Fundamental Theory of the Growth of Thick Oxide Films on Metals

Abstract

A theoretical development is presented for the growth kinetics of thick oxide films on metals. Transport of ions and electrons through the oxide layer is considered to occur by diffusion in the presence of space-charge and surface-charge fields, with local space-charge neutrality being a good approximation in the oxide interior remote from the interfaces. The kinetics are predicted to be parabolic, namely L(t)∝t^1⁄2, where L(t) is the oxide film thickness at time t; the corresponding built-in voltage across the oxide is predicted to have a thickness-independent value. The derived expressions relate the parabolic rate constant, the built-in electric field, and the electrostatic potential to the mobilities of the diffusing ions and electrons and to the fixed excess concentrations of these species established near the two interfaces of the oxide layer which are in contact with the parent metal and the gaseous oxygen.