Study of melt convection and interface shape during sapphire crystal growth by Czochralski method

Global simulation is performed to predict electromagnetic field, heat transfer, melt flow, and interface shape during the different growth stages of sapphire crystal by RF-heated Czochralski (Cz) process. Melt flow in the Cz-sapphire growth system includes Marangoni convection due to the variation of surface tension at the free surface, natural convection due to the complex thermal boundary conditions on the crucible walls, and forced convection due to the crystal rotation. As the crystal grow longer, the effects of the convections on the melt flow, temperature distribution and interface shape varies due to the drop of melt, which can be characterized by Grashof number (Gr) with the melt height as the characteristic length. It is found that as melt height reduces, natural convection gets weaker, and the interface becomes flatter. To examine systematically the effects of the convections on the crystal growth process, three dimensionless parameters, Nσ, Gr/Re2 and Nσ2, are further introduced. Nσ denotes the influence of surface tension in the boundary layer as compared with buoyancy in the melt, Gr/Re2 is the ratio of convective forces to the normalizing convective velocities with viscosity, and Nσ2 represents the relative strength of Marangoni flow to forced convection. The effects of the parameters on the melt flow and heat transfer are examined, and their relationships to the interface convexities are obtained. The understanding of melt convection and interface shape is not only important for the optimization of a stable sapphire crystal growth, but also critical for an accurate modeling of the growth process.