A note on the linear-parabolic law of phase formation

Abstract

One of the two equations (reaction rate) on which the Deal—Grove model of Si oxidation is based, assumes that the reacting Si is in thermodynamic equilibrium. The diffusion of injected interstitials, necessarily along a chemical potential gradient, provides evidence of an increase of the chemical potential of the substrate atoms at the interface. This must be accounted for in any kinetic equation of oxide formation and growth. A first approximation model based on this observation leads to a modified linear—parabolic equation which gives an improved match between the calculated growth curve and experimental data. The physico-chemical values that can be extracted from the model are compatible with commonly accepted ideas about the properties of silicon and of SiO2. The approach is deliberately general and is thought to be valid not only for the oxidation of silicon, but also for the oxidation of metals and for all solid-state chemical reactions. The model derived should be valid for many solid phase formations, e.g. metal oxidation or silicidation, and not be limited only to silicon oxidation. © 1991 Taylor & Francis Group, LLC.