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

Abstract

The capability of the atomic force microscope (AFM) and the scanning tunnelling microscope (STM) to image surfaces with atomic resolution is still amazing us. Theory has been for a long time and in certain respects remains to the present day in debt to experiment. The aim of this review is to describe the development of theoretical models of the AFM, which serves both as an imaging tool and as a tool for manipulating atoms and molecules at surfaces. Models based on classical and quantum mechanical treatment of tip-sample interaction in the AFM are reviewed with emphasis on the explanations of atomic resolution that they provide. The attempts to understand atomic resolution in the STM on metal surfaces started with the local charge-density concept; however, even exact theories based on three-dimensional scattering theory, using different models for the tip and the sample, cannot provide an understanding of the large corrugation amplitudes of the tip height in the constant-current scanning mode in STM on densely packed metal surfaces. A recently developed dynamic theory of STM, regarding the tunnelling as an excited-state property of the interacting tip-plus-sample system, provides an insight into the physical background of atomic resolution in these cases. Other issues in the theory of STM and scanning tunnelling spectroscopy (STS) addressed relate to the equivalence of the current-density formulation of STM theory and the generalized Ehrenfest theorem, tunnelling via surface states and resonances, the mirror theorem of STS, image reversal in STM, many-particle effects in STM. With the prospect of converting the AFM and STM into tools for surface technology on the nanoscopic scale, theory will be challenged to suggest models going beyond the single-particle approaches and the adiabatic approximation.

Advances in atomic force microscopy

“…Simple cantilevers can even be cut from household aluminum foil (Rugar and Hansma, 1990) and etched tungsten wires . Later, silicon micromachining technology was employed to build cantilevers in 1 More information about tip-sample forces can be found in Ciraci et al (1990); Israelachvili (1991); Sarid (1994); Perez et al (1997Perez et al ( , 1998; Shluger et al (1997Shluger et al ( , 1999; Abdurixit et al (1999); Drakova (2001); Ke et al (2001Ke et al ( , 2002 parallel production with well-defined mechanical properties. The first micromachined cantilevers were built at Stanford in the group of Calvin F. Quate.…”

First-principles study of the tunnel current between a scanning tunneling microscopy tip and a hydrogen-adsorbedSi(001)surface

“…1͒ has made it possible to observe the structures at surfaces with atomic resolution and has provided much useful information on surface configurations. 2 It is well known that the STM image is not directly related to the atomic configuration but depends on the electronic structure at the surface. For example, in the case of H, Cl, or NH 3 -adsorbed dimers of Si͑001͒ surfaces, the adsorbed dimers look geometrically lower than bare dimers in STM images.…”

Energy-resolved STM mapping ofC60on metal surfaces: A theoretical study

“…The STS signal, on the other hand, is strongly influenced by the nature of the contact and the structure of the tip, and extraction of information on the physical and chemical properties of the measured sample is possible only with the support of electronic structure calculations with an atomistic description of the system. [3][4][5] In this paper we discuss from a theoretical point of view the powerful combination between microscopy and spectroscopy which is peculiar of STM and STS. The accuracy of recent STM experiments on C 60 monomers on metallic surfaces 6,7 represents a rigorous benchmark for any theoretical modeling of STM imaging and spectroscopy.…”