Thin Layers and Triple Points
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
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,
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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