Charge transport in molecular junctions: From tunneling to hopping with the probe technique

We demonstrate that a simple phenomenological approach can be used to simulate electronic conduction in molecular wires under thermal effects induced by the surrounding environment. This “Landauer-Büttiker’s probe technique” can properly replicate different transport mechanisms, phase coherent nonresonant tunneling, ballistic behavior, and hopping conduction. Specifically, our simulations with the probe method recover the following central characteristics of charge transfer in molecular wires: (i) the electrical conductance of short wires falls off exponentially with molecular length, a manifestation of the tunneling (superexchange) mechanism. Hopping dynamics overtakes superexchange in long wires demonstrating an ohmic-like behavior. (ii) In off-resonance situations, weak dephasing effects facilitate charge transfer, but under large dephasing, the electrical conductance is suppressed. (iii) At high enough temperatures, k_BT/ϵ_B > 1/25, with ϵ_B as the molecular-barrier height, the current is enhanced by a thermal activation (Arrhenius) factor. However, this enhancement takes place for both coherent and incoherent electrons and it does not readily indicate on the underlying mechanism. (iv) At finite-bias, dephasing effects may impede conduction in resonant situations. We further show that memory (non-Markovian) effects can be implemented within the Landauer-Büttiker’s probe technique to model the interaction of electrons with a structured environment. Finally, we examine experimental results of electron transfer in conjugated molecular wires and show that our computational approach can reasonably reproduce reported values to provide mechanistic information.