GREEN-FUNCTION THEORY OF SCANNING TUNNELING MICROSCOPY - TUNNEL CURRENT AND CURRENT-DENSITY FOR CLEAN METAL-SURFACES

A theory of scanning tunneling microscopy (STM) is presented that acco unts for a realistic treatment of the electronic structure of the samp le surface. The sample is represented by a semi-infinite crystal built from muffin-tin potentials describing the atomic structure and surfac e electronic wave functions of s, p, d, etc., electrons. The other ele ctrode carrying the tip atom is a planar free-electron metal surface. The potential of the tip atom is expanded in a localized basis set. Wi thin the single-particle approach, the exact equation for the scatteri ng wave for the combined system (tip plus sample) is derived. It is ev aluated using a Green-function technique. From the scattering wave fun ction the spatial distribution of the current density is obtained. The method is applied to study the tunnel current to clean Al(111), Pd(11 1), and Pd(100) surfaces. At typical tip-sample separations (greater-t han-or-equal-to 3 angstrom) the substrate atoms appear as protrusions. Quite remarkable, the contrast is found to be larger in the Al(111) i mages than in the Pd(111) and Pd(100) images. This is a consequence of the tip-sample interaction. As a further consequence of tip-sample in teractions we find that at close distances between the tip and the Pd surfaces the interstitial regions appear as maxima in the variation of the tunnel current. The theory covers a broad range of tip-sample sep arations, including those where perturbation treatments of STM theory (as, e.g., developed by Tersoff and Hamann) break down. A systematic a nalysis of the different aspects that may affect the tunnel current is presented.