Dislocation Density Analyses of Bulk Semiconductor Single Crystal during CZ Growth Process (Effects of Crystal Anisotropy).

Abstract

A computer code was developed for continuous simulation of dislocation density in a bulk single crystal during the Czochralski (CZ) growth process. In this computer code, the effects of crystal anisotropy such as the elastic constants and the slip directions were approximately taken into account by averaging the Young's modulus, the Poisson's ratio and the resolved shear stresses along the azimuthal direction. Axisymmetric finite element analysis can be applied to quantitative estimation of dislocation density during single crystal growth process by using this averaging technique together with the Haasen-Sumino model as a creep constitutive equation of a single crystal at elevated temperatures. Dislocation density analyses were performed both for [001] growth direction and [111] growth direction of InP single crystal. As a result, although the [111] growth direction has the higher average Young's modulus than the [001] growth direction, the former gives lower dislocation density than the latter. This result represents the effects of crystal anisotropy and is consistent with the previous qualitative analysis and steady state analysis of dislocation density.