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 STM and STS of Bulk Insulators
2 STS of Thin Film Insulators
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
Possible Additional Effects
Acknowledgments & References

II.2 Tunneling Barrier Parameters

The first approximation is to assume that both the tip and the sample are essentially metallic and have the same work function φ and constant density of states. The assumption of a constant tip density of states is often made, lacking detailed knowledge of the tip states. The Si density of states has little structure at the energies under consideration, i.e., about 4 eV above the valence band maximum.

Assume that the tunneling probability through the vacuum is given by:

T_vac(E,V) = tunneling probability , where a-term

which corresponds to WKB approximation for tunneling through a barrier of the average height.

Assume that the total tunneling probability T(E,V) = T_vac(E,V)T_ins(E,V).

The following are the values of the "fixed" tunneling barrier and environment parameters:

φ = 4 eV — work function for the tip and the sample,
kT = 0.026 eV — assume room temperature,
d_tip= 11 Å — tip-sample separation (typical value for sample bias of 3–4 V),
d_ins — thickness of the insulator film in Å.

These are the values used in all the following models, unless specified otherwise.

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