Theoretical Study of the Growth of a Perfect GaAs Crystal by MLEC method

对LEC法晶体生长过程进行了建模和仿真。晶体生长模型包含了该方法的基本特征，并得到了晶体和熔体的温度。晶体的温度分布和热应力：精确求解了有限和半无限圆柱体的温度和热应力。对于短晶，强应力发生在晶体表面的顶部中心，对于长晶，最大热应力发生在靠近固液界面的晶体外围。为了找到热应力最小的生长方向，研究了不同生长方向下热应力的生长方向依赖性。此外，还提出了从热应力中得到位错阵图的方法。毕竟，要得到无位错的晶体，就必须降低晶体中的热应力，只要减少晶体侧面的热损失就可以满足。熔体内温度分布和流体对流：设计了计算轴向磁场作用下熔体温度和流体对流的计算机模拟程序。熔体中的对流受到磁场的抑制。存在一种可能性，即晶体下的自由对流主导流被磁场抑制和逆转，熔体被晶体旋转引起的强制对流主导流所占据，也存在一种可能性，即熔体-流体边界附近存在由表面张力梯度引起的马兰戈尼对流。得到了不同磁场强度下的马兰戈尼对流，发现马兰戈尼对流与自由对流有相似之处。最后，坩埚的旋转和磁场也能有效地抑制和二维化熔体中的对流。

The Process of the crystal growth by the LEC method is modeled and simulated. The crystal growth model includes the essential features of the method and the temperatures in the crystal and melt are obtained.1. Temperature distribution and thermal stress in the crystal: The temperature and thermal stress in the crystal are exactly solved for a finite and semi-infinite cylinders. For a short crystal a strong stress occurs at the top center of the crystal surface and for a long crystal the maximum thermal stress occurs at the crystal periphery near the solid-liwuid interface. To find the growth direction for which the thermal stress becomes minimum, the growth direction dipendence of the thermal stress is investigated for various growth directions. Furthermore, the procedure to obtaine the dislocation array pattern from the thermal stress is postulated. After all, to obtaine a dislocation free crystal, it is necessary to reduce the thermal stress in the crystal and it will be satisfied if the heat loss from the crystal side surface is reduced.2. Temperature distribution and fluid convection in the melt: A computer simulation code to obtaine the temperature and fluid convection under an axial magnetic field is devised. The convection in the melt is suppressed by the magnetic field. There is a possibility that the free convection doninant flow is suppressed and reversed under the crystal by the magnetic field and that the melt is occupied by a forced convection dominant flow caused by crystal rotation There is also a possibility that there exists a marangoni convection caused by a surface tension gradient near the melt-fluid boundaries. The marangoni convections are obtained for various magnetic field strengths and found that the marangoni convection has a similarity as the free convection. Finally, the crucible rotation as well as the magnetic field is also effective to suppress and to two-dimensionalise the convection in the melt.