Effect of Oxygen on Thermocapillary Convection in a Molten Silicon Column under Microgravity

Abstract

X-ray flow visualization in a half-zone molten silicon bridge was carried out under microgravity at a variety of oxygen partial pressures in an ambient atmosphere. The flow velocity of thermocapillary convection was found to decrease with increased oxygen partial pressure. Thermocapillary flow stabilized when the oxygen partial pressure at the inlet p O 2 was increased to 10 Ϫ4 MPa. The dependence of the flow velocity and flow mode on p O 2 can be explained in terms of the decrease in the temperature coefficient of surface tension due to the increase in oxygen partial pressure. Single crystals of semiconductor silicon have been widely used for advanced computer and mobile communication devices. To improve the quality of silicon single crystals, the transfer of heat and mass at the solid-liquid interface during crystal growth must be better understood. In industrial crystal growth processes, such as the Czochralski ͑CZ͒ or the float-zone ͑FZ͒ methods, there are three types of convection: buoyancy, forced, and thermocapillary convection. Of these, the thermocapillary effect at the free surface is dominant, especially under microgravity. 1 Thermocapillary convection also plays a significant role in forming dopant striations in the crystal growth process. Eyer et al. 1 carried out silicon crystal growth in a float-zone system under microgravity and showed that timedependent thermocapillary convection caused the dopant striations. Cröll et al. 2 found that the critical Marangoni number, M a c2 , for the transition from steady to time-dependent flow was 150 Ϯ 50. The thermocapillary flow in a molten silicon bridge has previously been investigated by measuring temperature fluctuations and visualizing flow. 3-7 Nakamura et al. 7 observed thermocapillary flow by using X-ray radiography with tracer particles in a molten silicon bridge, and they showed that the frequency of the tracer motion in the bridge formation process differed from that of the complete bridge. There have also been many reports on numerical simulations of thermocapillary convection in a half-zone bridge in low Prandtl number fluids such as molten silicon. [8][9][10][11][12][13][14][15] These simulations indicated that transition processes occur first, from an axisymmetric flow to a three-dimensional steady flow and then from a threedimensional steady flow to a three-dimensional oscillatory flow. Most studies, however, have not taken into consideration the influence of oxygen partial pressure in the ambient atmosphere on thermocapillary convection of molten silicon.The Marangoni number, which indicates the potential for thermocapillary convection, depends on the temperature coefficient of surface tension, the temperature difference between the upper and lower interfaces, and the height of the molten zone. In many investigations of thermocapillary convection in molten silicon, the temperature coefficient of surface tension has been assumed to be constant. However, in the case of molten silicon, oxygen partial pressure in an ambient atmosphere is though t...

Thermophysical Properties of Molten Silicon

“…4.17(a) and (b). The oxygen partial pressure dependence of the Marangoni flow velocity for molten silicon observed under microgravity conditions [81] was well explained by taking account of the oxygen partial pressure dependence of the temperature coefficient of surface tension.…”

Silicon

“…The Marangoni flow shows a marked dependence on oxygen partial pressure of an ambient atmosphere, i.e. oxygen concentration in the melt [37]. This flow shows a unique behavior at the surface of the Czochralski melt, because the oxygen concentration is high in the melt adjacent to the crucible wall and low in the vicinity of the growing crystal.…”

Effect of oxygen partial pressure on silicon single crystal growth by floating zone technique: surface oxidation and Marangoni flow

“…This idea has been based on the measurement of surface tension of molten silicon as a function of temperature and oxygen partial pressure; both surface tension and temperature coefficient show marked dependence on the ambient oxygen partial pressure [22]. We found that both flow velocity and instability mode of the Marangoni flow are consequently affected by oxygen partial pressure [12,13]. We have tried to find the effect of oxygen partial pressure on striation formation of the silicon crystals, because striation is introduced by instability of the Marangoni flow.…”

“…Prof. Benz's group and our group shared these challenging subjects and collaborated. Research activities of the Japanese group featured diagnostics of the Marangoni flow from the viewpoint of hydromechanics, i.e., temperature fluctuation measurements using multiple thermocouples [10], in-situ visualization of the Marangoni flow using an X-ray technique [11] and observation of the effect of oxygen partial pressure on the Marangoni flow [12,13]. The existence of the critical Marangoni number Ma c3 , where an oscillatory flow with a single frequency changes into that with multiple frequencies, was observed for the first time [11,13].…”