Global analysis of heat transfer in CZ crystal growth of oxide taking into account three-dimensional unsteady melt convection: Effect of meniscus shape

Abstract

A global model of heat transfer analysis for the Czochralski crystal growth of oxides, in which a three-dimensional unsteady melt flow was taken into account, was developed in our recent study. In the model, however, the focal point was the methodology of formulating the model by coupling a conventional global model of heat transfer, which is based on a pseudosteady axisymmetric assumption, with a model of a three-dimensional, unsteady melt flow via two interface models. Therefore, for simplicity, the shape of the melt free surface was assumed to be flat. In this study, the global model was further developed by considering the meniscus of the melt free surface. It was found that the meniscus of the melt free surface caused the melt flow to be more unstable and shifted the critical Reynolds number at which the melt/crystal interface inversion occurs toward a much lower value.