A Generalized Mathematical Framework for Thermal Oxidation Kinetics

TL;DR

This paper introduces a comprehensive mathematical model for thermal oxidation that extends classical theories by incorporating detailed interface reactions and transport processes, unifying various oxidation rate laws into a single framework.

Contribution

The paper develops a generalized model that captures all stages of oxidation, relaxing previous assumptions and unifying different rate laws within one comprehensive framework.

Findings

Identifies three distinct oxidation regimes: reaction-controlled, transitional, and diffusion-controlled.

Shows that the classical Deal-Grove model is a lower order approximation of the new model.

Unifies various oxidation rate laws into a single, comprehensive model.

Abstract

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.