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直拉法晶体生长过程非稳态流体热流耦合

黄伟超 刘丁 焦尚彬 张妮

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直拉法晶体生长过程非稳态流体热流耦合

黄伟超, 刘丁, 焦尚彬, 张妮

Thermo-fluid coupling of unsteady flow in Czochralski crystal growth

Huang Wei-Chao, Liu Ding, Jiao Shang-Bin, Zhang Ni
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  • 为了改善复杂对流形态下的晶体生长品质, 提出了一种改进的格子Boltzmann方法研究非稳态熔体流动和传热的耦合性质. 该方法基于不可压缩轴对称D2Q9模型, 构建了包含旋转惯性力和热浮力等外力项的演化关系, 实现了对轴对称旋转流体的速度、温度和旋转角速度的计算与分析. 结果表明, 非稳态熔体中的流、热耦合性质与格拉斯霍夫数和雷诺数的相互作用有关; 通过调节高雷诺数, 可有效抑制熔体中的自然对流, 改善温度分布, 有助于提高单晶的品质. 数值计算结果与实际硅单晶生长试验均证明了所提方法的正确性及有效性.
    In a crystal growth system, the crystal quality is greatly affected by the coupling properties between unsteady melt flow and thermal transfer. In this paper, an improved lattice Bolzmann method is proposed. This incompressible axisymmetric model based method transforms the fluid equations of cylindrical coordinate into those of the two-dimensional Cartesian coordinate and constructs the evolutionary relationship of the external force terms, such as rotational inertia force and the thermal buoyancy. In the unsteady melt, the temperature distribution and the rotational angular velocity are determined based on the D2Q4 model and the velocity of axisymmetric swirling fluid is calculated based on the D2Q9 model. The mirror bounce format is adopted as the boundary conditions of the free surface and the axis symmetry. For the remaining boundary conditions, the non-equilibrium extrapolation format is used. In the simulation, 12 sets of flow function results are obtained by choosing different sets of Grashof number and Reynolds number. By comparing with the finite crystal growth results, the effectiveness of the proposed method can be shown. Furthermore, by studying the convection shape and the temperature distribution of the melt under coupling between high Grashof number and high Reynolds number, it can be concluded that the thermal coupling properties and flow in the unsteady melt relate to Grashof number and Reynolds number. By adjusting the high Reynolds number generated by the crystal and crucible rotation, the strength of the forced convection in the melt can be changed. Therefore, the natural convection in the melt can be suppressed effectively and the temperature distribution results can be improved significantly. In addition, it is worth mentioning that the findings in this paper can be straightforwardly extended to the silicon single crystal growth experiment by turning the dimensionless crystal rotation Reynolds number and crucible rotation Reynolds number into the actual rotation speed.
    • 基金项目: 国家自然科学基金重点项目 (批准号: 61533014)、国家重点基础研究发展计划(批准号: 2014CB360500)和高等学校博士学科点专项科研基金(批准号: 2013611813001)资助的课题.
    • Funds: Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 61533014), the National Basic Research Program of China (Grant No. 2014CB360500), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 2013611813001).
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    Sabanskis A, Bergfelds K, Muiznieks A, Schröck Th, Krauze A 2013 J. Cryst. Growth 377 9

    [3]

    Niemietz K, Galindo V, Pätzold O, Gerbeth G, Stelter M 2011 J. Cryst. Growth 318 150

    [4]

    Xing H, Chen C L, Jin K X, Tan X Y, Fan F 2010 Acta Phys. Sin. 59 8218 (in Chinese) [邢辉, 陈长乐, 金克新, 谭兴毅, 范飞 2010 物理学报 59 8218]

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    Liu Q Z, Kou Z M, Han Z N, Gao G J 2013 Acta Phys. Sin. 62 234701 (in Chinese) [刘邱祖, 寇子明, 韩振南, 高贵军 2013 物理学报 62 234701]

    [6]

