A shock-tracking algorithm for surface evolution under reactive-ion etching

A new algorithm that determines the evolution of a surface eroding under reactive-ion etching is presented. The surface motion is governed by both the Hamilton–Jacobi equation and the entropy condition for a given etch rate. The trajectories of ‘‘shocks’’ and ‘‘rarefaction waves’’ are then directly tracked, and thus this method may be regarded as a generalization of the method of characteristics. This allows slope discontinuities to be accurately calculated without artificial diffusion. The algorithm is compared with ‘‘geometric’’ surface evolution methods, such as the line-segment method.