Metal oxidation kinetics and the transition from thin to thick films

Abstract

We report an investigation of growth kinetics and transition from thin to thick films during metal oxidation. In the thin film limit (<20 nm), Cabrera and Mott's theory is usually adopted by explicitly considering ionic drift through the oxide in response to electric fields, where the growth kinetics follow an inverse logarithmic law log(dl/dt) ∝ 1/l. It is generally accepted that Wagner's theory, involving self-diffusion, is valid only in the limit of thick film regime (>1 μm) and leads to parabolic growth kinetics dl/dt ∝ 1/l, where l is the oxide film thickness. Theory presented here unifies the two models and provides a complete description of oxidation including the transition from thin to thick film. The range of validity of Cabrera and Mott's theory and Wagner's theory can be well defined in terms of the Debye–Hückel screening length. The transition from drift-dominated ionic transport for thin film to diffusion-dominated transport for thick film is found to strictly follow the direct logarithmic law log(dl/dt) ∝ −l that is frequently observed in many experiments.