轴向磁场下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方法是一种新型的晶体生长方法,它完美结合了传统Czochralski提拉法和Bridgman定向凝固法的优点,生长出的晶体质量较为理想,尤其是在生长对热应力比较敏感的CdZnTe晶体方面颇具优势。目前,这种新型晶体生长方法在微重力条件下虽然取得了一些成功,但是结果并不令人非常满意。究其原因,关键在于由表面张力作用诱导的熔体内部的热毛细对流影响了晶体的生长质量。为了削弱熔体内部的热毛细对流,本文尝试通过施加磁场影响熔体内部的流动,研究结果可为新型分离结晶Bridgman方法的应用提供理论参考。
本文重点针对微重力条件下,轴向磁场作用下新型分离结晶法生长CdZnTe晶体过程的熔体部分建立三维物理模型和数学模型,采用有限差分法进行数值模拟,得到了熔体内部的流场分布和温度分布,分析了磁场对熔体内部流动的影响作用。
研究结果表明:(1)通过施加轴向磁场可有效地削弱熔体内部的流动,有利于分离结晶过程的进行。(2)当熔体顶部为固壁时,在狭缝处自由表面张力的作用下,会在熔体底部形成一个流胞。轴向磁场可以有效地抑制这个流胞的强度,并且使流胞中心向自由表面迁移,流胞区域变小。在相同的Ma数下,磁场对熔体内部流动的抑制作用随着Ha数的增加而逐渐增强,同时自由表面上温度分布的非线性随着Ha数的增加而逐渐减弱。在相同的Ha数下,自由表面上的速度和温度分布的非线性随着Ma数的增加而逐渐增强。随磁场强度的增加,临界Ma数增大。(3)当熔体顶部为自由表面时,由于上下自由表面张力的作用,在熔体内部会形成两个流动方向相反的流胞。施加轴向磁场以后,熔体内部的两个流胞均会受到洛伦兹力的抑制作用。随磁场强度的增加,两个流胞的流动强度降低,同时上部流胞的流型随着Ha数的增加变得更加简单。在相同的Ma数下,上下自由表面上的速度均随Ha数的增加而减小。随磁场强度的增加,临界Ma数增大。
Detached Bridgman technique is a new method of melt growth, combining the advantages of both classical Bridgman and Czochralski methods, and better quality crystals can be obtained. So, the method is good at growing CdZnTe crystal growth which is more sensitive to heat stress. This new method of crystal growth has some success in microgravity conditions,but the results are not satisfactory. The reason lies that the free surface tension drives the thermocapillary convection in the melt. In order to weaken the strength of the flow in the melt, the axial magnetic field is applied. The results can provide a theoretical basis of detached Bridgman technique successfully growth of CdZnTe crystals.
In this paper, the three-dimensional physical model and governing equations for CdZnTe in detached solidification are established under axial magnetic field and microgravity. Numerical simulations of flow in the melt with different values of Ha and Ma are conducted using the finite-difference method. The distributions of streamline and isotherm of the melt and free surface are obtained. Meanwhile, the effect of axial magnetic field on the melt flow is analyzed.
The results showed: (1) The axial magnetic field significantly suppresses the thermocapillary convection in the melt. (2)When the top surface of the melt is solid wall, a toroidal roll is caused in the melt by the surface tension gradient on the free surface. The axial magnetic field significantly weaken the strength of the toroidal roll and make the center of it approach to the free surface, as well as the flow cell area become smaller. When the value of Ma is fixed, the inhibition effect of magnetic field is enhanced gradually with Ha increasing, and the non-linear temperature distribution gets decreased on the free surface. When Ha is kept at a certain value, with Ma increasing, both the velocity and the non-linear temperature distribution on the free surface get increased. The critical Ma gets increased as the intensity of magnetic field increasing. (3) When the top surface of the melt is free surface, two roll cells with opposite direction are observed in the melt driven by both the surface tension gradient on the two free surfaces. When axial magnetic field is applied, both toroidal roll cells in the melt will be inhibited by the Lorentz force. And their intensities are gradually reduced with the increase of magnetic field. At the same time, the structures of upper roll cell are significantly simplified with the increase of Ha. When the value of Ma is fixed, with Ha increasing, the velocity on the free surface is gradually reduced. The critical Ma gets increased as the intensity of magnetic field increasing.
本文重点针对微重力条件下,轴向磁场作用下新型分离结晶法生长CdZnTe晶体过程的熔体部分建立三维物理模型和数学模型,采用有限差分法进行数值模拟,得到了熔体内部的流场分布和温度分布,分析了磁场对熔体内部流动的影响作用。
研究结果表明:(1)通过施加轴向磁场可有效地削弱熔体内部的流动,有利于分离结晶过程的进行。(2)当熔体顶部为固壁时,在狭缝处自由表面张力的作用下,会在熔体底部形成一个流胞。轴向磁场可以有效地抑制这个流胞的强度,并且使流胞中心向自由表面迁移,流胞区域变小。在相同的Ma数下,磁场对熔体内部流动的抑制作用随着Ha数的增加而逐渐增强,同时自由表面上温度分布的非线性随着Ha数的增加而逐渐减弱。在相同的Ha数下,自由表面上的速度和温度分布的非线性随着Ma数的增加而逐渐增强。随磁场强度的增加,临界Ma数增大。(3)当熔体顶部为自由表面时,由于上下自由表面张力的作用,在熔体内部会形成两个流动方向相反的流胞。施加轴向磁场以后,熔体内部的两个流胞均会受到洛伦兹力的抑制作用。随磁场强度的增加,两个流胞的流动强度降低,同时上部流胞的流型随着Ha数的增加变得更加简单。在相同的Ma数下,上下自由表面上的速度均随Ha数的增加而减小。随磁场强度的增加,临界Ma数增大。
Detached Bridgman technique is a new method of melt growth, combining the advantages of both classical Bridgman and Czochralski methods, and better quality crystals can be obtained. So, the method is good at growing CdZnTe crystal growth which is more sensitive to heat stress. This new method of crystal growth has some success in microgravity conditions,but the results are not satisfactory. The reason lies that the free surface tension drives the thermocapillary convection in the melt. In order to weaken the strength of the flow in the melt, the axial magnetic field is applied. The results can provide a theoretical basis of detached Bridgman technique successfully growth of CdZnTe crystals.
