Abstract
The effect of solutal Marangoni convection on flow instabilities in the presence of thermal Marangoni convection in a Si-Ge liquid bridge with different aspect ratios As has been investigated by three-dimensional (3D) numerical simulations under zero gravity. We consider a half-zone model of a liquid bridge between a cold (top plane) and a hot (bottom plane) disks. The highest Si concentration is on the top of the liquid bridge. The aspect ratio (As) drastically affects the critical Marangoni numbers: the critical solutal Marangoni number (under small thermal Marangoni numbers (MaTAs≲1800)) has the same dependence on As as the critical thermal Marangoni number (under small solutal Marangoni numbers (400≲MaCAs≲800)), i.e., it decreases with increasing As. The azimuthal wavenumber of the traveling wave mode increases as decreasing As, i.e., larger azimuthal wavenumbers (m=6,7,11,12, and 13) appear for As=0.25, and only m=2 appears when As is one and larger. The oscillatory modes of the hydro waves have been extracted as the spatiotemporal structures by using dynamic mode decomposition (DMD). The present study suggests a proper parameter region of quiescent steady flow suitable for crystal growth for smaller aspect ratios of the liquid bridge.
Highlights
Semiconductor single crystals with high purity are a vital requirement for novel optoelectronic devices in various fields of information technology
As well as MaC are larger, the flow becomes 3D oscillatory or 3D steady depending on the aspect ratio of the liquid bridge
The dependency of MaC,cri on As for weak solutal Marangoni convection is in good agreement with the previous results of the case of pure thermal Marangoni convection for high-Pr number fluids
Summary
Semiconductor single crystals with high purity are a vital requirement for novel optoelectronic devices in various fields of information technology. The floating zone (FZ) method is one of the most promising techniques to obtain silicon germanium (SiGe) single crystals with superior purity. During this process, a small free melt zone stabilized by surface tension is suspended between the polycrystalline feed rod and the grown single crystal. The crystal growth is achieved by a relatively slow movement of the crystal and feed rod through the molten zone. This container less configuration is beneficial since it eliminates possible crucible contamination. The temperature and concentration gradients along the free surface of the liquid bridge give rise to surface tension gradients that can induce strong thermo-solutal Marangoni convective flows
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