Inelastic electron tunneling spectroscopy in molecular junctions: Peaks   and dips
  We study inelastic electron tunneling through a molecular junction using the non-equilibrium Green function (NEGF) formalism. The effect of the mutual influence between the phonon and the electron subsystems on the electron tunneling process is considered within a general self-consistent scheme. Results of this calculation are compared to those obtained from the simpler Born approximation and the simplest perturbation theory approaches, and some shortcomings of the latter are pointed out. The self-consistent calculation allows also for evaluating other related quantities such as the power loss during electron conduction. Regarding the inelastic spectrum, two types of inelastic contributions are discussed. Features associated with real and virtual energy transfer to phonons are usually observed in the second derivative of the current I with respect to the voltage when plotted against the latter. Signatures of resonant tunneling driven by an intermediate molecular ion appear as peaks in the first derivative d(current)/d(voltage) and may show phonon sidebands. The dependence of the observed vibrationally induced lineshapes on the junction characteristics, and the linewidth associated with these features are also discussed. 
Michael Galperin, Mark A. Ratner, Abraham Nitzan