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为了了解双向温度梯度作用下Cz液池内复杂流动和传热特性,利用有限容积法对底部施加不同垂直热流密度(3.0~4.0 W/cm2)的Cz结构内硅熔体流动进行了三维数值模拟.结果表明,当3.0 W/cm2≤q≤3.4 W/cm2时,液池内为稳态轴对称流动,自由表面上温度波动呈直辐条结构,液池内最高温度出现在坩埚侧壁(即Th);当3.6 W/em2≤q≤4.0W/cm2时,流动失稳,液池内总体温度水平提高,最高温度高于壁面温度,其出现的位置离开壁面逐渐向液池中心移动.

参考文献

[1] Maxim Teitel;Dietrich Schwabe;Alexander Yu. Gelfgat .Experimental and computational study of flow instabilities in a model of Czochralski growth[J].Journal of Crystal Growth,2008(7/9):1343-1348.
[2] P.Hintz;D.Schwabe;H.Wilke .Convection in a Czochralski crucible - Part 1: non-rotating crystal[J].Journal of Crystal Growth,2001(1/2):343-355.
[3] Takeshi Azami;Shin Nakamura;Minoru Eguchi .The role of surface-tension-driven flow in the formation of a surface pattern on a Czochralski silicon melt[J].Journal of Crystal Growth,2001(1/2):99-107.
[4] Schwabe D. .Buoyant-thermocapillary and pure thermocapillary convective instabilities in Czochralski systems[J].Journal of Crystal Growth,2002(Pt.3):1849-1853.
[5] V. Kumar;G. Biswas;G. Brenner;F. Durst .Effect of thermocapillary convection in an industrial Czochralski crucible: numerical simulation[J].International Journal of Heat and Mass Transfer,2003(9):1641-1652.
[6] You-Rong Li;Nobuyuki Imaishi;Lan Peng;Shuang-Ying Wu;Taketoshi Hibiya .Thermocapillary flow in a shallow molten silicon pool with Czochralski configuration[J].Journal of Crystal Growth,2004(1/3):88-95.
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