Microscopic study of electrical transport through individual molecules with metallic contacts. I. Band lineup, voltage drop, and high-field transport

We present the first in a series of microscopic studies of electrical transport through individual molecules with metallic contacts. We view the molecules as “heterostructures” composed of chemically well-defined atomic groups, and analyze the device characteristics in terms of the charge and potential response of these atomic groups to the perturbation induced by the metal-molecule coupling and the applied bias voltage, which are modeled using a first-principles based self-consistent matrix Green’s function (SCMGF) method. As the first example, we examine the devices formed by attaching two benzene-based molecular radicals—phenyl dithiol (PDT) and biphenyl dithiol (BPD)—symmetrically onto two semi-infinite gold electrodes through the end sulfur atoms. We find that both molecules acquire a fractional number of electrons with similar magnitude and spatial distribution upon contact with the electrodes. The charge transfer creates a potential barrier at the metal-molecule interface that modifies significantly the frontier molecular states depending on the corresponding electron density distribution. For both molecules, the metal Fermi level is found to lie closer to the highest-occupied-molecular-orbital (HOMO) than to the lowest-unoccupied-molecular-orbital (LUMO). Transmission in the HOMO-LUMO gap for both molecules is due to the metal-induced gap states arising from the hybridization of the metal surface states with the occupied molecular states. Applying a finite bias voltage leads to only minor net charge injection due to the symmetric device structure assumed in this work. But as current flows, the electrons within the molecular junction redistribute substantially, with resistivity dipoles developing in the vicinity of potential barriers. Only the delocalized $\pi$ electrons in the benzene ring can effectively screen the applied electric field. For the PDT molecule, the majority of the bias voltage drops at the metal-molecule interface. But for the BPD molecule, a significant amount of the voltage also drops in the molecule core. The field-induced modification of the molecular states (the static Stark effect) becomes significant as the bias voltage increases beyond the linear-transport region. A bias-induced reduction of the HOMO-LUMO gap is observed for both molecules at large bias. The Stark effect is found to be stronger for the BPD molecule than the PDT molecule despite the longer length of the former. For both molecules, the peaks in the conductance are due to electron transmission through the occupied rather than the unoccupied molecular states. The calculation is done at room temperature, and we find that the thermionic-emission contribution to the current-voltage characteristics of both molecules is negligible.