A Level Set Approach to a Unified Model for Etching, Deposition,
and Lithography, II: Three-dimensional Simulations
D. Adalsteinsson and J.A. Sethian
Journal Computational Physics, Vol. 122, No. 2, pp. 348-366, 1995.
We apply a level set formulation to the problem of surface advancement
in 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. The equations of motion of a unified
model, including the effects of isotropic and unidirectional deposition
and etching, visibility, surface diffusion, reflection, and material
dependent etch/deposition rates are presented and adapted to a level set
Part I of this paper, the
basic equations and algorithms
for two dimensional simulations were developed. In this paper, the
extension to three dimensions is presented. We show a large collection
of simulations, including three-dimensional etching and deposition into
cavities under the effects of visibility, directional and source flux
functions, evolution of lithographic profiles, discontinuous etch rates
through multiple materials, and non-convex sputter yield flux functions.
Part III of this paper,
effects of reflection, re-emission,
surface diffusion, and multiple materials will be presented.
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