The effect of curved interface shape on thermal stress during Czochralski crystal growth

Analytical solutions of the quasi-steady-state thermal stresses in the crystal with finite length during Czochralski growth are obtained. In the temperature analysis, both the temperature distribution and the shape of the solid-liquid interface are simultaneously solved. It is found that the shape of the interface is parabolic-like and the Biot number is the dominating parameter. In the thermal stress analysis, we found that the results of the curved interface model are qualitatively similar to, but quantitatively different from those of the planar interface model. In addition, we also find that the effect of the crystal length should not be neglected, especially when the length is small.