VGF growth method is of raising relevance for 4-6(8)-inch GaAs, InP and GaSb crystals. Cost reduction, convection and stoichiometry control, exemption from ...
PRESENT STATE AND FUTURE TASKS OF III-V BULK CRYSTAL GROWTH Peter Rudolph Institute for Crystal Growth, Max-Born-Str.2, 12489 Berlin, Germany Semiconductor III-V compounds are now and in future of central importance for human life. The leading position of GaAs will be continuously developed further. Single crystalline yield of InP needs to increase essentially. Very high growth rates are expected for GaSb, GaN and AlN. Accordingly, the mastering of the melt-solid, vapour-solid and flux-solid phase transitions on higher technological level by more detailed fundamental knowledge is absolutely essential. VGF growth method is of raising relevance for 4-6(8)-inch GaAs, InP and GaSb crystals. Cost reduction, convection and stoichiometry control, exemption from boron, in situ prevention of precipitate generation, inclusion trapping, dislocation density and patterning as well as twinning are the main tasks of defect engineering. I.
Introduction
The outstanding role of III-V semiconductors is undisputed. In addition to applications in opto- and laser electronics in the narrow- (InSb, InAs, GaSb), middle(GaAs, InP, GaP) and wide-band (AlAs, GaN, AlN) regions these materials gain increasing importance fore high-frequency microelectronics (GaAs, InP, GaN), photo- (GaAs) and thermovoltaics (GaSb), high-power electronics (GaN, AlN), as well as UV-, IR- and γradiation detectors (GaN, InSb, GaAs, respectively). Now as before, the epitaxial processes for device production require high-quality substrate crystals. GaAs is still in a leading position. The today worldwide production capacity of semiconducting (SC) and semiinsulating (SI) GaAs wafers yields about 200 000 kcm2 increasing by a factor of ~3 up to 2010. Due to the more complicated material parameters the share of InP wafers amounts to 5000 kcm2 only. High growth rates are expected for GaSb used in thermovoltaic and IR-detection devices. Due to their favourable wide gap characteristics GaN and AlN come more and more to the fore. Although the low crystal growth rates from vapour and solution in five years a remarkable yield of the nitride bulk production over some hundred kcm2 can be approximated. Industrially, SI GaAs crystals with diameters up to 150 mm are grown by the Liquid Encapsulated Czochralski (LEC) and Vertical Gradient Freeze (VGF) methods. Recently, for both techniques the principal mastering of 200-mm diameter was demonstrated successfully [1]. Also InP, GaP and GaSb crystals are growing by LEC and VGF. Diameters up to 100 and 150 mm are reported on Czochralski- and VGF-grown InP crystals [2]. Generally, during the last ten years a replace of the LEC by VGF is running. This is due to the better control of melt convection, uniaxiality and homogeneity of the heat transfer. However, for both methods there are still some essential problems to be solved. Mostly they are related to economical parameters, like increase of yield and reduction of price. For instance, to enlarge the crystal
length per run higher melt columns are required that promotes the - convective turbulences in LEC arrangements and, as the result, the growth instability. - In case of VGF higher melts affect the control of the growing interface morphology and extent the interaction time between melt and container wall. Further, there are still some deficiencies of the current crystal qualities challenging the defect engineering in principle, i.e. - uncontrolled non-stoichiometric growth conditions leading to relatively high intrinsic point defect content being responsible for harmful precipitation of second phases particles during cooling down of the crystal and diffusion-drived dislocation mobility; - enhanced boron incorporation when B2O3 encapsulant is applied that influence the intrinsic point defect situation, i.e. Ga vacancy concentration, EL2 and Si efficiencies in GaAs; - collective rearrangements of dislocations into cellular structures and cross-like walls at densities above 5x103 cm-2 and lower than 102 cm-2, respectively, responsible for physical and mechanical inhomogeneities along the wafer area; - twinning along the {111} facets changing the ingot orientation from [001] to [122] (or [111] to [115]) being, hence, the most problematic drawback for materials with low stacking fault energies, like InP and InAs.
