水平硅带生长过程的数值研究

Numerical study on the growth process of horizontal silicon

建立了水平凝固生长模型,采用凝固动力学和变形几何追踪凝固前沿,通过求解N-S方程和能量方程获得生长模型的速度场、温度场和压强场的分布。进行适当的参数研究,研究射流冷却速度、拉伸速度、Marangoni流对凝固结晶的具体影响。结果表明:凝固结晶过程的温度分布主要取决于热扩散而非流体流动;相对于射流冷却速度,Marangoni应力、拉伸速度对熔体流动更具影响力;Marangoni流对生长过程影响可以忽略;硅片厚度随射流冷却速度的增大而增大,与之相反,随拉伸速度的增大而减小;最大拉速取决于热移除条件,移除热量的速度越快,对应的极限拉伸速度越高。

A level of solidification growth model model is developed for solving the Navier-Stokes and energy equations to obtain the flow, pressure, and temperature fields for solidification process. Using solidification dynamics and deformation geometry to track solidification frontier. The effects of jet cooling rate, pull speed, Marangoni flow and solidification front boundary conditions on the solidification crystallization were studied. The results show that the temperature contours of grouth should mainly be determined by heat diffusion rather than the flow. The Marangoni stress and the pull velocity have more influence on the melt flow than the jet cooling rate. Marangoni flow on the growth process can be ignored. The thickness of the wafer increases with the increase of the jet cooling rate, and on the contrary, decreases with the increase of the tensile speed. The maximum pull speed attainable depends on the heat removal conditions; the faster the heat is removed, the corresponding limit The higher the stretching speed.