扰动法非线性晶体生长过程数值模拟研究

Numerical Simulation Study on Nonlinear Crystal Growth Process Using Perturbation Method

采用扰动法对使用Cz(Czochralski)法非线性晶体生长过程中提拉速度和熔液平均温度场进行了数值模拟研究,实验结果可用于实现晶体等径生长中提拉速度和熔液平均温度的预测控制。研究表明,熔液平均温度(提拉速度)不变时,提拉速度(熔液平均温度)随环境毕奥数的增加和/或熔液毕奥数的减小而增大。进一步研究,熔液若不会组分过冷,可以得到提拉速度的最大值,并在整个生长过程中,必须控制提拉速度小于它的临界上限,否则晶体生长过程将失败。

The nonlinear dynamic process of Czochralski crystal growth（CZCG）is studied by the perturbation method. The solutions of this method can be used to predict, quantitatively, how a crystal growth with constant crystal radius is perfectly controlled by the desired of crystal pull rate and bulk melt temperature. It is found that for growth under constant bulk temperature （pull rate）,the pull rate （bulk melt temperature） will increase with increasing ambient Biot number and/or decreasing melt Biot number. Furthermore, if the melt cannot be supercooled, we can formulate the maximum pull rate analytically. The pull rate must not exceed this maximum value, otherwise the CZCG process will break down.