勾形磁场下直径300mm CZ Si熔体中氧浓度分布的数值模拟

Numerical Simulation of Oxygen Transportation in 300mm Diameter CZ Si Crystal Growth Under Cusp Magnetic Field

采用低雷诺数K-ε紊流模型，考虑自然对流、晶体旋转和坩埚旋转等因素，对晶体直径为300mm，磁场强度变化范围在0～0．12T条件下，熔体硅内流场及氧的浓度分布、磁场分布等作了数值模拟．计算中采用有限体积法，运用SIMPLE(semi—implicit method for pressure linked equations)算法耦合压力和速度场，动量方程、能量方程中对流项的离散采用QUICK(quadratic upwind interpolation of convective kinematics)格式，紊动能和耗散项方程中对流项的离散采用迎风格式．数值模拟结果表明，在勾形磁场作用下，熔体硅内的流场、氧的浓度分布与无磁场作用相比有较大不同，随着磁场强度的增加，生长界面处氧的浓度降低，并且磁场确实能有效地抑制熔体内的紊流，有利于晶体生长．

A low Reynolds number K ε turbulence model,which combines effects of buoyancy,crystal rotation and crucible rotation,is used to simulate the convection and oxygen transportation in a 300mm diameter CZ Si crystal growth under the cusp magnetic field,strength ranged from 0 to 0 12T.Based on a finite volume method,the QUICK scheme is used to discretize the convection term in the momentum and energy equations,and the up wind scheme is used to discretize the convection term in the kinetic energy and dissipation rate equations.The SIMPLE algorithm is employed to couple velocity and pressure field.The simulation results indicate flow patterns and oxygen concentration in the melt are significantly different,when a cusp magnetic field is applied.The oxygen concentration at the growth interface is decreasing as the magnetic field strength increasing,and the turbulence intensities have been effectively dampened by the magnetic fields,which is benefit to the crystal growth.