# A Generalized Mathematical Framework for Thermal Oxidation Kinetics

## 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 detail. 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.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1033070

- Report Number(s):
- PNNL-SA-78995

Journal ID: ISSN 0021-9606; JCPSA6; KC0201020; TRN: US201202%%572

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 135; Journal Issue: 2; Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; APPROXIMATIONS; DIFFUSION; KINETICS; MATHEMATICAL MODELS; OXIDATION; OXIDES; OXIDIZERS; STOICHIOMETRY; TRANSPORT

### Citation Formats

```
Xu, Zhijie, Rosso, Kevin M., and Bruemmer, Stephen M..
```*A Generalized Mathematical Framework for Thermal Oxidation Kinetics*. United States: N. p., 2011.
Web. doi:10.1063/1.3607984.

```
Xu, Zhijie, Rosso, Kevin M., & Bruemmer, Stephen M..
```*A Generalized Mathematical Framework for Thermal Oxidation Kinetics*. United States. doi:10.1063/1.3607984.

```
Xu, Zhijie, Rosso, Kevin M., and Bruemmer, Stephen M.. Tue .
"A Generalized Mathematical Framework for Thermal Oxidation Kinetics". United States. doi:10.1063/1.3607984.
```

```
@article{osti_1033070,
```

title = {A Generalized Mathematical Framework for Thermal Oxidation Kinetics},

author = {Xu, Zhijie and Rosso, Kevin M. and Bruemmer, Stephen M.},

abstractNote = {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 detail. 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.},

doi = {10.1063/1.3607984},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 2,

volume = 135,

place = {United States},

year = {2011},

month = {7}

}