Three-dimensional thermal stresses in on-axis grown SiC crystals

For SiC single crystals grown on-axis by the modified Lely method, thermoelastic stresses are computed. The crystal boundary temperatures are obtained by an axisymmetric heat transfer analysis of the whole growth furnace. By adding a small azimuthally varying temperature disturbance to the axisymmetric background temperature field, three-dimensional thermal stresses are generated. This problem is solved by decomposing all field variables into Fourier series whereby the Fourier coefficient fields are still two-dimensional ones. The azimuthal integration of the weak form of the finite element method (FEM) is performed analytically, while all coefficient fields as well as the intentional axisymmetric reference problem are solved numerically in the domain of radius and z-axis only. For several growth stadiums, the total three-dimensional shear stresses are compared to the axisymmetric background shear stresses.