Study of twisting of β-Ga2O3 crystals based on optical absorption and thermal conductivity anisotropy in the crystals grown by the Czochralski method

Abstract

The effects of internal radiation and thermal conductivity anisotropy in β-gallium oxide crystals on heat and mass transfer in the Czochralski method were numerically studied. Specifically, we calculated the temperature and velocity distributions in a crystal and/or melt and the interface shape between the crystals and melt for the Czochralski method. We used the Rosseland approximation to include the internal radiation in the crystals to calculate the heat transfer in the crystal. Moreover, the thermal conductivity anisotropy in the crystals was considered to study the asymmetric temperature distribution.The results indicated that the temperature gradient in the semitransparent crystal was smaller than that in the opaque crystal. This result is attributed to the absorption of the outgoing heat flux from the interface between the crystal and melt in the crystal. We studied the asymmetric temperature distributions in the crystals caused by thermal conductivity anisotropy as a function of the crystal absorption coefficient.The results also indicated that the interface shape between a semitransparent crystal and the melt was convex to the melt, whereas the shape between an opaque crystal and the melt was almost flat.