基于LBM-CA耦合模型的定向凝固多晶硅小平面枝晶生长数值模拟

Numerical Simulation of Small Plane Dendrite Growth in Directionally Solidified Polysilicon Based on LBM-CA Coupling Model

为了更好的研究高各向异性小平面枝晶生长。提出了一种综合考虑动力学各向异性和界面能各向异性的小平面枝晶生长的格子Boltzmann方法-元胞自动机(LBM-CA)耦合模型,对硅小平面枝晶的生长过程及生长形状进行模拟;验证所采用的新动力学各向异性方程的正确性;研究了界面能各向异性、动力学各向异性和过冷度对小平面枝晶生长的影响。结果表明:小平面枝晶较非小平面枝晶表现出更强的各向异性;界面能各向异性系数的增大,小平面枝晶生长的各向异性显著增大,生长速率变化、部分取向缺失;过冷度的增大,硅晶体由小平面晶粒生长变为小平面枝晶,其各向异性也显著增强,取向缺失增加,棱角更加明显,二次枝晶臂生长速率加快;动力学各向异性增大,二次枝晶臂生长速率、长度和数量均有增加。

To investigate the growth of high anisotropic planar dendrites,the growth process and the shape of silicon planar dendrites considering both dynamic anisotropy and interfacial energy anisotropy were simulated by a lattice Boltzmann method coupled based on a cellular automata(LBM-CA)model.The related dynamic anisotropic equation was proposed and verified.The effects of interfacial energy anisotropy,dynamic anisotropy and undercooling on the growth of planar dendrites were analyzed.The results show that the planar dendrites exhibit more intense anisotropy than non-planar dendrites,the anisotropy of planar dendrites increases with the increase of interfacial energy anisotropy coefficient,and the anisotropy of planar dendrites increases significantly with the growth rate and partial orientation loss.The planar dendrites grow,and the anisotropy and orientation loss increase with the increase of undercooling.The growth rate,length and number of secondary dendrite arms increase with the increase of kinetic anisotropy.