A SHOCK-TRACKING ALGORITHM FOR SURFACE EVOLUTION UNDER REACTIVE-ION ETCHING

A new algorithm that determines the evolution of a surface eroding und er reactive-ion etching is presented. The surface motion is governed b y both the Hamilton-Jacobi equation and the entropy condition for a gi ven 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 di scontinuities to be accurately calculated without artificial diffusion . The algorithm is compared with ''geometric'' surface evolution metho ds, such as the line-segment method.