Optical Measurement of Resonant Oscillation and Marangoni Convection-Induced Oscillation in a Molten Silicon Surface

Surface oscillation due to oscillatory Marangoni flow in a liquid bridge of molten silicon was observed through interferometry. To obtain higher resolution, interferograms taken from a molten silicon surface and a reference sample were converted to phase-distribution profiles by using spatial phase-measurement. We analyzed the phase-distribution profiles by measuring the radial displacement, azimuthal phase value gradient, and axial phase value gradient. The total radial displacement was about 1.5 µm over a 2.0-s period. The radial displacement and axial phase value gradient showed in-phase correlation, which suggests a traveling wave in the azimuthal direction. The Fourier spectrum of the radial displacement showed several peaks from 0.5 to 5 Hz. These frequencies corresponded to the frequencies of Marangoni flow reported based on other methods. The spectrum also showed two single peaks at 21 and 24.5 Hz. These frequencies agreed well with theoretical resonant frequencies of the liquid bridge.