THERMAL STRESS ESTIMATION FOR LARGE DIAMETER SILICON SINGLE CRYSTAL USING MATERIAL PROPERTIES OBTAINED FROM MOLECULAR DYNAMICS METHOD

以下是本研究的结果。(1)开发了计算单晶热膨胀系数和弹性常数的分子动力学程序。这些值为α-铁成功地获得了中间温度使用分子动力学代码。在升高的温度下，不能获得稳定的溶液，因为热振荡随着温度的升高而变大。获得高温下的热膨胀系数和弹性常数，如熔点，仍然是未来的问题没有解决。(2)开发了半导体块体晶体生长过程中位错密度的计算机模拟程序。Haasen-Sumino模型被用作单晶在高温下的本构方程。用该程序对Si、GaAs和InP的位错密度进行了模拟，结果表明该程序是有效的。计算结果表明，在实际的GaAs和InP提拉生长中，可以观察到GaAs和InP单晶中W型位错密度沿直径的分布，该程序可作为研究和开发高质量块状单晶的有力工具。(3)根据直拉法生长直径为8英寸的无位错单晶体的实际情况，估算了硅单晶在熔点附近的杨氏模量。当将由Si单晶的临界分辨剪应力与相应应变之间的实验关系获得的杨氏模量用于8英寸直径Si单晶的位错密度模拟时，结果获得了无位错的单晶。因此，对于大直径CZ硅晶体例如16英寸直径晶体的位错密度模拟，推荐使用该杨氏模量。

The following are results of the present research.(1) A molecular dynamics code was developed to calculate thermal expansion coefficient and elastic constants of single crystals. These values for alpha-Fe were successfully obtained up to intermediate temperatures using the molecular dynamics code. At elevated temperatures, stable solutions cannot be obtained, because thermal oscillation becomes large with temperature increase. To obtain thermal expansion coefficient and elastic constants at the elevated temperatures such as the melting point remains unsolved as a future problem.(2) A computer code was developed for simulations of dislocation density in semiconductor bulk crystals during growth process. The Haasen-Sumino model was used as a constitutive equation for single crystals at elevated temperatures. Dislocation density simulations were perfomed using this computer code for Si, GaAs and InP to show the effectiveness of the computer code. The results indicate W-type dislocation density distributions across the diameter in GaAs and InP single crvstals that can be observed in practical Czochralski (CZ) growth of GaAs and InP.This computer code can be used as a powerful tool for research and development of high quality bulk single crystal.(3) The Young's modulus of Si single crystal near the melting point was estimated in accordance with the fact that dislocation-free bulk single crystals with 8-inch diameter are produced commonly by meana of the practical CZ growth. When the Young's modulus obtained from the experimental relation between the critical resolved shear stress and the corresponding strain for Si single crystal was used in the dislocation density simulation of a 8-inch diameter Si single crystal, dislocation-free single crystal was obtained as a result.Therefore, the use of this Young's modulus is recommended for dislocation density simulations for large diameter CZ silicon crystals such as 16-inch diameter crystals.