Studies on dislocation patterning and bunching in semiconductor compound crystals (GaAs)

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Abstract

The origins of formation of two not yet completely understood structural defects in undoped semiconductor compound crystals, mainly GaAs, are analysed and discussed—(i) dislocation patterning in cells and (ii) dislocation bunching. The dependences of the mean cell diameter d on the dislocation density N and acting thermo-mechanical stress σ in VCz GaAs crystals are investigated and compared with metallic crystals. The rules of correspondence dNb−1/2 and dGbσ−1 (G—shear modulus, b—Burgers vector) have been confirmed. The superposition of two genesis paths is proposed: formation of dislocation networks by dynamical polygonization and cell patterning by dissipative structuring. Possible reasons for the absence of missing of cells in InP crystals are proposed. The concepts of dislocation bunching are reviewed. Newer simulation results in the field of metals demonstrate the possible importance of oscillating growth conditions like melt convection, turbulences or heating temperature fluctuations. Experimentally, the probability of appearance of dislocation bundles in VCz GaAs crystals as function of the growing interface shape is investigated. Considering the radial distribution of von Mises tensors a bunching by glide collision is possible.

Introduction

The demand of high-quality semiconductor compound wafers with large diameters of 100–150 mm (4–6 inch, respectively) for epitaxy-based devices in micro-, opto- and nanoelectronics is increasing and the structural quality becomes more and more crucial. Because the growth of undoped dislocation-free semiconductor compound crystals is still impossible, today, the targets are low dislocation densities of uniform distribution. During the last decade the methodical efforts were directed to reach these aims by applying low-temperature gradient growth methods like vertical Bridgman (VB), vertical gradient freeze (VGF) and vapour pressure controlled Czochralski (VCz) techniques. However, there are still two serious inhomogeneous structural inaccessibilities involving structural and electrical parameter variations, the formation mechanisms of which are not yet completely clarified: (i) the dislocation arrangements in cell patterns and (ii) dislocation bunching. Both types of defects are observed in GaAs crystals independently on the above-mentioned growth techniques and they are well known from conventional horizontal Bridgman (HB) and liquid encapsulation Czochralski (LEC) method too [1].

Dislocation cells cause mesoscopic wafer inhomogeneity of the electrical parameters. In as-grown GaAs crystals the EL2 defects are enriched in the cell walls the levelling of which requires costly steps of post-growth treatment. Dislocation bundles propagate from the substrate crystal into the epitaxial layers affecting device performance markedly.

Cellular structures are not only typical for melt-grown GaAs. They appear also in other undoped crystals of III–V (e.g. GaP), II–VI (e.g. CdTe and ZnSe) and IV–VI (e.g. PbTe) compounds. Especially in crystallized metals and metallic alloys the dislocation arrangement in cells is a characteristic feature. Dislocation bundles, often described as gnarls, tangles or clusters, mostly appear sporadically and in isolation. Once nucleated they may propagate through the whole growing crystal, typically, parallel to the direction of solidification. Such defects have been detected in GaAs and InP crystals. They are observed in cast silicon ingots. They are also known from plastically deformed metallic crystals and often called veins.

Despite a large number of publications dealing with both defect types their genesis is not yet understood exactly. Are cell patterns driven by energetical (enthalpy production) or dissipative (ordering, i.e. entropy reducing) processes or do they result from a combination of both? Are dislocation bundles generated stochastically, e.g. by locally acting heterogeneous origins, or definitely e.g. by the thermo-mechanical stress field appearing in a cooling crystal? In order to clarify these questions, careful experimental studies in combination with the theory of dislocation reactions in ensemble, i.e. dislocation dynamics, are required. During the last few years, most related progress was made in the field of single crystalline metals [2], [3]. Unfortunately, no profitable knowledge has been transferred to semiconductor compounds yet. Obviously, this is due to the marked difference of dislocation densities and, hence, varying long-range interaction dimensions between dislocations. Whereas in metals dislocation densities of 108–1010 cm−2 and cell diameters of 1–10 μm are typical, semiconductor crystals show much lower numbers of dislocations in the range of 103–105 cm−2 forming much greater cells with diameters of 100–1000 μm. Hence, the small sizes of 3D simulation boxes, typically 20–25 μm3 maximum, are presently available for modelling such processes and they work well for metals but fail for materials with markedly lower dislocation density. Nevertheless, as will be shown below, already today the semiconductor crystal grower can learn proper informative facts from the metal physicists. It is time to bring them together more closely to develop further the modelling capacity and improve the methodology even for the production of semiconductor compound crystals.

The present paper will contribute to the clarification of the nature of both defect types on the basis of experimental facts mainly obtained on GaAs crystals. To correlate them with the acting thermal stress at growth temperatures, global computer modelling of the von Mises components was used. The results are discussed considering newer concepts from metal physics.

Section snippets

Experimental procedure

Undoped 4- and 6-inch 〈1 0 0〉-oriented GaAs crystals used for defect analysis were grown by the VCz method, the specifics of which were described elsewhere in detail [4]. An axial temperature gradient of about 20 K cm−1 was applied at the growing interface. Pulling rates between 4 and 6 mm h−1 were selected. In order to control the thermal and thermo-mechanical stress fields via the shape of the growing phase boundary the following parameters were varied: crucible start position, power ratio between

Cellular structure

Typically, in undoped GaAs crystals the dislocations are arranged in cellular patterns (Fig. 1a). The majority of dislocations are concentrated in the cell walls, the interiors are mostly dislocation free. In general, such arrangement agrees very well with dislocation patterns observed in metals, e.g. in deformed Cu–Mn single crystals (see Fig. 1 in Ref. [8], for example). As was revealed by depth integrating LST, the cells are of globular shape [5] as can be deduced from Fig. 1a (note in the

Summary

We analysed two not yet completely understood defects in melt-grown semiconductor compound crystals: (i) dislocation patterning in cells and (ii) dislocation bunching. The dependences of the mean cell diameter d on the dislocation density N and acting thermo-mechanical stress σ were investigated and compared with metallic crystals. We confirmed the rules of correspondence dN−1/2 and dGbσ−1 and deduced identical formation mechanism. Concerning our observations two genesis paths are superposed:

Acknowledgements

The authors are grateful to M. Czupalla and M. Pietsch for growing the crystals, B. Lux, Th. Wurche and M. Imming for wafer preparation, H. Baumüller for EPD and striation analysis (all from IKZ), and Dr. B. Brinkmann (Frauenhofer Institute Erlangen) for helpful discussions. They are pleased to mention the work was supported by the German Federal Ministry of Education, Science, Research and Technology (contract nos. 01 BM 501-0, 501-A) and Freiberger Compound Materials GmbH.

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