A Level Set Approach to a Unified Model for Etching, Deposition, and Lithography II: Three-Dimensional Simulations
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Journal of Computational Physics 122 (2): 348--366 (December 1995)

We apply a level set formulation to the problem of surface advancement in three-dimensional topograhy 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 formulation. In 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. In Part III of this paper, effects of reflection and re-emission and surface diffusion will be presented.
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