Physics Department, University of Wisconsin, Madison, WI, USA (1999)
In the simplest approximation one can neglect the effect of a finite temperature and consider sharp step functions instead of the Fermi function f(E) for metallic density of states. The tunneling probability through the insulator T_{ins} is assumed to be:
T_{ins}(E,V) = exp[ 2a (E_{CBM}eVE)^{½ }d_{ins}] for eV+E < E_{CBM}
T_{ins}(E,V) = 1 for eV+ E > E_{CBM}
Electrons tunneling into the gap see a constant height barrier, and electrons tunneling into the conduction band of the insulator propagate freely.
Fig. 3 Normalized conductance calculated including the
contribution from the tunneling probability only.
Adjustable parameters:
d_{ins} = 3 Å
E_{CBM} = 3 eV
Amazingly enough, even this simplest model produces the resonant peak at CBM in normalized conductance (Fig. 3), and the absolute values that are not too far from the observed ones (compare to Fig. 2). Typical values are assumed for the insulator thickness d_{ins} and E_{CBM}.