Slip in GaAs substrates during molecular beam epitaxial growth: an X-ray topographicsurvey

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1 Journal of Crystal Growth 224 (2001) Slip in GaAs substrates during molecular beam epitaxial growth: an X-ray topographicsurvey P. Mo ck 1 Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, England, UK Received 7 February 2000; accepted 19 January 2001 Communicated by J.B. Mullin Abstract Synchrotron X-ray transmission topography has been used to study different types of dislocation bundle in 2-inch diameter, (0 0 1) oriented GaAs substrates after growth of a variety of heteroepitaxial III V compound semiconductor structures. The dislocation bundles of the majority type start at the sample edges in regions of up to about 258 around the four h100i peripheral areas, glide typically up to about 1.5 cm into the bulk of the wafer following [1 1 0] and ½1 10Š line directions and form, depending on the dopant type, pseudo-symmetric four- or two-fold sets. The dislocation bundles were observed in samples that were grown in three different makes of molecular beam epitaxy machine. Eradication of the bundles was achieved by modifications to the sample holder of an MBE machine built at the Defence Evaluation and Research Agency, Great Malvern, UK. # 2001 Elsevier Science B.V. All rights reserved. PACS: Ea; Kk; Ff Keywords: A1. Stresses; A1. Substrates; A1. X-ray topography; A3. Molecular beam epitaxy; B2. Semiconducting gallium arsenide 1. Introduction Towards the end of a series of synchrotron based double-crystal X-ray reflection topography and diffractometry studies of misfit dislocation nucleation and multiplication processes in (In,Ga)As on GaAs [1 4], we observed in some epitaxial structures severe plastic deformation that was not associated with misfit strain. Plastic deformation that does not relieve misfit strain, address: (P. Mo ck). 1 Present address: Department of Physics (MC 273), University of Illinois at Chicago, 845 West Taylor Street, Chicago, IL , USA. associated with screw dislocations, has previously been reported in epitaxial layers [5] and such dislocations were also observed in our most recent double-crystal X-ray reflection topography study. A comprehensive, synchrotron based, singlecrystal X-ray transmission topography study under conditions of high anomalous transmission was initiated to work out the cause of this deformation and some results of this study are presented and discussed in this paper. Some results of the above mentioned double-crystal X-ray reflection topography study and of a Makyoh (MagicMirror [6]) topography inspection will also be presented for comparison purposes. The discussion of our results will include comparisons /01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S (01)

2 12 P. Mo ck / Journal of Crystal Growth 224 (2001) with earlier results from the literature, which have mainly been obtained by means of standard Nomarski microscopy. 2. Experimental details Fifteen (In,Ga)As single and double heterostructures and one (Al,Ga)As/GaAs multiquantum-well structure were grown in molecular beam epitaxy (MBE) machines of three different makes. While the first of these MBE machines was a purpose built piece of equipment for in-situ X-ray imaging of relaxation processes in strained epitaxial layers [7], the second was a commercial Varian GEN II. The third MBE machine was a commercial VG Semicon machine. The sample holders of these three MBE machines are all of the radiatively heated non In-bonding type. Undoped, 2-inch diameter, (0 0 1) vertical gradient freeze Bridgman (VGFB) GaAs wafers of the standard thickness ( 450 mm) as well as a few Si (10 18 cm 3 ) doped, two-inch diameter, (0 0 1) VGFB GaAs wafers of the standard ( 450 mm) and more than twice the standard thickness ( 1 mm) were used as substrates. The epitaxial samples possessed a wide variety of structural parameters and were either fully strained, partly relaxed, or almost completely relaxed. While the In content in the (In,Ga)As layers ranged from nominally 2 to 10%, the thickness of the strained layers ranged from nominally 60 nm to 2.7 mm. Where applicable, the thickness of the GaAs capping layers ranged from nominally 10 nm to 4 mm. Before the growth of the epitaxial structures commenced, buffer layers of up to 0.5 mm were grown at temperatures of typically about 6008C, preceded by surface oxide desorption at up to 6508C. An undoped, 2-inch diameter (0 0 1) VGFB substrate of the standard thickness as well as two Si-doped 2-inch diameter (0 0 1) VGFB substrate of the standard thickness and of about 1 mm thickness, all without epitaxial layers (and without alternative thermal treatment), were also included