Tunneling at the Oxide-Covered Electrode

The rate of electron transfer from the electrolyte to an electronic level in the metal with an energy E (with respect to the Fermi level) can be expressed in the form 

The matrix element for an electronic transition from a state e) in the redox electrolyte via a localized impurity state r) in the film to a state m) in the metal is according to second-order perturbation theory  

Inserting Eq. (90) into Eq. (89) gives for the anodic resonance current due to the impurity state r) 

For reasonably thick barriers (a 10 A), the width of the Lorentzian distribu-tion of resonance state is smaller than the range over which the other factors 

the following expression for the anodic current density can be obtained after integration  

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