Model of resonant quantum tunneling through isolated molecules

Abstract

A model is described for the resonant-tunneling current between two metal electrodes with an isolated molecule situated between them. The most significant parameters governing this process are the couplings between the electrode and molecular electronic states. The calculation of these couplings using the full atomic-scale treatment of the molecular system, and extended to include the proximal surface atoms of the metal electrode, becomes computationally prohibitive for most systems. However, for a weakly coupled system, the eigenstates of the molecule and electrodes can be considered separable, and the isolated molecule can be analyzed independently from the tunneling dynamics. Following the formalism originally developed by Oppenheimer to analyze field ionization of atoms and extended by Bardeen to general tunneling phenomena, an integral expression is written down for the explicit determination of the electrode-molecule coupling, using as an input the independently computed molecular wave functions. These couplings can then be used as inputs to a rate-equation treatment of the electronic transport between the electrodes and through the intermediate molecule. This treatment is then applied to a simple idealized system consisting of an isolated hydrogen atom situated between two metal electrodes. The current, differential conductivity, and level occupation probabilities are computed, plotted, and discussed. An interesting bias dependence of the tunneling current is observed and discussed.