3.2.2 Separating Material Interfaces

Some interactions between different materials during the oxidation process may not be described using the suggested LS labeling from Figure 1.2. An example is the movement of the $\Phi _{up}$ surface with a mask present. Instead, materials must be labeled separately and fully enclosed within their own volume, as shown in Figure 3.4.

Figure 3.4: Geometry of a mask and its LS labeling when the mask is used for a material growth or deposition process.

$\includegraphics[width=0.481\linewidth]{chapter_oxidation_modeling/figures/LS_labels_vol.eps}$	$\includegraphics[width=0.481\linewidth]{chapter_oxidation_modeling/figures/LS_labels.eps}$
(a) Material regions and their	(b) Level Set representation

This allows for interactions between different surfaces which do not necessarily result in those surfaces joining, but rather being completely separate entities. Such an event is shown in Figure 3.5, where the system from Figure 3.3 undergoes simultaneous growth at a velocity of 0.75 at the top surface and -0.25 at the bottom surface.

Figure 3.5: The initial and final geometry after surface evolution of $\Phi _{down}$ downward and $\Phi _{up}$ upward at rates of -0.25 and 0.75, respectively.

$\includegraphics[width=0.481\linewidth]{chapter_oxidation_modeling/figures/masked_initial.eps}$	$\includegraphics[width=0.481\linewidth]{chapter_oxidation_modeling/figures/masked_final.eps}$
(a) Initial interfaces	(b) Final interfaces

L. Filipovic: Topography Simulation of Novel Processing Techniques