Isotropic Deposition and Etching
Physical Effects/Overview of Mechanism:
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In isotropic etching/deposition, the speed function F of the
interface in its normal direction is independent of the orientation
of the interface. In this case, inward pointing sharp corners are
rounded when they etch inwards, and are outward pointing corners
remain sharp when etched (the opposite situation takes place under
deposition). This corresponds to the selection of the correct weak
solution to the equations of motion (see the discussion and
references in the recent book on
level set methods.
Level Set Methodology:
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The level set methodology advances the surface by solving the
appropriate initial value partial differential equation, using the
correct viscous limit of the Hamilton-Jacobi equation. Thus, the normal
is correctly defined as the weak limit in places where differentiability
is lost. In the case of isotropic etching and deposition, this means
that corners will be smoothly rounded (as expected) when the extrude into the
depositing material, and remain sharp selecting the correct singularity when
the point away from the deposition source.
Sample Simulations:
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A square contact hole is isotropically etched with a uniform etch
rate F=1; results show the expected rounding of corners at the bottom of
the well and the maintained top sharp corners.
Isotropic Etching into a well: (129K)
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