Global analysis of heat transfer in CZ crystal growth of oxide taking into account three-dimensional unsteady melt convection: Investigation of the coupling method between 2D and 3D models

Abstract

The global model of heat transfer analysis for the Czochralski crystal growth of oxides developed in our previous studies, in which a three-dimensional unsteady melt flow was taken into account, was modified. Here, the Reynolds’ averaged form of the energy equation was used for the melt in the 2D global model in order to consider the effect of unsteady three-dimensional melt convection, i.e., the heat fluxes resulting from the instantaneous three-dimensional velocity fluctuations in the melt, on the thermal field in the 2D global model. As a result, it was revealed that the effect of the time-dependent melt convection can be accounted for well by the Reynolds’ average form of the energy equation. Also, the effect of crystal rotation on melt convection and the melt/crystal interface shape was investigated numerically.