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The thermal stress analysis of a silicon bulk single crystal with a diameter of 6 or 8 inches is performed in the cases of the [001] and [111] pulling directions by using a three-dimensional finite element program developed for calculating thermal stress in a bulk single crystal during the 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 single crystal which are required for the thermal stress analysis are obtained from a computer program for a transient heat conduction analysis which is specialized for the Czochralski growth. 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 relation between these parameters and the shape of the crystal-melt interface is discussed.

Numerical simulation was conducted to study the thermal history of Czochralski growth of large silicon single crystals. The computations were performed for various crystal diameters and emissivities of the crucible inner wall. The analysis gives the change of temperature distribution in the crystal and the shape of the solid-melt interface. The computed results show the importance of the effects of radiation from the crucible inner wall and the melt free surface on crystal growth. Also, increasing crystal diameter decreases the pull speed and increases the concavity of the solid-melt interface into the crystal. The result of this analysis is in good agreement with measurement of the pull rate on production apparatus, and the shape of the crystal-melt interface showed a tendency to qualitatively agree with the observations of X-ray diffraction.