Contribution to a theory of vibrational scanning tunneling spectroscopy of adsorbates: Nonequilibrium Greenʹs function approach

Formal theory of a phonon-assisted tunneling between a metal surface with an adsorbate and a metal scanning tip through an adsorbate (i.e., vibrational scanning tunneling spectroscopy (STS)) has been presented on the basis of the self-consistent nonequilibrium Keldyshʹs diagram technique. Within this approach, it is possible to take into account a finite lifetime of vibrational excitation, and the balance between elastic and opening inelastic tunneling channels. The relaxation of the vibrational degrees of freedom is included into the phonon Keldysh–Green function and plays a very important role both in the elastic and the inelastic tunneling through the adsorbate. The tunnel current (the total as well as the inelastic one) is calculated in terms of the one-particle nondiagonal substrate–adsorbate Keldysh–Greenʹs function supplemented with the vibrational lifetime and filling factors of adsorbate orbital and phonons. The general expression of the inelastic tunnel current and conductance via the excitation of phonons is also presented in terms of the phonon occupation number and the phonon damping function in the stationary condition.