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

对LEC法生长晶体的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，得到了晶体和熔体中的温度。晶体中的温度分布和热应力：对于有限和半无限长的圆柱体，晶体中的温度和热应力都得到了精确的求解。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的热应力对生长方向的影响。此外，还提出了从热应力中获得位错阵列图案的步骤。毕竟，要获得无位错的晶体，降低晶体中的热应力是必要的，只要减少晶体侧面的热损失就能满足要求。熔体内的温度分布和流体对流：编制了计算轴向磁场作用下熔体内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。这可能是由于磁场抑制和扭转了晶体下的自由对流，熔体被晶体旋转引起的强制对流占据，也有可能在熔体-流体边界附近存在由表面张力梯度引起的Marangoni对流。得到了不同磁场强度下的Marangoni对流，发现Marangoni对流与自由对流有相似之处。此外，坩埚旋转和磁场也能有效地抑制熔体内的对流并使其二维化。

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.