A thermal elastic model for constrained crystal growth with facets

Abstract

Abstract. In this paper we present a model for computing thermal stress inside a crystal with facets. Using a systematical perturbation analysis, a semi-analytical thermal stress solution is obtained for constrained directional growth with small lateral heat flux. Our solution can be applied to crystals grown by various growth techniques such as the Czochralski method. The semianalytical nature of the solution allows us to compute thermal stress in crystals with facets much more efficiently, compared to a full 3D simulation. Examples are given for crystals pulled in a variety of seed orientations.