Marangoni flow of molten silicon

Marangoni flow of molten silicon was studied for a half-zone liquid-bridge configuration. Through flow visualization using an X-ray radiography technique with tracer particles and temperature oscillation measurements, the instability mode for the Marangoni flow was determined. It was found that m=1 and 2 modes appeared depending on the aspect ratio (Gamma =height h/radius r) of the liquid bridge. The critical Marangoni number for transition from an oscillatory flow with single frequency to that with multiple frequencies was deduced to be about Ma = 1300, based on the calibrated-temperature difference between hot and cold solid/liquid interfaces. A transition was also observed when the oxygen partial pressure of the ambient atmosphere was changed. The flow velocity observed using a tracer particle also showed a dependence on the oxygen partial pressure; the velocity decreased with increasing oxygen partial pressure. By observing surface oscillation using a spatial-phase measurement technique, Marangoni oscillation at the melt surface was successfully distinguished from natural oscillation with eigenfrequencies. Marangoni oscillation (> 1 Hz) that was not revealed by flow Visualization and temperature measurement using thermocouples was also observed. Marangoni flow at a flat surface should be studied, so that the heat and mass transfer process for the Czochralski system can be more clearly understood and controlled. (C) 2001 Elsevier Science Ltd. All rights reserved.