On the derivation of heterogeneous reaction kinetics from a homogeneous reaction model

A simple homogeneous reaction model in one dimension is presented in the context of silicon oxidation. We investigate two different (canonical) regimes for the oxidant diffusivity and show how these lead in the limit of fast bulk reactions to distinct sharp interface models for oxidation. The resulting heterogeneous models are moving boundary problems which correspond to the classical Stefan problem or to the Stefan problem with kinetic undercooling. The results are relevant for more general reactions but illustrate some of the peculiarities associated with silicon oxidation.