Abstract
This paper describes the computation of the tunneling current in a scanning tunneling microscope (STM) up to the geometric contact of the tip with atoms in a cluster adsorbed on a flat conducting surface. The calculation accounts for the three-dimensional scattering taking place simultaneously in the top atomic layer of the sample and in the apex of the probing tip. The model is built with the following ingredients: (a) the tip is represented by a cluster of atoms attached to an otherwise planar free-electron metal surface, and (b) the analysed sample is a planar free-electron metal with a local potential corrugation induced by an isolated molecule or adatom. The potential barrier includes the strong bending effect due to the image-charge occuring as the tunneling electron crosses the gap between the tip and the sample. The specific theoretical approach designed to solve this scattering problem exploits the fast Fourier transforms algorithm to construct a transfer-matrix in a mixed real- and momentum-space representation. The theory is used here to simulate the current image of a model-aluminium atom on a free-electron metal substrate using electrons focussed by a single-atom tungsten tip.
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