NUMERICAL-SIMULATION OF THE INTERFACE INVERSION IN CZOCHRALSKI GROWTH OF OXIDE CRYSTALS

The well-known inversion of the crystal-melt interface occuring in oxide crystal growth due to a transition of the melt flow from free to combined free and forced convection is simulated numerically. The mathematical model includes the time-dependent flow and temperature fields in the melt and the lower part of the crystal. The shape of the crystal-melt interface is calculated as part of the solution. Two different system geometries have been investigated with material parameters corresponding to Al2O3. In case of a small crystal diameter a flat crystal-melt interface is obtained when the boundary between free and forced convective flow lies beneath the crystal periphery. This occurs at a certain crystal rotation rate which may be termed as "critical". For a large crystal diameter this is no longer true. The interface is never flat during the transition but has a concave-convex shape within a large range of the crystal rotation rate. So the inversion is better characterized by a critical range of the crystal rotation rate. © 1990.