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.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 f 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:

Tvac(E,V) = , where

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

Assume that the total tunneling probability T(E,V) = Tvac(E,V)Tins(E,V).

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

f = 4 eV - work function for the tip and the sample

kT = 0.026 eV - assume room temperature

dtip = 11 Å - tip-sample separation (typical value for sample bias of 3-4 V)

dins - thickness of the insulator film in Å

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

Next Section: II.3 The Simplest Model for T(E,V)

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