EXPERIMENTAL-OBSERVATION AND NUMERICAL-SIMULATION OF WAVE PATTERNS IN A CZOCHRALSKI SILICON MELT

Azimuthal m-folded (m = 2, 3, 4,...) wave patterns have been observed in a Czochralski silicon melt by analysis of temperature measurements. Three-dimensional time dependent simulations of the unsteady melt flow in the down-scaled Czochralski configuration were executed and qualitatively compared with the experimental data. Both experimental and numerical results show processing wave patterns. The wave drift direction relative to the crucible rotation reveals a transition from co-rotation to counter-rotation with increasing crucible rotation rate. The higher the crucible rotation rate the faster is the phase velocity of the wave drift. Slow co-rotating and fast counter-rotating modes were also reported by Goldstein et al. [Journal of Fluid Mechanics, 248 (1993) 583], when investigating rotational Rayleigh-Benard convection in fluids of relatively high Prandtl numbers by means of an analytical approach. Moreover, experimental investigations of baroclinic waves in low-Prandtl number fluids [Fein and Pfeffer, Journal of Fluid Mechanics 75 (1976) 81] definitely showed counter-rotation for smaller and co-rotation for higher annulus rotation rates. Hence it is suggested that the m-folded waves may be due to the mechanism of Kuppers-Lortz instabilities, which mainly occur in flow configurations with a dominant vertical temperature gradient.