壁面材质和温度场对熔融硅润湿角的影响

许多; 丁建宁; 袁宁一; 张忠强; 程广贵; 郭立强; 凌智勇

doi:10.7498/aps.64.116801

摘要

本文建立了毛细模型, 采用微流动两相流水平集法计算了熔融态硅液与壁面的润湿角, 以人造金刚石作为壁面材料的计算结果与实验结果进行比较, 验证了该模型和计算方法的正确性. 在此基础上, 分别选用碳化硅、石墨和人造金刚石作为壁面材料, 探讨了不同壁面材料表面张力和壁面黏附力对润湿角的影响规律. 结果发现, 相同温度下的毛细力作用使得熔融硅液出现起伏上升现象; 润湿角均有不同程度的减小然后增大, 最终趋于稳定; 初始阶段, 由于气/熔融硅液表面张力与气/壁面表面张力之差变化较大, 液面起伏波动较大; 随后趋于稳定上升. 同时发现石墨作为壁面材料时, 以上变化更易趋于稳定. 该研究为熔体中生长晶体硅获得更稳定的生长环境提供了理论依据.

关键词:

润湿角 /
熔融硅 /
稳定性 /
毛细效应

Abstract

A capillary model is developed for calculating the wetting angle of molten silicon on different walls by using the microfluidic two-phase flow level set method and studying the characteristics of the rising process. A mathematical model formulation rigorously accounts for the mass and momentum conservation by using the improved Navier-Stokes equation and considering the Marangoni effect. Compared with the experimental data, the change of the wetting angle on the chemical vapor deposition (CVD) diamond wall indicates the grids independence and the validity of the numerical algorithm. We also discuss the influence of surface tension, and Marangoni stress induced by the gradient of surface tension coefficient, and wall adhesion to the change of wetting angle for three different walls, which include SiC wall, graphite wall, and CVD diamond wall, at different temperatures (1683-1873 K). Result shows that at the same temperature, the thermal-capillary effects that induce the molten silicon to undulation are raised. The wetting angle is reduced after first being increased and finally stabilized. At the initial stage, the fluctuation of the liquid-air interface is volatile due to the large changes of the liquid-air and the wall-air surface tensions, and subsequently, the fluctuation tends to be stable while the wetting angle is close to a fixed value. It is also found that with the graphite wall, these changes are more likely to be stable. This research provides a theoretical guide to obtain a stable growth environment for silicon belt fabricated from the molten silicon.

Keywords:

作者及机构信息

1.
江苏大学微纳米科学技术研究中心, 镇江 212013;

2.
常州大学低维材料微纳器件与系统研究中心, 常州 213164;

3.
江苏省光伏科学与工程协同创新中心(常州大学), 常州 213164;

4.
江苏省光伏工程科学国家重点实验室培育建设点, 常州 213164

基金项目: 国家自然科学基金重点项目(批准号:51335002)、国家自然科学基金(批准号:11472117)和江苏高校优势学科建设工程资助的课题.

Authors and contacts

1.
Micro/Nano Science and Technology Center, Jiangsu University, Zhenjiang 212013, China;

2.
Low-dimension Material Micro/Nano Device and System Center, Changzhou 213164, China;

3.
Collaborative Innovation Center of Photovolatic Science and Engineering, Changzhou University, Changzhou 213164, China;

4.
The breeding construction point of State Key Laboratory of Photovoltaic Engineering Science, Changzhou University, Changzhou 213164, China

Funds: Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 51335002), the National Natural Science Foundation of China (Grant No. 11472117), and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

参考文献

[1]	Qian J, Zerda T W, He D, Daemen L, Zhao Y 2003 Journal of Materials Research 18 1173
[2]	Ekimov E A, Gavriliuk A G, Palosz B, GierlotkaS, Dluzewski P, Tatianin E, Kluev Y, Naletov A M, Presz A 2000 Applied Physics Letters 77 954
[3]	Xu S H, Zhou H W, Wang C X, Wang L W, Sun Z W 2013 Acta Phys. Sin. 62 134702 (in Chinese) [徐升华, 周宏伟, 王彩霞, 王林伟, 孙祉伟 2013 62 134702]
[4]	Yamamoto Y, Tokieda K, Wakimoto T, Ito T, Katoh K 2014 International Journal of Multiphase Flow 59 106
[5]	Li Y Q, Liu L, Zhang C H, Duan L, Kang Q 2013 Acta Phys. Sin. 62 024701 (in Chinese) [李永强, 刘玲, 张晨辉, 段俐, 康琦 2013 62 024701]
[6]	Messmer B, Lemee T, Ikebukuro K, Ueno I, Narayanan R 2014 International Journal of Heat and Mass Transfer 78 1060
[7]	Daggolu P, Yeckel A, Bleil C E, Derby J J 2012 Journal of Crystal Growth 355 129
[8]	Sasaki H, Tokizaki E, Huang X M 1995 Japanese journal of applied physics 34 3432
[9]	Sedlmeier F, Janecek J, Sendner C, Bocquet L, Netz R R, Horinek D 2008 Biointerphases 3 FC23
[10]	Landau L D, Lifshitz E M (translated by Li Z) 2013 Fluid Mechanics (Beijing:Higher Education Press) pp267-269 (in Chinese) [朗道, 栗夫席兹著(李植译) 2013 流体动力学(第五版)(北京:高等教育出版社)第267-269页]
[11]	Peng L, Li Y R, Zeng D L 2004 JournaI of Chongging University 27 60 (in Chinese) [彭岚, 李友荣, 曾丹苓 2004 重庆大学学报:自然科学版 27 60]
[12]	Peng L, Zhang W, Li X R, Meng H Y 2011 Journal of Synthetic Crystals 40 556 (in Chinese) [彭岚, 张伟, 李友荣, 孟海泳 2011 人工晶体学报 40 556]
[13]	Wang C X, Xu S H, Sun Z W, Hu W R 2010 International Journal of Heat and Mass Transfer 53 1801
[14]	Mlungwane K, Sigalas I, Herrmann M, Rodríguez M 2009 Ceramics International 35 2435
[15]	Li Y Q, Liu L 2014 Acta Phys. Sin. 63 214704 (in Chinese) [李永强, 刘玲 2014 63 214704]
[16]	Hitoshi S, Eiji T, Kazutaka T, Shigeyuki K 1994 Jpn. J. Appl. Phys. 33 6078
[17]	Huang X M 1997 Physics 26 37 (in Chinese) [黄新明1997 物理 26 37]
[18]	Rowlinson J, Widom B 1982 Molecular Theory of Capillarity (Oxford:Oxford University Press) p86
[19]	Li Y R, Deng N B, Wu S Y, Peng L, Li M W 2005 Chinese Journal of Materials Research 19 395 (in Chinese) [李友荣, 邓努波, 吴双应, 彭岚, 李明伟 2005 材料研究学报 19 395]
[20]	Son G H 2014 International Communications in Heat and Mass Transfer 58 156
[21]	Daggolu P 2013 Ph. D. Dissertation (Minnesota:University of Minnesota)