in the X-ray transmission topography study. We used epitaxial samples for most of our study because they were readily available and, as demonstrated in Refs. [8 11], completely adequate for this purpose. This series of papers proves, as the discussion in Section 3.2 will show, that it is not the epitaxial growth process itself which causes slip in GaAs substrates but the thermal treatments that are associated with it. All of these 19 samples were assessed 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). Fine-grained Agfa-Gevaert Structurix D4 X-ray film (as a cheap alternative to Ilford L4 nuclear plates) was mainly used for the recordings of the topograms. However, a few L4 nuclear plates were also used when we aimed for the recordings of finer contrast details such as images of misfit dislocations. At least one topogram was taken from each of the samples at a wavelength of 0.13 nm (where the product mt is about 11, m: linear absorption coefficient, t: sample thickness 450 mm). A complete set of symmetry related 111, 111,202,313,and topograms was taken in transmission geometry from an undoped substrate (with a fully strained quantum-well structure) in order to determine the crystallographicparameters of the dislocations in the majority type dislocation bundles. In addition, several synchrotron based double-crystal X-ray reflection topograms were recorded on Ilford L4 nuclear plates and reflections of the substrates were employed under the experimental condition that are described in Refs. [2,3]. 3. Results and discussion 3.1. Results of this study From the observation that the contrast of the dislocation bundles was quite similar regardless of which side of a sample was exposed first to the incoming X-ray beam [12], we conclude that the dislocation bundles are distributed through the whole thickness of the substrates rather than in the epitaxial structures. Fig. 1a, a transmission topogram taken from an undoped GaAs substrate (with a fully strained (Al,Ga)As/GaAs multiquantum-well structure) depicts predominantly a

3 P. Mo ck / Journal of Crystal Growth 224 (2001) Fig. 1. (a) single-crystal X-ray transmission topogram, (b) Makyoh topogram of an undoped VGFB GaAs substrate of 0.45 mm thickness (with a fully strained (Al,Ga)As/GaAs multiquantum-well structure). The major diameter of the ellipse in Fig. 1a equals 4.8 cm, i.e. 2-inch minus about 2.5 mm obstruction due to the mounting of the sample relative to the X-ray beam. This topogram represents, as the other X-ray transmission topogram (Fig. 2a) an X-ray analogue to a photographicpositive (where enhanced X-ray intensity corresponds to increased brightness in the image). The clearly visible cellular dislocation structure is typical for undoped, as purchased VGFB GaAs substrates. Marker MF stands for the major flat of the wafer in Fig. 1a. The Makyoh topogram, Fig. 1b, depicts the whole 2-inch diameter sample minus some very minor obstruction due to mounting. The orientation of the major flat of this wafer is clearly discernable in Fig. 1b and an anti-clockwise rotation of this figure by 458 leads to the same wafer orientation as in Fig. 1a. (The same orientation relationship applies to Figs. 2a and b.) typical, pseudo-symmetric, four-fold set of dislocation bundles that was present in most of the samples of our study. These dislocation bundles are starting at the sample edges in regions of up to about 258 around the four h100i peripheral areas and glide in this particular sample up to about 1.8 cm into the bulk of the wafer following [1 1 0] and ½1 10Š line directions. Details on the Burgers vector assessments of different dislocation bundles and a classification of the dislocation bundles into different types are given elsewhere [12]. The most important results of the analysis of dislocation bundles of the majority type are: the extended segments of the dislocations within each bundle are of the 608 type and there are dislocations which possess two different Burgers vectors in each of these bundles. There are in Fig. 1a two more types of dislocation bundles (minority types) at and opposite to the major flat in the ½ 1 10Š and [1 1 0] peripheral area. In other samples, the latter types of dislocation bundles have been found to exist in the two ½ 110Š peripheral areas as well, but only occasionally were dislocation bundles of the minority types present in all four h110i peripheral areas. It was observed in a variety of samples by means of Makyoh topography, visible light interferometry, and standard Nomarski microscopy [13] that while dislocation bundles of the first minority type tend to be located at or rather close (5 108) to a h110i pole, dislocation bundles of the other minority type(s) typically deviate from about 108 up to about 358 from a h110i pole, partially overlapping the areas that are occupied by the pseudo-symmetricset of majority type dislocation bundles. An example of a Makyoh topogram is given in Fig. 1b, presenting the epilayer side of the same (Al,Ga)As/GaAs multiquantum-well sample as Fig. 1a. The Makyoh topogram, Fig. 1b, facilitates the distinction

