Ab initio calculations of scanning tunneling microscopy images within a scattering formalism

A procedure for the simulation of scanning tunneling microscopy (STM) images is presented. it combines a density-functional theory (DFT) determination of the electronic wave functions and a scattering formalism for the tunneling current calculation. The atomic structures of the sample and the tip are fully described. The coupling of the surface and the tip apex with their respective bulk reservoirs together with the tip-surface interactions are completely taken into account. The whole system being infinite, the DFT calculations were performed on fragments of the system. From the calculated Hamiltonian and overlap matrix elements, the tunnel current was evaluated with a Green's-function technique. We applied this method both to the Cu(001) surface probed by a Cu tip (contaminated or not) and to a Cu(001)+p(2X2)-S surface probed by a Cu tip. The calculated current as a function of the tip-surface distance, with a decay of one decade per A, and the corrugations in the zero-bias limit are in good agreement with experimental data. The analysis of the atomic orbital contributions to the tunnel current can provide insights into the STM contrast mechanism, as shown with selected examples.