Transition voltage spectroscopy in vacuum break junction: The standard tunneling barrier model and beyond

Abstract

Recent experiments on transition voltage (V t ) spectroscopy in mechanically controllable vacuum break junctions have been interpreted theoretically by using a Simmons WKBtype approach of the transport by tunneling based on the standard vacuum barrier picture (work function þ source-drain bias þ charge images). In the first part of the paper, we present an analysis demonstrating the inconsistencies of that approach. Then, we report detailed results obtained by exactly solving the Schrödinger equation, which show that the standard tunneling barrier model fails to describe the experimental vacuum transition voltage spectroscopy (TVS) data. This indicates that the physical description within that model is incomplete. In the attempt to go beyond the standard barrier model, we report results demonstrating that the inclusion of electron states at the electrodes' surface significantly improves the agreement with experiment. This applies both to the d-dependence of V t and to the jump in the linear conductance when approaching the atomic contact limit.

A quantum chemical study from a molecular transport perspective: ionization and electron attachment energies for species often used to fabricate single-molecule junctions

“…13 has recently drawn attention, is to what extent is it legitimate to approximate a real molecular orbital as a point charge. Within classical electrostatics, the interaction energy of an electron located at z with the image charges created in two infinite planar electrodes can be exactly expressed by 56,57 …”

Concurrent conductance and transition voltage spectroscopy study of scanning tunneling microscopy vacuum junctions. Does it unravel new physics?

“…ν-values are given in the legend. Image charge effects are included using the exact classical interaction 10,11,15 , which is cutoff close to electrodes using the procedure described elsewhere 17 . 3,20 .…”

“…For two planar electrodes, the exact expression of φ im 8 can be used to numerically find the exact transmission coefficient 10,11 .…”

“…So, a ghost current may be at the ori- . Image charge effects are included using the exact classical interaction 10,11,15 , which is cutoff close to electrodes using the procedure described elsewhere 17 . gin of both Ohmic conductances saturating at larger d's and transition voltages that decrease with 1/d. We have checked that this trend is not affected if the realistic effects discussed in the preceding subsection and the ESI † are included in calculations.…”

Modified Superexchange Model for Electron Tunneling Across the Terminated Molecular Wire

“…The Simmons's model works well in analyzing the characteristics in metal–dielectric–metal systems, but difficulties arise upon its application to the molecular wires. The problem is the choice of physically validated parameters, especially the barrier height and the effective tunneling mass m * . The model of superexchange tunneling across the molecular wire provides an alternative approach and uses the parameters, such as couplings and energy gaps, that are more appropriate for description of the electron‐transfer processes in molecular junctions.…”