Thermal Stress Analysis of Silicon Single Crystal during Czochralski Growth

Thermal stress analyses of a silicon bulk single crystal with 6 or 8 inches in diameter are performed in the case of [001] and [111] pulling directions by using a three-dimensional finite element program developed for calculating thermal stress in a bulk single crystal during Czochralski growth. Elastic anisotropy and temperature dependence of material properties are taken into account in this program. The temperature distribution and shape of a silicon bulk crystal which are required for the thermal stress analysis are obtained from a computer program for a transient heat conduction analysis. The stress components obtained from the thermal stress analysis are converted into the parameters related with dislocation density. The time variations of these parameters are shown in this paper. The relationship between these parameters and the shape of the crystal-melt interface is discussed.