Numerical simulation of heat and mass transfer during Czochralski silicon crystal growth under the application of crystal-crucible counter- and iso-rotations

Abstract

In this study, the effects of different rotational combinations between the crystal and the crucible on the flow, heat and mass transfer in the melt are discussed based on numerical simulations. Both crystal-crucible counter- and iso-rotations are investigated. The simulation results for the growth of crystal 200 mm in length show that the oxygen concentration along the crystal-melt interface is determined by competition between the mechanisms of convection and diffusion. When the differences in rotation between the crystal and crucible are low during iso-rotation, the melt velocity is significantly weakened and the effect of the diffusion process on oxygen transport in the melt becomes stronger than the effect of convection. The melt flow is more sensitive to changes in the crystal rotation rate. The distribution of oxygen atoms and the temperature of the melt are more significantly affected by the flow pattern in cases of counter-rotation than iso-rotation. Moreover, it is found that a flow transition occurs in the silicon melt when the crystal and crucible have the same iso-rotation rate (ReS/ReC = 0.5842). A lower concentration and more uniform radial distribution of oxygen can be obtained by using the iso-rotation conditions. Rotating the crystal and crucible in the same direction also produces a flatter defect transition with lowering and flattening of the growth parameters Vcr/Gc along the crystal-melt interface.