A LEVEL SET APPROACH TO A UNIFIED MODEL FOR ETCHING, DEPOSITION, AND LITHOGRAPHY .1. ALGORITHMS AND 2-DIMENSIONAL SIMULATIONS

We apply a level set formulation to the problem of surface advancement in a two-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 a nd cusp development, a nd 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. The development of this model and algorithm naturally extends to three dimensions in a straightforward manner and is described in part II of this paper (in press). (C) 1995 Academic Press, Inc.