施引文献

[1]	Qian J, Zerda T W, He D, Daemen L, Zhao Y 2003 Journal of Materials Research 18 1173
[2]	Ekimov E A, Gavriliuk A G, Palosz B, GierlotkaS, Dluzewski P, Tatianin E, Kluev Y, Naletov A M, Presz A 2000 Applied Physics Letters 77 954
[3]	Xu S H, Zhou H W, Wang C X, Wang L W, Sun Z W 2013 Acta Phys. Sin. 62 134702 (in Chinese) [徐升华, 周宏伟, 王彩霞, 王林伟, 孙祉伟 2013 62 134702]
[4]	Yamamoto Y, Tokieda K, Wakimoto T, Ito T, Katoh K 2014 International Journal of Multiphase Flow 59 106
[5]	Li Y Q, Liu L, Zhang C H, Duan L, Kang Q 2013 Acta Phys. Sin. 62 024701 (in Chinese) [李永强, 刘玲, 张晨辉, 段俐, 康琦 2013 62 024701]
[6]	Messmer B, Lemee T, Ikebukuro K, Ueno I, Narayanan R 2014 International Journal of Heat and Mass Transfer 78 1060
[7]	Daggolu P, Yeckel A, Bleil C E, Derby J J 2012 Journal of Crystal Growth 355 129
[8]	Sasaki H, Tokizaki E, Huang X M 1995 Japanese journal of applied physics 34 3432
[9]	Sedlmeier F, Janecek J, Sendner C, Bocquet L, Netz R R, Horinek D 2008 Biointerphases 3 FC23
[10]	Landau L D, Lifshitz E M (translated by Li Z) 2013 Fluid Mechanics (Beijing:Higher Education Press) pp267-269 (in Chinese) [朗道, 栗夫席兹著(李植译) 2013 流体动力学(第五版)(北京:高等教育出版社)第267-269页]
[11]	Peng L, Li Y R, Zeng D L 2004 JournaI of Chongging University 27 60 (in Chinese) [彭岚, 李友荣, 曾丹苓 2004 重庆大学学报:自然科学版 27 60]
[12]	Peng L, Zhang W, Li X R, Meng H Y 2011 Journal of Synthetic Crystals 40 556 (in Chinese) [彭岚, 张伟, 李友荣, 孟海泳 2011 人工晶体学报 40 556]
[13]	Wang C X, Xu S H, Sun Z W, Hu W R 2010 International Journal of Heat and Mass Transfer 53 1801
[14]	Mlungwane K, Sigalas I, Herrmann M, Rodríguez M 2009 Ceramics International 35 2435
[15]	Li Y Q, Liu L 2014 Acta Phys. Sin. 63 214704 (in Chinese) [李永强, 刘玲 2014 63 214704]
[16]	Hitoshi S, Eiji T, Kazutaka T, Shigeyuki K 1994 Jpn. J. Appl. Phys. 33 6078
[17]	Huang X M 1997 Physics 26 37 (in Chinese) [黄新明1997 物理 26 37]
[18]	Rowlinson J, Widom B 1982 Molecular Theory of Capillarity (Oxford:Oxford University Press) p86
[19]	Li Y R, Deng N B, Wu S Y, Peng L, Li M W 2005 Chinese Journal of Materials Research 19 395 (in Chinese) [李友荣, 邓努波, 吴双应, 彭岚, 李明伟 2005 材料研究学报 19 395]
[20]	Son G H 2014 International Communications in Heat and Mass Transfer 58 156
[21]	Daggolu P 2013 Ph. D. Dissertation (Minnesota:University of Minnesota)

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