The Scattering Theoretical Approach to the Scanning Tunneling Microscope

Abstract

In the interpretation of Scanning Tunneling Microscopy (STM) one often adopts the somewhat simplistic view that the tunnel current should be proportional to the local surface charge density at the position of the tip. More often than not this gives a reasonable interpretation of the STM -images. But in some cases it leads to an apparent contradiction with other available information on the sample surface. These contradictions are not always easy to resolve and some have been puzzling the STM-community for years.If STM is considered as a probe of the local sample charge density at the Fermi level, this suggests a comparison to results obtained from 2] where the total sample charge density is probed at distances which are roughly equivalent to those accessible by STM. Table 3.1 contains this comparison, which demonstrates that for clean and adsorbate covered close-packed metal surfaces there are problems in interpretating the STM images. For the given examples a picture of the local charge density differs qualitatively from the images seen in STM. In these cases the vertical coordinate of the probe tip that maintains a constant tunneling current will not coincide with what is usually imagined as the topography of the surface. The local charge density picture can be theoretically justified in the case of large tip-sample separation where the interaction between the two electrodes is negligible [3.3]. It is hence concluded that tip-sample interaction plays an important role in some STM-experiments and that a more general theory is needed to achieve a general understanding of the STM imaging process.A general theory has to reliably treat the quantum properties of electrons of a few eV kinetic energy. These electrons interact with structures of dimensions of the order of their wavelength. It has been recognized in the literature that realistic potentials and an exact solution of the three-dimensional scattering problem are required [3.4-8] In this article, theories of the Scanning Tunneling Microscope (STM) are reviewed which use a localized Green function approach to calculate the current beyond perturbation theory. The potential of the tip atom is expanded in a localized basis set. The scattering wave functions yielding the spatial current

Theoretical modelling of scanning tunnelling microscopy, scanning tunnelling spectroscopy and atomic force microscopy

“…Once we have calculated the exact Green functions we can evaluate the tunnelling current exactly. This strategy can be used independently of the particular one-particle model and this is the approach to STM theory followed by Doyen et al (1993a, b), Doyen and Drakova (1996), Koetter et al (1996), andNoguera (1996).…”