4 14 P. Mo ck / Journal of Crystal Growth 224 (2001) between majority type and minority type dislocation bundles in overlapping spatial areas of Fig. 1a since, as we will discuss in the next Section, it shows only minority type dislocation bundles. As Fig. 1a indicates, the area that is directly affected by the dislocation bundles and the threading dislocations associated with them is about one third of the whole 2-inch diameter wafer. The individual dislocations in the bundles are threading either up through the epilayers and potentially harm opto- and micro-electronic devices which may be built into these layers or extend downwards to the back side of the substrate. As expected, the three substrates without epilayers (and without alternative thermal treatments) did neither possess the pseudo-symmetric sets of majority type dislocation bundles nor the dislocation bundles of the minority types. From all of the samples, the one with the highest growth temperature, as shown in Figs. 1a and b, possesses the highest dislocation content. No significant influence of the length of time at which the samples were held at the growth or annealing temperatures on the severity of the plasticdeformation was observed. As Fig. 2a shows, the n+ doping of some of the substrates changed the pseudo four-fold symmetry of the majority type dislocation bundle set to pseudo two-fold. The dislocation bundles that were gliding in the (fast) ½ 110Š directions were on average about twice as long as their counterparts in the (slow) [1 1 0] directions. This might be an effect of selective impediment of the mobility of certain types of dislocations which is known to Fig. 2. X-ray topograms of a 1 mm thick, Si doped VGFB GaAs substrate (with a fully strained (In,Ga)As double heterostructure) (a) single-crystal transmission geometry, (b) double-crystal reflection geometry. The major diameter of the ellipse in Fig. 2a equals 4.8 cm. Marker MF stands for the major flat of the wafer in Fig. 2a. Fig. 2b represents the whole 2-inch diameter sample minus about 2.5 mm obstruction by a slit in the white radiation X-ray beam line (marker S). Conversely to the transmission topograms (Figs. 1a and 2a), the reflection topogram (Fig. 2b) represents a photographic negative (where enhanced X-ray intensity appears as enhanced blackening). Some surface scratches which are due to sample handling are visible in both images and Fig. 2b shows, in addition, some phase contrast artefacts [3]. The orientation of the major flat of the wafer is clearly discernable in Fig. 2b and an anticlockwise rotation of this figure by 458 leads to the same wafer orientation as in Fig. 2a. (The same orientation relationship applies to Figs. 1a and 1b.)

5 P. Mo ck / Journal of Crystal Growth 224 (2001) be dopant and doping level dependent [14]. Possibly due to the Si dopant and moderately high doping level, the area that is affected by the dislocations bundles in this particular sample is only about one quarter of the whole 2-inch diameter wafer. It should be noted that both pseudo-symmetries only apply to the visual appearance of the majority type dislocation bundle sets, i.e. their lengths and spatial distribution. As the complete Burgers vector analysis showed, the crystallographic dislocation parameters are, in agreement to Curie s symmetry principle, indeed symmetrically related by a combination of a four-fold inversion axis, two perpendicular mirror planes, and two perpendicular two-fold axes, i.e. the symmetry elements of the point group 42 m [12]. Any elasticdeformation of the samples at room temperature (wafer warp) was sensed by means of double-crystal X-ray reflection topograms. While samples with 0.45 mm thick substrates where at room temperature so heavily bent (i.e. elastically deformed) that typically only approximately 20 30% of a sample could be imaged by the monochromatic X-ray beam, Fig. 2b, which is taken from a 1 mm thick substrate, shows an almost complete image. There are again minority type dislocation bundles at and opposite to the major flat in the ½ 1 10Š and [1 1 0] peripheral areas depicted in Figs. 2a and b. Note that the dislocation bundle in the area of the major flat has a particularly pronounced X-ray topography contrast, indicating a rather high dislocation density in this bundle. As a matter of fact, slip-line