `A1' in Fig. 1(a).
Such calculations were compared with experimental obser-
vations from other dislocation bundles of the pseudo-
symmetric set of majority-type dislocation bundles and
enabled checks on the internal consistency of the crystal-
lographic indices of all re¯ections, and the direct- and reci-
procal-lattice vectors that are given in this paper. In addition,
it becomes obvious from these calculations and from consid-
erations of the multiplicity of general and speci®c poles in the
point group �42m, that the set of majority-type dislocation
bundles is complete, indicating that all other dislocation
bundles in the sample must belong to different types.
From the fact that the widths and contrast of the quarter
subset (markers `A1' and `A2' in Fig. 1a) with the `extinction of
shadow contrast' in the 1�11, 1�33 and 3�13 topograms (Figs. 2a,
2b and 2c) are similar in the 0�22, 202 and �20�2 topograms (Figs.
1a, 2b, 2c and 1b), where dislocations with either one or the
J. Appl. Cryst. (2001). 34, 65±75 P. MoÈck � Dislocation bundles 67
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Figure 1Single-crystal transmission topograms (taken at � = 0.13 nm): (a) 0�22 re¯ection, (b) �20�2 re¯ection. The major diameter of the ellipses is about 4.8 cm.These topograms and those in Figs. 2, 3 and 4(a) represent X-ray analogues of photographic positives (i.e. increased X-ray radiation intensitycorresponds to increased brightness in the images). The Burgers vectors, line directions, glide planes and peripheral areas of origin of the majority-typedislocation bundles, denoted by the markers `A1' to `D2' in (a), are listed in Table 1. All topograms of this paper, except (b) above, are indexed on thebasis of a right-handed axis system with the [001] direction pointing downwards with respect to the observer. For (b), a right-handed axis system has beenused where the [00�1] direction points downwards with respect to the observer. As the indexing of the topograms indicates, different sides of the waferwere initially exposed to the incoming X-ray beam when (a) and (b) were recorded. In (a), the majority-type dislocation bundles follow a clockwisesequence in alphabetical order (`A1', `A2', `B1', `B2', `C1', `C2', `D1', `D2') that starts from the 12 o'clock position. In (b), these dislocation bundlesfollow an anticlockwise sequence in alphabetical order that starts from the 9 o'clock position. There are several artefacts caused by moving and mountingthe sample by means of tweezers. These artefacts are particularly numerous at the region around the major ¯at (10:30 o'clock position in both images)and facilitate comparisons of the contrast of individual dislocation bundles for different re¯ections.
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68 P. MoÈck � Dislocation bundles J. Appl. Cryst. (2001). 34, 65±75
other Burgers vector are extinct, it
is concluded that the number of
dislocations of each of the two
Burgers vectors are similar as well.
There is a clear difference in the
contrast of the quarter subset that
is denoted as `B1' and `B2' in Fig.
1(a) in the 0�22 and 202 topograms
(Figs. 1a, 2b and 2c). While about
half of the dislocations in this
quarter subset seem to be extinct
in the 202 topogram, all of the
dislocations are responsible for the
pronounced Borrmann shadow of
this quarter subset in the 0�22topogram. Based on these and
similar observations from the rest
of the 220-type topograms, it is
concluded that about one quarter
of the dislocations in a pseudo-
symmetric set of majority-type
dislocation bundles is extinct in
any one 220-type re¯ection.
While Figs. 1, 2 and 3 have been
reproduced in order to illustrate
the `extinction of shadow contrast'
effects for the main sample of this
analysis, Figs. 4(a) and 4(b), and
Figs. 4(d) and 4(e) show sections of
several topograms from the same
sample in higher magni®cations.
As can be clearly seen in Figs. 4(a)
and 4(b), the constituent disloca-
tions of a majority-type dislocation
bundle follow more or less straight
lines that are parallel to h110idirections which are perpendicular
to the surface normal. These
dislocations start at the rim of the
wafer and end in segments that
typically form a small hook and
eventually thread to the free wafer
surfaces [i.e. the (001) and (00�1)planes]. Hair-pin-shaped ends of
dislocations were occasionally
observed as well.
Fig. 4(c) shows, for comparison
purposes only, a section of a
majority-type dislocation bundle of
the second sample. Since this
topogram has been recorded on a
nuclear plate rather than a less-
expensive X-ray ®lm, the resolu-
tion is much higher. A majority-
type dislocation bundle with a
signi®cantly higher dislocation
density is shown in Fig. 4(c) to
g
g
g
( )a
( )b
( )c
Figure 2Single-crystal X-ray transmission topograms: (a) 1�11 re¯ection, (b) 0�22 (right) and 1�33 (left) re¯ections,(c) 3�13 (left) and 202 (right) re¯ections. The major diameter of the ellipse of the 1�11 topogram (a) is4.8 cm. The straight line across this topogram is caused by the pasting together of the upper and lowerhalves of the topogram, as the height of the X-ray beam was not suf®cient to record the re¯ected-transmitted intensity from the whole wafer in one image. The 0�22, 1�33, 202 and 3�13 topograms are framedby the edges of a set of slits that reduced the dimensions of the incoming X-ray beam. The wider slitdistance in these topograms is about 4.1 cm for (b) and about 4 cm for (c). The regions of enhanced X-rayintensity (i.e. the bright stripes) at the lower left edge (third quadrant, 7:30 o'clock position) of the 3�13topogram (c), and at the left-hand side (9:00 o'clock position) in the 1�11 topogram (a), are caused bydiffusely scattered white X-ray radiation that passed through the sample mounting at the major ¯at of thesample. The majority-type dislocation bundles in (a) follow a clockwise sequence in alphabetical orderthat starts with `A1' at the 10:30 o'clock position. Since (b) is in the same orientation as Fig. 1(a), the samesequence of majority-type dislocation bundles applies for both images. In (c), the majority-typedislocation bundles follow a clockwise sequence in alphabetic order that starts with `A1' at the 9 o'clockposition. The majority-type dislocation bundles `A1' and `A2' show `extinction of shadow contrast' in the1�11, 1�33 and 3�13 topograms.
