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

本文的研究成果如下：(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。利用分子动力学程序成功地获得了中温以下的α-Fe的这些值。在高温下，由于热振荡随着温度的升高而增大，因此不能获得稳定的解。获得在熔点等高温下的热膨胀系数和弹性常数仍是一个有待解决的问题。(2)开发了一个用于模拟半导体大块晶体生长过程中位错密度的计算机程序。采用Haasen-Sumino模型作为高温下单晶的本构方程。用该程序对Si、GaAs和InP进行了位错密度模拟，验证了该程序的有效性。结果表明，在实际的提拉法(CZ)生长中，可以观察到GaAsInP单晶中沿直径方向的W型位错密度分布。该计算机程序可作为研究和开发高质量块体单晶的有力工具。(3)根据实际CZ法生长直径为8英寸的无位错大块单晶的特点，估算了熔点附近的硅单晶的杨氏模数。将由临界剪切应力与应变的实验关系得到的杨氏模数用于8英寸直径的硅单晶的位错密度模拟，得到了无位错的单晶。因此，对于16英寸直径的大直径直拉硅单晶，建议使用该杨氏模数来模拟位错密度。

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.