Theory of scanning tunneling microscopy and scanning tunneling spectroscopy based on the resonant tunneling model: can we observe surface states?

A theory based on a simple model for resonant tunneling processes is presented to calculate the current in the scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). A simple expression of the current is given, which consists of three parts: one for the electron occupation, one for the change of the electronic states by admixtures between the tip and the sample, and the third for current from the surface to the electrode attached to the sample. It is shown that the surface states do not contribute to the tunneling current if they lie in the gap of the bulk band, because we can construct only evanescent waves in such an energy range. However when the surface states appear in a gap at certain wave vectors parallel to the surface but energetically degenerate to bulk states with different parallel wave vectors, they can be observed because the translational symmetry parallel to the surface is broken by the tip. The present theory can be applied to the detailed analysis of the tunneling current combined with suitable electronic state calculations.