Tip and Surface Determination from Experiments and Simulations of Scanning Tunneling Microscopy and Spectroscopy

Abstract

We present a very efficient and accurate method to simulate scanning tunneling microscopy images and spectra from first-principles density functional calculations. The wave functions of the tip and sample are calculated separately on the same footing and propagated far from the surface using the vacuum Green function. This allows us to express the Bardeen matrix elements in terms of convolutions and to obtain the tunneling current at all tip positions and bias voltages in a single calculation. The efficiency of the method opens the door to real time determination of both tip and surface composition and structure, by comparing experiments to simulated images for a variety of precomputed tips. Comparison with the experimental topography and spectra of the $\mathrm{S}\mathrm{i}(111)\mathrm{\text{−}}(7\times 7)$ surface shows a much better agreement with Si than with W tips, implying that the metallic tip is terminated by silicon.