A mathematical model was developed for ionic conduction in amorphous oxide films. The model was based upon a hypothetical defect-cluster mechanism according to which metal and O ions were both involved in transport. The defect clusters were created by the inward displacement of O ions, around an O vacancy-like defect, due to the electric field of the vacancy. Metal ions were assumed to migrate easily within the gap between the first and second layers of O ions around the vacancy. The model took account of the polarization of the conductive gap in the applied electric field, the exchange of mobile metal ions in the cluster with stationary metal ions in the surrounding oxide, and a space charge which was generated in the films by clusters and oxide non-stoichiometry. The rate-limiting step was jumping of the O vacancy in the cluster. It was found that polarization of the cluster led to a stoichiometric excess of metal ions in the cluster, and that this excess produced a net transport of metal ions due to the motion of the cluster. The metal-ion transport number increased with the electric field and depended upon the dielectric constant and cluster size. The field dependence agreed with that which was found experimentally. The calculated transport numbers were in quantitative agreement with experimental data for Ta, Nb and W oxides, but were smaller than the experimental values for Al oxide. The field coefficient in the high-field conduction-rate expression was predicted, and agreed with experimental data to within 10%.

Metal and Oxygen Ion Transport during Ionic Conduction in Amorphous Anodic Oxide Films. M.H.Wang, K.R.Hebert: Journal of the Electrochemical Society, 1999, 146[10], 3741-9