Numerical analysis of fluid flow of rotating squared crystal in the pulling method and its effect on growth shape

Abstract

Abstract A numerical analysis of the effect of a rotating squared crystal on the environmental solution flow in the pulling method was performed. These calculation results show a drastic change in the velocity boundary layer thickness around the squared edge at a certain condition. This velocity boundary layer thickness has generally a strong relation with a solute boundary layer thickness and that corresponds to the difference of the crystal growth rate. We calculate the crystal surface spiral ledge growth rate assuming typical BCF model and with the different solute boundary layer thickness at different positions. This solute boundary layer thickness difference brought different ledge growth rates. We calculate ledge growth rate in the case of the small solute boundary layer thickness near the spiral center and large thickness far from the spiral center. At the region of the two solute boundary layer thickness exists, the higher growth rate ledge that located near the spiral center about to reach the far located and low growth rate ledge. So as a result, the ledge spacing becomes smaller at the boundary of the two different thickness boundary layers.