II. Control of convection flows Increasing melt columns as prerequisite for growth of longer crystals with diameters of 150 - 200 mm need first of all the proper control of increasing non-steady flows within the huge melt crucibles. According the relation between Rayleight and Taylor numbers, i.e. buoyancy vs. artificial (rotational) convection, the Rossby stability criterion [3] is not more fulfilled in LEC systems with melt heights ≥100 mm. Strong convection flow densities
of some hundred N m-3 and temperature oscillations over ± 10 °C make the stable growth of single crystals very difficult. In VGF melt columns the characteristic toroidal convection pattern promotes the undesirable concave interface morphology. An effective countermeasure proves to be wellcontrolled penetrating Lorentz forces. Even longitudinally travelling magnetic fields (TMF), inducing toroidal flow patterns of opposite flow directions, may damp the buoyancy-drived convection very effectively. Compared to steady fields TMF requires much lower induction forces of some mT only [4]. However, for the growth of dissociating compounds such as III-Vs within characteristic thick-walled high-pressure vessels, the necessary magnetic induction forces are an order of magnitude greater when the inductor coils are placed outside. Hence, for adoption in well-established industrial growth machines, location of the coils inside the growth container is favoured. Optimizing the frequency and phase a well-controllable dynamic program for melt and interface stabilization has to be developed. In case of VGF the guarantee of a constant flat growing interface with slightly convex curvature at the container wall is quite important. To optimize sophistic accompanying global 3D numeric simulations are absolutely necessary.
III. Near-stoichiometric growth In compound crystals, such as III-Vs, one of the most important and complicated parameter to be controlled is the stoichiometry or a given deviation from it. Non-stoichiometric composition enhances the generation of intrinsic point defects (vacancies, interstitials, antisites) that affect the type of conductivity, carrier concentration, absorption behaviour, diffusivity, efficiency of dopant incorporation etc. It promotes the generation, multiplication and spatial movement of dislocations. Finally, the incorporation of the excess component at the interphase in the form of inclusions and the nucleation of second phase in the form of precipitates during the cooling process of the as-grown crystal can impair the wafer and device quality markedly. Hence, the maturity of in situ control of stoichiometry during growth is one of the key targets [5,6].
a
b
Fig. 1. The existence regions of (a) GaAs [6,7] and (b) InP, InAs, and InSb [8] (∆δ - deviation from stoichiometry, l liquidus, s – solidus, 1-3 different references; see [8]).
diagram, i.e. deviation from stoichiometry. In GaAs its maximum widths ∆δmax amounts at 1170 °C to ~10-4-10-3 mole fractions. The congruent melting point is located at arsenic excess of ~10-4 regarding stoichiometry (Fig. 1a). Concerning newer calculations, the solidus crosses the stoichiometry at markedly Ga-rich melt with mole fractions xL < 0.40 or is even completely located on the Asrich side [7]. In InP the phase extent is studied less. One order of magnitude smaller width (∆δmax ≈ 1x10-5) and stoichiometry deviations towards both component sides has been calculated [8] (Fig. 1b). Usually, SI GaAs crystals are grown from slightly arsenic-rich melts in order to control the AsGa antisite deep donor (EL2) concentration and to compensate by controlled addition of the shallow acceptor carbon [1]. However, to avoid the precipitation of arsenic excess and inclusion a near-stoichiometric growth is required. For that the vapour pressure controlled Czochralski (VCz) technique without boric oxide encapsulation [9] proves to be usable. The related Ga-rich mole fraction of the melt is controlled by partial arsenic pressure via the temperature of an installed As-source. Note at such growth conditions from Ga-rich melt the concentration of EL2 falls below 1016 cm–3. Therefore, the concentrations of the compensating shallow acceptor carbon and residual impurities must be reduced drastically in order to meet the precondition [EL2] > [C] + (NΣA - NΣD) > 0 with NΣA,D the total concentrations of acceptors (A) and donors (D) shallower than EL2. In the VCz experiments of the author’s team [9] a proper in situ carbon control down to 1×1015 cm–3 was adjusted. This was solved by CO gas streaming communicating with the inner VCz chamber. Furthermore, only highly purified chamber internals were used to minimize the residual impurity content (note no impurity gettering by the B2O3 encapsulant takes place as in the LEC method). Additionally, the growth rate and temperature gradient were chosen undercritically in order to prevent morphological instability and Ga-inclusion incorporation. Considering all these measures perfect near-stoichiometric SI GaAs single crystals with electrical resistivity 3×108 Ωcm have been grown successfully. EL2 and C concentrations of 8.0×1015 and 6.3×1015 cm-3 were obtained, respectively. It has been shown that pulling of GaAs crystals from Garich melt minimizes the contents of As precipitates, BGa substitutes and dislocations [9]. For VGF the in situ stoichiometry control is discussed and tested for a long time past but not yet solved on industrial scale. As a result VGF crystals show still characteristic features of nonstoichiometry such as precipitates, inclusions of the excess phase and, partially, cellular dislocation patterns (see below). To establish an in situ stoichiometry control the continuously decreasing height of the melt column during the normal freezing process would require a well-controlled source temperature program well fitting the real growth rate.
