Make your own free website on

Scanning Tunneling Spectroscopy of Insulating Films

Paper for Advanced Solid State Physics class, Dmitri Y. Petrovykh.

Physics Department, University of Wisconsin, Madison, WI, USA (1999)

  1. 1 STM and STS of Bulk Insulators
    2 STS of Thin Film Insulators
  2. 1 Tunneling Current Theory
    2 Tunneling Barrier Parameters
    3 The Simplest Model for T(E,V)
    4 Thermal Broadening Included
    5 More Accurate Tunneling Probabilities
  3. Possible Additional Effects
  4. Acknowledgments & References

II.3 The Simplest Model - T(E,V) Dependence Only

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 Tins is assumed to be:

Tins(E,V) = exp[ 2a (ECBMeVE)½ dins]   for  eV+E < ECBM

Tins(E,V) = 1    for    eV+ E > ECBM

Electrons tunneling into the gap see a constant height barrier, and electrons tunneling into the conduction band of the insulator propagate freely.

calculated normalized conductance

Fig. 3 Normalized conductance calculated including the contribution from the tunneling probability only.
Adjustable parameters:
dins = 3 Å
ECBM = 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 dins and ECBM.

Main page: Chemical contrast STM | Next section: Thermal Broadening Included »

horizontal spacer