Theory of Scanning Tunneling Spectroscopy Based on the Resonant Tunneling Model II: Relation between Different Approaches

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Abstract
The expression for scanning tunneling microscopy current given in a previous paper [Jpn. J. Appl. Phys. 33 (1994) 3657] is rewritten into a simpler form in terms of the time-derivative of the occupation number of states connected to the sample electrode. Assumptions made in the previous theory, such as infinitely wide and flat surface, are lifted. It is shown that the resonant width for the cluster orbitals, where the tunneling current flows, is different, in general, from the transition rate to states which carry the current to the electrodes. It is emphasized that the ratio of the sample-cluster tunneling matrix elements to those of cluster-tip tunneling, which increases with decreasing tip-sample distance, affects the scanning tunneling spectrum due to the multiple scattering effect.

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