Grain-boundary diffusion in thin films. II. Multiple grain boundaries and surface diffusion

Abstract

Diffusion in polycrystalline thin films is investigated using both analytical and numerical methods. Bulk, grain‐boundary, and interfacial diffusion are all included in the analysis, and the conditions under which each process influences the concentration profile are evaluated. The thin film is treated as a slab of finite thickness containing uniformly spaced grain boundaries that are perpendicular to the plane of the film. One surface of the slab is assumed to be in contact with an infinite reservoir of the diffusing species. Three limiting cases are considered in which the second surface is (i) a barrier to diffusion, (ii) a plane with an infinite surface diffusion coefficient, and (iii) a zero‐concentration surface.