Efficient method for the simulation of STM images. I. Generalized Green-function formalism

We present a theoretical formalism specially suited for the simulation of scanning tunneling microscopy (STM) images. The method allows for a realistic description of the STM system, taking fully into account its three-dimensional nature. Bias effects may also be considered since the theory is not restricted to the low-bias limit. The starting point is the previously applied Landauer-B\"uttiker formula, which expresses the current at the STM junction as a sum of transmission coefficients linking eigenstates at each electrode. The transmission coefficients are directly obtained from the scattering matrix which is, in our approach evaluated through Green-function techniques; in particular, we employ the surface Green-function matching (SGFM) method to find the Green function at the interface, and explicitly derive simple expressions for the current. Additionally, the formalism goes beyond the elastic-scattering limit by considering inelastic effects via an optical potential. We also present a method to analyze the current in terms of contributions arising from individual atomic orbital interactions and their interference with other interactions. To this end, the SGFM method is replaced by a first-order expansion of the interface Green function.