Marangoni flow of molten silicon

Abstract

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 ( Γ= 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.