A numerical simulation study for the Czochralski growth process of Si under magnetic field |
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| Affiliation: | 1. Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Cauerstrasse 4, D-91058 Erlangen, Germany;2. Department of Mechanical Engineering, University of Victoria, Victoria, BC, Canada V8W 3P6;1. Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China;2. Institute for Computational Modeling in Civil Engineering, Technische Universität, Braunschweig 38106, Germany;1. Department of Materials Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan;2. Department of Crystalline Materials Science, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan;3. Crystal Growth Laboratory, University of Victoria, Victoria, BC V8W 3P6, Canada;1. SUMCO Corp./Technology Div., 1-52 Kubara, Yamashiro-cho, Imari, Saga, Japan;2. Nippon Steel & Sumitomo Metal Corp., 20-1 Shintomi, Futtsu, Chiba, Japan;1. STR Japan K.K., East Tower 15F, Yokohama Business Park, 134, Goudo-cho, Hodogaya-ku, Yokohama, Kanagawa 240-0005, Japan;2. STR Group—Soft-Impact, Ltd., Bolshoi Sampsonievskii pr. 64, Build. “E”, 194044 St. Petersburg, Russia;3. GlobalWafers Japan Co., Ltd., 6-861-5 Higashiko, Seiro, Niigata 957-0197, Japan;4. Okayama Prefectural University, 111 Kuboki, Soja, Okayama 719-1197, Japan |
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| Abstract: | The article presents results of the numerical simulations carried out for the transport phenomena occurring during the Czochralski crystal growth process. Due to computational constraints, the simulations were kept limited to axisymmetric geometries. The simulation model gives special attention to the crystal–melt interface and oxygen transport, and treats the crystal–melt interface according to Stefan’s balance, by explicitly moving the grids. Oxygen evaporation at the free surface is expressed by balancing the corresponding fluxes. Marangoni convection due to temperature gradients is also incorporated into the model. The role of an applied axial magnetic field in controlling fluid flow, interface shape, and oxygen levels is studied in detail. The effect of crystal and crucible rotations is also examined under the influence of the magnetic field. Simulation results show that the application of an axial magnetic field leads to flatter interfaces and lower oxygen concentration levels, but makes the oxygen distribution non-uniform at the crystal–melt interface. |
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