Efficient Method for Fast Simulation of Scanning Tunneling Microscopy with a Tip Effect

Abstract

On the basis of Bardeen's perturbation theory on electron tunneling and inspired by Paz et al.'s study, a new expression for the tunneling current between the scanning tunneling microscopy (STM) tip and sample has been obtained, and it provides us with an efficient method to simulate STM images. The method can be implemented in any code of first-principles computing software, which offers the wave functions of the tip and sample, calculated independently at the same footing, as input. By calculating the integral with fast Fourier transform (FFT), simulating the STM image of a given sample surface by a database of different tips on a PC turns out to be not a time-consuming work. Compared with Paz et al.'s method, our method abandons the application of the vacuum Green function and possesses better computing efficiency, fewer parameters, and more reasonable simulated results especially at lower computing cost. Simple tip-sample systems, such as H-H and Pd2-Ag2, are taken as benchmarks to test our method. The topographic images of a CO molecule adsorbed on a Cu(111) surface obtained by using a tungsten tip and a CO-terminated tip are also simulated, and the simulated results are in good agreement with the experimental ones.