Computer Simulation of the AFM/LFM Imaging Process: Hexagonal versus Honeycomb Structure on Graphite

Abstract

Although the atoms in cleavage planes of graphite are arranged in a honeycomb structure, it is well known from experimental work that atomic force microscopy (AFM) yields a hexagonal structure, a phenomenon that has not been understood so far. Here, computer simulations of the atomic-scale imaging process on graphite by AFM are reported, showing that this behaviour can be explained within a simple model of elastic tip-sample interaction. Both the topographic (AFM) images and the friction force or lateral force microscopy (LFM) images were simulated as a function of the scanning direction relative to the graphite lattice and as a function of the cantilever force constant. The scan distortions and the skipped area due to the AFM/LFM imaging process were evaluated. Simulations were performed both in the presence and in the absence of atomic-scale stick-slip processes. It is shown that neither stick-slip processes nor an inequivalence of the A- and B-sites of graphite is necessary to generate a hexagonal AFM image when scanning an atomic honeycomb structure. Rather, the simulations demonstrate that due to the two-dimensional elastic lateral displacement of the cantilever, the potential maxima-which correspond to the positions of the honeycomb lattice-are avoided by the scanning path of the tip apex, resulting in a hexagonal structure of the AFM and LFM images.