Stress distributions in growing polycrystalline oxide films

Abstract

We analyze the generation of stresses in polycrystalline oxide films formed via the oxidation of a substrate using a new continuum model. The model includes a description of the polycrystalline microstructure in two dimensions. The diffusion of all independent components, the rate of the oxidation reaction and the effect of stresses on these are accounted for in a thermodynamically self-consistent manner. Grain boundaries serve both as high diffusivity paths and as sites for oxide formation. Different diffusion controlled oxidation regimes (rapid oxygen/cation diffusion, comparable oxygen/cation diffusivities) and different grain boundary/bulk diffusivity ratios are examined within this framework. Numerical solutions reveal large lateral stress gradients, with stresses concentrated around the grain boundaries. While the average in-plane stress is compressive and the stress at the film/substrate interface near the grain boundary highly so, large tensile stresses are observed near the grain boundary at the film surface. These predictions are consistent with experimental observations on polycrystalline oxide growth. We also present analytical approximations for the stress distribution in the film that capture the essential features of the numerical results.