Thermodynamics of phosphorus in molten silicon
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I.
INTRODUCTION
SOLAR energy will shortly be in great demand, since it is inexhaustible and cleaner than any conventional energy resources. At present, expensive off-grade silicon for semiconductor (SEG-Si) is used for a solar cell to convert solar energy into electricity. For this reason, the solar cell system has not been developed widely until now. Using relatively inexpensive metallurgical grade silicon (MG-Si) as a starting material for making solar grade silicon (SOG-Si) is believed to be one of the ways to make solar cell less expensive. Phosphorus is a typical impurity in silicon, and the required maximum limit for phosphorus content is 1025 [mass pct P] for SOG-Si. Unfortunately, the segregation coefficient of phosphorus in silicon is large (0.35), so it is difficult to remove phosphorus by zone or unidirectional refining. Although some attempts to remove phosphorus by vacuum treatment have been carried out,[1,2] quantitative analysis has not been made due to lack in thermodynamic properties of phosphorus in molten silicon. In the present study, the Gibbs energy change of phosphorus dissolution into silicon was determined by using a chemical equilibration technique. II.
EXPERIMENTAL
A molten silicon-phosphorus alloy was equilibrated in a controlled phosphorus partial pressure. The dissolution reaction of phosphorus into silicon and its Gibbs energy change are expressed by Eqs. [1] and [2], respectively. 1 P (g) 5 P (mass pct, in Si) 2 2 DG7 5 2RT ln
fP z [mass pct P] p1/2 P2
[1] [2]
TAKAHIRO MIKI, Graduate Student, KAZUKI MORITA, Associate Professor, and NOBUO SANO, Professor, are with the Department of Metallurgy, The University of Tokyo, Tokyo 113, Japan. Manuscript submitted September 25, 1995. METALLURGICAL AND MATERIALS TRANSACTIONS B
where R is the gas constant, fP is the activity coefficient of phosphorus in liquid silicon relative to 1 mass pct, and pP2 is the partial pressure of phosphorus. At low phosphorus concentration, the activity coefficient of phosphorus, fP, may be assumed as unity. The Gibbs energy change of phosphorus dissolution can be calculated by measuring phosphorus content of silicon at constant temperature and phosphorus partial pressure according to Eq. [2]. Temperature dependence of the Gibbs energy change has been measured from 1723 to 1848 K. Ten grams of silicon-phosphorus alloy in a graphite crucible (30-mm o.d., 25-mm i.d., and 60-mm length) or 3g of silicon-phosphorus alloy in an alumina crucible (16-mm o.d., 14-mm i.d., and 55-mm length) was held in a graphite holder and equilibrated at temperatures ranging from 1723 to 1848 K controlled within 50.5 K in a deoxidized argon and phosphorus gas mixture. A portion of the sample was withdrawn by sampling by a quartz tube and was subjected to chemical analysis. Phosphorus content of silicon was analyzed by spectrophotometry. Equilibration time was determined as 1.51 3 102 ks by preliminary experiment. Silicon-phosphorus alloy was prepared by the following procedure. After melting high-purity polycrystalline silicon in a
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