IV. Dislocation dynamics A. Dislocation cell structuring
The concentration of intrinsic point defects is related to the width of the compound phase extent in the phase
In most as-grown crystals the stored dislocations rearrange in characteristic cell patterns (Fig. 2), which are
not desirable since physical parameter inhomogeneities are caused. For instance, across semi-insulating {100} GaAs wafers a mesoscopic resistivity variation is observed due to the accumulation of AsGa antisite defects (EL2) within the cell walls [10]. As a result a costly postgrowth homogenization step by annealing is required. Cells are also well known from another material groups like metals, alloys, dielectrics independently which growth method was used [11]. The cells are of globular type and their size decreases with increasing average dislocation density [12]. Many deformation experiments below the melting point revealed their correlation with mechanical stress linking cell structure with dynamical polygonization. However, there is not yet direct experimental correlation with thermoelastic strain during growth due to the impossibility of in situ stress measurements. Thus, for the first time the author’s team scaled the cell diameters d with dislocation density ρ , revealed by EPD analysis and thermoelastic stress τ , obtained by global numeric modelling in growing GaAs crystals [13]. In progress, the non-steady equation of plastic deformation was solved giving the duration period until the main dislocation interactions are completed. The terms were then transformed into spatial coordinates by the modified Alexander-Haasen equation. Setting growth rate and material parameters the history of the elastic and plastic parts along the crystal coordinates were obtained [14].
Fig. 2. Cellular dislocation structures in undoped GaAs crystals revealed by (a) KOH etching of a 4-inch wafer [13], (b) LST analysis with integrated depth of 2 mm [12], and (c) X-ray synchrotron topography [11].
From the numeric calculations follows [14] that in growing GaAs crystals the plastic relaxation is completed after a distance of only some mm behind the interface within time period of 1 - 2 hours. One can expect that the prevailing part of cell formation process is transpired during that time. In fact, there are experimental proofs from real-time synchrotron x-ray topography on crystallizing Al [15] and mechanical stressed Cu crystals [16] that the appearance of cellular structures does coincide with the onset of plastic deformation. This fact substantiated the procedure to take the calculated elastic strain at the interface for correlation with the cell dimensions measured in the post-grown wafers (of course, one has to consider possible renewed increase of the elastic
stress during the cooling down course of the crystal even at LEC when it emerges from the boric oxide encapsulant and contacts the relatively cold gas atmosphere). It was found [13,14] that at thermoelastic stresses above 1 MPa, typically for LEC, the universal relations of d = Kρ -1/2 and d = αKGbτ -1 (K,α - constants, G shear modulus, b - Burgers vector) [11] are fulfilled. However, at lower stresses, typically for VCz and VGF, deviations from the d~τ -1 correlation with exponents less than -1 have been obtained. Probably, the diffusion creep via native point defects gains the upper hand over dislocation glide. However, in VGF crystals the longer stay time at high temperatures as well as the somewhat enhanced residual elastic stress due to the lower dislocation density are responsible for better accordance of the cell diameters with the universal rule d~τ -1. Generally, at dislocation densities below 5x103 cm-2 the cell walls begin to disintegrate into fragments. Compared to GaAs and GaP as-grown InP crystals do not show well-developed dislocation cell structures. Obviously, due to the smaller compound phase extent (Fig. 1b) less native point defects are available that reduce the cell formation probability by limiting the climb process [11,17]. Further, cross glide, being important precondition for spatial cell formation too [18], is in InP markedly reduced due to its extremly high stacking fault probability. Cell formation can be reduced by doping. No cell structuring was observed in GaAs doped with In or Si at concentrations > 1018 cm–3. Such an effect is due to the impurity gettering at the dislocation core leading to dislocation locking. Dislocation patterning is also prevented when very low dislocation densities are presented as in the case of minimum thermoelastic stress. Another way is the minimization of the intrinsic point defect content by in situ control of stoichiometry. Recently, the author’s team demonstrated by using the VCz arrangement without boric oxide encapsulant that the cellular structure dissolves when the GaAs crystals grow from a wellcontrolled