  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.
