分离结晶过程中熔体热毛细对流的三维数值模拟
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摘要
新型分离结晶Bridgman法结合了传统Czochralski提拉法和Bridgman定向凝固法的优点,既能够保证晶体在较低的热梯度条件下进行晶体的分离生长,又可以为晶体生长提供一个不受约束的、自由的生长环境,因此它可以被看作是一种理想的从熔体中生长晶体的方法。CdZnTe晶体是一种十分重要的功能材料,具有能在室温下工作、高灵敏度、高能量分辨率、高量子效率、低漏电率、高电阻率等诸多优点,在医学成像与诊断、工业测量与控制、核材料非破坏分析、环境监测和天体物理等领域有着广泛的应用。因此,开展新型分离结晶Bridgman法制备CdZnTe晶体的相关研究,具有重要的工程意义和理论价值。
本文重点研究在微重力条件下,新型分离结晶Bridgman法生长CdZnTe晶体过程中熔体内部的流动特征。针对建立的三维数学物理模型,采用有限差分法对熔体内部的流动过程进行数值模拟,获得了熔体内部的温度分布和流场分布,分析了熔体内部的流动特征,确定了流动转变的临界条件。
研究结果表明:(1)熔体顶部为固壁时,当Ma数较小时,在下部自由表面上表面张力梯度的作用下,在熔体内部下自由表面附近将会产生一个小流胞,此时熔体内部的流动较弱且为稳态流动;当Ma数逐渐增大,熔体内部的流动范围将会逐渐增大,流胞的流动强度逐渐增强,熔体内部温度的非线性分布也逐渐加剧;当Ma数超过某一临界值以后,流动将转变为非稳态流动。(2)熔体顶部为自由表面时,当Ma数较小时,在上部和下部自由表面的表面张力梯度作用下,在熔体内部会产生两个流动方向相反的流胞,此时流动较弱且为稳态流动;当Ma数逐渐增大,熔体内部流动范围亦随之增大,流胞的流动强度会逐渐增强;与熔体顶部为固壁时的临界Ma数相比,此时的临界Ma数有所减小。(3)熔体内部流动失稳的物理机制可以解释为流速与阻力的变化之间存在着滞后。
The traditional methods about crystal growth from melt are the Bridgman method and the Czochralski method. Both the advantages and drawbacks exist in these two crystal growth methods. The detached Bridgman technique combines superiorities of both the Bridgman and Czochralski methods, so grows better quality crystals.
We establish the three-dimensional physical model and mathematic governing equations for CdZnTe in detached solidification in the paper. In order to understand the fundamental characteristics of thermocapillary convection in melt in detached solidification under microgravity, the finite-difference method is used to carry on the three-dimensional numerical simulation for the thermocapillary convection in detached solidification. As a result, we obtain the velocity and temperature distributions of melt in detached solidification. Meanwhile, the critical Marangoni numbers can be obtained.
The numerical simulation results show that: (1)In the case of the top is non-slip wall,when Marangoni number is small, there is one steady toroidal roll cell near the lower free surface, the flow of melt is steady and weak. And with Ma number increasing, the flow is expanded toward the inner part of melt gradually and the velocity of flow on the lower free surface increases. When Ma number exceeds the critical value, the flow of melt becomes unstable. (2)In the case of the top is free surface, when Marangoni number is small, there are two steady toroidal roll cells in the melt which flow counter caused by the gradients of surface tension in the upper and lower free surfaces. And with Marangoni number increasing, the flow is expanded toward the inner part of melt gradually. When Marangoni number exceeds the critical value, the flow is unstable. Comparing with the top being solid wall, the critical Marangoni number is lower. (3)We can explain the physical mechanism of this unstable thermocapillary convection as following: there is the hysteresis between the variety of the velocity and the resistance.
本文重点研究在微重力条件下,新型分离结晶Bridgman法生长CdZnTe晶体过程中熔体内部的流动特征。针对建立的三维数学物理模型,采用有限差分法对熔体内部的流动过程进行数值模拟,获得了熔体内部的温度分布和流场分布,分析了熔体内部的流动特征,确定了流动转变的临界条件。
研究结果表明:(1)熔体顶部为固壁时,当Ma数较小时,在下部自由表面上表面张力梯度的作用下,在熔体内部下自由表面附近将会产生一个小流胞,此时熔体内部的流动较弱且为稳态流动;当Ma数逐渐增大,熔体内部的流动范围将会逐渐增大,流胞的流动强度逐渐增强,熔体内部温度的非线性分布也逐渐加剧;当Ma数超过某一临界值以后,流动将转变为非稳态流动。(2)熔体顶部为自由表面时,当Ma数较小时,在上部和下部自由表面的表面张力梯度作用下,在熔体内部会产生两个流动方向相反的流胞,此时流动较弱且为稳态流动;当Ma数逐渐增大,熔体内部流动范围亦随之增大,流胞的流动强度会逐渐增强;与熔体顶部为固壁时的临界Ma数相比,此时的临界Ma数有所减小。(3)熔体内部流动失稳的物理机制可以解释为流速与阻力的变化之间存在着滞后。
The traditional methods about crystal growth from melt are the Bridgman method and the Czochralski method. Both the advantages and drawbacks exist in these two crystal growth methods. The detached Bridgman technique combines superiorities of both the Bridgman and Czochralski methods, so grows better quality crystals.