Ga-rich melt composition [9]. B. Is there any hope of dislocation-free growth? To grow III-V compound crystals without dislocations is a long-term vision of the crystal growers. Dislocationfree GaAs and InP wafers would to be very promising for optoelectronic devices, especially high-brightness LEDs and high-power LDs. However, the main problem making such perfectness uncertain are the unfavourable material parameters like very low critical resolved shear stress τCRSS (~ 0.5 MPa near to the melting point) and relatively high content of native point defects. So arises the question is there any chance at all ? It is well established that the density and distribution of dislocations in melt-grown crystals are due to thermoplastic relaxation of thermally induced stress during growth [19]. Therefore, the content of dislocations is determined by the (time and space dependent) stress level during growth. The level of thermal stress is related to the temperature field in the growing crystal and cool-
ing-down procedure. The higher the temperature field nonlinearities (in first approximation correlating with temperature gradients and crystal radius), the higher the mechanical stress. This correlation together with the low natural τCRSS makes very difficult to grow crystals of larger diameters with low dislocation density or even dislocation-free. From methodical point of view lowtemperature-gradient growth techniques like VGF and VCz are clearly preferred in order to meet this goal. In fact, compared to LEC crystals much lower residual stresses |Sr - St| ≈ 10-6 are typically for these methods. Hence, the careful engineering of the temperature field, assisted by global computer modelling, at all process stages are of essential significance. Recently, Pendurti et al. [20] reported the global numeric modelling of the non-stationary elastic stress and related dislocation development in growing LEC InP crystals by implying the history of the thermal field in the crystal as well as the convection in the melt and vapour phase. A close correlation between the calculated elastic stress history and related dislocation density evolution does exist at various crystal points. It was found out that the gas convection has a significant effect on the total dislocation density - a quite important fact that was not yet considered so far.
[100]
a
[110]
b
Fig. 3. Cross-like rearrangement of residual dislocations in a Si-doped GaAs VGF crystal (a) [24] and sketched sectional view of the cone region of VGF crystals demonstrating the getting caught of the {111} facets (b).
Generally, to pave the way for dislocation-free growth of large III-V crystals the proper combination of the following conditions are required: i) use of dislocationfree seed crystals, probably, with the same diameter as the crystal to be grown, ii) strongly uniaxial heat flow with very small temperature gradients, i.e. nearly flat isotherms at all stages of the growth process, iii) leave out of boric oxide encapsulant the presence of which introduces markedly thermomechanical stresses at the crystal periphery and, maybe, its replacement by a capillary stable detached growth mode, iv) in-situ stoichiometry control in order to reduce the intrinsic point defect content which promotes high-temperature dislocation multiplication by climb, and v) avoidance of all parameter instabilities especially melt and gas flow fluctuations. From today point of view the VGF (probably also further developed VCz) is the most suitable method to meet these demands in ensemble. But at conventional VGF growth the conical part between seed and cylindrical crystal body proves to be the most dangerous region due to the getting caught of the {111} facets (Fig. 3b). If only very few residual dislocations are presented (< 200
cm–2) in [001]-oriented GaAs crystals they are accumulated cross-like along the directions (Fig. 3a). This is connected with the pronounced joint of the {111} facets along the directions in the crystal cone [21] (Fig. 3b). Probably, dislocations can be generated by lattice misfits between the meeting Ga and As facets [22]. Such an explanation would favour the growth with a flat bottom from a seed of the same diameter [23] in order to maintain the rotational symmetry without pronounced faceting (above named condition i). Until today, lowest dislocation densities of less than 100 cm-2 are obtained in 4” GaAs VGF crystals doped with Si [24]. Undoped crystals of the same diameter contain still around 103 cm-2. Despite of such noteworthy progress during the last decade at the present it is not yet clear of which consequences would to be a total absence of dislocations in compound crystals. Possibly, missing dislocations could lead to much higher supersaturation of native point defects and their clustering as micro voids and agglomerates, as it is well known from silicon.