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consist of dislocations with the same arrangement as the
dislocations depicted in Figs. 4(a) and 4(b).
3.3. Assessments of minority-type dislocation bundles
Figs. 3(a) and 3(b) show `extinction of shadow contrast' in
the 111 and �111 topograms for a dislocation bundle of the ®rst
minority type (denoted as `MT 1' in Fig. 1a) that exists in the
[110] peripheral area opposite the major ¯at of the wafer. This
dislocation bundle is also extinct in the �133 re¯ection (topo-
gram not shown), leading to a Burgers vector of�12[0
�11]. Since
the line direction of this bundle is [�1�10],the constituent dislocations belong to
the 60� type.Fig. 4(d) shows this dislocation bundle
in �202 re¯ection in a higher magni®ca-
tion. In comparison with all other dislo-
cation bundles in the wafer, this
particular bundle has a very low dislo-
cation density. From a comparison of this
®gure with Figs. 4(a) and 4(b) and the
discussions above, it is obvious that this
particular dislocation bundle belongs to
a type that is different from the majority
type.
The minority-type dislocation bundles
of the second type, e.g. marker `MT 2' in
Fig. 1(a), were more dif®cult to access
since they seem to consist partly of
thermal-treatment-induced dislocations
that have interacted with grown-in dislocations. This led to
ambiguities in the determination of possible `extinction of
shadow contrast' conditions for various re¯ections. There
were, in addition, experimental limitations such as obstruc-
tions caused by the X-ray beam reducing slits in several of the
topograms, which occasionally prevented the imaging of these
dislocation bundles.
Fig. 4(e) shows the area where such a dislocation bundle
comes into close contact with a branch of the majority-type
dislocation bundle `B2', in higher magni®cation for the 1�11re¯ection. From a comparison of Fig. 4(e) with Fig. 4(d) and
the discussions above, it is obvious that this particular dislo-
cation bundle belongs to a type that differs from both the
majority and the ®rst minority type.
4. Discussion
4.1. Nucleation and arrangement of dislocations in majority-type dislocation bundles
Yonenaga & Sumino (1993), Matsui (1987) and Brown et al.
(1983) suggested that dislocation bundles with h110i line
directions and {111} glide planes in plastically deformed GaAs
are nucleated at surface sources. The dislocation arrangements
given in these papers resemble closely the arrangement of the
dislocations in the majority-type dislocation bundles, as given
in x3.2. Therefore, following the suggestion by Yonenaga &
Sumino (1993), Matsui (1987) and Brown et al. (1983), it is
assumed that the nucleation of majority-type dislocation
bundles took place as half-loops at the wafer edges.
After nucleation, the half-loops could have expanded by
glide processes and either the upper or the lower parts of them
could have been lost by gliding out of the specimen, leaving, as
observed experimentally, partial half-loops that consist of
dislocation segments perpendicular to the wafer normal and
segments that are threading either up through the epitaxial
J. Appl. Cryst. (2001). 34, 65±75 P. MoÈck � Dislocation bundles 69
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( )ag
( )bFigure 3Single-crystal X-ray transmission topograms: (a) 111 re¯ection, (b) �111 re¯ection. The majordiameter of these topograms is 4.8 cm. In (a), the majority-type dislocation bundles follow analphabetical sequence (`B1', `B2', `C1', `C2', `D1', `D2', `A1', `A2') clockwise starting with `B1' atthe 10:30 o'clock position. The minority-type dislocation bundle `MT 1' as well as the majority-typedislocation bundles `B1' and `B2' show `extinction of shadow contrast' in (a). In (b), the majority-type dislocation bundles follow an alphabetical sequence (`C1', `C2', `D1', `D2', `A1', `A2', `B1',`B2') clockwise from `C1' at the 10:30 o'clock position. The region of enhanced X-ray intensity (i.e.the bright stripe) at the right-hand side of (b) is caused by diffusely scattered white X-ray radiationthat passed through the sample mounting at the major ¯at of the sample. The minority-typedislocation bundle `MT 1' as well as the majority-type dislocation bundles `C1' and `C2' show`extinction of shadow contrast' in (b).
Table 1Summary of the parameters of all of the dislocations that belong to thepseudo-symmetric fourfold set of majority-type dislocation bundles [asdenoted (A1±D2) in Fig. 1(a)].
(a) Line directions and Burgers vectors.
