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 functions.

Return to Main Outline Page