A three-dimensional numerical study of Marangoni convection in a floating full zone
A three-dimensional numerical study of Marangoni convection in a floating full zone
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DOI：
10.1504/ijmpt.2005.005762
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发表时间：
2005
影响因子：
0.5
通讯作者：
H. Minakuchi;Y. Okano;S. Dost
中科院分区：
文献类型：
--
作者：
H. Minakuchi;Y. Okano;S. Dost
本文对浮区法生长掺硅锗晶体过程中的输运现象进行了三维数值模拟研究。通过数值模拟研究了零重力条件下Marangoni对流在全区域结构中的作用。模型中还考虑了晶体旋转和晶区长径比的影响。采用有限差分法离散液相场方程及相应的边界条件，并采用HSMAC（Highly Simplified Marker And Cell）方法求解。结果表明，流场和温度场最初是二维的，有两对相同大小的涡，随着时间的推移，流场变成三维的，尽管假设的轴对称边界条件。浓度场的三维化要比流场早得多。浮区的纵横比有一个突出的影响，在三维流动结构发生的临界Marangoni数，以及对方位波数和溶质浓度的均匀性沿着在熔体中的晶体生长界面。晶体旋转的应用有利于获得沿着生长界面更均匀的溶质浓度分布。
The article presents a three-dimensional computational study for the transport phenomena occurring during the growth of Si-doped Ge crystals by the Floating-Zone (FZ) technique. Numerical simulations were performed to examine the role of the Marangoni convection in a Full-zone configuration under zero gravity. The effects of crystal rotation and zone aspect ratio were also considered in the model. The field equations of the liquid phase and the associated boundary conditions were discretised by the finite difference method, and solved by the HSMAC (Highly Simplified Marker And Cell) method. Results show that the flow and temperature fields are initially two-dimensional with two pairs of vortexes of the same size, as time proceeds, however the flow field becomes three-dimensional in spite of assumed axisymmetric boundary conditions. The concentration field becomes three-dimensional much earlier than the flow field. The float zone aspect ratio has a prominent effect on the critical Marangoni number at which three-dimensional flow structures occur, and as well as on the azimuthal wave number and the uniformity of the solute concentration along the crystal growth interface in the melt. It was also shown that the application of a crystal rotation is very beneficial in obtaining a moreuniform solute concentration distribution along the growth interface.