Establishment of new method of crystal growth with well-controlled convection by electro-magnetic force

在硅直拉（CZ）晶体生长中施加磁场是控制熔体-晶体界面形状、控制坩埚内熔体对流从而提高晶体质量的有效方法。由于坩埚中的熔体质量较大，熔体流动不稳定，这种方法对直径较大的晶体更有效，横向磁场在控制熔体流动方面具有很大的潜力。在横向磁场的影响下，坩埚中的熔体流动以及因此炉内的全局热场主要是三维（3D）的。虽然已经有许多优秀的数值模拟TMCZ生长的工作，这些模型仅限于熔体或熔体和晶体，由于需要大量的计算机内存和计算时间的要求。然而，由于TMCZ生长炉是一种高度不稳定的生长炉， 关于我们 非线性和共轭体系，三维全球建模显然是必要的。Liu和Kakimoto最近提出了一种部分3D全局模型，该模型使部分3D全局建模可行，并且对计算机资源和计算时间的要求适中。将该程序应用于熔晶界面附近的温度分布分析，以阐明晶体内部的温度梯度，它决定了晶体内部点缺陷和空洞的分布;对横向磁场作用下的小型直拉硅单晶炉进行了部分三维的全局数值分析，以阐明熔晶界面附近的温度分布。计算了熔体-晶体界面形状和界面附近固液轴向温度梯度随磁场强度和晶体提拉速率的变化关系。结果表明，晶体中的轴向温度梯度随拉晶速率的增大而增大，熔体中的轴向温度梯度在界面附近减小。随着磁场强度的增加，晶体和熔体中的轴向温度梯度均增大。熔体对流的影响随磁场强度或拉晶速率的增大而减小。熔体-晶体界面向上移动的拉晶速率和晶体中的温度梯度之间的比率或所施加的磁场强度的增加。少

Application of magnetic fields in silicon Czochralski (CZ) crystal growth is an effective method for controlling the shape of the melt-crystal interface and for controlling melt convection in a crucible and therefore for improving crystal quality. Such a method is more effective for crystals with large diameter, since flow in a crucible becomes unstable due to large mass of the melt in a crucible.A transverse magnetic field applied to silicon CZ growth processes (TMCZ) has great potential for controlling melt flow. The melt flow in a crucible and, hence, the global thermal field within the furnace are principally three-dimensional (3D) under the influence of a transverse magnetic field. Although there are many excellent published works on numerical modeling of TMCZ growth, these models are limited to the melt or to the melt and the crystal due to the requirement of large computer memory and the requirement of a long time for computation. However, since a TMCZ growth furnace is a highly … More nonlinear and conjugated system, 3D global modeling is obviously necessary. Liu and Kakimoto recently proposed a partial 3D global model that makes partial 3D global modeling feasible with moderate requirements of computer resources and computation time. We applied the newly developed code to the analysis of temperature distribution near the melt-crystal interface to clarify the temperature gradient in a crystal, which determines distribution of point defects and voids in a crystal.A partly three-dimensional (3D) global analysis was carried out numerically for a small silicon Czochralski furnace in a transverse magnetic field to clarify temperature distribution near a melt-crystal interface. The melt-crystal interface shape and the axial temperature gradients in solid and liquid near the interface were calculated as functions of the magnetic field intensity and the pulling rate of a crystal. It was found that the axial temperature gradient in the crystal increases with increase in the crystal-pulling rate and that in the melt decreases near the interface. With increase in intensity of the magnetic field, the axial temperature gradients in both crystal and melt increase. The influence of melt convection becomes smaller with increase in either the magnetic field intensity or the crystal-pulling rate. The melt-crystal interface moves upward with increase in either the ratio between crystal pulling rate and temperature gradient in the crystal or the intensity of the applied magnetic field. Less