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模拟。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.晶体中的温度分布和热应力：精确求解了有限长和半无限长圆柱体的晶体中的温度和热应力。对于短晶体，最大热应力出现在晶体表面的顶部中心，而对于长晶体，最大热应力出现在晶体的周边，靠近固液界面。为了找到热应力最小的生长方向，研究了不同生长方向的热应力的生长方向依赖性。此外，还提出了由热应力获得位错排列图的步骤。毕竟，要获得无位错的晶体，就必须降低晶体中的热应力，只要降低晶体侧面的热损失就可以满足.熔体中的温度分布和流体对流：设计了一个计算机模拟程序来获得轴向磁场下的温度和流体对流。熔体中的对流被磁场抑制。有一种可能性，自由对流doninant流动被抑制和扭转下的晶体由磁场和熔体被占领的强制对流占主导地位的流动所造成的晶体旋转。也有一种可能性，存在一个marangoni对流所造成的熔体-流体边界附近的表面张力梯度。得到了不同磁场强度下的马兰哥尼对流，发现马兰哥尼对流与自由对流有相似之处。最后，坩埚旋转以及磁场也是有效的，以抑制和二维的熔体中的对流。

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.