分离结晶过程中熔体热毛细对流的二维数值模拟
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摘要
新型分离结晶Bridgman法结合了传统Bridgman定向凝固法和Czochralski提拉法的优点,既能保证晶体生产过程中较低的热梯度,又能提供一个晶体不受约束、自由生长的环境,他是一种理想的从熔体中生长晶体的方法,可以生产出高质量、大体积的CdZnTe晶体,而CdZnTe晶体是一种应用广泛的半导体功能材料,研究CdZnTe材料分离结晶过程中熔体的流动特征,可以为在地面条件下采用分离结晶法制备CdZnTe晶体提供指导,具有重要的理论意义和使用价值。
本文针对新型分离结晶Bridgman法生长CdZnTe晶体过程中的熔体流动建立了二维物理模型和数学模型,采用有限差分法对不同条件下的流动进行数值模拟,得到了熔体内的速度分布和温度分布,确定了流动转化的临界条件,分析了熔体内部的流动特征及流动失稳的物理机制。
结果表明:(1)微重力条件下,熔体顶部为固壁时,狭缝处自由表面上的表面张力梯度驱使熔体内部产生了热毛细对流。当Ma数较小时,流动为稳态流动;当Ma数超过某一临界值后,流动转化为非稳态的热毛细对流。临界Ma数随着高径比的减小而增大,随着狭缝宽度的增大而增大。流动失稳的物理机制可以解释为某种作用所引起的速度扰动使得流速的变化和温度的变化之间形成了一个滞后。(2)微重力条件下,熔体顶部为自由表面时,上下两个自由表面上的表面张力梯度驱使熔体内部产生了两个流动方向相反的流胞,与熔体顶部为固壁时得到的结果进行比较发现:高径比A=1时的临界Ma数减小,A=2时的临界Ma数增大。(3)常重力条件下,熔体顶部为自由表面时,Ma数较小时浮力对熔体内部流动的影响作用很弱;随着Ma数的增大,浮力的影响作用增强,使得上部流胞强度减小,下部流胞强度增大;另外,浮力使得临界Ma数减小了一个数量级。
Detached Bridgman technique, combining appealing characteristics of both the classical Bridgman and Czochralski methods, can provide a low temperature gradient and an environment of crystal freely growth in the process of crystal solidification. It is a good method for the crystal growth and can yield high quality and bulk mass crystals of CdZnTe which is a good semi-conducting material of using widely. It can instruct experiment of growing crystal on the earth of studying the fundamental characteristics of detached solidification of the CdZnTe. So our research is significant and valuable.
In this paper, the two-dimensional physical model and governing equations for CdZnTe in detached solidification are established. Numerical simulations of flow in the melt with different conditions are conducted using the finite-difference method. As a result, the distribution profiles of temperature and stream function of the melt and the critical Marangoni numbers are obtained. As well as the fundamental characteristics of flow and the physical mechanism of the unstable convection are analyzed.
The results showed that: (1) When the top surface of the melt is solid wall under microgravity condition, the thermocapillary convection is caused in the melt by the surface tension gradient on the free surface. As the Marangoni number is small, the flow is steady thermocapillary convection; With the Marangoni number exceeds the critical value, the steady flow converts into unstable thermocapillary convection. The critical Marangoni number climbs with the ratio of height and radius decreasing and the gap width increasing. The physical mechanism of the unstable thermocapillary convection can be explained as a hysteretic phenomenon between the variety of velocity and temperature which caused by a velocity turbulence. (2) When the top surface of the melt is free surface under microgravity, two roll cells with opposite direction are observed in the melt, which are driven by both the surface tension gradient on the upper and lower free surfaces; Comparing the results of this part with that obtained under condition of solid wall of the top surface, it can be found that the critical Marangoni number decreases as the ratio of height and radius equals to 1 and increase as it equals to 2. (3) When the top surface of the melt is free surface under gravity condition, the effect of the buoyancy on the flow is little as the Marangoni number is small; With the Marangoni number increasing, the effect of the buoyancy increases, which makes the upper roll cell weaken and the lower roll cell strengthen; In addition, the critical Marangoni number decreases by one order of magnitude as a results of effect of buoyancy.
