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We study inelastic electron tunneling through a molecular junction using the nonequilibrium Green's function 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 Phi when plotted against Phi. Signatures of resonant tunneling driven by an intermediate molecular ion appear as peaks in the first derivative dI/dPhi 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.
Galperin et al. (Tue,) studied this question.