Numerical Study of the Micro-Pulling-Down Process for Sapphire Fiber Crystal Growth

Numerical simulation is conducted to study the micro-pulling-down process for the growth of sapphire fiber crystal. Using the CrysMAS package, the fundamental equations for heat transfer, fluid flow, the melt/crystal interface, and the electromagnetic field are solved simultaneously to address the characteristics of the growth system. We found that, in the melt, Marangoni convection is dominant, and the buoyancy convection is negligible. Gas convection is strong, due to the large temperature difference in various parts of the furnace. Heat transfer around the crucible region is dominated by radiation due to the high temperature. The results also show a hot spot near the top of the crucible, and a ring design is further proposed to obtain a uniform temperature field in the crucible. The predicted melt/crystal interface has a convex shape protruding into the melt, which is consistent with the experimental observation. The simulated temperature distribution on the surface of the crucible cone is in good agreement with experimental measurements. The three-dimensional effect of the observation windows is also studied. The results show that using three observation windows on the afterheater is helpful to achieve more symmetrical temperature fields. The effects of furnace elements including the RF coil, crucible, afterheater, and insulation on the axial temperature gradient at the solid and liquid (S/L) interface are further investigated. The results provide important information to improve the growth procedure of a single crystal using the micro-pulling-down method.