    Shi D Y, Wang Z K, Zhang A M 2014 Acta Phys. Sin. 63 074703 (in Chinese) [史冬岩, 王志凯, 张阿漫 2014 物理学报 63 074703]

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    Xie J F, Zhong C W, Zhang Y, Yin D C 2009 Chin. J. Theor. Appl. Mech. 41 635 (in Chinese) [解建飞, 钟诚文, 张勇, 尹大川 2009 力学学报 41 635]

    [8]

    Halliday I, Hammond L A, Care C M, Good K, Stevens A 2001 Phys. Rev. E 64 011208

    [9]

    Peng Y, Shu C, Chew Y T, Qiu J 2003 J. Comput. Phys. 186 295

    [10]

    Weinstein O, Miller W 2010 J. Cryst. Growth 312 989

    [11]

    Huang H B, Lu X Y, Krafczyk M 2014 Int. J. Heat Mass Tran. 74 156

    [12]

    Guo Z L, Shi B C, Wang N C 2000 J. Comput. Phys. 165 288

    [13]

    He X, Luo L 1997 J. Stat. Phys. 88 3

    [14]

    Guo Z, Shi B, Zheng C 2002 Int. J. Numer. Meth. Fl. 39 325

    [15]

    Zou Q, He X 1997 Phys. Fluids 9 1591

    [16]

    Bansch E, Davis D, Langmach H, Reinhardt G, Uhle M 2006 Comput. Fluids 35 1400

  • [1]

    Gu X, Li R, Tian Y 2014 J. Cryst. Growth 390 109

    [2]

    Sabanskis A, Bergfelds K, Muiznieks A, Schröck Th, Krauze A 2013 J. Cryst. Growth 377 9

    [3]

    Niemietz K, Galindo V, Pätzold O, Gerbeth G, Stelter M 2011 J. Cryst. Growth 318 150

    [4]

    Xing H, Chen C L, Jin K X, Tan X Y, Fan F 2010 Acta Phys. Sin. 59 8218 (in Chinese) [邢辉, 陈长乐, 金克新, 谭兴毅, 范飞 2010 物理学报 59 8218]

    [5]

    Liu Q Z, Kou Z M, Han Z N, Gao G J 2013 Acta Phys. Sin. 62 234701 (in Chinese) [刘邱祖, 寇子明, 韩振南, 高贵军 2013 物理学报 62 234701]

    [6]

    Shi D Y, Wang Z K, Zhang A M 2014 Acta Phys. Sin. 63 074703 (in Chinese) [史冬岩, 王志凯, 张阿漫 2014 物理学报 63 074703]

    [7]

    Xie J F, Zhong C W, Zhang Y, Yin D C 2009 Chin. J. Theor. Appl. Mech. 41 635 (in Chinese) [解建飞, 钟诚文, 张勇, 尹大川 2009 力学学报 41 635]

    [8]

    Halliday I, Hammond L A, Care C M, Good K, Stevens A 2001 Phys. Rev. E 64 011208

    [9]

    Peng Y, Shu C, Chew Y T, Qiu J 2003 J. Comput. Phys. 186 295

    [10]

    Weinstein O, Miller W 2010 J. Cryst. Growth 312 989

    [11]

    Huang H B, Lu X Y, Krafczyk M 2014 Int. J. Heat Mass Tran. 74 156

    [12]

    Guo Z L, Shi B C, Wang N C 2000 J. Comput. Phys. 165 288

    [13]

    He X, Luo L 1997 J. Stat. Phys. 88 3

    [14]

    Guo Z, Shi B, Zheng C 2002 Int. J. Numer. Meth. Fl. 39 325

    [15]

    Zou Q, He X 1997 Phys. Fluids 9 1591

    [16]

    Bansch E, Davis D, Langmach H, Reinhardt G, Uhle M 2006 Comput. Fluids 35 1400

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出版历程
  • 收稿日期:  2015-05-19
  • 修回日期:  2015-06-18
  • 刊出日期:  2015-10-05

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