3D etching profile evolution simulation using sparse field level set method

Abstract

Level set method, introduced by Osher and Sethian [1], is a highly robust and accurate computational technique for tracking of moving interfaces in etching, deposition and photolithography processes. It originates from the idea to view the moving front as a particular level set of a higher dimensional function, so the topological merging and breaking, sharp gradients and cusps can form naturally, and the effects of curvature can be easily incorporated. The corresponding equations of motion for the propagating surfaces, which resemble Hamilton-Jacobi equations with parabolic right-hand sides, can be solved using methods for solving hyperbolic conservation laws, ensuring in that the way correct entropy-satisfying solution [2]. In this paper we describe an application of the sparse field method for solving level set equations in 3D plasma etching simulations. Sparse field method itself, developed by Whitaker [3] and broadly used in image processing community, is an alternative to the usual combination of narrow band and fast marching procedures for the computationally effective solving of level set equations. The obtained results for convex and non-convex Hamiltonians show correct behavior of etching profiles in simple model cases.