Scanning Tunneling Spectroscopy of Thin Insulating Films.

D. Y. Petrovykh
Department of Physics, University of Wisconsin-Madison
Abstract

Contents:    









Figures:    		 I.1  STM and STS of Bulk Insulators
I.2  STS of Thin Film Insulators
II.1 Tunneling Current Theory
II.2 Tunneling Barrier Parameters
II.3 The Simplest Model for T(E,V)
II.4 Thermal Broadening Included
II.5 More Accurate Tunneling Probabilities
III   Possible Additional Effects
IV   Acknowledgments
References
1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12

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

and   Tins(E,V) = 1   for    eV+ E > ECBM

That is 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:
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.

Next Section: II.4 Thermal Broadening Included

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