3. Advanced Oxidation Model

In case of oxidation there exist two segments, one for silicon and one for SiO, with an interface. It is not a problem to make a mesh for such structures, but the SiO-growth results in a moving boundary problem, which means that the interface should move after each simulation step. In order to reach the new position of the interface, new grid points are inserted and a remeshing step has to be performed [61,63]. These mesh operations demand complicated algorithms.

The basic idea of this model is to define the regions of and SiO on a single and static mesh with a separating parameter . In this model plays a key role, because the main interest of oxidation simulation is to predict the shape of the SiO-domain. Since the newly formed SiO leads to a significant volume increase and so to large displacements or stresses, the modeling of the mechanics also plays an important role. Besides the oxidant diffusion and the change of , the mechanics is an important part of the mathematical formulation.

- 3.1 The Diffuse Interface Concept
- 3.2 Mathematical Formulation
- 3.2.1 Oxidant Diffusion
- 3.2.2 Dynamics of
- 3.2.3 Volume Expansion of the New Oxide
- 3.2.4 Diffusion Coefficient and Reaction Layer
- 3.2.5 Mechanics

- 3.3 Model Overview

Ch. Hollauer: Modeling of Thermal Oxidation and Stress Effects