Image effects in transport at metal-molecule interfaces

Abstract

We present a method for incorporating image-charge effects into the description of charge transport through molecular devices. A simple model allows us to calculate the adjustment of the transport levels, due to the polarization of the electrodes as charge is added to and removed from the molecule. For this, we use the charge distributions of the molecule between two metal electrodes in several charge states, rather than in gas phase, as obtained from a density-functional theory-based transport code. This enables us to efficiently model level shifts and gap renormalization caused by image-charge effects, which are essential for understanding molecular transport experiments. We apply the method to benzene di-amine molecules and compare our results with the standard approach based on gas phase charges. Finally, we give a detailed account of the application of our approach to porphyrin-derivative devices recently studied experimentally by Perrin et al. [Nat. Nanotechnol. 8, 282 (2013)], which demonstrates the importance of accounting for image-charge effects when modeling transport through molecular junctions.

Transport gap renormalization at a metal-molecule interface using DFT-NEGF and spin unrestricted calculations

“…The gate is applied to the orbitals of the electrons of the molecule (see the supplementary material of Ref. 17) and we obtain the electronic configuration of the system after the self-consistent procedure within the DFT-NEGF framework.…”

“…The charge excess in the molecule is calculated with respect to the neutral state of the isolated molecule. 17 In the first two regimes, as the partial charge transfer at zero gate is very small, the molecule is expected to be neutral. This simplifies the process to determine the IP and EA.…”

“…[11][12][13][14] The reduction of the IP and EA of the molecule is mainly due to the Coulomb interaction between the added charge on the molecule and the screening electrons in the leads. This feature, called the imagecharge effect, 4,5,[15][16][17] becomes more relevant as the molecule gets closer to the metallic surface.…”

“…In the weak coupling regime, other methods like constrained density functional theory (CDFT) and density functional theory together with non-equilibrium Green's function (DFT-NEGF) technique have been implemented to analyze the level alignment at the interfaces. 17,[31][32][33] In the work presented by Souza et al, 31 CDFT is used to determine the charge-transfer energy of a molecule physisorbed on a metallic surface. This method gives quantitatively accurate results at small molecule-metal separations; however, in order to obtain quantitatively converged results, large metal cluster sizes are needed for large distances, and metal atoms with a few valence electrons must be used in order to keep the calculations manageable.…”

“…Using classical electrodynamics, it is possible to predict the level shifts close to a metallic surface. 4,5,[15][16][17] In a previous paper, we calculated the energy level adjustment of a molecule in the junction caused by image-charge effects using classical electrostatics. 17 Atomic charges for the molecule in the junction (from a NEGF-DFT calculation) rather than in the gas phase were used for the image-charge calculation.…”