Linedirection²
Burgers vector,type 1
Burgers vector,type 2
`Effective' Burgersvector³
A1 [110] �12[011] �1
2[10�1] �1
2[110]A2 [�1�10] �1
2[0�1�1] �1
2[�101] �1
2[�1�10]
B1 [�110] �12[0
�11] �12[10
�1] �12[1
�10]B2 [1�10] �1
2[01�1] �1
2[�101] �1
2[�110]
C1 [�1�10] �12[0
�11] �12[
�10�1] �12[
�1�10]C2 [110] �1
2[01�1] �1
2[101] �12[110]
D1 [1�10] �12[011] �1
2[�10�1] �1
2[�110]
D2 [�110] �12[0
�1�1] �12[101] �1
2[1�10]
(b) Glide planes and peripheral area of origin.
Glideplane
Type of plane accordingto Gatos & Lavine (1960)
Peripheral areasof origin
A1 and A2 (1�11) B [0�10], [100]B1 and B2 (111) A [100], [010]C1 and C2 (�111) B [010], [�100]D1 and D2 (�1�11) A [�100], [0�10]
² Sign follows the assumed glide direction from the wafer rim into the bulk of thewafer. ³ After `pairing up' of dislocations, `effective' Burgers vectors are obtained byformally adding the Burgers vector types 1 and 2 of the constituent dislocations of amajority-type dislocation bundle.
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70 P. MoÈck � Dislocation bundles J. Appl. Cryst. (2001). 34, 65±75
structure or downwards to the back side of the substrate.
Taking into account that the radius of the wafer is about 50
times larger than the sample thickness, the result of the gliding
out of one of the 60� segments could be that the partial half-
loops are headed by screw segments that are, as observed
experimentally, trailed by 60� segments.
The sketches of Figs. 5(a), 5(b) and 5(c) illustrate the origin
and ®nal arrangement of a dislocation pair (as discussed
below) in a majority-type dislocation bundle. Note that the
®nal con®guration is in good agreement with the experimen-
tally observed arrangement, as shown in suf®cient detail in
Figs. 4(a), 4(b) and 4(c).
g
1 cm( )a
( )b 0.5 mm
0.5 mm 0.5 mm
0.5 mm
g g
( )c
g g
(d) ( )e
Figure 4Higher magni®cation images ofdifferent types of dislocation bundlesin various re¯ections. (a) Majority-typedislocation bundles `D2' (left) and `A1'(right); 0�22 re¯ection; X-ray analogueof a photographic positive. (b) Sectionof one branch of a majority-typedislocation bundle `D1' where it endsin the bulk of the wafer; �20�2 re¯ection;X-ray analogue of a photographicnegative. (c) Section of one branch ofa majority-type dislocation bundle ofthe second sample; 1�11 re¯ection; X-rayanalogue of a photographic negative.This image is reproduced for compar-ison with (b). As the comparison of (b)and (c) shows, majority-type dislocationbundles have the same microscopicarrangement in thermally processedGaAs wafers. Since a medium with aby-far superior resolution has been usedfor the recording of this topogram, moredetails of the dislocation arrangementcan be seen, although the dislocationdensity is signi®cantly higher. While thedislocations in the majority-type dislo-cation bundle run horizontally from leftto right, one set of 1
2h110i{111}-typemis®t dislocations runs vertically andthe corresponding horizontal set ofmis®t dislocations is extinct for thisparticular re¯ection. The mis®t disloca-tions appear predominantly in theirkinematical image since they arelocated at a depth of only 140 nm belowthe exit surface of the X-ray beam (seealso MoÈ ck & Smith, 2000). The disloca-tions in the majority-type dislocationbundles, however, appear in their dyna-mical images since they are distributedthroughout the whole thickness of theGaAs wafer (see also AppendicesA andB, and MoÈ ck & Smith, 2000). (d)Section of the ®rst minority-type dislo-cation bundle `MT 1' where it ends inthe bulk of the wafer; 1�11 re¯ection; X-ray analogue of a photographic nega-tive. (e) Area in the 1�11 topogramwhere a minority-type dislocationbundle of the second type comes inclose contact with one branch of themajority-type dislocation bundle `B2';X-ray analogue of a photographicnegative. The majority-type dislocationbundle runs vertically and the minority-type dislocation bundle makes a smallangle with the horizontal edge of the®gure.
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4.2. Dislocation pairs in majority-type dislocation bundles
As Fig. 6(a) reveals, majority-type dislocation bundles show
pronounced contrast in infrared polariscopy maps of residual
shear strains. Although the constituent dislocations of
majority-type dislocation bundles are of the 60� type, i.e.
should, if isolated, possess Burgers vector components parallel
to the wafer normal which would cause surface steps, Fig. 6(b)
shows that majority-type dislocation bundles are not revealed
as surface steps in a Makyoh topogram.
