An Asymptotic Analysis for A Model of Chemical Vapor Deposition on A Microstructured Surface

We consider a model for chemical vapor deposition, the process of adsorption of gas onto a surface together with the associated deposition of a chemical reactant on the surface. The surface has a microscopic structure which, in the context of semiconductor manufacturing, arises from a preprocessing of the semiconductor wafer. Using singular perturbation analysis, a boundary condition for the corresponding diffusion equation is derived, which allows for the replacement of the microstructured surface by a flat boundary. The asymptotic analysis is numerically verified with a simple test example.