In this paper, the three-dimensional physical model and governing equations for CdZnTe in detached solidification are established under axial magnetic field and microgravity. Numerical simulations of flow in the melt with different values of Ha and Ma are conducted using the finite-difference method. The distributions of streamline and isotherm of the melt and free surface are obtained. Meanwhile, the effect of axial magnetic field on the melt flow is analyzed.
The results showed: (1) The axial magnetic field significantly suppresses the thermocapillary convection in the melt. (2)When the top surface of the melt is solid wall, a toroidal roll is caused in the melt by the surface tension gradient on the free surface. The axial magnetic field significantly weaken the strength of the toroidal roll and make the center of it approach to the free surface, as well as the flow cell area become smaller. When the value of Ma is fixed, the inhibition effect of magnetic field is enhanced gradually with Ha increasing, and the non-linear temperature distribution gets decreased on the free surface. When Ha is kept at a certain value, with Ma increasing, both the velocity and the non-linear temperature distribution on the free surface get increased. The critical Ma gets increased as the intensity of magnetic field increasing. (3) When the top surface of the melt is free surface, two roll cells with opposite direction are observed in the melt driven by both the surface tension gradient on the two free surfaces. When axial magnetic field is applied, both toroidal roll cells in the melt will be inhibited by the Lorentz force. And their intensities are gradually reduced with the increase of magnetic field. At the same time, the structures of upper roll cell are significantly simplified with the increase of Ha. When the value of Ma is fixed, with Ha increasing, the velocity on the free surface is gradually reduced. The critical Ma gets increased as the intensity of magnetic field increasing.
引文
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[2]王季陶,刘明登主编.半导体材料.北京:高等教育出版社. 1990.
[3]蒋民华.我国人工晶体的发展与展望[J].硅酸盐学报, 1993, 21(6): 548-553.
[4]蒋民华.中国晶体生长和晶体材料五十年.功能材料信息, 20085(4): 11-16.
[5]吴建生,张寿柏编著.材料制备新技术.上海:上海交通大学出版社. 1996.
[6]姚连增编.晶体生长基础.合肥:中国科学技术大学出版社. 1995.
[7]李万万,桑文斌,王昆黍,闵嘉华,张斌. CdZnTe核辐射探测器材料与器件研究进展[J].上海有色金属, 2004, 25(2): 87-94.
[8]张岚,李元景,毛绍基,邓智,朱维彬,李树伟.像素CdZnT e探测器的研制[J].核电子学与探测技术, 2006, 26(3): 307-309.
[9]王涛,徐亚东,查钢强,刘伟华,徐凌燕,白旭旭,傅莉,介万奇.室温辐射探测器用CdZnTe晶体生长及其器件制备[J].机械科学与技术, 2010, 29(4): 546-550.
[10]孙茂友,万群,秦福.水平磁场对熔体热对流抑制作用的理论分析. 1989.
[11] Y. S. Lee, Ch. H. Chun. Experiments on the oscillatory convection of low Prandtl number liquid in Czochralski crystal growth under an axial magnetic field [J]. J. Crystal Growth, 1999, 198/199: 147-153.
[12] Yasuto Miyazawa. Effect of Magnetic Field on Melt Flow and Crystal Growth of Oxide Crystals [J]. Progress in Crystal Growth and Characterizationof Materials, 1999, 261-272.
[13] Y. S. Lee, Ch. H. Chun. Effects of Axial Magnetic Field on The Oscillatory Convection Coupled With Crucible Rotation in Czochralski Crystal Growth [J]. Adv. Space Res, 1999, 24(10): 1375-1378.
[14] L. Gorbunov, A. Klyukin, A. Pedchenko, et al. Melt Flow Instability and Vortex Structures in Czochralski Growth under steady magnetic fields [J]. Energy Conversion and Management, 2002, 43:317-326.
[15] Erich Tomziga, Janis Virbulisa, Wilfried von Ammon, et al. Application of dynamic and combined magnetic fields in the 300mm silicon single-crystal growth [J]. Materials Science in Semiconductor Processing, 2003, 5: 347–351.
[16] Bok-Cheol Sim, In-Kyoo Lee, Kwang-Hun Kim, et al. Oxygen concentration in the Czochralski-grown crystals with cusp-magnetic field [J]. J. Cryst. Growth, 2005, 275: 455–459.
[17]蓝慕杰,叶水驰,鲍海飞等.外加横向磁场下Bridgman法生长HgCdTe晶体的实验研究[J].哈尔滨工业大学学报, 1996, 31(3): 8-10.
[18]蓝慕杰,叶水驰,鲍海飞等.在横向磁场中用Bridgman法生长HgCdTe晶体[J].材料研究学报, 2000, 14(1): 76-81.
[19] T. Alboussiere, A. C. Neubrand, J.P. Garandet, et al. Segregation during horizontal Bridgman growth under an axial magnetic field [J]. J. Cryst. Growth, 1997, 181: 133-144.
[20] Y.Y.Khine, J.S. Walker. Thermoelectric Magnetohydrodynamic Effects during Bridgman Semiconductor Crystal Growth with a Uniform Axial Magnetic field [J]. J. Cryst. Growth, 1998, 183: 150-158.
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