Effect of crucible and crystal rotations on the convexity and the thermal stress in large size sapphire crystals during Czochralski growth

In this study, the effect of the temperature and flow fields generated by the rotation of the crucible and the crystal on the convexity of a c-axis, large-diameter sapphire crystal during the Czochralski growth process is investigated numerically. The thermal stress distributions in different sizes of crystal are also considered. The computational results show that the convexity and the thermal stress of the crystal are strongly dependent on the crucible and crystal rotation rates. The counter rotation between the crucible and the crystal results in a flatter crystal-melt interface, compared to the case of no crucible rotation or crystal rotation. Maximum thermal stress occurs at the highest curvature of the crystal-melt interface which appears near the center of the growing crystal, and the value is directly proportional to the crystal's size. Moreover, there is a significant decrease in the von Mises stress for the crystal-melt interface with lower convexity due to a reduction in the temperature gradient in the radial direction along the interface. As the crystal length gets larger, the maximum von Mises stress rapidly reduces.