The theory of inelastic electron tunneling spectroscopy (IETS) and motions of single adsorbed atoms and molecules on metal surfaces induced by vibrational excitation with a scanning tunneling microscope (STM) is reviewed. The theory of STM-IETS is described using the adsorbate-induced resonance model. Elementary processes of how an adsorbate overcomes the potential barrier along the reaction coordinate (RC) by inelastic tunneling current are described with a focus on direct excitation of the RC mode by coherent and incoherent vibrational ladder climbing and an indirect one through anharmonic coupling to a mode excited by tunneling electrons. Action spectroscopy of single molecule motions is also discussed. The latter allows a direct access to the vibrational density of states, which can not be otherwise observed in the STM-IETS because of a competition between the elastic and inelastic tunneling currents.
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