Protocol for disentangling the thermally activated contribution to the tunneling-assisted charge transport. Analytical results and experimental relevance†
In this paper we present results demonstrating that the charge transport by tunneling in molecular junctions can exhibit a substantial temperature dependence. We deduce an accurate analytical interpolation formula for the low bias conductance G enabling disentangling into a temperature independent contribution and a thermally activated contribution. The latter is found to have a temperature dependence more general than the ubiquitous Arrhenius form, which it recovers as a limiting case, and permits to extract the energy offset of the molecular orbital that dominates the charge transport. Importantly, the interpolation formula is general; it can be utilized for fitting experimental conductance data for any form of transmission (e.g., Lorentzian, Gaussian, generalized exponential or else). Furthermore, from the fitting parameters thus obtained, valuable information on the energy dependence of the transmission function can be gathered, which is hard to obtain from other methods. For illustration, available experimental transport data at variable temperature for molecular junctions are analyzed within the present theoretical framework. From a more general perspective, the results reported here are important because they attempt to give a constructive answer to the question of discriminating between the (single-step) tunneling and (two-step) hopping mechanisms based on the temperature dependence of the conductance. Namely, they suggest performing variable temperature G-measurements on nanojunctions fabricated by contacting a given molecular species to different electrodes and monitoring the metal dependence of the activation energy.