3D Anisotropic Stress Analysis during Kyropoulos Growth of Sapphire Single Crystal

By using 3D finite element calculations, numerical simulations are performed to predict the thermal field as well as the thermal stress in a c-axis sapphire single crystal grown by Kyropoulos technique. The effects of additional resistive heating (placed under the crucible bottom) and crystal rotation are investigated and a comparison is made between the isotropic and anisotropic analysis. The anisotropy of the elastic constants and thermal expansion coefficients as well as their temperature dependence are considered in the anisotropy calculations while Young's modulus and the Poisson ratio are used in the isotropic analysis. Thermal stress is found to be smaller in the anisotropy analysis than that in the isotropic analysis and significant differences are found in their respective distribution patterns. Additional resistive heating acts to decrease both of the crystal-melt interface convexity and the von Mises stress. In addition, crystal rotation combined with additional resistive heating decreases significantly the thermal stress inside the sapphire crystal and along the melt-crystal interface. Therefore, optimizing the heating conditions and using a suitable crystal rotation rate seem to be favorable to control the growth interface shape and to reduce thermal-stress-related defects during the growth process.