本文针对新型分离结晶Bridgman法生长CdZnTe晶体过程中的熔体流动建立了二维物理模型和数学模型,采用有限差分法对不同条件下的流动进行数值模拟,得到了熔体内的速度分布和温度分布,确定了流动转化的临界条件,分析了熔体内部的流动特征及流动失稳的物理机制。
结果表明:(1)微重力条件下,熔体顶部为固壁时,狭缝处自由表面上的表面张力梯度驱使熔体内部产生了热毛细对流。当Ma数较小时,流动为稳态流动;当Ma数超过某一临界值后,流动转化为非稳态的热毛细对流。临界Ma数随着高径比的减小而增大,随着狭缝宽度的增大而增大。流动失稳的物理机制可以解释为某种作用所引起的速度扰动使得流速的变化和温度的变化之间形成了一个滞后。(2)微重力条件下,熔体顶部为自由表面时,上下两个自由表面上的表面张力梯度驱使熔体内部产生了两个流动方向相反的流胞,与熔体顶部为固壁时得到的结果进行比较发现:高径比A=1时的临界Ma数减小,A=2时的临界Ma数增大。(3)常重力条件下,熔体顶部为自由表面时,Ma数较小时浮力对熔体内部流动的影响作用很弱;随着Ma数的增大,浮力的影响作用增强,使得上部流胞强度减小,下部流胞强度增大;另外,浮力使得临界Ma数减小了一个数量级。
Detached Bridgman technique, combining appealing characteristics of both the classical Bridgman and Czochralski methods, can provide a low temperature gradient and an environment of crystal freely growth in the process of crystal solidification. It is a good method for the crystal growth and can yield high quality and bulk mass crystals of CdZnTe which is a good semi-conducting material of using widely. It can instruct experiment of growing crystal on the earth of studying the fundamental characteristics of detached solidification of the CdZnTe. So our research is significant and valuable.
In this paper, the two-dimensional physical model and governing equations for CdZnTe in detached solidification are established. Numerical simulations of flow in the melt with different conditions are conducted using the finite-difference method. As a result, the distribution profiles of temperature and stream function of the melt and the critical Marangoni numbers are obtained. As well as the fundamental characteristics of flow and the physical mechanism of the unstable convection are analyzed.
The results showed that: (1) When the top surface of the melt is solid wall under microgravity condition, the thermocapillary convection is caused in the melt by the surface tension gradient on the free surface. As the Marangoni number is small, the flow is steady thermocapillary convection; With the Marangoni number exceeds the critical value, the steady flow converts into unstable thermocapillary convection. The critical Marangoni number climbs with the ratio of height and radius decreasing and the gap width increasing. The physical mechanism of the unstable thermocapillary convection can be explained as a hysteretic phenomenon between the variety of velocity and temperature which caused by a velocity turbulence. (2) When the top surface of the melt is free surface under microgravity, two roll cells with opposite direction are observed in the melt, which are driven by both the surface tension gradient on the upper and lower free surfaces; Comparing the results of this part with that obtained under condition of solid wall of the top surface, it can be found that the critical Marangoni number decreases as the ratio of height and radius equals to 1 and increase as it equals to 2. (3) When the top surface of the melt is free surface under gravity condition, the effect of the buoyancy on the flow is little as the Marangoni number is small; With the Marangoni number increasing, the effect of the buoyancy increases, which makes the upper roll cell weaken and the lower roll cell strengthen; In addition, the critical Marangoni number decreases by one order of magnitude as a results of effect of buoyancy.
引文
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[6] P. Gille, B. Bauer. Single crystal growth of Al13Co4 and Al13Fe4 from Al-rich solutions by the Czochralski method [J]. Cryst. Res. Technol., 2008, 43(11): 1161-1167.
[7] K. Mazaev, V. Kalaev, E. Galenin, et al. Heat transfer and convection in Czochralski growth of large BGO Crystals [J]. J. Cryst. Growth, 2009, 311: 3933-3937.
[8] M. Ishii, K. Harada, N. Senguttuvan, et al. Crystal growth of BSO (Bi4Si3O12) by vertical Bridgman method [J]. J.Cryst. Growth, 1999, 205: 191-195.
[9] N. Tsutsui, Y. Ino, K. Imai, et al. Growth of large size LBO(Li2B4O7) single crystals by modified Bridgman technique [J]. J.Cryst. Growth, 2000, 211: 271-275.
