大直径硅单晶生长过程中固/液界面形状及熔体流动的数值分析

Numerical Simulation of Melt/Crystal Interface and Melt Flow during Large Diameter Single Silicon Crystal Growth

数值模拟技术是提升大直径硅单晶质量、降低晶体制备成本的有效工具。利用切克劳斯基法生长硅单晶时,固/液界面的形变程度是衡量晶体质量的关键参数。由于单晶炉体内的高温环境导致对界面的直接观察极为困难,因此本文采用有限元法对生长16英寸直径硅单晶过程中,不同生长阶段的固/液界面形状及熔体流动情况进行计算。数值计算结果表明:在本文所用的热场及工艺参数条件下,随着晶体长度的不断增加,固/液界面的形变量增加同时晶体内部的热应力加大;通过对晶体提拉速率及晶体转速-坩埚转速的比值的调整,我们发现,降低晶体的提拉速率以及精确的控制转速比可以使晶体各个阶段都获得比较理想的界面形状。

Numerical simulation is an effective tool for improving the large diameter single silicon crystal quality and reducing the preparation cost. The deflection of solid/liquid interface in Czochralski （Cz） method is a key issue for crystal quality. Owing to the high-temperature environment and in-situ observation are quite di^cult, the finite element analysis was applied to research the interface shape and melt flow during the crystal growth. Using the thermal field and control parameters in this paper, we concluded that the maximum deflection of interface shape and Von Mises stress increases as the crystal length increasing and that solid/liquid interface shape and melt flow are sensitive to the pulling rate and the rotation rate of crystal and crucible. Interface with low deflection can be achieved for low pulling rate or for certain combination of crystal and crucible rotation rates.