Modeling of the float zone process

The interaction of heat, mass, and momentum transport in the floating zone method for growing single crystals from the melt is examined. Methods for detailed numerical simulation of the transport phenomena in a floating zone are developed. Results of the calculations are combined with experiments to determine the effects of solidification induced, surface tension driven, and buoyancy driven convection in establishing dopant redistribution in the melt and the roles of heat transfer in crystal and melt and melt/solid interface shape in determining crystal quality. State of the art finite element techniques were developed for calculating the influence of natural convection in the melt on the shape of a melt/crystal interface and dopant segregation in the crystal. These techniques are demonstrated for solidification by the Bridgman technique. Numerical techniques are developed that calculate the shapes of both the melt/solid and melt/gas interfaces simultaneously with the thermal fields in melt and solid. Models for the fluid flows due to the rotation of the feed and crystal rods are completed and the effects of these flows on dopant segregation are studied, especially in the case of zones longer than can be achieved on Earth.