A LEVEL SET APPROACH TO A UNIFIED MODEL FOR ETCHING, DEPOSITION, AND LITHOGRAPHY .2. 3-DIMENSIONAL SIMULATIONS

We apply a level set formulation to the problem of surface advancement in three-dimensional topography simulation of deposition, etching, an d lithography processes in integrated circuit fabrication. The level s et formulation is based on solving a Hamilton-Jacobi-type equation for a propagating level set function, using techniques borrowed from hype rbolic conservation laws. Topological changes, corner and cusp develop ment, and accurate determination of geometric properties such as curva ture and normal direction are naturally obtained in this setting. The equations of motion of a unified model, including the effects of isotr opic and unidirectional deposition and etching, visibility, surface di ffusion, reflection, and material dependent etch/deposition rates are presented and adapted to a level set formulation. In Part I of this pa per, the basic equations and algorithms for two-dimensional simulation s 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 lithog raphic 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. (C) 1995 Academic Press, Inc.