Conductance of a STM contact on the surface of a thin film
  The conductance of a contact, having a radius smaller than the Fermi wave length, on the surface of a thin metal film is investigated theoretically. It is shown that quantization of the electron energy spectrum in the film leads to a step-like dependence of differential conductance G(V) as a function of applied bias eV. The distance between neighboring steps in eV equals the energy level spacing due to size quantization. We demonstrate that a study of G(V) for both signs of the voltage maps the spectrum of energy levels above and below Fermi surface in scanning tunneling experiments. 
N. V. Khotkevych, Yu. A. Kolesnichenko and J. M. van Ruitenbeek
cond-mat.mes-hall