bunches where visible to the unaided human eye over a wide range of illumination and observation angles in the area of the major flat of this sample. These slipline bunches were clearly visible both on the epilayer side and the back side of this sample and could, although less pronounced, also be observed by the unaided human eye on other samples that were grown either in the same on in any of the other two MBE machines on substrates of the standard thickness. Thus, the area of the major flat is obviously a region of enhanced resolved shear stress during molecular beam epitaxial growth. While all eight samples (including the samples of Figs. 1 and 2) grown in a Varian GEN II MBE machine at the Defence and Evaluation Research Agency, Great Malvern, showed pseudo-symmetricsets of majority type dislocation bundles and some minority type dislocation bundles, both of them occurred only in one out of four samples that had been grown in a VG Semicon MBE machine at the IRC Semiconductor Materials of Imperial College London. Eradication of the dislocation bundles was achieved by modifications to the sample holder of the purpose built MBE machine [7] which was originally designed as a copy of its counterpart in the Varian GEN II machine. This demonstrates clearly that the problem of severe plasticdeformation during molecular beam epitaxial growth is caused in our case by the particular sample holder design. For more information on the sample holder of a Varian GEN II MBE and the modifications that have been made, see Appendix A and Ref. [15]. After the modifications were made, annealing studies comprising temperatures of up to 7458C and holding times of up to 48 h at the growth temperature did not cause plastic deformation of the substrates. We observed that samples which showed both severe plasticdeformation and wafer warp effects were prone to break into pieces along {1 1 0} cleavage planes much more readily than other samples that did not contain sample holder and heat treatment induced dislocation bundles. This can be understood as a result of the existence of residual stresses at room temperature [16] which lower the mechanical load that is required for cleaving significantly Comparison of our results to the results of previous studies Stripes of reduced residual shear strain with a similar spatial distributions as in our study have been observed in scanning infrared polariscopy (SIP) maps of GaAs substrates after heat treatments in a MBE growth chamber at temperatures between C [8,9]. After 1 mm of homoepitaxial growth by means of MBE at 5308C and after thermal treatments of GaAs wafers in the

6 16 P. Mo ck / Journal of Crystal Growth 224 (2001) same temperature range as above without epitaxial growth in the same MBE growth chamber, dislocation bundles with a similar spatial distribution as in our study have been detected by means of X-ray reflection topography [9 11]. As already mentioned in the experimental details chapter, this series of papers demonstrates conclusively that it is neither the process of the molecular beam epitaxial growth nor the epitaxial structure itself which causes the observed plastic deformation of the substrates, but the heat treatments to which the substrates have been subjected. The detrimental influence of pre-existing plastic deformation, residual strains and stresses in GaAs wafers on the stability against further plasticdeformation during subsequent thermal treatments has also been demonstrated [10,11]. From the SIP images in Refs. [8,9] and the X-ray reflection topograms in Refs. [9 11], one can speculate that these heat treatments have led to the same kinds of dislocation bundles, utilising the same mechanisms, as observed in our study. Two rather similar models [17 19] that are based on the resolved thermal shear stresses for the {1 1 1} h1 10i glide systems have been put forward by two different groups in order to account for the occurrence of heat treatment induced plastic deformation in GaAs wafers. It is concluded in Refs. [17,18] that temperature gradients across the GaAs wafer are responsible for the formation of slip lines. Ref. [19], on the other hand, stresses the crucial role the MBE sample holder design, especially the ledge on which a radiatively heated GaAs wafer rests, plays in the formation of temperature gradients. It should, however, be noted that the plastic deformation will be helped by surface irregularities [20,21] and its spatial distribution is unlikely to be solely associated with the spatial distribution of the thermal stresses. This ties in with our observations on one particular sample, where there was only one single, short, and very narrow majority type dislocation bundle running in the ½ 1 10Š