The indicated red lines are edges and corners, which are tracked and treated specially in our front tracking simulation.
Whether sharp features evolve sharply or round off is very much physics dependent.
Our group consists of J. Glimm, H. Kranzer, J. Pinezich, S. Simanca , D. Tan, F. Tangerman, and G. Vanderwoude. In collaboration with Dr. Satoshi Hamaguchi at the IBM Watson Research Center, we started last year with the development of a three dimensional process simulation code, which is focused on the evolution of three dimensional structures: edges and corners, and the formation of voids during the process.
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The initial geometry for many of our experiments is a rectangular
or square hole in the plane, shown here from on top. The indicated red lines are edges and corners, which are tracked and treated specially in our front tracking simulation. Whether sharp features evolve sharply or round off is very much physics dependent. |
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Shown is the rectangular hole, from below.
For this computation we assumed an isotropic deposition process where the efficiencies are angle independent. Examples are chemical etching processes or low pressure processes. As a result, the edges at the top of the hole round off, while the other remain sharp. In this image we show a comparison between a computation using a coarse and one using a fine (twice refined) grid. Shown are the edges and tracked curves (red) in the triangulation for the coarse mesh and the surface (without edges shown) for the fine mesh. They are only slightly different (i.e. much less than a coarse mesh spacing) near the rounded region, near the top of the hole. |
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Shown is the result from a `double well' efficiency etching simulation.
Such efficiencies can occur for crystalline materials where a specific
non orthogonal angle has maximum yield, the cutting angle.
Such an efficiency results
in a double well Hamiltonian. See examples.
The one-dimensional Riemann problems for are nontrivial in this case: The sharp curves around the top of the hole, bifurcate into what is referred to as beveling: two sharp curves, surrounding the hole, separated by a smooth surface. Since bifurcation is not yet automated in our code, we initialized this geometry as slightly bifurcated already, and track the result. |
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For the same `double well' efficiency we
show a side view of the etched hole.
We specifically show the initial hole, shown from below, without triangle edges as well as the etched hole, showing only the edges and curves, but not the surface. In this way it is possible to make a geometric comparison. A striking feature is the tapering at the bottom, correctly predicted through the solution of Riemann problems. |
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A Void!
Resputtering, i.e., the non sticking of the incoming material,
is one of the main mechanisms for the creation of undesigned
voids in a computer chip.
In many instances, the volume occupied by the
void is intended to be filled with a conducting material (wire).
Voids therefore contribute to overheating, and thus shorten
the chip's lifetime.
View From the Side:
In this simulation we prescribed a point source,
close to the chip's surface, with a efficiency at a point equal
to the cosine of the angle between normal and point-to-source.
The sticking probability is taken as 0.8.
Although a point source this close to the chip's surface is
somewhat unphysical its effect is quite similar to area source
whose particle beam widens with distance.
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View From the Bottom: |
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View From the Bottom at The Attachment Point: |
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