V. Twinning Growing-in twins are one of the most serious macroscopic defects the presence of which make a crystal of no use to wafer preparation because of the twin-induced growth misorientation over the whole crystal body (Fig. 4a). Up to now there is not yet an absolute reliable prevention measure due to their stochastic character of appearance even in InP crystals (Fig. 4b). However, one can list a ranking of the most responsible material and growth parameters enhancing the twinning probability. Gottschalk et al. [25] correlated it with the stacking fault energy whereupon the highest danger of twinning exists in materials with high ionicity showing the lowest stacking fault energies. In fact, InP with degrees of ionicity of 42 % and stacking fault energy of 18 x 10-7 J cm-2 shows an extremely high twinning statistics among the semiconductor compounds. Growth conditions enhancing twin appearance are - i) temperature instabilities, i.e. remelting of the interface, ii) presence of impurities, iii) foreign particles swimming on the melt surface, iv) interface contact with wetting inner container walls, and v) morphological instability of the crystallization front. Hurle [26] has provided a possible thermodynamic description, which can explain the key features of the process. The model demonstrates that, because of the orientation dependence of interfacial energies in the presence of facets, there is a configuration of the 3-phase boundary for which, for sufficiently large supercooling, the free energy of formation of a critical nucleus is actually lowered by forming that nucleus at the 3-phase boundary in twinned orientation. This will occur only if a critical angle of conical growth presenting a portion of crystal surface normal to is sampled during the growth. Such a twinned nucleus is thermodynamically favoured if the supercooling exceeds the critical value δT* = A* (σ Tm / h ∆H) with σ the twin plane energy, Tm melting temperature, h the nucleus height, ∆H the latent heat of
fusion, and A* the reduced work of formation of a nucleus intersecting the 3-phase boundary (its detailed derivation is given in Ref. [26]).
ced compared to conventional PID control. The proposed control method has been successfully tested on 2” InP and GaAs in the IKZ labs showing high accuracy, reproducibility, and robustness. At VGF growth the twinning stochastics can be reduced if flat bottom container is used [23].
VI. GaN and AlN bulk crystals
Fig. 4. The formation of growing-in twins in LEC crystals. (a) Sketch showing different kinds of twins and related crystal misorientation when a [001]-oriented seed is used. (b) Twinning on {111} facets (white arrows) at the shoulder region of a InP crystal revealed by Inada [27]. (c) Scheme demonstrating the 2D-growth mode along the {111} facets when a misoriented (i.e. twinned) nucleus is generated at the three-phase boundary.
Many LEC and Bridgman experiments have demonstrated that the twin probability is markedly reduced if the temperature fluctuations δT of the growth system, and therefore excursions of the angle of the contacting meniscus, are minimised. In fact Japanese producers succeeded in twin-free InP crystal growth with diameters up to 100 (150) mm by careful maintenance of thermal stability during growth that was achieved by applying damping magnetic fields around the melt [28,29]. In this connection well-developed control systems are of increasing importance. Recently Neubert et al. from IKZ Berlin [30] developed a model-based feedback controller of Czochralski processes. The basic strategy includes the use of nonlinear observers for the reconstruction of not directly measured quantities (e.g., crystal diameter and conical growth angle) and a combination of model-based and PID controllers for tracking of crystal diameter and growth velocity trajectories. The system quantities derived by means of the observer are less noisy and more accurate than those yielded by simple numerical differentiation. Furthermore, the growth velocity can be calculated from the values reconstructed by the observer. Due to the model the intricate meniscus dynamics is fully taken into account. Reconstruction by the observer and feedback control show excellent performance and the parameterization effort is remarkably redu-
For the growth of GaN bulk crystals several growth techniques are still under investigation [31]. Beside highpressure flux growth, low-pressure solution growth (LPSG), metal halide vapour phase epitaxy (HVPE) and epitaxial layer overgrowth (ELOG) for obtainment of free-standing thick layers, the direct synthesis from vapour phase under NH3 flow on alternative or native substrates is a quite hopeful bulk growth variant which is also investigated at the IKZ Berlin [32]. Metallic Ga is evaporated and reacts with nitrogen from an ammonia and nitrogen gas mixture. Relatively low pressures in the region of 100-800 mbar and moderate growth temperatures of 1000-1300 °C are used. The still small crystals of mm-dimension show improved structural quality compared to flux grown material. Also the growth of AlN crystals is under investigation at IKZ [33]. For manufacturing of UV-LEDs the mixed crystal system of (Al,Ga,In)N needs to deposit on substrates (e.g. GaN). However, due to the large lattice misfit between layer and foreign substrates AlN homosubstrates grown by sublimation process seems to be a hopeful variant. The required high growth temperatures ≥ 2000 °C and the aggressive aluminium gas species limit the choice for crucible materials. TaC proves to be a usable candidate showing low partial pressures, high temperature and chemical stability. The optimization of a self-seeding process with subsequent growth and bulk n-doping are under development. In general, the growth of both materials with cmdimensions proves to be one of the key challenges for the crystal grower community during the next years.
