  We present a generalized mathematical model for thermal oxidation and the
growth kinetics of oxide films. The model expands long-standing classical
models by taking into account the reaction occurring at the interface as well
as transport processes in greater details. The standard Deal-Grove model (the
linear-parabolic rate law) relies on the assumption of quasi-static diffusion
that results in a linear concentration profile of, for example, oxidant species
in the oxide layer. By relaxing this assumption and resolving the entire
problem, three regimes can be clearly identified corresponding to different
stages of oxidation. Namely, the oxidation starts with the reaction-controlled
regime (described by a linear rate law), is followed by a transitional regime
(described by a logarithmic or power law depending on the stoichiometry
coefficient m), and ends with the well known diffusion-controlled regime
(described by a parabolic rate law). Deal-Grove's theory is shown to be the
lower order approximation of the proposed model. Various oxidation rate laws
are unified into a single model to describe the entire oxidation process.
