Linear and non-linear stability of melt flows in magnetic fields

This review considers the stability of melt motion in two simplified models of semiconductor crystal growth by either vertical gradient freeze (VGF) or Czochralski (Cz) processes under the influence of various magnetic fields. In VGF the crystal is grown at the bottom of the crucible, resulting in a stable thermal stratification of the melt. The presence of a stabilizing temperature gradient surprisingly decreases the stability of the flow driven by a rotating magnetic field (RMF). The instability of the travelling magnetic field (TMF)-driven flow, in contrast, is significantly delayed by thermal stratification in VGF. The TMF may, thus, be used in VGF to control the shape of the solidification interface or the radial dopant distribution without causing undesirable flow oscillations. The crystal is pulled out from the melt in the Cz process, producing an unstable temperature gradient below the crystal. The RMF is able to force the resulting unstable buoyant flow into a state of small-scale, high-frequency turbulence that may be regarded as stable for practical purposes. This effect is experimentally observed over a wide range of Grashof numbers, up to 10⁹, characteristic for a large Cz system.