direction in the [0 1 0] peripheral area, obscuring the four-fold pseudo-symmetry of the whole set almost completely. This particular sample showed as well the highest amount of wafer warp. There is a direct correspondence between X-ray transmission topograms and SIP images, since the former map the distribution of the dislocations (i.e. in a sense, the carriers of plastic deformation) and the latter map the residual strain [13]. We agree, thus, with Ref. [17] that true slip lines which are seen by standard Nomarski microscopy and pseudo-slip lines which can be detected by any one of the two transmission methods, mentioned above, are not necessarily the same phenomenon. While the former method can only sense the free surface, the latter two methods integrate over the whole sample thickness. This argument is supported by our standard Nomarski microscopy, visible light interferometry observations, e.g., see Fig. 1d in Ref. [22], and Makyoh topograms, e.g., Fig. 1b. These three surface sensitive techniques showed that pronounced slip-line contrast (i.e. minority type dislocation bundles) could be observed on several samples in the area of the major flat and, to a lesser extent, in other peripheral areas around h110i, but that this contrast was not present around the four h100i peripheral areas, (where majority type dislocation bundles have been proven to exist by the transmission methods, e.g. Fig. 1a). In correspondence to these observations, the mainly surface sensitive double-crystal X-ray reflection topography technique enhances, as a comparison of Figs. 2a and b shows, the visibility of dislocation bundles of the minority types and, thus, helps to distinguish between different types of dislocation bundles in cases when their spatial distribution overlaps. The spatial distribution of slip lines that is predicted by the models [17 19] differs significantly from the experimentally observed spatial distribution of the majority type dislocation bundles. It seems, however, to be roughly in agreement with our observation of dislocation bundles (Figs. 1b and 2b) around h110i peripheral areas, i.e. minority type dislocation bundles. One of the reasons for this partial discrepancy between experiment and theory [17 19] is most probably the assumption that the dislocations within a dislocation bundle do not interact [17]. While this might be a good approximation for the dislocations in the bundles of the minority types, it

7 P. Mo ck / Journal of Crystal Growth 224 (2001) does, to our opinion, not hold true for the dislocations in the majority type dislocation bundles. As mentioned earlier, there are dislocations with two different Burgers vectors in the latter type of dislocation bundle which could in effect pair up [12], enhancing the driving force on dislocation movements in the h100i peripheral areas significantly. Since a comprehensive discussion of this hypothesis is given in Ref. [12] and a new model that accounts for both majority and minority dislocation bundles in thermally processed GaAs wafers is presented in Ref. [23], we will provide some theoretical support for the existence of dislocations pairs in majority type dislocation bundles only concisely in Appendix B. Observations that corroborate the pairing up hypothesis and, thus, support our model [23] experimentally are presented in Refs. [13,22]. It is noteworthy that the plasticdeformation that is realised by the majority type dislocation bundles is much more severe than the one that is realised by the minority type dislocation bundles. While the majority type dislocation bundles are typically up to about 1.5 cm long, the dislocation bundles of the minority types extend at most for a few mm. In addition, majority type dislocation bundles are much more numerous than dislocation bundles of the minority types. Added together, we estimate from a variety of undoped samples that there is typically a difference of about 50 times in the amount of plasticdeformation that is realised by these two different types of dislocation bundles. Thus, the currently accepted models [17 19] account only for a small percentage of the whole plasticdeformation although they describe the preference of minority type dislocation bundles at the substrate orientation flat well. Bearing in mind that a fourth type of MBE machine (i.e. another user built piece of equipment that employed a radiatively heated, non Inbonding sample holder [24]) has been used for the thermal treatments described in Refs. [8 11], it seems to be the case that the problem of severe plasticdeformation of GaAs substrates in MBE sample holders is rather widespread. 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 [9 11,18,19]. 