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 techni que with tracer particles and temperature oscillation measurements, the ins tability 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 dif ference between hot and cold solid/liquid interfaces. A transition was also observed when the oxygen partial pressure of the ambient atmosphere was ch anged. The flow velocity observed using a tracer particle also showed a dep endence on the oxygen partial pressure; the velocity decreased with increas ing oxygen partial pressure. By observing surface oscillation using a spati al-phase measurement technique, Marangoni oscillation at the melt surface w as successfully distinguished from natural oscillation with eigenfrequencie s. Marangoni oscillation (> 1 Hz) that was not revealed by flow Visualizati on and temperature measurement using thermocouples was also observed. Maran goni flow at a flat surface should be studied, so that the heat and mass tr ansfer process for the Czochralski system can be more clearly understood an d controlled. (C) 2001 Elsevier Science Ltd. All rights reserved.