Physical Effects/Overview of Mechanism:
In many problems, more than two materials are involved, for example, in the so-called scum problem. As an example. we imagine an initial block, in which a mask covers a substrate, and envision a simultaneous etch and deposition process. We imagine that one material (which will be shown as light gray)is isotropically deposited on both the mask (shown in dark gray) and substrate (shown in black). At the same time that this material is being deposited, it is being etched under an ion-milling/sputter law, such that the etch rate in the substrate is twice as fast as the etch rate in the mask.
The net effect is the development of a thin sidewall deposition layer; on the more horizontal faces, the ion-milling component overpowers the deposition term, and the total effect produces etching.
Level Set Formulation:
A level set formulation of this problem is straightforward, and involves evolving triple points. No special treatment is required of these points; we also note that subgrid resolution occurs.
Results and Sample Simulations:
We show the sequence of profile evolution under these effects. We note the development of the thin nano-layer which covers the side walls, but is fully etched away along the top and the bottom; we also note the existence of evolving triple points. We also note that the ion-milling sputter etching speed law promotes faceting, as expected. We stress that the grid used for this calculation is significantly larger than the size of the nano-layer; thus our algorithms provide for significant sub-grid resolution without resorting to adaptive mesh technology.
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