Masanobu Sumiji

Optical observation of solid-melt interface fluctuation due to Marangoni flow in a silicon liquid bridge

We observed fluctuation of the three-phase (solid, melt and ambient atmosphere) boundary position in silicon liquid bridges. We proved by measuring interface fluctuation and temperature fluctuation simultaneously that this interface fluctuation is caused by the formation and fluctuation of asymmetrical temperature field due to Marangoni flow instability. The amplitude of interface fluctuation decreased with increasing oxygen partial pressure. This decrease in interface fluctuation suggests that oxygen partial pressure is a factor that influences Marangoni flow in molten silicon.

Two-directional observation of solid–melt interface fluctuation induced by Marangoni flow in a silicon liquid bridge

We observed microscopic fluctuation of the solid–melt interface position (interface fluctuation) in silicon liquid bridges fromtwo points, 135 1 apart along the azimuthal direction. We found both in-phase, anti-phase relationships and null correlation between the two interface fluctuations. These relationships can be explained by the formation of a non-axisymmetric temperature field and the coupling between instabilities of stationary m ¼ 2 mode and oscillatory m ¼ 1 mode. r 2002 Elsevier Science B.V. All rights reserved.

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.

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.

DIRECT OBSERVATION OF MARANGONI CONVECTION-INDUCED OSCILLATION AT SILICON MELT SURFACE

Marangoni convection-induced oscillation at the molten silicon surface of a half-zone liquid column was directly observed using real-time moire phase-shift interferometry. The oscillation frequency was analyzed by applying the Fourier transformation to the data of relative displacement versus time relationship of the melt surface. Several peaks of oscillation frequencies were observed at 0.5–5 Hz, being higher than the frequencies at 0.1–0.3 Hz observed in the previous studies by the temperature measurement using thermocouples and the x-ray flow visualization technique.

Surface Tension Driven Flow of Molten Silicon: Its Instability and the Effect of Oxygen

Surface-tension-driven flow of molten silicon, which is one of mechanisms of heat and mass transfer during crystal growth, was investigated by using a liquid-bridge configuration under microgravity and on earth. Using microgravity is a convenient way to study surface-tension-driven flow, because buoyancy flow can be suppressed so that only surface-tension-driven flow can be distinguished. In the liquid-bridge configuration, which corresponds to floating-zone growth, flow instability and its three-dimensional structure were investigated through measurement of temperature-oscillation, flow visualization, optical pyrometry of the melt surface, observation of oscillation of the melt/crystal interface, and observation of surface oscillation by phase-shift interferometry. Azimuthal wave number m for instability structure depends on the aspect ratio of the bridge, Γ, which is defined as the ratio of height h to radius r.

Non-invasive techniques for observing the surface behavior of molten silicon

The behavior of molten silicon surfaces was observed by using non-invasive techniques such as laser microscopy, phase-shift Michelson interferometry and CCD thermometry. The formation and oscillation of a non-axisymmetric temperature field due to surface-tension-driven flow instability was revealed in a molten silicon bridge, which simulates floating zone configuration. For a flat surface, which represents a Czochralski melt, a hydrothermal wave was plausibly observed when the melt was shallow, whereas a cell pattern was observed during crystal growth when the melt was deep. The cell pattern was modified by application of a magnetic field.

The Effect of Oxygen Partial Pressure on Marangoni-Flow-Induced Dopant Striations in Floating-Zone Silicon Crystals

A silicon crystal was grown after the floating-zone (FZ) method under oxygen partial pressures (Po2 in) of 2.0×10-8 MPa and 5.8×10-6 MPa, which were measured at the entrance of a furnace. It was found that dopant striations showed a single-peak spectrum at 0.19 Hz in this crystal, and a crystal grown at Po2 in of 2.0×10-8 MPa showed multiple frequencies. This result is explained by a decrease in the Marangoni number with increasing oxygen partial pressure. It has thus been concluded that Marangoni flow in FZ silicon crystal growth can be controlled by introducing oxygen gas, independently of the temperature field control in the vicinity of the crystal/melt interface.

Observation of surface oscillation in a molten silicon column using moire interferometry

Surface oscillation due to oscillatory Marangoni flow in a liquid bridge of molten silicon was observed using phase- shift interferometry. The molten silicon surface was described by phase-distribution profiles with a sampling rate of 30 Hz. From the phase-distribution profiles, we analyzed the oscillation of the radial displacement, axial gradient, and azimuthal gradient of the molten silicon surface. The oscillation of the radial displacement, axial gradient showed an in-phase relationship. However, in-phase oscillation was not observed between the radial displacement and the azimuthal gradient. Marangoni frequencies was observed at 0.1 to 5 Hz in which the frequencies higher than 1Hz had not previously been observed by conventional methods. We also found eigenfrequencies of the liquid bridge at 8.8Hz and 11.5Hz.