Convective effects in float-zone and Czochralski melts

The hydrodynamics of crystal-growth melts is a relatively new research area. Numerical modeling of these processes is necessary. The work discussed herein is in two parts: numerical simulations of the flow in a Czochralski melt, and also of that in a float zone. In addition, for the float-zone case, energy stability theory will be used to determine stability bounds for the onset of oscillatory thermo-capillary flow. Convective effects in crystal-growth melts arise from a variety of mechanisms. Temperature gradients both in the direction of gravity and normal to it give rise to convection due to buoyancy effects. Rotation of the crucible and/or crystal causes a forced convection which may augment or oppose the buoyancy-driven flow. Finally, thermo-capillary forces (due to the variation of surface tension with temperature) drive surface motions which in turn generate convection in the bulk fluid. All of these mechanisms are present in either Czochralski or float-zone growth. The objective of the Czochralski modeling is to develop an accurate numerical simulation of the flow in a Czochralski silicon melt and to investigate the effects of various parameters on the flow properties. Like some earlier investigations, the intent is to simulate the effects of buoyancy, forced and thermo-capillary convection, including unsteady effects. Unlike earlier work, the aim is to include the effects of a variable free surface and freezing interface and, possibly incorporate nonaxisymmetric effects.