In-depth concentration profile equation for cations in thin oxide film under the inverse logarithmic growth law of low-temperature oxidation

Abstract

The inverse logarithmic growth law of initial oxidation has been derived by Cabrera-Mott under the conditions that cation concentration is constant and growth rate is limited by the diffusion of metal ion under a strong electric field. Mott theory has been developed by Fromhold's numerical flux equation and Dignam's analytical ion current equation. In this paper, we derive the inverse logarithmic law from Dignam's flux equation for cations. Then an in-depth concentration profile equation of mobile ion defects can be obtained by using the experimental result for inverse logarithmic growth rate, i.e. an intercept of a coordinate time axis and a gradient. We apply the equation to the low-temperature oxidation experimental results of Al (aluminum). Numerical calculations of the derived approximate equation as applied to initial oxidation of Al are presented for various conditions. The results obtained by calculation are as follows. 1. The concentration of mobile cation defects at the surface of oxide/gas depends strongly on the potential barrier, U, and changes greatly with an increase in the electric field, E. 2. The change of the concentration in the vicinity of metal/oxide interface decreases with increasing E.