The numerical modelling of dislocation generation in semiconductor crystals during Czochralski growth

Abstract

The dislocation densities in semiconductor compound crystals have been found to be affected by the growth orientation, crystal radius and the ambient temperature employed during the Czochralski (CZ) growth process. The objective of this paper is to investigate the influence of these growth parameters on the dislocation density and spell out ways to control the growth parameters in order to reduce the dislocation density. The finite-element technique is utilized to solve the governing equations of the quasi-steady-state (QSS) heat transfer and the thermoelasticity to obtain the temperature distribution and the thermal stresses in a growing crystal. The resolved shear stresses (RSSs) in each slip system are obtained through the transformation of thermal stresses. The RSSs are then employed to calculate the plastic deformation and dislocation density in each slip system of the crystal using the constitutive equation. The total dislocation densities in the crystal are obtained by summing the dislocation densities in all the slip systems. The results indicate that ambient temperature and growth direction can be effectively used to reduce the dislocation density in the CZ process.