数值模拟自然对流对直拉单晶硅的影响(英文)

Numerical Simulation of the Natural Convection Influence on Silicon Single Crystal by CZ

在直拉单晶硅生长的过程中,自然对流对晶体界面的形状、温度场及应力分布影响很大。本文采用二维模型对熔体内自然对流对单晶硅的影响作了数值模拟,在低雷诺数时采用层流模型,高雷诺数时采用紊流模型,Gr的变化范围从3×106到3×1010,这样涵盖了从小尺寸到大尺寸的直拉单晶硅生长系统。数值结果表明熔体的流动状态不仅与熔体的Gr有关,还与熔体高度和坩埚半径的比值密切相关。当Gr>108时,熔体内确实存在紊流现象,层流模型不再适合,随着Gr的增大,紊流现象加剧,轴心处的等温线变得更为陡峭,不利于晶体生长。

Natural convective has significant effects on the crystal-meh interface shape, temperature field and the stress distribution in Czochralski （CZ） crystal growth. In this paper, two-dimensional numerical simulations were carried out to clarify the effect of buoyancy force on melt motion in a CZ crystal system. At low Reynolds numbers, a laminar model was used, while at large Reynolds numbers, a turbulence model was employed. The present paper investigates the natural convection from a low Grashof number 3 × 10^6 to a large Grashof number 3 ×10^10 ,which corresponding to small-size CZ system to large-size CZ system. The numerical results show that the flow state is not only related to Grashof number but also the ratio of the melt height to the crucible radius. When Gr is large than a critical value 10^8, the flow becomes unstable, the laminar model is no longer suitable, and it is found that with the increase of Grashof number, the turbulence flow and intensity becomes stronger and temperature gradient near the interface becomes sharper, which is harmful to the crystal growth.