Active Oxidation of Liquid Silicon in the Presence of Hydrogen: Extension of the Ratto Model
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INTRODUCTION
LIQUID silicon oxidation is a driving phenomenon in purification processes used in the ‘‘metallurgical route’’ to produce silicon for solar cells, at a lower energy cost than the classical chemical route used for electronic grade silicon.[1] A plasma process has been proposed to remove boron from liquid silicon, first investigated on silicon drops,[2] then at large scale in Japan with arc torches[3] and in France with inductive plasmas.[4,5] Other boron extraction processes were tested using gas mixtures in place of plasma torches.[6,7] All those processes use a common reaction mechanism at the interface between molten silicon and gas, involving silicon and boron in the liquid phase and hydrogen and oxygen in the gas phase (generally mixed with argon). Despite its industrial application, this mechanism is not completely understood, especially the rate limiting step that could be the surface reaction itself or the diffusion of oxidizing species toward the surface.[7,8] One key point of such a process is that silicon is oxidized (to form SiO or SiO2) in parallel with boron that mainly produces HBO in the gas phase.[4,7] The concept of thermodynamic equilibrium at the surface[8] enables to deduce the boron extraction rate from the silicon oxidation rate. The core of this paper is to study the mechanism of silicon oxidation for typical conditions used in the purification processes mentioned previously: atmospheric pressure, silicon temperature between 1683 K and 2073 K (1410 C and 1800 C), and a gas mixture blown on the surface, containing argon with some percents of
oxygen (or water vapor) and a variable proportion of hydrogen. The oxidation of liquid silicon by dioxygen in a neutral gas was described in the literature,[10,11] but those models did not include hydrogen. A 1D model has been developed using the work of Ratto et al.[11] as a basis and adding new species due to the presence of hydrogen. This model is described in part 2. The main results are described in part 3, for conditions that could be encountered in purification processes. In part 4, the flow of silicon oxidized from the melt is predicted using a combination of our numerical model with the theoretical predictions of the mass transfer boundary layer thickness for an impinging jet. These predictions are applied for a set of experiments of silicon purification with steam for which the mass loss was measured.[12] In part 5, we applied the same model to a plasma purification experiment to predict silicon oxidation rate, and from this value, a speed of removal of boron which was compared to the experimental value.[8] The discussion shows perspectives on the prediction of purification kinetics. II.
OXIDATION MODEL IN THE PRESENCE OF HYDROGEN
Following Reference 11, we use the concept of a stagnant film to study the transport of species across the gaseous boundary layer just above the liquid silicon. The flow of each gaseous species is then only diffusive, whereas chemical reactions in the gas produce some source terms in each transport equation for i
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