OSCILLATORY CONVECTION IN LOW-ASPECT-RATIO CZOCHRALSKI MELTS

Modeling of the crucible in bulk crystal growth simulations as a right circular cylinder may be adequate for high aspect ratio melts but this may be unrealistic when the melt height is low. Low melt height is a unique feature of a solid feed continuous Czochralski growth process for silicon single crystals currently under investigation. At low melt heights, the crucible bottom curvature has a dampening effect on the buoyancy-induced oscillations, a source of inhomogeneities in the grown crystal. The numerical results demonstrate how the mode of convection changes from vertical wall-dominated recirculating flows to Benard convection as the aspect ratio is lowered. This phenomenon is strongly dependent on the boundary condition at the free surface of the melt, which has been generally considered to be either adiabatic or radiatively cooled. A comparison of the flow oscillations in crucibles with and without curved bottoms at aspect ratios in the range of 0.25 to 0.50, and at realistic Grashof numbers (10(7) < Gr < 10(8)) illustrate that changing the shape of the crucible may be an effective means of suppressing oscillations and controlling the melt flow.