Resonant-tunneling theory of imaging close-packed metal surfaces by scanning tunneling microscopy

We propose a resonant-tunneling theory of scanning tunneling microscopy (STM) by considering the general characteristics of a probe tip in which an electron trap, or impurity, causing the resonance is assumed to adsorb on an insulating contamination layer at the tip. The resulting constant-current STM image is the sum of two terms. The first term is due to the spatial variation of the conductance between surface and impurity, and the second term is due to the spatial variation of the force between surface and impurity. The relative contribution of the two terms to the image corrugation is determined by a constant K, which depends on the properties of insulating layer. Under the assumption of single atom adsorbed on a clean tip, our result reduces to the Tersoff-Hamann formalism, as expected. However, for a contaminated-tip approximation, we find that atomic corrugation of STM images can be dominated by the force corrugation between impurity and surface similar to that of atomic-force microscopy. The theory provides good agreement with experimental data on the corrugation as a function of z-axis piezoelectric element driving distance recently reported [J. Wintterlin et al., Phys. Rev. Lett. 62, 59 (1989)] for the Al(111)surface.