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3.1 The Diffuse Interface Concept


The diffuse interface concept avoids a moving interface problem, because there is not a sharp interface between silicon and SiO$ _2$ in contrast to the standard models [64,65]. Because of the missing sharp interface there different segments for silicon and SiO$ _2$ do not exist. In order to determine where is silicon and where is SiO$ _2$, a parameter named normalized silicon is defined [66]

$\displaystyle \eta(\vec{x},t) = \frac{C_{Si}(\vec{x},t)}{C_{0,Si}}.$ (3.1)

Here $ C_{Si}(\vec{x},t)$ is the silicon concentration at time t and point $ \vec{x} \mathrm{(x, y, z)}$ and $ C_{0,Si}$ is the concentration in pure silicon. $ \eta $ is 1 in pure silicon and 0 in pure silicon dioxide.

Instead of a sharp interface there is a so-called reaction layer where the diffusion of oxidants, the chemical reaction, and the volume increase occur simultaneously. This reaction layer has a spatial finite width (see Fig. 3.1), where the values of $ \eta $ lie between 0 and 1 [66]. The $ \eta $ curve always starts with 0 near silicon and ends at 1 near oxide, as shown in Fig. 3.2. The shape of this curve is given by the calculated $ \eta $ distribution in the reaction layer, which depends on the parameters in the model.



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Next: 3.2 Mathematical Formulation Up: 3. Advanced Oxidation Model Previous: 3. Advanced Oxidation Model

Ch. Hollauer: Modeling of Thermal Oxidation and Stress Effects