The Solid-Liquid Interface Shape during Crystal Growth by the Czochralski Method

Abstract

The solid-liquid interface shapes are obtained by solving the Laplace's equation computationally assuming a model adequately simplified. The conditions which are indispensable for the crystal growth are mentioned in detail; the interface shape is given as a function of the convective heat loss, the crystal length, the crystal radius, and the crucible temperature for germanium. There exists a simple relation between the growth rate and the deviation from the flat interface and we can determine the growth rate for realizing the nearly flat interface. Our results are in qualitatively agreement with the experimental data hitherto obtained. Furthermore it is explained by present results why the dislocation-free crystal can be grown.