Etching: a two-dimensional mathematical approach

A mathematical model for the etching of a semi-infinite active surface is presented. The model assumes that the transport of the active species occurs solely by diffusion. It is shown that, when the diffusion field propagates much faster than the etched surface, the problem can be solved by a singular perturbation technique, which distinguishes a near field in the area where the moving surface and the non-etchable mask meet, and a far field where edge effects may be disregarded to first order. The leading terms of a composite expansion are given, from which the shape of the moving boundary can be determined at all times.