Acknowledgement The author is indebted to his co-workers Dr. M. Neubert, Dr. F.-M. Kiessling, Dr. Ch. Frank-Rotsch, Dr. U. Juda, D. Jockel, M. Czupalla (all from IKZ Berlin) for their works essentially contributing to the present chapter. He is grateful for numerous interesting discussions with Dr. M. Jurisch, Dr. St. Eichler and Dr. B. Weinert from Freiberger Compound Materials GmbH.
References [1] M. Jurisch F. Börner, Th. Bünger, St. Eichler, T. Flade, U. Kretzer, A. Köhler, J. Stenzenberger and B. Weinert, “LEC- and VGF-growth of SI GaAs single crystals-recent developments and current issues”, J. Crystal Growth 275, pp. 283-291, 2005.
[2]
K. Iwasaki, K. Sato, K. Aoyama, S. Numao, I. Honma, S. Sugano, T. Hoshina and T. Sato, “6-in diameter InP single crystals grown by the hot-wall LEC method and the mirror wafers”, IEEE Trans. Semicond. Manufact. 16, pp. 360-364, 2003.
[3]
H.T. Rossby, “A study of Benard convection with and without rotation”, J. Fluid Dynamics 36, 309335, 1969. [4] P. Schwesig, M. Hainke, J. Friedrich and G. Müller, “Comparative numerical study of the effects of rotating and travelling magnetic fields on the interface shape and thermal stress in the VGF growth of InP crystals“, J. Crystal Growth 266, pp. 224-228, 2004. [5] J. Nishizawa and Y. Oyama, “Stoichiometry of III-V compounds”, Mat. Sci. Eng. R 12, pp. 273426, 1994. [6] P. Rudolph, “Non-stoichiometry related efects at the melt growth of semiconductor compound crystals - a review”, Crystal Res. Technol 38, pp. 542554, 2003. [7] W. Dreyer and F. Duderstadt, “On the modelling of semi-insulating GaAs including surface tension and bulk stresses”, Treatise No. 995, WeierstraßInstitute of Berlin 2004. [8] G.V. Semenova, T.P. Sushkova, A. Morozova and E.G. Goncharov, “ Processing of defect formation and deviation from stoichiometry in semiconductor AIIIBV and AIVBV comounds”, Inst. Phys. Conf. Ser. No. 160, IOP Publishing Ltd., pp. 385388 , 1997. [9] P. Rudolph and F.-M. Kiessling, “Growth and characterization of GaAs crystals produced by the VCz method without boric oxide encapsulation”, J. Crystal Growth 292, pp. 532-537, 2006. [10] J.R. Niklas, W. Siegel, M. Jurisch and U. Kretzer, “GaAs wafer mapping by microwave-detected photoconductivity”, Mat. Sci. Eng. B 80, pp. 206209, 2001. [11] P. Rudolph, “Dislocation patterning in semiconductor compounds”, Crystal Res. Technology 40, pp. 7-20, 2005. [12] M. Naumann, P. Rudolph, M. Neubert and J. Donecker, “Dislocation studies in VCz GaAs by laser scattering tomography”, J. Crystal Growth 231, pp. 22-33, 2001. [13] Ch. Frank-Rotsch, U. Juda, F.-M. Kiessling and P. Rudolph, „Dislocation patterning during crystal growth of semiconductor compounds (GaAs)”, Mat. Sci. Technol. 21, pp. 1450-1454, 2005. [14] P. Rudolph, Ch. Frank-Rotsch, U. Juda, St. Eichler and M. Scheffer-Czygan, phys. stat. sol. (to be published). [15 ] G. Grange, C. Jourdan, A.L. Coulet and J. Gastaldi, “Observation of the melting-solidification process of an Al crystal by synchrotron X-ray topography”, J. Crystal Growth 72, pp. 748-752, 1985. [16] B. Jacobson, H.F. Poulson, U. Lienert, J. Almer, S.D. Shastri, H.O. Sorensen, C. Gundlach and W. Pantleon, “Formation of subdivision of deformation structures during plastic deformation”, Science 312, pp. 889-892, 2006. [17] B. Bako, I. Groma, G. Györgyi and G. Zimanyi, “Dislocation patterning: The role of climb in meso-scale simulations”, Comp. Mat. Sci. 38, pp. 22-28, 2006.
