A Level Set Approach to a Unified Model for Etching, Deposition,
and Lithography, III: Re-Deposition and Re-Emission
D. Adalsteinsson and J.A. Sethian
Journal of Computational Physics, 138, 1, pp. 193-227, 1997.
In previous work, we have applied the level set formulation to the problem of
surface advancement in two and three-dimensional topography simulation of
deposition, etching, and lithography processes in integrated circuit
fabrication. The level set formulation is based on solving
a Hamilton-Jacobi type equation for a propagating level set function,
using techniques borrowed from hyperbolic conservation laws. Topological
changes, corner and cusp development, and accurate determination of
geometric properties such as curvature and normal direction are
naturally obtained in this setting.
Part I of this paper presented
the basic equations and algorithms
for two dimensional simulations, including the effects of
isotropic and unidirectional deposition
and etching, visibility, surface diffusion, reflection, and material
dependent etch/deposition rates.
Part II focussed on the
extension to three dimensions is presented.
This paper completes the series, and add the effects of
re-deposition, re-emission, and surface diffusion for fully three-dimensional
topographic simulations. This requires the solution of the transport
equations for arbitrary geometries, and leads to simulations that
contain simultaneous and multiple competing effects of
visibility, directional and source flux
functions, complex sputter yield flux functions, wide ranges of sticking
coefficients and various forms for the re-emission and re-deposition
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