Numerical Investigation on the Effect of Marangoni Convection in an Industrial Czochralski Crucible

Abstract

The quasi direct numerical simulations (DNS) of the flow and the thermal fields in an industrial Czochralski crucible have been carried out in order to investigate the effect of thermocapillary or Marangoni convection employing an optimised parallel-vector block-structured Navier-Stokes equations solver. The simulations have been performed without and with the Marangoni effect at a specified rotation of the crucible during the synthesis of mono-crystalline Silicon (Pr=0.011). The time-averaged flow field reveals that the inward radial velocity at the free surface of the melt is quite high for the case with Marangoni convection. The flow is directed towards the solid crystal due to the presence of significant surface tension gradients at the free surface. A stronger downward flow has been observed at the center of the crucible owing to this strong radial velocity. Due to the superposition of the Marangoni convection, temperature fluctuations are reduced under the free surface and at the crystal interface. Thus the fluctuations in the growth rate are reduced. The turbulent kinetic energy, k is smaller below the crystal at different depths in the melt for the cases without any effect of the Marangoni convection as compared to the cases with Marangoni convection. The temperature along the free surface of the melt is increased when the thermocapillary effect is included.