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A theory which was proposed by Scheid et al. in 2010 (Scheid B, van Nierop E A, Stone H A 2010 Appl. Phys. Lett. 97 171906) suggests that very thin ribbons of molten material can be drawn out of a melt by adequately tuning the temperature gradient along the dynamic meniscus that connects the static meniscus at the melting bath to the region of the drawn flat film. Based on this theory, one-step manufacturing ultra-thin silicon wafer by pulling out from a molten silicon bath has attracted considerable attention in recent year due to its many attractive performances such as low cost, simple process, etc. By using this method, solar cell can have intensive applications due to its low cost and stable output efficiency. The results show that the thermal capillarity effect plays a great role in preparing the ultra-thin silicon. The thickness of the silicon wafer is sensitive to the capillary length and the strength of the surface tension variation as well. In order to reveal the mechanism for the effect of thermal capillary on the fabrication of ultra-thin silicon wafer, a thermal capillary finite element model is developed for the horizontal ribbon growth system to study the wetting behaviors of molten silicon on graphite. The mathematical model is established and simulated by using the commercial software; several parameters such as mass, viscous stress and capillary force are calculated. The wetting processes are tested by changing surface roughness (Ra=0.721 m and Ra=0.134 m), system temperatures (17371744 K), and durations (1030 s) at constant temperature on a high-temperature, high-vacuum contact angle measurement instrument. It is found that the wetting angle of silicon droplet on graphite decreases with surface roughness and temperature increasing; the wetting angle comes down with time going by (lasting 30 s) at constant temperature, which is consistent with the theoretical result of Wenzel. The influence of surface tension on wetting process is studied by analyzing the distributions of pressure and velocity field. It is shown that the differential pressure at the solid-liquid interfaces, induced by thermal capillary effect, decreases in the wetting process and reaches a balance which prevents the droplet from being wetted. At T=1700 K, the wetting angle and the shape of droplet change quickly within 0.4 ms and eventually become stable after 5 ms as shown in the simulation. The spreading length L and droplet height h at the steady-state are calculated with considering the influence of droplet radius on the wetting process. The results show that both L and h are directly related to the steady-state of wetting angle. The surface tension dominates the wetting process for droplet radius R0 5mm; while for R0 5 mm, the wetting process is dominated by gravity.
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Keywords:
- molten silicon /
- wetting angle /
- capillary effect /
- surface roughness
[1] Wang A, Zhao J, Wenham S R, Green M A 1996 Prog. Photovolt. Res. Appl. 4 55
[2] Green M A 2009 Prog. Photovolt. Res. Appl. 17 183
[3] Zhang Y N, Stokes N, Jia B H, Fan S H, Gu M 2014 Sci. Rep. 4 4939
[4] Ren Z P, Zhang N L, Luo R 1987 J. Eng.Thermophys. 8 70 (in Chinese)[任泽霈, 张能力, 罗锐1987工程热物理8 70]
