Numerical study of natural convection in Czochralski crystallization

Natural convection in the melt phase of the Czochralski crystal growth syst em is unavoidable due to the gravitational field. Both horizontal and verti cal temperature gradients influence the stability of the melt convection. F or a tall crucible, a boundary layer type of convection is dominant, while Rayleigh-Benard-type convection occurs for a shallow crucible. A low Reynol ds number kappa-epsilon model was employed, but found to be inadequate for prediction and a more sophisticated model is required. (C) 1998 Elsevier Sc ience S.A. All rights reserved.