Stress distributions in growing oxide films

We present a new continuum model for the growth of an oxide film that examines the generation of self-stresses. The model self-consistently accounts for the thermodynamics and kinetics of the evolution of film thickness, diffusion of all components, oxidation reaction rates and the effects of stresses on these. Numerical solution of the models shows that large compressive stresses and significant stress gradients can be developed across the oxide layer. The signs of the stress and stress gradients are consistent with experimental observations. Following an initial transient, the concentration profiles and stresses settle into a steady-state, in which the concentration profiles and stresses are independent of the relative magnitudes of the oxygen and cation diffusivities. We have developed an approximate, analytical solution for the composition and stress that accurately matches the steady-state results obtained numerically.