Thermal Stress Analysis During the Czochralski Melt Growth of Optical Crystals

This paper presents a finite element method for studying Czochralski melt growth of optical crystals with an emphasis on thermal and stress analyses of axisymmetric problems. A heat transfer analysis is performed to determine the temperature distribution in the crystal. The heat transfer problem is solved with a mixed computational model including the hybrid finite/boundary element for electromagnetism, the Galerkin finite element method for transport equations, the Galerkin boundary element method for external surface energy exchanges and the discontinuous finite element method for internal radiation. The temperature results are directly input as loads to determine the stresses caused by the temperature loading. Thermal stress analyses of a Gadolinium gallium garnet (Gd₃Ga₅O₁₂) crystal are performed in the cases of the [100] pulling direction. Then, we can evaluate the crystal quality based on the thermal stress analysis. Three real operating cases for Gadolinium gallium garnet crystal growth processes are studied with the method presented in this paper.