Theory of scanning tunneling microscopy

Abstract

The present theoretical understanding of imaging clean and adsorbate covered metal surfaces in scanning tunneling microscopy is examined with special emphasis on a possible theoretical foundation for the observed unexpectedly large corrugation on close-packed metal surfaces. Several suggestions for explaining these experimental findings are investigated. Resonance tunneling via tip d-orbitals might be a possible mechanism of amplifying small lateral structure of electronic or elastic origin. Two complementary theoretical methods are applied. The first one concentrates on a realistic description of the potential and wave functions of the sample surface whereas the second one attempts to model a more realistic transition metal tip. In the first approach the tip is represented by a Gaussian protrusion on an otherwise planar free-electron metal surface. The sample surface is built from muffin-tin potentials accounting for the atomic structure and the d-electrons. The spatial current distribution near the tip region is obtained by summing the contributions of all scattered waves. The method has been applied to study the current to Al(111) and Pd(100) surfaces. The corrugation obtained is rather small and cannot explain the experimental observations. The second approach studies two transition metal tips consisting of a single tungsten atom adsorbed on a flat W(110) surface and on a group of four other W atoms. The cluster of four W atoms is coupled to a flat W(110) surface by using an embedding method. The basis set on the W atoms includes 6s-, 6p-, and 5d-orbitals. The electronic structure of the tip exhibits a 5d2-resonance near the Fermi level. The effects of tip d-orbitals and resonance tunneling on the lateral contrast in STM are analyzed.