Important issues facing model-based approaches to tunneling transport in molecular junctions†
Extensive studies on thin films indicated a generic cubic current–voltage I–V dependence as a salient feature of charge transport by tunneling. A quick glance at I–V data for molecular junctions suggests a qualitatively similar behavior. This would render model-based studies almost irrelevant, since, whatever the model, its parameters can always be adjusted to fit symmetric (asymmetric) I–V curves characterized by two (three) expansion coefficients. Here, we systematically examine popular models based on tunneling barriers or tight-binding pictures and demonstrate that, for a quantitative description at biases of interest (V slightly higher than the transition voltage Vt), cubic expansions do not suffice. A detailed collection of analytical formulae as well as their conditions of applicability is presented to facilitate experimentalist colleagues to process and interpret their experimental data obtained by measuring currents in molecular junctions. We discuss in detail the limits of applicability of the various models and emphasize that uncritically adjusting the model parameters to experiment may be unjustified because the values deduced in this way may fall in ranges rendering a specific model invalid or incompatible to ab initio estimates. We exemplify with the benchmark case of oligophenylene-based junctions, for which the results of ab initio quantum chemical calculations are also reported. As a specific issue, we address the impact of the spatial potential profile and show that it is not notable up to biases V ≳ Vt, unlike at higher biases, where it may be responsible for negative differential resistance effects.