Theory of vibrational tunneling spectroscopy of adsorbates on metal surfaces

A theoretical model for studying elementary processes in vibrational scanning tunneling microscopy/spectroscopy is presented. General formulae for the elastic and inelastic tunneling currents are derived on the basis of the Anderson Hamiltonian coupled to a vibrational degree of freedom. Our treatment includes the vibrational damping due to electron–hole pair excitations. It is found that the non-equilibrium situation plays a crucial role for opening of the inelastic channel and excitations of adsorbate phonons. Elementary processes for both elastic and inelastic tunneling currents are clarified in a qualitative manner. The distribution function of adsorbate phonons is derived and may be of great importance for the understanding of the recently observed current-induced dynamical motions of adsorbates.