Isotropic Deposition and Etching

Physical Effects/Overview of Mechanism:

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:

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:

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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