Dislocation Dynamics During the Czochralski Growth of Silicon

The thermal stresses induced by temperature variations that exist during steady-state Czochralski growth produce plastic deformations in the crystal by dislocation motion and generation. The temperature variations in the crystal are calculated numerically by the finite element method (FEM). Employing the Haasen-Sumino viscoplastic response function for silicon and the calculated temperature profile, the thermal stresses, the dislocation densities, and the residual stresses in the crystal are also calculated. Only low dislocation densities are of interest and hence the associated viscoplastic deformations are found to be small. The assumption is made that there is a very low dislocation density along the solid-melt interface. The Haasen-Sumino material model is modified to include a back-stress to account for the locking effects due to the impurity concentration in the crystal. This analysis provides guidance for growing large diameter crystal of materials with known constitutive relations which have a low dislocation density and low thermal stresses.