Numerical Simulation of Phosphorus Removal from Silicon by Induction Vacuum Refining
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INTRODUCTION
The equilibrium partial pressure of silicon is
PHOSPHORUS
is an impurity in silicon difficult to remove. For solar cell applications, there are limitations on the level of impurities as in semiconductor-grade silicon, but the acceptable levels are substantially higher. The maximum permissible concentrations of individual impurities in solar-grade silicon are defined by studying the conversion efficiency of solar cells as a function of impurity concentration. As is shown in Figure 1, the limits on impurity concentrations in p-type silicon for solar cells are reported by Bathey et al.,[1] Gribov et al.,[2] and Dietl.[3] The required maximum limit for phosphorus content in solar grade silicon should be less than 0.1 ppma. Vacuum refining is one of the conventional processes in metallurgy, and phosphorus can be expected to evaporate preferentially from silicon melt under vacuum refining with its higher vapor pressure than silicon. Experiments to remove phosphorus under vacuum conditions were investigated by Zheng et al.,[4] Miyake et al.,[5] Yuge et al.,[6] Suzuki et al.,[7] Pires et al.,[8] and Ikeda and Maeda,[9] and the thermodynamics of phosphorus in molten silicon was also presented by Miki et al.[10] and Zaitsev et al.[11] In the present study, a numerical model for phosphorus removal in vacuum induction refining of silicon is developed and compared to experimental data. II.
THERMODYNAMIC EQUILIBRIUM
Understanding of the thermodynamics and kinetics of evaporation of volatile impurities from a liquid metal bath held under vacuum requires information on the vapor pressure of constituent gas species above the melt. SONGSHENG ZHENG, Postdoctoral candidate, and XUE-TAO LUO, Professor, are with the Department of Materials Science and Engineering, Xiamen University, Xiamen 361005, People’s Republic of China. Contact e-mail: [email protected] THORVALD ABEL ENGH and MERETE TANGSTAD, Professors, are with the Department of Material Science and Engineering, Norwegian University of Science and Technology, Trondheim 7034, Norway. Manuscript submitted July 15, 2010. Article published online February 15, 2011 2214—VOLUME 42A, AUGUST 2011
peSi ¼ p0Si cSi xSi
½1
where p0Si is the vapor pressure of pure silicon; cSi is the Raoultian activity coefficient of silicon, taken as unity here; and xSi is the molar fraction of silicon. The vapor pressure is calculated by the Van Laar equation:[12,13] log poSi ¼ 20; 900T1 0:565 log T þ 12:9
½2
The partial pressure of phosphorus vapor above liquid silicon is complex since phosphorus has three significant gaseous species. As is reported by Schlesinger,[14] vaporizing red or liquid phosphorus forms a gas consisting primarily of P4, which is the predominant form below 973 K (700 C). Above this temperature, the presence of P2 vapor becomes noticeable and increasingly dominant above 1533 K (1260 C). At much higher temperatures, monatomic phosphorus vapor begins to appear. Therefore, the partial pressure of phosphorus vapor above liquid silicon is decided by the thermodynamic pr
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