Nd∶YAG晶体生长过程中熔体液流速度场的数值模拟

Numerical Simulation Study on Fluid Velocity Field in Melt During the Growth of Nd∶YAG Crystals

采用有限差分法对使用Cz(Czochralski)法生长Nd∶YAG激光晶体过程中熔体中的液流速度场进行数值模拟研究。首先给出了Nd∶YAG晶体生长系统的数学模型 ,然后对上述数学模型进行无量纲化处理 ,最后给出相应的边界条件 ,使用有限差分法求解上述方程。应用上述方法编制仿真程序 ,仿真了改变工艺条件后熔体中液流速度场的变化情况 ,分析了各种工艺条件对液流速度场变化的影响。

A numerical simulation study on fluid velocity field in melt was reported in this paper by using Finite Differential Method (FDM) during the growth of Nd∶YAG crystals by Cz (Czochralski) method. First, the mathematical model of Nd∶YAG crystal growth was given out. The momentum conservation equation of melt, the continuity equation of melt, the heat conservation equation of melt, the mass conservation of melt, the heat conservation equation of crystal and the heat conservation equation of crucible were included in the model. Then, the dimensionless equations were given for solving the equations by the numerical method. Finally, the boundary conditions were given and the equations were solved by FDM. The simulation program was given by above method and then the changes of fluid velocity field in melt were described by simulation program. The effects of processing conditions on fluid velocity field in melt were analyzed. The effects of simulation time, the effects of crystal rotation speed during the crystal growth, the effects of the crystal diameter and the effects of the crucible size were considered. The results of simulation indicated: 1. The forced convection in the melt is weaker than the natural convection during the process of simulation, so that it can't be shown in the figure of fluid velocity field, and the forced convection will become weaker and weaker with the simulation time increased. 2. As the rotation speed of crystal is increased, the natural convection in the melt will become stronger and stronger, and the effective area of natural convection will become bigger than it is in initial cases. 3. The natural convection in the melt will become weaker when either the diameter of crystal or the ratio of the crucible diameter to its depth is increased. Although the above method is employed to simulate the fluid velocity field during the crystal growth of Nd∶YAG, it can also be used to simulate some other single crystal growth by Cz method, such as the growth of silicon single crystal, the GaAs single crystal and the GGG single crystal and so on. It is essential to adapt the parameters of the equations and the simulation program to the new materials.