Both experimental observations may be explained by the
existence of dislocation pairs with `effective Burgers vectors'
that relieve shear strains effectively, on the one hand, and
cancel the surface steps of the two constituent 60� dislocations,on the other hand (see also MoÈ ck et al., 1999, 2001; MoÈck &
Smith, 2000; MoÈck, 2000b). The `effective Burgers vectors' of
Table 1(a) are obtained by formally adding the Burgers vector
types of the constituent dislocations of a majority-type dislo-
cation bundle. This formal addition can be performed since it
was concluded in x3.2 that there are about equal numbers of
dislocations with either one of two different Burgers vectors in
each majority-type dislocation bundle. As can be easily seen,
the `effective Burgers vectors' of Table 1(a) do not possess
components parallel to the wafer normal, i.e. cannot give rise
to surface steps, but are most effective in relieving shear
strains between the h100i and h010i axes that are perpendi-
cular to the wafer normal.
J. Appl. Cryst. (2001). 34, 65±75 P. MoÈck � Dislocation bundles 71
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Figure 5Sketches that illustrate the origin and arrangement of a dislocation pair ina majority-type dislocation bundle. (a) Nucleation of two half-loops atsurface inhomogeneities. (b) Formation of a dislocation pair and glidingout of one part of a half-loop. (c) Final arrangement after a part of theother half-loop has glided out and the force on the dislocation pair is nolonger suf®cient to sustain its movement.
↑ ↑[ [- -- -1 110] 10]
MT 2
5 × 10–5
( )a ( )b
Figure 6Complementary experimental results (slightly modi®ed after MoÈ ck et al., 1999, 2001); comparison of a scanning infrared polariscopy map with a Makyohtopogram of the wafer from which Figs. 1, 2, 3, 4(a), 4(b), 4(d) and 4(e) were taken. Except for small mounting and imaging artefacts, the whole two-inch-diameter wafer is depicted in both images. (a) Scanning infrared polariscopy map. Residual shear strains between the h100i directions that areperpendicular to the wafer normal are shown. Residual strain maps of complementary strain tensor components are given by MoÈ ck et al. (1999). Thequantifying marker of the strain is linear. The majority-type dislocation bundles follow in alphabetical order clockwise from `A1' at the 1:30 o'clockposition. Majority-type dislocation bundles and two minority-type dislocation bundles are clearly visible, for only they relieved a suf®cient amount ofshear strain during the thermal treatment of the wafer. Careful examination of the original of this ®gure demonstrated that the minority-type dislocationbundle of the second type, denoted as `MT 2' in (b) and Fig. 1(a), did indeed cause a low level of shear strain relief, but the related contrast has been lostin the reproduction of this image. (b) Makyoh topogram. The surface topography is shown with a height sensitivity of about 50 nm and a spatialresolution of about 1 mm (Laczik et al., 1995). Only those minority-type dislocation bundles that consist of a suf®cient number of dislocations with asigni®cant Burgers vector component parallel to the surface normal are visible. Marker `MT 2' stands for the minority-type dislocation bundle of thesecond type, as in Fig. 1(a). The two minority-type dislocation bundles which show pronounced contrast in (a) are also clearly visible. Since majority-typedislocation bundles do not cause discernable surface steps, they are not visible in a Makyoh topogram. The most obvious imaging artefacts in (a) arebright spots, which are caused by dust particles on the free wafer surfaces. The most obvious imaging artefact in (b) is a circular speck in the secondquadrant, which is caused by a surface inhomogeneity in one of the employed optical elements. Both images are in the same orientation and the major¯at of the wafer, i.e. the [�1�10] direction, points up towards the top of the page. It is assumed that the low dislocation density in the minority-typedislocation bundle of the ®rst type, marker `MT 1' in Fig. 1(a), is the reason why there is no discernable contrast for it in both the scanning infraredpolariscopy map (a) and the Makyoh topogram (b).
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72 P. MoÈck � Dislocation bundles J. Appl. Cryst. (2001). 34, 65±75
As the dislocation density in the
majority-type dislocation bundles is too
high for X-ray topography to resolve either
individual dislocations or dislocation pairs,
the proposed formation of dislocation pairs
is so far only a hypothesis. Theoretical
support for the existence of dislocation
pairs has been obtained, however, from the
semi-quantitative modelling of thermal-
treatment-induced plastic deformation in
GaAs wafers (MoÈ ck, 2000b). In short, the
main theoretical arguments are as given in
the following section.
4.3. Theoretical support for the existenceof dislocation pairs in majority-type dislo-cation bundles
For the strain levels that were actually
encountered during the thermal treatment
of the wafer (MoÈ ck, 2000b), the critical
resolved shear stresses on the eight actually
operational slip systems were calculated, as
given in Table 1, employing the formulae
and material data given by MoÈ ck (2000b).
These calculations predict for the outer-
most margin of a GaAs wafer under the
given thermal treatment conditions four
curves for the eight resolved thermal shear
stresses �1 = �2, �3 = �4, �5 = �6 and �7 = �8,over an angular coordinate with respect to
the [100] direction (see Fig. 7a, where the
subscripts are explained).
As Fig. 7(a) shows, there are only eight
small angular regions where the resolved
thermal shear stresses possess values that
are larger than the experimentally derived
threshold for dislocation generation
(Kiyama et al., 1997) in the applicable
deformation geometry (Reid, 1973). In
other words, the model predicts that there
are only eight angular regions where
minority-type dislocation bundles of the
second type may glide after they have been
nucleated by some mechanism. In good
agreement with Figs. 1, 2, 3, 6(a) and 6(b),
and the X-ray topograms that are
presented by MoÈ ck (2000a) and MoÈck &
Smith (2000), the theoretical prediction is
that these areas range from about 10� to
about 35� around both sides of the h110ipoles. It should be noted, and will be brie¯y
discussed in Appendix C, that Figs. 7(a)
and 7(b) are compatible with the experi-
mentally derived point symmetry group�42m (see also MoÈ ck, 2000b).
