CUSP磁场对直拉硅单晶氧浓度分布影响的数值模拟

Numerical Simulation of CUSP Magnetic Field on Oxygen Concentration Distribution in CZ-Si Crystal Growth

利用有限元分析软件对Φ300 mm直拉硅单晶生长过程进行模拟,分析了保持CUSP磁场对称面与熔体坩埚界面交点处的径向分量不变的情况下,硅单晶中氧浓度分别随CUSP磁场通电线圈距离、通电线圈半径的变化规律。随着通电线圈距离和半径的增大,晶体熔体固液界面氧浓度均逐渐降低。随着通电线圈距离和半径的增大,硅熔体径向磁场强度逐渐增大,对坩埚底部熔体向晶体熔体固液界面处对流的抑制作用加强,固液界面下方熔体轴向流速减小,使得从坩埚底部运输上来的富氧熔体减少,继而固液界面处的氧浓度降低。随着线圈距离和半径的增大,为保持所需磁场强度,施加电流也逐渐增大,从而能耗增大,与增大通电线圈距离相比,增大通电线圈半径所需的电流较大。通过实验,将CUSP磁场对单晶中氧浓度分布影响的数值模拟结果与实际晶体生长进行了对比,实验结果验证了数值模拟的结果。

Finite element analysis software femag-CZ was used for the simulation of the effect of CUSP magnetic field on the oxygen concentration in CZ-Si crystal growth.Keeping the CUSP radial component in the intersection of CUSP and the crucible melt interface constant,the law of oxygen concentration distribution along melt/crystal interface was studied.With the increase of the distance and radius of CUSP current coils,oxygen concentration in the m-c interface decreased gradually.Keeping the CUSP radial component in the intersection of CUSP and the crucible melt interface constant,CUSP magnetic field current coils distance and radius was adjusted.With the increase of coils distance and radius,the radial magnetic field strength in melt increased gradually,causing the axial melt convection velocity decreased.The melt containing more oxygen content from the bottom of crucible decreased,so the oxygen concentration in m-c interface decreased.With the increase of the distance and radius of coils,the applied current and then energy consumption also increased,compared with the increase of the electric coils distance,the increase of coils radius needed a larger current.Compared the numerical analysis with experiment,the two results gave the same variation tendency.