Melt-motion during the Czochralski growth of silicon crystals with a cusp magnetic field

The relative importance of the three melt-motion components (thermocapillary convection, the buoyant convection, and centrifugal-pumping flow) during the Czochralski growth of silicon crystals with a cusp magnetic field is investigated by combining the separate asymptotic solutions. The top boundary layer, which is adjacent to the crystal-melt interface and to the free surface, is very important because the thermocapillary and centrifugal-pumping flows are confined to this layer, and because the flow here determines the radial distributions of oxygen and dopants in the crystal, as well as the rate of oxygen evaporation from the free surface. The buoyant convection is not confined to the top layer, extends over the entire melt, and is the only component of the melt motion which affects the melt temperature for 0(1) thermal Peclet numbers. The analysis of the thermal problem with convective heat transport is presented. The effects of varying the Hartmann number, the thermal Peclet number, and the angular velocity of the crystal on the balance between the three melt-motion components in the top layer are investigated.