The effect of vibrations on Marangoni convection and melt mixing during crystal growing by the Czochralski method

Vibrational melt flows in Czochralski crystal growth are investigated numerically on the basis of unsteady Navier-Stokes-Boussinesq formulation for incompressible fluid. The finite element code ASTRA is used for calculations. It is found that the vibrations provide much more effective mixing of the melt flow compared to the rotation of the crystal and the crucible. Numerical modeling indicates the existence of standing vibrational waves on the free melt surface. It is demonstrated that the vibrations can be used to weaken and to compensate the influence of the thermo-capillary Marangoni convection for normal and microgravity environments.