Resonance-Tunneling Spectroscopy of Atoms Adsorbed on Metal Surfaces: Theory

Abstract

Using a perturbational approach, we consider the theory of resonance tunneling of field-emitted electrons through atoms adsorbed on metal surfaces, first treated by Duke and Alferieff. It is shown how one can proceed from the observed total energy distributions to information concerning the energy-level spectrum of the atom perturbed by the metal surface. The major alteration of the spectrum manifests itself in a shift and lifetime broadening of the atomic energy levels due to configuration interactions with the continuum of metal states. In past work, this shift and broadening have been theoretically calculated by various workers. Theories have also been advanced for calculating dipole moments and, consequently, work-function changes and binding energies in which the final expressions for these quantities require knowledge of the perturbed atomic energy-level scheme. The plan in the present paper is to present a method of analyzing the data obtained in resonance-tunneling spectroscopy so that values for the shift and broadening of the energy levels can be obtained. To proceed towards this end, a simplified model is treated in a mathematically systematic manner. We believe, however, that the present approach maintains sufficiently close contact with the physics of the processes involved and thus, because of its transparency, is a potentially more valuable tool than past theories. The first experimental data of resonance tunneling in field emission, obtained by Plummer and Young and reported on in the preceding paper, are analyzed within the context of the present theory. These data include tunneling through single Zr atoms in which a single brand ground-state level is seen, tunneling through Ba atoms in which both a broad ground state of $6s^2$ character and two narrow excited $6s5d$ states are seen, and tunneling through Ca in which a somewhat narrow $4s4p$ excited state is seen. Most aspects of the data are satisfactorily accounted for in the present theory, and the observed shifts and broadenings of the levels are in good agreement with past calculations.