Figure 7Calculated resolved thermal shear stresses at the rim of the thermally processed wafer as afunction of an angular coordinate with respect to [100]. Both theoretically predicted graphs areentirely compatible with the experimental results that are presented in Table 1. (a) The resolvedthermal shear stresses on isolated dislocations in all symmetry-related minority-type dislocationbundles of the second type are shown. The slip systems of these minority-type dislocationbundles are as follows: (1) �1
2[0�11](111); (2) �1
2[011](�1�11); (3) �1
2[0�11] (�111); (4) �1
2[011](1�11);
(5) �12[10
�1](111); (6) �12[
�10�1](�1�11); (7) �12[
�10�1](�111); (8) �12[10
�1](1�11). Themarker with the annotation `MT 2' at the angular coordinate value 149� indicates the locationof the respective minority-type dislocation bundle with the same denotation as in Figs. 1(a) and6(b). This marker has been annotated in order to indicate that the symmetry of the model isfourfold, as discussed brie¯y in Appendix C, rather than eightfold. (b) The resolved thermalshear stresses on the four types of dislocation pairs that may be formed in the slip planes (111),(�111), (�1�11) and (1�11) are shown. The respective angular positions of the majority-typedislocation bundles that may result from the formation of dislocation pairs are annotated incorrespondence to Fig. 1(a) by the markers `B1', `B2', `C1', `C2', `D1', `D2', `A1' and `A2'.
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Fig. 7(a) indicates that minority-type dislocation bundles
cannot exist in peripheral areas closer than about �10� to a
h110i pole. This prediction shows that dislocation bundles of
the ®rst minority type are not accounted for by the model,
which assumes a perfectly circular wafer. It is believed,
therefore, that minority-type dislocation bundles of the ®rst
type are the result of the in¯uence of the crystal orientation
¯ats on the distribution of the thermal stresses.
The startling conclusion from Fig. 7(a) is, however, if
dislocation pairs could not exist, a few minority-type disloca-
tion bundles of the second type would be all that is possible to
relax the actually encountered thermal strains in the thermally
processed GaAs wafers. If, however, dislocation pairs are
taken into account, the situation changes completely.
The resolved thermal stresses for the four types of dislo-
cation pairs (P�15 = �1 + �5 =
P�26 = �2 + �6,
P�37 = �3 + �7 =P
�48 = �4 + �8) are, for nearly all angular regions, above the
threshold for dislocation glide (Kiyama et al., 1997). The
generation of dislocation pairs is, however, limited by the pre-
existence of dislocation sources, which are most numerous
around the h100i peripheral areas (MoÈck, 2000b). Taking this
limitation into account, the fourfold symmetry of the model
becomes obvious and the angular range of majority-type
dislocation bundles is, as the good agreement of Fig. 7(b) with
Figs. 1, 2, 3 and 6(a), and the X-ray topograms that are
presented by MoÈ ck (2000a) and MoÈck & Smith (2000) indi-
cate, about 22� around both sides of the h100i poles.
4.4. Discussion of minority-type dislocation bundles on thebasis of both the complementary experimental results and thesemi-quantitative model
Since the symmetry of the crystallographic parameters of
the pseudo-symmetric fourfold set of majority-type disloca-
tion bundles is a consequence of the applicable deformation
geometry (Reid, 1973), it is expected that the crystallographic
parameters of the dislocation bundles of the second minority
type will possess the same symmetry. The crystallographic
parameters of the minority-type dislocation bundles of the
®rst type, i.e. those dislocation bundles that are located at and
opposite to the wafer orientation ¯ats, on the other hand, are
expected to possess a lower symmetry since it is believed that
they are caused by an asymmetric disturbance of the applic-
able deformation geometry.
While the minority-type dislocation bundle of the second
type, which is denoted as `MT 2' in Fig. 1(a), is discernable in
the Makyoh topogram (Fig. 6b), it is only hardly visible in the
original of the scanning infrared polariscopy map of residual
shear stains (original of Fig. 6a). According to the model
(MoÈ ck, 2000b), the dislocations in this bundle should have
Burgers vectors of either �12[101] or �1
2[10�1] or possibly a
combination of both.
The two minority-type dislocation bundles in the [110]
peripheral area (adjacent to both the dislocation bundle of the
®rst minority type, which is denoted as `MT 1', and the two
majority-type dislocation bundles, denoted as `B1' and `B2' in
Fig. 1a) show pronounced contrast in both the scanning
infrared polariscopy map (Fig. 6a) and the Makyoh topogram
(Fig. 6b). According to the model (MoÈ ck, 2000b), the Burgers
vectors of the dislocations in one of the bundles should be
either �12[10
�1] or �12[101], or possibly a combination of both.
The other bundle should consist of dislocations with Burgers
vectors of either�12[0
�11] or�12[011], or possibly a combination
of both.
