COMPUTATION OF SCANNING TUNNELING MICROSCOPE IMAGES

This article describes the computation of the tunnel current in a scanning tunneling microscope (STM). The calculation accounts for the three-dimensional scattering taking place simultaneously in the first atomic layers 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 analyzed 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 formation occurring 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 transform algorithm to construct a transfer matrix in a mixed real- and momentum-spaces representation. The total current is obtained by summing the contributions of all scattered waves traveling in the barrier between the tip and the sample, and it is studied in this article for various positions of the tip relative to the adsorbed atomic cluster. The theory is used here to simulate the scan of a model-aluminum atom on a free-electron metal substrate using electrons focused by a single-atom tungsten tip.