Sparse field level set method for non-convex Hamiltonians in 3D plasma etching profile simulations

Level set method [S. Osher, J. Sethian, J. Comput. Phys. 79 (1988) 12] is a highly robust and accurate computational technique for tracking moving interfaces in various application domains. 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 resulting equations, describing interface surface evolution, are of Hamilton–Jacobi type and they are solved using techniques developed for hyperbolic equations. In this paper we describe an extension of the sparse field method for solving level set equations in the case of non-convex Hamiltonians, which are common in the simulations of the profile surface evolution during plasma etching and deposition processes. Sparse field method itself, developed by Whitaker [R. Whitaker, Internat. J. Comput. Vision 29 (3) (1998) 203] 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 developed procedure is applied to the simulations of 3D feature profile surface evolution during plasma etching process, that include the effects of ion enhanced chemical etching and physical sputtering, which are the primary causes of the Hamiltonian non-convexity.