NUMERICAL-ANALYSIS OF FLUID-FLOW OF ROTATING SQUARED CRYSTAL IN THE PULLING METHOD AND ITS EFFECT ON GROWTH SHAPE

A numerical analysis of the effect of a rotating squared crystal on th e environmental solution flow in the pulling method was performed. The se calculation results show a drastic change in the velocity boundary layer thickness around the squared edge at a certain condition. This v elocity boundary layer thickness has generally a strong relation with a solute boundary layer thickness and that corresponds to the differen ce of the crystal growth rate. We calculate the crystal surface spiral ledge growth rate assuming typical BCF model and with the different S olute boundary layer thickness at different positions. This solute bou ndary layer thickness difference brought different ledge growth rates. We calculate ledge growth rate in the case of the small solute bounda ry layer thickness near the spiral center and large thickness far from the spiral center. At the region of the two solute boundary layer thi ckness exists, the higher growth rate ledge that located near the spir al 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. (C) 1998 Published by Elsevi er Science Ltd. All rights reserved.