A Level Set Approach to a Unified Model for Etching, Deposition, and Lithography

Abstract

Previously, Adalsteinsson and Sethian 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 presented the basic equations and algorithms for two dimensional simulations, including the effects of isotropic and uni-directional deposition and etching, visibility, reflection, and material dependent etch/deposition rates. Part II focused on the extension to three dimensions. This paper completes the series, and add the effects of redeposition, reemission, and surface diffusion. This requires the solution of the transport equations for arbitrary geometries, and leads to simulations that contain multiple simultaneous competing effects of visibility, directional and source flux functions, complex sputter yield flux functions, wide ranges of sticking coefficients for the reemission and redeposition functions, multilayered fronts and thin film layers.