[5] Karapetsas G, Sahu K C, Sefiane K, Matar O K 2014 Langmuir 30 4310
[6] Liu C S 2008 J. Qingdao Technol. Univ. 29 9 (in Chinese)[刘长松2008青岛理工大学学报29 9]
[7] Wang F, Peng L, Zhang Q Z, Liu J 2015 Acta Phys. Sin. 64 140202 (in Chinese)[王飞, 彭岚, 张全壮, 刘佳2015物理学报64 140202]
[8] Daggolu P, Yeckel A, Bleil C E, Derby J J 2012 J.Cryst. Growth 355 129
[9] Scheid B, van Nierop E A, Stone H A 2010 Appl. Phys. Lett. 97 171906
[10] Scheid B, van Nierop E A, Stone H A 2012 Phys. Fluids 24 032107
[11] Liu Z H, Jin W Q, Pan Z L, Cheng N 1998 J.Inorg. Mater. 13 113 (in Chinese)[刘照华, 金蔚青, 潘志雷, 程宁1998无机材料学报13 113]
[12] Chen S X, Li M W 2007 J. Inorg. Mater. 22 15 (in Chinese)[陈淑仙, 李明伟2007无机材料学报22 15]
[13] Yu Q H, Liu L J, Geng A N, Jiang B W, Li Z Y, Xu Y Y, Xue K M 2014 J. Cryst. Growth 385 49
[14] Ranjan S, Balaji S, Panella R A, Ydstie B E 2011 Comput. Chem. Eng. 35 1439
[15] Shockley W 1962 US Patent 3031275
[16] Jeong H M, Chung H S, Lee T W 2010 J. Cryst. Growth 312 555
[17] Hess U, Pichon P Y, Seren S, Schöneckerb A, Hahna G 2013 Sol. Energ. Mat. Sol. C 117 471
[18] Xu D, Ding J N, Yuan N Y, Zhang Z Q, Cheng G G, Guo L Q, Ling Z Y 2015 Acta Phys. Sin. 64 116801 (in Chinese)[许多, 丁建宁, 袁宁一, 张忠强, 程广贵, 郭立强, 凌智勇2015物理学报64 116801]
[19] Legendre D, Magnaudet J, Mougin G 2003 J. Fluid Mech. 497 133
[20] Merle A, Legendre D, Magnaudet J 2005 J. Fluid Mech. 532 53
[21] Bretherton F P 1961 J. Fluid Mech. 10 166
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[1] Wang A, Zhao J, Wenham S R, Green M A 1996 Prog. Photovolt. Res. Appl. 4 55
[2] Green M A 2009 Prog. Photovolt. Res. Appl. 17 183
[3] Zhang Y N, Stokes N, Jia B H, Fan S H, Gu M 2014 Sci. Rep. 4 4939
[4] Ren Z P, Zhang N L, Luo R 1987 J. Eng.Thermophys. 8 70 (in Chinese)[任泽霈, 张能力, 罗锐1987工程热物理8 70]
[5] Karapetsas G, Sahu K C, Sefiane K, Matar O K 2014 Langmuir 30 4310
[6] Liu C S 2008 J. Qingdao Technol. Univ. 29 9 (in Chinese)[刘长松2008青岛理工大学学报29 9]
[7] Wang F, Peng L, Zhang Q Z, Liu J 2015 Acta Phys. Sin. 64 140202 (in Chinese)[王飞, 彭岚, 张全壮, 刘佳2015物理学报64 140202]
[8] Daggolu P, Yeckel A, Bleil C E, Derby J J 2012 J.Cryst. Growth 355 129
[9] Scheid B, van Nierop E A, Stone H A 2010 Appl. Phys. Lett. 97 171906
[10] Scheid B, van Nierop E A, Stone H A 2012 Phys. Fluids 24 032107
[11] Liu Z H, Jin W Q, Pan Z L, Cheng N 1998 J.Inorg. Mater. 13 113 (in Chinese)[刘照华, 金蔚青, 潘志雷, 程宁1998无机材料学报13 113]
[12] Chen S X, Li M W 2007 J. Inorg. Mater. 22 15 (in Chinese)[陈淑仙, 李明伟2007无机材料学报22 15]
[13] Yu Q H, Liu L J, Geng A N, Jiang B W, Li Z Y, Xu Y Y, Xue K M 2014 J. Cryst. Growth 385 49
[14] Ranjan S, Balaji S, Panella R A, Ydstie B E 2011 Comput. Chem. Eng. 35 1439
[15] Shockley W 1962 US Patent 3031275
[16] Jeong H M, Chung H S, Lee T W 2010 J. Cryst. Growth 312 555
[17] Hess U, Pichon P Y, Seren S, Schöneckerb A, Hahna G 2013 Sol. Energ. Mat. Sol. C 117 471
[18] Xu D, Ding J N, Yuan N Y, Zhang Z Q, Cheng G G, Guo L Q, Ling Z Y 2015 Acta Phys. Sin. 64 116801 (in Chinese)[许多, 丁建宁, 袁宁一, 张忠强, 程广贵, 郭立强, 凌智勇2015物理学报64 116801]
[19] Legendre D, Magnaudet J, Mougin G 2003 J. Fluid Mech. 497 133
[20] Merle A, Legendre D, Magnaudet J 2005 J. Fluid Mech. 532 53
[21] Bretherton F P 1961 J. Fluid Mech. 10 166
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