Model for the Steady-State Growth of Porous Anodic Alumina Films

Abstract

Simulations were developed for the distributions of electrical potential and incorporated anions in porous anodic alumina (PAA) films during steady-state growth. Predictions of a model for the potential distribution based on Laplace's equation were compared to those of the current continuity equation in conjunction with high-field conduction. It was found that Laplace's equation, which has been used previously in PAA models, resulted in strong violations of charge conservation, when the current density was evaluated using the high field conduction equation. Interface motion predicted by the current continuity equation was nearly uniform except near convex ridges on the metal-film interface. This model was extended to predict the distribution of anions in the film, since incorporated anions may provide suppression of conduction near the ridge. The spatial distribution of acid anions predicted by the model agreed with experimental observations. Simulations were developed for the distributions of electrical potential and incorporated anions in porous anodic alumina (PAA) films during steady-state growth. Predictions of a model for the potential distribution based on Laplace's equation were compared to those of the current continuity equation in conjunction with high-field conduction. It was found that Laplace's equation, which has been used previously in PAA models, resulted in strong violations of charge conservation, when the current density was evaluated using the high field conduction equation. Interface motion predicted by the current continuity equation was nearly uniform except near convex ridges on the metal-film interface. This model was extended to predict the distribution of anions in the film, since incorporated anions may provide suppression of conduction near the ridge. The spatial distribution of acid anions predicted by the model agreed with experimental observations.