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在直拉单晶硅生长的过程中,自然对流对晶体界面的形状、温度场及应力分布影响很大。本文采用二维模型对熔体内自然对流对单晶硅的影响作了数值模拟,在低雷诺数时采用层流模型,高雷诺数时采用紊流模型,Gr的变化范围从3×106到3×1010,这样涵盖了从小尺寸到大尺寸的直拉单晶硅生长系统。数值结果表明熔体的流动状态不仅与熔体的Gr有关,还与熔体高度和坩埚半径的比值密切相关。当Gr>108时,熔体内确实存在紊流现象,层流模型不再适合,随着Gr的增大,紊流现象加剧,轴心处的等温线变得更为陡峭,不利于晶体生长。
In the process of Czochralski crystal growth, natural convection has a great influence on the shape, temperature field and stress distribution of the crystal interface. In this paper, the two-dimensional model is used to simulate the influence of natural convection in the melt on the single crystal silicon. The laminar flow model is used at low Reynolds number and the turbulence model is used at high Reynolds number. Gr varies from 3 × 106 to 3 × 1010, which covers the Czochralski crystal growth system from small to large size. The numerical results show that the flow state of the melt is not only related to the Gr of the melt, but also to the ratio of the melt height to the radius of the crucible. When Gr> 108, turbulent flow does exist in the melt, and the laminar flow model is no longer suitable. As Gr increases, the turbulent phenomenon aggravates and the isotherm at the axis becomes steeper, which hinders the crystal growth .