Effect of RF coil position on spoke pattern on oxide melt surface in Czochralski crystal growth

摘要

Three-dimensional numerical simulations of LiNbO_3 melt flow in a Pt crucible (47mm~Φ x 47mm~H x 1.5mm~T) in the Czochralski oxide crystal growth configuration have been performed to investigate the effect of RF coil position on spoke patterns observed on the free surface of oxide melt. The crucible temperature field calculation was coupled with the numerical simulations of melt flow to provide a realistic thermal boundary condition for the melt/crucible interface. The melt was assumed to be an incompressible Newtonian Boussinesq fluid, and the flow was laminar. The free surface of melt and the crystal/melt interface were flat. The heat loss from the free surface was due to thermal radiation alone. The heat generation rate of the crucible was obtained by analyzing the electromagnetic field; the outside surfaces of the crucible were adiabatic. The Marangoni effect was taken into account. It was found that the appearance of the spoke pattern is dependent on the RF coil position. When the RF coil was set low relative to the crucible, the spoke pattern appeared easily; otherwise, the spoke pattern was difficult to be generated. The results of the investigation validated the mechanism of spoke pattern formation reported in J. Crystal Growth 200 (1999) 204.