Propagator theory of scanning tunneling microscopy

We develop a quantum mechanical scattering theory for electrons which tunnel out of (or into) the tip of a scanning tunneling microscope. The method is based on propagators (or Green functions) for quasistationary scattering with the tip being an electron source (or sink). The results for the tunneling current generalize the Tersoff-Hamann approach of scanning tunneling microscopy. In contrast to previous calculations the present theory relates the tunneling current to the potential distribution of the sample. Expressions for the corrugation are available through a simple perturbation expansion scheme. Analytical model calculations are presented and compared with existing results.