4. Conclusions It has been shown that some sample holder designs of MBE machines can cause severe plastic deformation in 2-inch diameter GaAs substrates when the sample is heated up to about 6508C. The plastic deformation occurs mainly by means of bundles of 608 dislocations which start at the sample edges in the four h100i peripheral areas, glide into the bulk of the substrate, and form depending on the dopant type a pseudo-symmetric, four- or two-fold set. Fortunately, the problem can be overcome by means of modifications to the sample holder. Acknowledgements We thank Dr. Gilbert W. Smith from the Defence Evaluation and Research Agency (DERA), Great Malvern, for the provision of eight samples, his modifications to the sample holder of the user built MBE machine that led to the eradication of the dislocation bundles, and for the drafting of Appendix B. Christine Roberts from the Interdisciplinary Research Centre (IRC) for Semiconductor Materials of Imperial College London provided four samples. Dr. David Laundy, Beam-Line Scientist of station 7.6 of the synchrotron radiation source (SRS) at Daresbury Laboratory, is thanked for experimental support. Dr. Glyn MacPherson form the IRC Semiconductor Materials of Imperial College London assisted during the initial part of the X-ray transmission topographicwork at the SRS. We would like to thank Dr. Kaoru Mizuno from the Department of Materials Science of Shimane University for his assistance in taking two double-crystal X-ray reflection topograms at the SRS and for some photographicwork. Dr. Zsolt Laczik from the University of Oxford kindly provided the Makyoh topogram that it shown in our paper. For the critical reading of the manuscript and useful

8 18 P. Mo ck / Journal of Crystal Growth 224 (2001) comments, we are indebted to Prof. Masayoshi Yamada, Department of Electronics and Information Science of the Kyoto Institute of Technology, Dr. Graham R. Booker, Department of Materials, University of Oxford, and Prof. Brian K. Tanner, Department of Physics of Durham University. Financial support from the Engineering and Physical Science Research Council (EPSRC) and the Ministry of Defence is gratefully acknowledged and we are particularly grateful to the EPSRC for sponsoring the usage of the experimental facilities at the SRS in the framework of two Direct Access projects (Reference numbers and 31098). Appendix A. Modifications to the sample holder The standard Varian/Epi 2-inch wafer holder has the wafer resting on a thin annular Tantalum foil all round its circumference. The wafer is held in place with Molybdenum springs, which push on the back of the wafer. The employed modification was to remove the annular foil and replace it with three U-shaped pieces of Molybdenum wire which were spot welded to the holder such that the open end of the U was facing in towards the centre of the holder. This had at least two effects: the contact area between the wafer and the mount was reduced, thus increasing the thermal resistance between the two, and the thermal environment was made more uniform because the edge of the wafer was no longer hidden behind the annular foil. Appendix B. Theoretical support for the existence of dislocations pairs in majority type dislocation bundles Assuming a tangentially uniform residual strain distribution, we calculated the critical resolved shear stresses on the eight actually operation slip systems, as experimentally derived in Ref. [12], for a perfectly circular undoped GaAs wafer, employing the formulae and material data given in Ref. [23]. Such calculations predict for one half of the actually operating slip systems and the outermost margin of the residual strain annulus (i.e , see Fig. 1a in Ref. [13]) two curves for the resolved thermal shear stresses t 1;2 and t 5;6 Fig. 3. Predicted resolved thermal shear stress as a function of an angular coordinate that counts from [1 0 0] for the slip systems no. 1: ½0 11Š (1 1 1), no. 2: [0 1 1] ð1 11Þ, no. 5: ½101Š (1 1 1), and no. 6 ½101Šð1 11Þ, and dislocation pairs (i.e. nos. 1+5 and 2+6).

