Theory of vibrational mode intensities in inelastic electron tunneling spectroscopy

We use a transfer-Hamiltonian formalism to develop a theory for the intensity of vibrational modes in inelastic electron tunneling spectroscopy (IETS) of organic molecules in metal-insulator-metal junctions. The initial and final electron states are localized on opposite sides of the insulating barier and are described by Wentzel-Kramers-Brillouin (WKB) wave functions. The interaction potential between the tunneling electron and the vibrating molecule is a sum of Coulomb potentials; each element in the sum corresponding to a partial charge localized on an atom in the molecule. The theory predicts properly the magnitudes of the integrated intensities in IETS as well as the ratio of intensities for opposite bias voltages. It also predicts that Raman-active modes should be comparable in intensity to infrared modes, even neglecting bond polarizabilities, and that modes forbidden to optical spectroscopies may be observable in IETS. We further describe how the orientation of the doped molecules on the surface can be inferred from IETS intensities.