Effect of rotating magnetic field on instabilities of thermocapillary flow in a Czochralski silicon melt pool

Abstract

The effect of the rotating magnetic field on the thermocapillary flow instabilities in a Czochralski silicon melt pool was numerically investigated by means of linear stability analysis. We considered three cases, namely, the non-rotating crystal, the crystal rotating in the same direction as the magnetic field (co-rotating crystal), and the crystal rotating in the opposite direction of the magnetic field (counter-rotating crystal). The linear stability analysis results show that the basic flow becomes unstable against two oscillatory instability modes. With the increase of the magnetic Taylor number (Ta), the overall trend of the critical Marangoni number decreases in the cases of a non-rotating crystal and counter-rotating crystal. However, in the case of a co-rotating crystal, the rotating magnetic field significantly improves the flow stability, and an inversion of the propagation direction of the oscillatory wave is observed with the increase of Ta. Energy analyses reveal that the instabilities are hydrodynamic in nature, which are caused by the combination of the strain-induced instability mechanism and the centrifugal instability mechanism, and the rotating magnetic field only provides little energy for the flow instabilities even at large Ta.