9 P. Mo ck / Journal of Crystal Growth 224 (2001) over an angular parameter that counts from the [1 0 0] direction (see Fig. 3, where the subscripts are explained). Calculations for the other four operating slip systems and the outermost margin of the residual strain annulus lead to a graph with an angular shift of 908 that is otherwise completely analogous to Fig. 3. We are, thus, completely justified to restrict the following considerations to one half of the actually operating slip systems. There are only four small angular regions where t 1;2 and t 5;6 possess values that are bigger than the experimentally derived threshold for dislocation generation [18] in the applicable deformation geometry [25], i.e. only four peripheral areas where minority type dislocation bundles can exist. Fig. 3 shows in good agreement to our experimental results, Section 3.1, that these areas ranges from about 108 to about 358 around [1 1 0]. The startling conclusion one has to draw from Fig. 3 is, however, if dislocation pairs would not exist, a few minority type dislocation bundles would be all that is possible to relax the thermally induced strain. If we, however, take dislocation pairing up, i.e. a type of possible dislocation interactions that have been discarded by the older models [17 19], into account, the situation changes completely. The resolved thermal stresses t 1 þ t 5 ¼ t 2 þ t 6 for dislocation pairs are for nearly all angular regions above the threshold for dislocation glide. Thus, glide of dislocation pairs is in principal possible nearly everywhere at the wafer edge. The locations where the glide of dislocation pairs will actually happen, however, are determined by the spatial distribution of the density of dislocation sources [20,21], which seem to be highest around the h100i peripheral areas, Ref. [23, Appendix 5]. Taking this distribution into account, the angular range of majority type dislocation bundles is, as Fig. 3 in good agreement to our experimental results, Section 3.1, indicates, about 228 around h100i directions. In conclusion, only the formation of dislocation pairs can explain the bulk of the experimental results in general and the observed spatial distribution of majority type dislocation bundles in particular. We consider, therefore, the good agreement between our model [23] and experimental results, Section 3.1, as strong theoretical support for the proposed pairing up of dislocations in majority type dislocation bundles. References [1] P. Mo ck, B.K. Tanner, C.R. Li, A.M. Keir, A.D. Johnson, G. Lacey, G.F. Clark, B. Lunn, J.C.H. Hogg, Semicond. Sci. Technol. 11 (1996) 1051; Erratum [2] P. Mo ck, B.K. Tanner, G. Lacey, C.R. Whitehouse, G.W. Smith, Inst. Phys. Conf. Ser. 157 (1997) 165. [3] B.K. Tanner, A.M. Keir, P. Mo ck, C.R. Whitehouse, G. Lacey, A.D. Johnson, G.W. Smith, G.F. Clark, J. Phys. D 32 (1999) A119. [4] K. Mizuno, P. Mo ck, B.K. Tanner, G. Lacey, C.R. Whitehouse, G.W. Smith, A.M. Keir, J. Crystal Growth 198/199 (1999) [5] A.G. Turnbull, G.S. Green, B.K. Tanner, M.A.G. Halliwell, Mater. Res. Soc. Symp. Proc. 202 (1991) p. 513 (Chapter 112) [6] Z. Laczik, G.R. Booker, A. Mowbray, J. Crystal Growth 153 (1995) 1. [7] C.R. Whitehouse, S.J. Barnett, D.E.J. Soley, J. Quarrell, S.J. Aldridge, A.G. Cullis, G.F. Clark, W. Lamb, B.K. Tanner, S. Cottrell, B. Lunn, C. Hogg, W. Hagston, Rev. Sci. Instr. 63 (1992) 634. [8] M. Yamada, M. Fukuzawa, T. Kawase, M. Tatsumi, K. Fujita, Inst. Phys. Conf. Ser. 145 (1996) 447. [9] M. Tatsumi, T. Kawase, Y. Iguchi, K. Fujita, M. Yamada, in: M. Godlewski (Ed.), Proceedings of the Eighth Conference on Semi-insulating III V Materials, 6 10 June, 1994, Warsaw, Poland, World Scientific, Singapore, pp [10] M. Tatsumi, Y. Hosokawa, T. Iwasaki, N. Toyoda, K. Fujita, Mater. Sci. Eng. B 28 (1994) 65. [11] T. Kawase, T. Wakamiya, S. Fujiwara, K. Hashio, K. Kimura, M. Tatsumi, T. Shirakawa, T. Tada, M. Yamada, in: C.J. Miner, W. Ford, E.R. Weber (Eds.), Proceedings of the Seventh International Conference on Semi-insulating III V Materials, April, 1992, Ixtapa, Mexico, IOP Publ. Ltd., Bristol, American Institute of Physics, Colchester, 1993, pp (Chapter 52). [12] P. Mo ck, J. Appl. Crystallogr. 34 (2001) 65. [13] P. Mo ck, M. Fukuzawa, Z. Laczik, G.W. Smith, G.R. Booker, M. Yamada, B.K. Tanner, M. Herms, Inst. Phys. Conf. Ser. No. 164 (1999) 67. [14] I. Yonenaga, K. Sumino, J. Crystal Growth 126 (1993) 19. [15] P. Mo ck, G.W. Smith, Cryst. Res. Technol. 35 (2000) 541. [16] P. Penning, Philips Res. Repts. 13 (1958) 79. [17] M. Yamada, M. Fukuzawa, K. Ito, Inst. Phys. Conf. Ser. No. 155 (1997) 901. [18] M. Kiyama, T. Takebe, K. Fujita, Inst. Phys. Conf. Ser. No. 155 (1997) 945.

10 20 P. Mo ck / Journal of Crystal Growth 224 (2001) [19] S. Sawada, H. Yoshida, M. Kiyama, H. Mukai, R. Nakai, T. Takebe, M. Tatsumi, M. Kaji, K. Fujita, Technical Digest IEEE GaAs Integrated Circuit Symp. 74 (1996) 50. [20] H. Alexander, Rad. Effects and Defects in Solids 111 (1989) 1. [21] S. Tohno, S. Shinoyama, A. Katsui, H. Takaoka, Appl. Phys. Lett. 49 (1986) [22] P. Mo ck, Z.J. Laczik, G.R. Booker, Mater. Sci. Eng. B, in press. [23] P. Mo ck, Cryst. Res. Technol. 35 (2000) 529, Erratum [24] M. Yamada, Department of Electronics and Information Science, Kyoto Institute of Technology, private communication. [25] C.N. Reid, Deformation Geometry for Materials Scientists, Pergamon Press, Oxford, 1973.