We establish the three-dimensional physical model and mathematic governing equations for CdZnTe in detached solidification in the paper. In order to understand the fundamental characteristics of thermocapillary convection in melt in detached solidification under microgravity, the finite-difference method is used to carry on the three-dimensional numerical simulation for the thermocapillary convection in detached solidification. As a result, we obtain the velocity and temperature distributions of melt in detached solidification. Meanwhile, the critical Marangoni numbers can be obtained.
The numerical simulation results show that: (1)In the case of the top is non-slip wall,when Marangoni number is small, there is one steady toroidal roll cell near the lower free surface, the flow of melt is steady and weak. And with Ma number increasing, the flow is expanded toward the inner part of melt gradually and the velocity of flow on the lower free surface increases. When Ma number exceeds the critical value, the flow of melt becomes unstable. (2)In the case of the top is free surface, when Marangoni number is small, there are two steady toroidal roll cells in the melt which flow counter caused by the gradients of surface tension in the upper and lower free surfaces. And with Marangoni number increasing, the flow is expanded toward the inner part of melt gradually. When Marangoni number exceeds the critical value, the flow is unstable. Comparing with the top being solid wall, the critical Marangoni number is lower. (3)We can explain the physical mechanism of this unstable thermocapillary convection as following: there is the hysteresis between the variety of the velocity and the resistance.
引文
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[2]蔡丽光,黄美松.人工晶体材料的生长技术[J].湖南有色金属, 2008, 24(3): 29-31.
[3] W.R. Wilcox, J.F. Yee, M.C. Lin, et al. Directional Solidfication of InSb-GaSb alloys [J]. American Astronautical Society, Scientific Technology Series,1974, 3:27-41.
[4] A.F. Witt, H.C. Gatos, M. Lichtensteiger, et al. Crystal growth and steady-state segregation under zero gravity: InSb [J]. Journal of the Electrochemical Society,1975, 122(2):276-283.
[5]李万万,桑文斌,王昆黍等. CdZnTe核辐射探测器材料与器件研究进展[J].上海有色金属, 2004, 6(2): 87-94.
[6]陆敏,张建国,沈先荣.碲锌镉半导体探测器的研究进展[J].海军医学杂志, 2007, 28(4): 372-374.
[7]朱世富,赵北君,王瑞林等.室温半导体核辐射探测器新材料及其器件研究[J].人工晶体学报, 2004, 33(1):6-12.
[8] Y. Tao, S. Kou. Segregation reduction in vertical Bridgman crystal growth of CdZnTe [J]. Journal of Crystal Growth, 1997, 181(3): 301-303.
[9] T. Duffar, M.D. Serrano, C.D. Moore, et al. Bridgman solidification of GaSb in space [J]. Journal of Crystal Growth, 1998, 192(1-2): 63-72.
[10] A.G. Petrosyan, G.O. Shirinyan, C. Pedrini, et al. Bridgman growth and characterization of LuAlO3-Ce3+ scintillator crystals [J]. Crystal Research and Technology, 1998, 33(2): 241-248.
[11] F. Yiting, S. Renying, F. Shiji, et al. Vertical Bridgman growth and scintillation properties of doped Bi4Si3O12 crystals [J]. Crystal Research and Technology, 1999, 34(9): 1149-1156.
[12] A. Shimizu, J. Nishizawa, Y. Oyama, et al. Dislocation densities in InP single crystals grown under controlled phosphorus vapor pressure by the horizontal Bridgman method [J]. Journal of Crystal Growth, 2000, 209(1): 21-26.
[13] H. Hermon, M. Schieber, E.Y. Lee, et al. CZT detectors fabricated from horizontal and vertical Bridgman-grown crystals [J]. Nuclear Instruments and Methods in Physics Research, 2001, 458(1-2):503-510.
[14] J. Luo, S.J. Fan, J.C. Wang, et al. Growth of Ca4YO(BO3)3 crystals by vertical Bridgman method [J]. Journal of Crystal Growth, 2001, 229: 261-264.
[15] J. Zhou, Z.W. Zhong, J.Y. Xu, et al. Bridgman growth and characterization of nonlinear optical single crystals Ca4GdO(BO3)3 [J]. Materials Science and Engineering, 2003, 97(3): 283-287.
[16] J.M. Chen, D.Z. Shen, R.H. Mao, et al. Crystal growth of PbFCl by modified Bridgmanmethod [J]. Journal of Crystal Growth, 2003, 250(3-4): 393-396.
[17] K. Fritscher. Eutectic structures in the Ni-Co-Cr-Al system obtained by plasma spraying and by Bridgman growth [J]. Journal of Crystal Growth, 2003, 250(3-4): 546-557.
[18] X.J. Wu, J.Y. Xu, J.Z. Xiao, et al. Growth of ferroelectric lead germanate single crystal by the vertical Bridgman method [J]. Journal of Crystal Growth, 2004, 263(1-4): 208-213.
[19] H. Du, C.H. Champness, I. Shih, et al. Growth of Bridgman ingots of CuGaxIn1-xSe2 for solar cells [J]. Thin Solid Films, 2005, 480-481: 42-45.
[20] H.B. Chen, R.S. Li, C.X. Ge, et al. Bridgman growth of bismuth tellurite crystals [J]. Materials Letters, 2005, 59(28): 3608-3610.
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