EXPERIMENTAL-OBSERVATION AND NUMERICAL-SIMULATION OF WAVE PATTERNS INA 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 flo w in the down-scaled Czochralski configuration were executed and quali tatively compared with the experimental data. Both experimental and nu merical results show processing wave patterns. The wave drift directio n relative to the crucible rotation reveals a transition from co-rotat ion to counter-rotation with increasing crucible rotation rate. The hi gher the crucible rotation rate the faster is the phase velocity of th e wave drift. Slow co-rotating and fast counter-rotating modes were al so reported by Goldstein et al. [Journal of Fluid Mechanics, 248 (1993 ) 583], when investigating rotational Rayleigh-Benard convection in fl uids of relatively high Prandtl numbers by means of an analytical appr oach. Moreover, experimental investigations of baroclinic waves in low -Prandtl number fluids [Fein and Pfeffer, Journal of Fluid Mechanics 7 5 (1976) 81] definitely showed counter-rotation for smaller and co-rot ation for higher annulus rotation rates. Hence it is suggested that th e m-folded waves may be due to the mechanism of Kuppers-Lortz instabil ities, which mainly occur in flow configurations with a dominant verti cal temperature gradient.