The effect of interface shape on anisotropic thermal stress of bulk single crystal during Czochralski growth

Both three-dimensional nonlinear anisotropic thermoelastic and two-dimensional nonlinear heat conduction finite element programs, which take into consideration the effects of the shape of the solid-liquid interface, elastic anisotropy and temperature-dependent material properties, were developed and implemented in this article to calculate the distributions of the temperature and the thermal stress in bulk single crystals during Czochralski growth. Thermal stress analyses of a GaAs bulk single crystal were carried out for the general form and, therefore, could be performed in an arbitrary pulling direction. However, only the results in the cases of the 〈00 1〉 and 〈1 1 1〉, which are of practical significance, were studied in this article. The influence of the elastic anisotropy and the shape of the solid-liquid interface, modeled as parabolic, upon the distributions of temperature, stress and the dislocation density parameter were investigated and discussed.