Thermodynamics of Phosphorus in Solvent Refining of Silicon Using Ferrosilicon Alloys

The thermodynamics of phosphorus distribution between solid silicon and iron-silicon melt was studied to examine the degree of phosphorus removal from silicon by solvent refining with ferrosilicon alloys. The experiments were performed on silicon-iron-phosphorus alloys with ~80 wt pct silicon and ~20 wt pct iron. A phosphorus distribution coefficient, which is defined as the ratio of the mole fraction of phosphorus in solid to that of liquid is as follows: 0.22 ± 0.02 [1583 K (1310 °C)], 0.29 ± 0.02 [1533 K (1260 °C)], and 0.33 ± 0.02 [1483 K (1210 °C)]. The corresponding removal percentages of phosphorus were 86 pct [1583 K (1310 °C)], 75 pct [1533 K (1260 °C)], and 67 pct [1483 K (1210 °C)]. The average phosphorus content of the refined silicon in the current process would be more than two times less than that of the conventional solidification refining techniques. The values of interaction coefficient of phosphorus on iron (εFeP)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ (\varepsilon_{\text{Fe}}^{P} ) $$\end{document} at different temperatures were obtained as −3460 ± 155 [1583 K (1310 °C)], −3595 ± 159 [1533 K (1260 °C)], and −3694 ± 119 [1483 K (1210 °C)]. The self-interaction parameters of phosphorus εPP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left( {\varepsilon_{P}^{P} } \right) $$\end{document}at different temperatures are as follows: 68 ± 4 [1583 K (1310 °C)], 78 ± 10 [1533 K (1260 °C)], and 103 ± 19 [(1483 K 1210 °C)]. The calculated values for the distribution coefficients of phosphorus at infinite dilution are 0.22 ± 0.00 [1583 K (1310 °C)], 0.30 ± 0.00 [1533 K (1260 °C)], and 0.34 ± 0.00 [1483 K (1210 °C)]. Considering the solid (red phosphorus) standard state for solid silicon, the activity coefficient of phosphorus in solid silicon is estimated as lnγP \, in \, solid \, Si∘=-173951T+10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {{ln\gamma }}_{\text{P \, in \, solid \, Si}}^{^\circ } = - 17395\left( {\frac{1}{\text{T}}} \right) + 10 $$\end{document}.