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

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 an 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.