Burgers vectors of minority-type dislocation bundles of the
second type, such as predicted by the model, could explain the
contrast in Figs. 6(a) and 6(b), would be related to each other
by the point symmetry group �42m, and would be compatible
with most of the experimental data that are contained in the
published X-ray topograms.
As far as dislocation bundles of the minority type are
concerned, obviously more work has to be performed to
elucidate the crystallographic parameters of the dislocations in
these bundles. The present X-ray topography study, however,
delivered a ®rst step towards such investigations by identifying
two different types of minority dislocation bundles.
5. Conclusions
Different types of dislocation bundles have been identi®ed in
a plastically deformed two-inch-diameter GaAs wafer that was
subjected to temperatures of up to about 923 K in a
commercial molecular beam epitaxy machine. The dislocation
bundle types differ in the crystallographic parameters of the
constituting dislocations and in their respective spatial distri-
bution. Dislocation bundles of the majority type form a
pseudo-symmetric fourfold set with h100i peripheral-area
orientation and are signi®cantly longer and much more
numerous than dislocation bundles of the minority types that
exist at and around h110i peripheral areas. The crystal-
lographic parameters of the whole set of majority-type dislo-
cation bundles are related by the point symmetry group �42m.
It is assumed that the constituent dislocations of the majority-
type dislocation bundles nucleated as half-loops at surface
irregularities at the rim of the wafer. The formation of dislo-
cation pairs in majority-type dislocation bundles has been
hypothesized in order to explain complementary experimental
results and is theoretically supported by a semi-quantitative
model of plastic deformation of GaAs wafers under conditions
that are typical for molecular beam epitaxy growth.
APPENDIX AKinds of X-ray transmission topography
The standard method for determining the Burgers vectors of
dislocations, as brie¯y outlined in Appendix B, works best for
isolated dislocations in a nearly perfect crystal of a thickness
(t) that is around 0.88 times the extinction distance of the
employed re¯ections (Tanner, 1996). Under such conditions, a
dislocation appears in its kinematical image on a photographic
positive as a brighter region (enhanced X-ray intensity) of
high contrast on a darker background. The magnitude of a
typical �t product (where � is the linear absorption coef®cient
of the diffracted radiation) at which the kinematical image
J. Appl. Cryst. (2001). 34, 65±75 P. MoÈck � Dislocation bundles 73
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74 P. MoÈck � Dislocation bundles J. Appl. Cryst. (2001). 34, 65±75
dominates the contrast is of the order of 1. X-ray transmission
topography is most commonly performed under such �tconditions and may be called `Lang-type topography'
(Authier, 1970).
There is an `awkward' (Lang, 1970) �t range of about 2±5
which should be avoided for straightforward experimental
determinations of Burgers vectors. X-ray transmission topo-
graphy under conditions of �t products of the order of
magnitude 10 is called anomalous transmission topography
(Authier, 1970), Borrmann-effect topography (Klapper &
Smolsky, 1998), or just Borrmann topography (Hildebrandt &
Wagenfeld, 1998), and will be discussed brie¯y in Appendix B.
APPENDIX BBurgers vector determination by means of X-raytransmission topography under conditions of highanomalous transmission
Since GaAs wafers of 0.45 mm thickness were used to record
the X-ray diffraction topograms, the experimental conditions
dictated working with large �t products. These products are
about 11 for � = 0.13 nm (i.e. for the 111, 1�11, �111, �20�2 and oneof the 0�22 re¯ections), 16 for � = 0.073 nm (i.e. for the other
0�22 and the 202 re¯ections) and about 7 for � = 0.053 nm (i.e.
for the 1�33 and 3�13 re¯ections).
This prevalent high anomalous transmission allowed the
usually much weaker dynamical-effect images of the disloca-
tions in a bundle to dominate the contrast in the transmission
topograms, while the usually much stronger corresponding
kinematical images were practically absorbed. Since the
anomalously high transmission depends strongly on the crys-
talline perfection, lattice defects such as dislocation bundles
reduce the effect and lead to a type of dynamical-effect image
that consists of diminished intensity (darker regions of
medium contrast on a brighter background in a photographic
positive), which is often called a Borrmann shadow (Klapper
& Smolsky, 1998). The sharpness of the Borrmann shadow
depends on the distance of the defect to the free surface where
the X-ray beam exits the crystal. As a direct consequence of
the Borrmann fan (Klapper & Smolsky, 1998), the further
away a dislocation is located from the exit surface, the more
blurred its Borrmann shadow will be.
There is another type of dynamical-effect image, also
known as an intermediate image, which arises from the
curvature of the wave®eld rays in the deformed regions
surrounding a dislocation and which leads to enhanced
intensity in some parts of the image (Klapper & Smolsky,
1998). In the cases of �t products of 10 to 20, the intermediate
image arises mainly from the regions near to the free surfaces
of the crystal (Authier, 1970). For thorough discussions of the
contrast in topograms taken under conditions of high anom-
alous transmission, see reviews by Tanner (1996), Petroff
(1983) and Authier (1970). Particular dislocation contrast
features in single-crystal X-ray transmission topograms
resulting from the use of a second-generation synchrotron
radiation source (such as that at Daresbury) have been
discussed by Bowen & Tanner (1998).
