Thermal stress analysis of bulk single crystal during Czochralski growth (comparison between anisotropic analysis and isotropic analysis)

A three-dimensional finite element program is developed for calculating the thermal stress in bulk single crystals during Czochralski growth. Elastic anisotropy is taken into account in this program. Thermal stress analyses of a GaAs bulk single crystal are performed in the cases of the [001] and [111] pulling directions, using its temperature distribution obtained from a heat conduction analysis and its material properties. The stress component and the dislocation density parameter are compared between the anisotropic analysis, taking account of elastic anisotropy, and the isotropic analysis, using Young's modulus and the Poisson ratio in the {111} plane. Significant differences are found in their values and distribution patterns between both analyses.