Effect of axisymmetric magnetic fields on heat flow and interfaces in floating-zone silicon crystal growth

A robust finite-volume/Newton method is used to simulate the heat transfer, fluid flow, and interface shapes of floating-zone silicon growth under an axisymmetric magnetic field generated by coils around the growth axis. The global method allows all the held variables, both the heat Bow and magnetic fields, and the interface variables, both the interfaces and the free surface, to be solved simultaneously in an efficient manner. Calculated results show that the suppression of convection by the applied magnetic fields is effective for both natural convection and forced convection due to rotation, but less effective for thermocapillary convection. As a result, the melt in the core region is quiescent and the effect of rotation also becomes trivial, while in the periphery the flow is still vigorous. The core size and Bow patterns depend on the applied magnetic strength and distribution. The calculated core size and dopant segregation for a growth in a mono-ellipsoid furnace are in good agreement with measured ones. The effects of rotation and finite electrical conductivity on current distribution are also illustrated.