In the particular case of dislocation bundles in GaAs, effects
such as As precipitation on the dislocation cores, splitting of
perfect dislocations into partial dislocations, superposition of
strain ®elds of dislocations that are in close proximity to one
another, and stress relaxation in the vicinity of dislocations
that thread towards the free crystal surfaces, may disturb the
extinction effects of both dynamical images for chosen
re¯ections. Some of these disturbances are expected to
increase with increasing �t.Although there is a signi®cant amount of anomalous
transmission present, it is believed that the set of topograms
depicted in Figs. 2(a), 2(b), 2(c), 3(a) and 3(b) allows the
correct determination of the Burgers vectors (bi) and types
[arccos(bi � li)] of the dislocations that are present in a quarter
subset of the pseudo-symmetric fourfold set of majority-type
dislocation bundles (`A1' and `A2' in Fig. 1a) and in a minority-
type dislocation bundle of the ®rst type (`MT 1' in Fig. 1a). The
Burgers vector determinations were performed by applying to
the Borrmann shadows the standard method, i.e. the well
known relation bi = gj � gk for gj � bi = 0 and gk � bi = 0
[isotropic elasticity, gj � (bi � li) = 0, gk � (bi � li) = 0], where giand gk are the reciprocal-lattice vectors of the re¯ections
employed and li are the line directions of the dislocations (see
e.g. Bowen & Tanner, 1998).
APPENDIX CSymmetry properties of the semi-quantitative model byMoÈck (2000b)
As demonstrated by MoÈ ck (2000b), models that are entirely
based on the angular distribution of the resolved thermal
shear stresses (Kiyama et al., 1997; Yamada et al., 1997;
Sawada et al., 1996) are over-simpli®cations since they disobey
Curie's symmetry principle (Shuvalov, 1988; Pau¯er, 1986;
Curie, 1894). The semi-quantitative model reported herein is
an improvement on the above-mentioned models since it
predicts, in agreement with the experimental results (Table 1),
the point symmetry group �42m for the crystallographic para-
meters of the thermal-treatment-induced plastic deformation.
This improvement has been achieved by including in the
model the naturally occurring distribution of dislocation
sources, dislocation pairs as basic constituents of the majority-
type dislocation bundles, and modi®cations of the stress
distribution during plastic ¯ow which is caused by dislocation
interactions in minority-type dislocation bundles.
As an indication of the fourfold symmetry of the model, the
angular coordinate value (149�) of the minority-type disloca-
tion bundle, denoted as `MT 2' in Figs. 1(a) and 6(b), has been
annotated in Fig. 7(a). This value is 8.5� less than the angular
coordinate value (157.5�) at which the local maximum of the
resolved thermal shear stress curves on the glide systems
�12[
�10�1](�111) and �12[10
�1](1�11) occurs. According to the old
models (Kiyama et al., 1997; Yamada et al., 1997; Sawada et al.,
1996), the dislocation bundle that is denoted as `MT 2' in Figs.
1(a) and 6(b) should exist exactly at this local maximum. In
addition, symmetry-related dislocation bundles should exist at
the angular positions of the other seven maxima of the
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resolved thermal shear stress curves in Fig. 7(a), i.e. at 22.5,
67.5, 112.5, 202.5, 247.5, 292.5 and 337.5�, leading to an
eightfold symmetry. As the comparison with the experimental
results (Fig. 1, 2, 3, 6a and 6b) shows, this is obviously not the
case.
The author is indebted to Dr G. W. Smith from the Defence
Evaluation and Research Agency, Malvern, for growing the
samples of this study, and would like to thank Dr D. Laundy
for advice and experimental support at the synchrotron
radiation source (SRS), Daresbury Laboratory. Previous
collaboration with Drs G. R. Booker, Z. J. Laczik and M.
Fukuzawa, as well as Professors M. Yamada and B. K. Tanner,
is kindly acknowledged. The author is grateful to both referees
for their comments. The Engineering and Physical Science
Research Council sponsored the usage of the experimental
facilities at the SRS in the framework of two `Direct Access'
projects (reference numbers 30047 and 31098).
References
Authier, A. (1970). Modern Diffraction and Imaging Techniques inMaterial Science, edited by S. Amelinckx, R. Gevers, G. Remaut &J. Van Landuyt, pp. 481±520. Amsterdam, London: North-Holland.(Proceedings of the International Summer Course on MaterialScience, Antwerp, Belgium, 28 July to 8 August 1969.)
Bowen, D. K. & Tanner, B. K. (1998). High Resolution X-rayDiffractometry and Topography, pp. 230±235. London: Taylor andFrancis.
Brown, G. T., Warwick, C. A., Young, I. M. & Booker, G. R. (1983).Inst. Phys. Conf. Ser. No. 67, pp. 371±376.
Curie, P. (1894). J. Phys. (Paris), 3, 393±415. (In French.)Flade, T., Jurisch, M., Kleinwechter, A., KoÈhler, A., Kretzer, U.,Prause, J., Reinhold, Th. & Weinert, B. (1999). J. Cryst. Growth,198/199, 336±342.
Gatos, H. C. & Lavine, M. C. (1960). J. Electrochem. Soc. 107, 427±433.
