Modulation of collective electronic effects in foils by the electron scanning tunneling microscope

In a recent paper the coupling of an STM probe tip to a hyperboloidal foil was examined with regard to the effect upon the foil's surface plasmon dispersion relation. The probe tip and foil were modeled in prolate spheroidal coordinates so as to provide a geometry appropriate to the STM, the probe tip being modeled as a hyperboloid of revolution. A similar model is presented here, but the case of a Cartesian foil is shown to be amenable to the calculations by use of transformation of solution of Laplace's equation. Due to the small distances involved, nonretarded electrodynamics is utilized, and since the main interest experimentally is in the spectrum of emitted photons, only a local dielectric function is used for the materials considered. The appropriate solutions to Laplace's equation and the transformation of the solutions are given in Section 2. In Section 3 the surface plasmon dispersion relation is given for the case of a prolate hyperboloidal STM probe tip near a thin flat metal foil on a dielectric substrate. Section 4 gives a discussion of the results. (orig.)