Mechanics of shaped crystal growth from the melt

Abstract

We present the numerical formulation of the thermal stress driven steady-state dislocation generation during the growth of shaped crystals from the melt, with Czochralski (CZ) growth of solid cylinder III–V compound semiconductors as an example. We use and compare the Haasen–Alexander model, coupling dislocation multiplication and creep strain rates, and the Jordan model, based on thermoelastic stresses. Growth parameters may be chosen so as to produce an overall approximately flat interface, leading to reduced dislocation density in the majority of the crystal's cross section. Calculation of final dislocation density requires the initial dislocation density and all stress components along the solid-liquid interface, microstructural features which depend on the physical processes leading to solidification. The final dislocation density is not sensitive to the initial dislocation density along the solid-liquid interface, but strongly depends on the interface stress. Significant stress relaxation at the interface is required to produce experimentally observed “W” shaped dislocation patterns. Crystal growth direction and crystalline anisotropy couple elastic (lattice) and plastic (slip systems) crystalline anisotropy.