[10] C. Marmn, A.G. Ostrogorsky. Growth of Ga-doped Ge0.98Si0.02 by vertical Bridgman with a baffle [J]. J.Cryst. Growth, 2000, 211: 378-383.
[11] C. H. Su, Y. G. Sha, S. L. Lehoczky, et al. Crystal growth of HgZnTe alloy by directional solidification in low gravity environment [J]. J.Cryst. Growth, 2002, 234: 487-497.
[12] C. Stelian, T. Duffar. Modeling of a space experiment on Bridgman solidification of concentrated semiconductor alloy [J]. J. Cryst. Growth, 2005, 275: 175-184.
[13] D. Schulz, S. Ganschow, D. Klimm, et al. Bridgman-grown zinc oxide single crystals [J]. J. Cryst. Growth, 2006, 296: 27-30.
[14] J. T. Yue, F. W. Voltmer. Influence of gravity-free solidification on solute micro segregation [J]. J. Cryst. Growth, 1975, 29: 329.
[15] A. F. Witt, H. C. Gatos, M. Lichtensteiger, et al. Crystal growth and steady-state segregation under zero gravity: InSb [J]. J. Electrochem. Soc., 1975, 122: 276.
[16] T. Duffar, I. Paret-Harter, P. Dusserre. Crucible de-wetting during Bridgman growth ofsemiconductors in microgravity [J]. J. Cryst. Growth, 1990, 100(1-2): 171-184.
[17] L. L. Regel, W.R. Wilcox. A Review of detached solidification in microgravity [J]. Microgravity Sci. Technol., 1999, 14: 152-166.
[18] T. Du?ar, M. D. Serrano, C. D. Moore, et al. Bridgman solidification of GaSb in space [J]. J. Cryst. Growth, 1998, 192: 63-72.
[19] P. Boiton, N. Giacometti, T. Duffar, et al, Bridgman crystal growth and defect formation in GaSb [J]. J. Cryst. Growth, 1999, 206: 159-165.
[20] M. Fiederle, T. Duffar, V. Babentsov1, et al. Dewetted growth of CdTe in microgravity (STS-95) [J]. Cryst. Res. Technol., 2004, 39(6): 481-490.
[21] T. Duffar, P. Dusserre, F. Picca, et al. Bridgman growth without crucible contact using the dewetting phenomenon [J]. J. Cryst. Growth, 2000, 211: 434-440.
[22] M. P. Volz, M. Schweizer, N. Kaiser, et al. Bridgman growth of detached GeSi crystals [J]. J. Cryst. Growth, 2002, 237-239: 1844-1848.
[23] H. Zhang, D. J. Larson Jr., C. L. Wang, et al. Kinetics and heat transfer of CdZnTe Bridgman growth without wall contact [J]. J. Cryst. Growth, 2003, 250: 215-222.
[24] N. Chevalier, P. Dusserre, J. P. Garandet, et al. Dewetting application to CdTe single crystal growth on earth [J]. J. Cryst. Growth, 2004, 261: 590-594.
[25] M. Fiederle, T. Duffar, J. P. Garandet, et al, Dewetted growth and characterisation of high-resistivity CdTe [J]. J. Cryst. Growth, 2004, 267: 429-435.
[26] J. B. Wang, L. L. Regel, W. R. Wilcox. Detached solidification of InSb on earth [J]. J. Cryst. Growth, 2004, 260: 590-599.
[27] W. Palosz, M. P. Volz, S. Cobb, et al. Detached growth of germanium by directional solidification [J]. J. Cryst. Growth, 2005, 277: 124-132.
[28] A. Zappettini, M. Zha, M. Pavesi, et al. Boron oxide fully encapsulated CdZnTe crystals grown by the vertical Bridgman technique [J]. J. Cryst. Growth, 2007, 307: 283-288.
[29] K. Takano, Y. Shiraishi, J. Matsubara, et al. Global simulation of the CZ silicon crystal growth up to 400mm in diameter [J]. J. Cryst. Growth, 2001, 229: 26-30.
[30] C. Wagner, R. Friedrich. Direct numerical simulation of momentum and heat transport in idealized Czochralski crystal growth configurations [J]. Int. J. Heat Fluid Flow, 2004, 25: 431-443.
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