Surface tension of molten silicon measured by the electromagnetic levitation method under microgravity
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g 5 735 2 0.074 (T 2 1687) where g is the surface tension (in mN/m) and T is the temperature (in K). The value was measured over a wide range of temperatures, from 230 K below the melting point (1687 K) to 1890 K. The scatter of the measured surface-tension values is much less than that measured by conventional methods.
I. INTRODUCTION
A NUMBER of attempts have been made to produce a higher-density large-scale integration (LSI), in order to increase productivity and lower costs. A computer simulation is an effective method to optimize the conditions for the production of a silicon single-crystal rod with a larger diameter and higher quality. Unfortunately, few reliable thermophysical-properties data for molten silicon are presently available to perform the simulation. Figure 1 shows the surface-tension values reported by other researchers,[1–11] and a large difference is noted among the reported values. In addition, each line is usually drawn from the experimental data, with a 3 to 5 pct scatter. These dispersions are probably caused by the fact that the surface tension of molten silicon is very sensitive to contaminants such as oxygen and that conventional methods have technical limitations in obtaining such values with a small degree of scatter. The electromagnetic levitation method was used in this study to overcome these problems. The sample does not come into contact with any crucible or substrate in this method, so contamination from these sources is prevented.[12] Consequently, the surface tension of the pure material can be measured even at a high temperature, and the values of the undercooled melt can also be measured. However, under terrestrial conditions, the surface-tension value cannot be measured with a high degree of accuracy by this technique, because the droplet shape is significantly distorted from that of a sphere due to gravity and the balanced electromagnetic force. Therefore, in this study, a microgravity condition was used to create a droplet with a spherical H. FUJII, Associate Professor, T. MATSUMOTO, Research Associate, and K. NOGI, Professor, are with the Joining and Welding Research Institute, Osaka University, Osaka 567-0047, Japan. N. HATA, formerly Graduate Student, Joining and Welding Research Institute, Osaka University, is Researcher, J.R. West Co., Ltd. T. NAKANO, formerly Graduate Student, Joining and Welding Research Institute, Osaka University, is Researcher, Sumitomo Osaka Cement, Co., Ltd. M. KOHNO, formerly Graduate Student, Joining and Welding Research Institute, Osaka University, is Researcher, Murata Manufacturing Co., Ltd. Manuscript submitted October 11, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
shape. In addition, the effect of the small shape distortion on the calculated surface-tension value was also investigated by controlling the droplet shape by changing the current ratio between two different coils. II. MEASUREMENT PRINCIPLE A levitated droplet is usually accompanied by a surface oscillation, because it is released from most restrictions. When the equil
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