J. Electroanal. Chem., 82 (1977) 65--80 65 © Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands A THEORY OF RESONANCE TUNNELLING AT FILM-COVERED METAL ELECTRODES * WOLFGANG SCHMICKLER Institut fiir Physikalische Chemie, Universith't Bonn, Wegelerstr. 12, 5300 Bonn (F.R.G.) (Received 31st January 1977) ABSTRACT Localized electronic states in the band gap of an oxide film deposited on a metal electrode can serve as intermediate states in electrochemical redox reactions. A theory of this process is presented which is based on the Franck-Condon approximation and second order perturba- tion theory with respect to the electronic matrix element. It is shown that states near the cen- tre of the barrier give the dominant contribution to the current. Calculated Tafel plots are markedly different from those for the direct tunnelling process: depending on the position of the impurity states one of the branches shows a downward bending at low overpotentials; at higher overpotentials straight, or almost straight, Tafel lines are obtained. Transfer coefficients in these regions are small, the cathodic coefficient being greater than the anodic, and their sum is tess than one. Depending on the barrier parameters and the position of the intermediate states, resonance tunnelling is estimated to be up to 102 times more effective than direct tun- nelling. (I) INTRODUCTION Resonance tunnelling via electronic states localized within a tunnelling barrier is a well-known phenomenon from field emission studies [1--4] and from elec- tron tunnelling through metal--insulator--metal junctions [ 5,6] and Schottky- barriers [7]. In the former process adsorbed atomic states with energies above the Fermi-level of the emitter can serve as virtual intermediate states giving rise to a considerable enhancement of the field emission current. An analysis of the resulting field emission energy distribution provides valuable information about the nature of the electronic levels of the adsorbate. Similarly trapping centres in Schottky-barriers or in metal--insulator--metal junctions can provide a resonance channel for electron tunnelling. This shows up as characteristic spikes in plots of the derivative of the total conductance vs. voltage and again information about the trapping centres can be inferred. As discussed in a previous paper [8], there is a considerable similarity between metal--insulator--metal junctions and metal-insulator-redox electrolyte systems. In the latter the insulator consists usually of an electrochemically generated oxide layer. Schultze, Vetter et al. [9] have studied redox reactions at metal electrodes covered by such thin oxide films, and interpreted their data in terms of direct elastic tunnelling. While their early work, which was restricted to oxide In honour of the 60th birthday of Benjamin G. Levich.