Hildebrandt, G. &Wagenfeld, W. (1998). Cryst. Res. Technol. 33, 511±515.
International Tables for X-ray Crystallography (1985). Vol. III,Physical and Chemical Tables, edited by C. H. MacGillavry & G. D.Rieck. Dordrecht: D. Reidel.
Kawase, T., Wakamiya, T., Fujiwara, S., Hashio, K., Kimura, K.,Tatsumi, M., Shirakawa, T., Tada, T. & Yamada, M. (1993). Semi-insulating III±V Materials, edited by C. J. Miner, W. Ford & E. R.Weberch, ch. 52, pp. 85±90. Bristol: Institute of Physics. (Proceed-ings of the 7th International Conference on Semi-insulating III±VMaterials, Ixtapa, Mexico, 21±24 April 1992.)
Kiyama, M., Takebe, T. & Fujita, K. (1997). Inst. Phys. Conf. Ser. No.155, pp. 945±948.
Klapper, H. & Smolsky, I. L. (1998). Cryst. Res. Technol. 33, 605±611.
Laczik, Z., Booker, G. R. & Mowbray, A. (1995). J. Cryst. Growth,153, 1±5.
Lang, A. R. (1970). Modern Diffraction and Imaging Techniques inMaterial Science, edited by S. Amelinckx, R. Gevers, G. Remaut &J. Van Landuyt, pp. 407±479. Amsterdam: North±Holland.(Proceedings of the International Summer Course on MaterialScience, Antwerp, Belgium, 28 July to 8 August 1969.)
Matsui, J. (1987). Inst. Phys. Conf. Ser. No. 87, pp. 249±258.MoÈ ck, P. (2000a). J. Cryst. Growth. Accepted.MoÈ ck, P. (2000b). Cryst. Res. Technol. 35, 529±540, 1131MoÈck, P., Fukuzawa, M., Laczik, Z., Yamada, M., Smith, G. W,Booker, G. R., Tanner, B. K. & Herms, M. (1999). Inst. Phys. Conf.Ser. No. 164, pp. 67±72. (Proceedings of the XI InternationalConference on Microscopy of Semiconducting Materials, Oxford,22±25 March 1999.)
MoÈ ck, P., Laczik, Z. J. & Booker, G. R. (2001). Mater. Sci. Eng. B.Accepted.
MoÈ ck, P. & Smith, G. W. (2000). Cryst. Res. Technol. 35, 541±548.
Pau¯er, P. (1986). Physikalische Kristallographie, pp. 28±34. Berlin:Akademie-Verlag. (In German.)
Petroff, J. F. (1983). Applications of X-ray Topographic Methods toMaterials Science, edited by S. Weissmann, F. Balibar & J. F. Petroff,pp. 75±96. New York: Plenum Press. (Proceedings France±USASeminar on Application of X-ray Topographic Methods toMaterials Science, Snowmass Village, Colorado, 7±10 August 1983.)
Reid, C. N. (1973).Deformation Geometry for Materials Scientists, pp.145±178. Oxford: Pergamon Press.
Sawada, S., Oida, K., Miyajima, H., Nambu, K., Nakai, R., Tatsumi,M., Fujita, K. & Nishida, Y. (1995). GaAs IC Symposium TechnicalDigest ± 17th Annual, ch. 72, pp. 115±118.
Sawada, S., Yoshida, H., Kiyama, M., Mukai, H., Nakai, R., Takebe,T., Tatsumi, M., Kaji, M. & Fujita, K. (1996). Technical Digest ±IEEE GaAs Integrated Circuit Symposium, Vol. 74, pp. 50±53.(Proceeding of the IEEE GaAs Integrated Circuit Symposium,Orlando, FL, 3±6 November 1996).
Shuvalov, L. A. (1988). Modern Crystallography IV, PhysicalProperties of Crystals, Vol. 37, pp. 46±49. Berlin: Springer.
Tanner, B. K. (1996). X-ray and Neutron Dynamical Diffraction ±Theory and Applications, edited by A. Authier, S. Lagomarsino &B. K. Tanner, NATO Advanced Science Institute Series, Series B,Physics Theory and Applications, Vol. 357, ch. 26, pp. 147±166. NewYork: Plenum Press. (Proceedings of the NATO Advanced StudyInstitute on X-ray and Neutron Dynamical Diffraction ± Theoryand Applications, Erice, Italy, 9±22 April 1996.)
Tatsumi, M., Hosokawa, Y., Iwasaki, T., Toyoda, N. & Fujita, K.(1994). Mater. Sci. Eng. B, 28, 65±71.
Tatsumi, M., Kawase, T., Iguchi, Y., Fujita, K. & Yamada, M. (1994).Proceedings of the 8th Conference on Semi-insulating III±VMaterials, Warsaw, Poland, 6±10 June 1994, edited by M.Godlewski, pp. 11±18. Singapore: World Scienti®c.
Yamada, M., Fukuzawa, K. & Ito, K. (1997). Inst. Phys. Conf. Ser. No.155, 901±904.
Yonenaga, I. & Sumino, K. (1993). J. Cryst. Growth, 126, 19±29.
J. Appl. Cryst. (2001). 34, 65±75 P. MoÈck � Dislocation bundles 75
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