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A technique for numerical simulation of the process of directional solidification of multisilicon in a square crucible is considered. The application of 2D axisymmetric geometry constructed for a vertical furnace cross section in the calculations is justified. The mathematical model describes the hydrodynamics of a melt, gas flow, global heat exchange, thermal stress, and evolution of the dislocation density in a growing crystal. The sensitivity of the stress and dislocation density to the Alexander–Haasen model parameters is determined.

Obtaining very high-purity germanium crystals with low dislocation density is a practically difficult problem, which requires knowledge and experience in growth processes. Dislocation density is one of the most important parameters defining the quality of germanium crystal. In this paper, we have performed experimental study of dislocation density during 4-in. germanium crystal growth using the Czochralski method and comprehensive unsteady modeling of the same crystal growth processes, taking into account global heat transfer, melt flow and melt/crystal interface shape evolution. Thermal stresses in the crystal and their relaxation with generation of dislocations within the Alexander-Haasen model have been calculated simultaneously with crystallization dynamics. Comparison to experimental data showed reasonable agreement for the temperature, interface shape and dislocation density in the crystal between calculation and experiment.

Текст статьи не публикуется в открытом доступе в соответствии с политикой журнала. To grow high-quality germanium crystals is one of the most important problems of growth industry. The dislocation density is an important parameter of the quality of single crystals. The dislocation densities in germanium crystals 100 mm in diameter, which have various shapes of the side surface and are grown by the Czochralski technique, are experimentally measured. The crystal growth is numerically simulated using heat-transfer and hydrodynamics models and the Alexander–Haasen dislocation model in terms of the CGSim software package. A comparison of the experimental and calculated dislocation densities shows that the dislocation model can be applied to study lattice defects in germanium crystals and to improve their quality.