W etting behaviors of the molten silicon on graph ite su rface∗

Cheng Guang-GuiZhang Zhong-QiangDing Jian-NingYuan Ning-YiXu Duo

1)(Micro/NanoScience and Technology Center,Jiangsu University,Zhenjiang 212013,China)2)(Low-d imension Material Micro/NanoDevice and SystemCenter,Changzhou University,Changzhou 213164,China)3)(Jiangsu Collaborative Innovation Center of Photovolatic Science and Engineering,Changzhou University,

Changzhou 213164,China)4)(The Breed ing Construction Point of State Key Laboratory of Photovoltaic Engineering Science,Changzhou University,

Changzhou 213164,China)

(Received 28 June 2016;revised manuscript received 8 November 2016)

W etting behaviors of the molten silicon on graph ite su rface∗

Cheng Guang-Gui1)3)†Zhang Zhong-Qiang1)3)Ding Jian-Ning1)2)3)4)‡Yuan Ning-Yi2)3)4)Xu Duo1)

1)(Micro/NanoScience and Technology Center,Jiangsu University,Zhenjiang 212013,China)2)(Low-d imension Material Micro/NanoDevice and SystemCenter,Changzhou University,Changzhou 213164,China)3)(Jiangsu Collaborative Innovation Center of Photovolatic Science and Engineering,Changzhou University,

Changzhou 213164,China)4)(The Breed ing Construction Point of State Key Laboratory of Photovoltaic Engineering Science,Changzhou University,

Changzhou 213164,China)

(Received 28 June 2016;revised manuscript received 8 November 2016)

Atheory which was proposed by Scheid et al.in 2010(Scheid B,van NieropE A,Stone HA2010 Appl.Phys.Lett.97 171906)suggests that very thin ribbons ofmolten material can be drawn out of amelt by adequately tuning the temperature gradient along the dynamicmeniscus that connects the staticmeniscus at themelting bath tothe region of the d rawn flat fi lm.Based on this theory,one-stepmanufacturing ultra-thin silicon wafer by pulling out froma molten silicon bath has attracted considerable attention in recent year due toitsmany attractive performances such as lowcost,simple process,etc.By using thismethod,solar cell can have intensive applications due toits lowcost and stab le output effi ciency.The results showthat the thermal capillarity eff ect plays a great role in preparing the ultra-thin silicon.The thickness of the silicon wafer is sensitive tothe capillary length and the strength of the surface tension variation aswell.In order toreveal themechanismfor the eff ect of thermal capillary on the fabrication of ultra-thin silicon wafer,a thermal capillary finite element model is developed for the horizontal ribbon growth systemtostudy the wetting behaviors of molten silicon on graphite.The mathematicalmodel is established and simulated by using the commercial software;several parameters such asmass,viscous stress and capillary force are calculated.The wetting processes are tested by changing surface roughness(Ra=0.721 µmand Ra=0.134 µm),systemtemperatures(1737–1744 K),and durations(10–30 s)at constant temperature on a high-temperature,high-vacuumcontact angle measurement instrument.It is found that the wetting angle of silicon d roplet on graphite decreaseswith 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 ofWenzel.The influence of surface tension on wetting process is studied by analyzing the distributions of pressure and velocity field.It is shown that the diff erential pressure at the solid-liquid interfaces,induced by thermal capillary eff ect,decreases in thewetting process and reaches a balancewhich prevents the droplet frombeing wetted.At T=1700 K,the wetting angle and the shape of droplet change quickly within 0.4ms and eventually become stab le 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 infl uence of d roplet radius on thewetting process.The results showthat both L and h are directly related tothe steady-state of wetting angle.The surface tension dominates the wetting process for droplet radius R0≪5 mm;while for R0≫5 mm,the wetting process is dominated by gravity.

molten silicon,wetting angle,capillary eff ect,surface roughness

10.7498/aps.66.036801

*Project supported by the Key Programof the National Natural Science Foundation of China(G rant No.51335002),the Key Support Projects of Strategic Emerging Industries in Jiangsu Province,China(G rant No.2015-318),and the Priority Academic ProgramDevelopment of Jiangsu Higher Education Institutions,China.

†Corresponding author.E-mail:ggcheng@u js.edu.cn

‡Corresponding au thor.E-mail:dingjn@u js.edu.cn