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

用三维有限元程序对提拉法生长的大块单晶Si、GaAs和InP在[001]和[111]两个方向上生长过程中的热应力进行了分析。该程序考虑了弹性各向异性。由热应力分析得到的应力分量被转换为表示滑动应变的有效应力的参数sigma_&lt；tot&gt；。利用(111)面上的杨氏模数和泊松比，比较了各向异性分析和各向同性分析的Sigma&lt；tot&gt；的数值和分布规律。得到了以下结论。(1)在拉力方向为[001]的情况下，各向同性分析比各向异性分析提供了更大的sigma_t；tot；(2)在[1111]拉力方向上，两种分析结果的不同之处在于σ的分布规律，而不是它的值。热应力a…用所开发的计算提拉法生长过程中块体单晶热应力的有限元程序，对[001]和[111]两种拉拔方向的6英寸和8英寸硅大块单晶进行了较多的分析。利用计算机程序进行了瞬时热传导分析，得到了进行热应力分析所需的块体单晶的温度分布和形状。将热应力分析得到的应力分量转化为与位错密度有关的参数。得到了以下结论。(1)位错密度参数在靠近固熔界面的底部中心或侧壁附近出现极大值。(2)位错密度参数的大小与固-熔体界面的形状有关。(3)位错密度参数值在[111]方向上小于[001]方向。较少

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