[18]
R. Madec, R. Devincre and L.P. Kubin, “Simulation of dislocation patterns in multislip”, Scripta Mat. 47, pp. 689-695 (2002).
[19]
J. Völkl, “Stress in cooling crystals”, in: D.T.J. Hurle (ed.), Handbook of Crystal Growth, Vol 2b, Elsevier, North-Holland 1994, pp. 821-874. S. Pendurti, V. Prasad and H. Zhang, “Modelling dislocation generation in high pressure Czochralski growth of InP single crystals: parts I and II”, Modelling Simul. Mater. Sci. Eng. 13, 249-297, 2005. B. Birkmann, J. Stenzenberger, M. Jurisch, J. Härtwig, V. Alex and G. Müller, “Investigations of residual dislocations in VGF-grown Si-doped GaAs”, J. Crystal Growth 276, pp. 335-346, 2005. G. Müller, P. Schwesig, B. Birkmann, J. Härtwig and S. Eichler, “Types and origin of dislocations in large GaAs and InP bulk crystals with very low dislocation densities”, Phys. stat. sol. (a) 202, pp. 2870-2879, 2005. P. Rudolph, F. Matsumoto and T. Fukuda, “Studies on interface curvature during vertical Bridgman growth of InP in a flat-bottom container”, J. Crystal Growth 158, pp. 43-48, 1996. B. Birkmann, M. Rasp, J. Stenzenberger and G. Müller, J. Crystal Growth 211, pp. 157-162, 2000. H. Gottschalk, G. Patzer and H. Alexander, “Stacking fault energy and ionicity of cubic III-V compounds”, phys, stat. Sol. (a) 45, pp. 207-217 (1978). D.T.J. Hurle, “A mechanism for twin formation during Czochralski and encapsulated vertical Bridgman growth of III–V compound semiconductors”, J. Crystal Growth 147, pp. 239-250, 1995. M. Shibata, Y. Sasaki, T. Inada and S. Kuma, “Observation of edge-facets in InP crystals grown by LEC method”, J. Crystal Growth 102, pp. 557-561, 1990. R. Pool, “Japan’s Showa Denko samples 6 inch InP wafers”, Compound Semiconductor 8, No. 4, p. 4, 2002; see also advertisement in III-Vs Review - The Advanced Semiconductor Magazine 15, p. 9 2002. T. Kawase, S. Fujiwara, M. Matsushima, Y. Hosokawa and R. Nakai in : Proc. 2001 Int. Conf. on InP and Related Mat., (13th IPRM), 14-18 May 2001 in Nara, p. 13. M. Neubert, “Model-based control” in: Annual Report 2005/06, Institute for Crystal Growth Berlin, 2006, pp. 82-84 (http://www.ikz-berlin.de). A. Denis, G. Goglio and G. Demazeau, “Gallium nitride bulk crystal growth processes: A review”, Mat. Sci. Engin. R50, pp. 167-194, 2006. D. Siche, Gallium Nitride” in: Annual Report 2005/06, Institute for Crystal Growth Berlin, 2006, pp. 50-51 (http://www.ikz-berlin.de). J. Wollweber, “Aluminium Nitride” in: Annual Report 2005/06, Institute for Crystal Growth Berlin, 2006, pp. 48-49 (http://www.ikz-berlin.de).
[20]
[21]
[22]
[23]
[24] [25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
