Estimation of Thermal Stress During Growth Process of Bulk Single Crystals used in Electronic Devices

采用三维有限元程序对Si、GaAs和InP块状单晶在[001]和[111]拉拔方向下的Czochralski生长过程进行了热应力分析。该方案考虑了弹性各向异性。将热应力分析得到的应力分量转换为参数sigma_< tott>，表示滑动应变的有效应力。利用（111）平面上的杨氏模量和泊松比，比较了各向异性分析和各向同性分析中sigma_< tott>的取值和分布规律。结果如下：(1)在拉向[001]的情况下，各向同性分析提供的sigma_< tott>值大于各向异性分析。(2)在拉向为[1111]的情况下，两种分析结果的差异在于sigma_< tott>的分布模式，而不是其值。采用上述用于计算块状单晶生长过程中热应力的有限元程序，对[001]和[111]拉向为6英寸或8英寸的硅块状单晶进行了更多的分析。利用瞬态热传导分析的计算机程序获得了热应力分析所需的块状单晶的温度分布和形状。将热应力分析得到的应力分量转换为与位错密度有关的参数。结果如下：(1)位错密度参数在靠近固-熔界面的底部中心或侧壁处达到最大值。(2)位错密度参数值与固-熔界面形状相关。(3)[111]拉向下位错密度参数值小于[001]拉向下位错密度参数值。少

Thermal stress analyses of Si, GaAs and InP bulk single crystals during Czochralski growth were performed in the cases of the[001] and[111] pulling directions by using a three-dimensional finite element program. Elastic anisotropy was taken into account in this program. The stress components obtained from the thermal stress analysis were converted into the parameter sigma_<tot> representing the effective stress for glide strains. The values and distribution patterns of sigma_<tot> were compared between the anisotropic analysis and the isotropic analysis using the Young's modulus and the Poisson's ratio in the (111) plane. The following were obtained. (1) In the case of the[001] pulling direction, the isotropic analysis provides larger sigma_<tot> values than the anisotropic analysis. (2) In the case of the[1111 pulling direction, the difference between the results obtained from both analyses consists in the distribution patterns of sigma_<tot> rather than in its values.Thermal stress a … More nalyses of silicon bulk single crystals with 6 or 8 inches were performed in the cases of the[001] and[111] pulling directions by using the above-mentioned finite element program developed for calculating thermal stress in a bulk single crystal during Czochralski growth. The temperature distribution and shape of a bulk single crystal which were required for the thermal stress analysis were obtained from a computer program for a transient heat conduction analysis. The stress components obtained from the thermal stress analysis was converted into the parameters related with dislocation density. The following were obtained. (1) The dislocation density parameters show the maximum value at the center of the bottom or the side wall near the solid-melt interface. (2) The values of the dislocation density parameters correlate with the shape of the solid-melt interface. (3) The values of the dislocation density parameters are smaller in the case of the[111] pulling direction than in the case of[001] pulling direction. Less