Analyzing Molecular Current-Voltage Characteristics with the Simmons Tunneling Model: Scaling and Linearization

Use of the Simmons model for analyzing tunneling transport across molecular junctions is reviewed, and its inherent limitations are examined, specifically for cases where there are no molecular length-dependent data (to extract a decay parameter), be it for experimental reasons or because of changes of the molecular energetics or packing with molecular length. The potential barrier across a molecular junction is shown to be strongly bias-dependent, much more so than is assumed in the commonly used version of the Simmons model. The means to distinguish true tunneling from conduction via pinholes (or hot spots) are also considered. Power expansion to the Simmons model shows that I/V vs V2 plots should be linear over that range, thus providing a simple and standardized parameter extraction. From such plots, we can extract values for the equilibrium conductance and for the "shape factor", a complementary parameter that describes the shape of the I−V relations. The applicability of these two parameters for describing actual transport is illustrated by analyzing data for three different types of molecular junctions. The linearity of the I/V vs V2 plots can be used to evaluate if, and if so, at which bias (and if at all) direct tunneling occurs and under which conditions this is not the case. The extracted equilibrium conductance and the "shape factor" provide an empirical method for quantifying electronic transport across practical molecular junctions where the exact packing of the molecules is rather uncertain. As such, the analysis can be used to weigh and classify the effect of chemical modifications to molecular junctions or compare contacting methods, so as to allow a deeper understanding of transport via molecular junctions.