Stress development during growth of oxide films

Abstract

The generation of stresses in polycrystalline oxide films formed via the oxidation of a substrate is analyzed 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 considered 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. A homogenized strain one-dimensional treatment captures the correct signs of stresses and through-thickness stress gradients observed in experiments. Numerical solution of the two-dimensional problem reveals 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. The grain boundary diffusivity has a significant effect on the stress gradients, with larger diffusivities leading to smaller stress gradients. The predictions compare favorably with experiment.