Models of the interaction of metal tips with insulating surfaces

We present the results of atomistic simulations of metallic atomic-force-microscopy tips interacting with ionic substrates, with atomic resolution. Chromium and tungsten tips are used to image the NaCl(001) and MgO(001) surfaces. The interaction of the tips with the surface is simulated by using density-functional-theory calculations employing a mixed Gaussian and plane-wave basis and cluster-tip models. In each case, the apex of the metal cluster interacts more attractively with anions in the surfaces than with cations, over the range of typical imaging distances, which leads to these sites being imaged as raised features (bright) in constant-frequency-shift images. We compare the results of the interaction of a chromium tip with the NaCl surface, with calculations employing exclusively plane-wave basis sets and a fully periodic tip model, and demonstrate that the electronic structure of the tip model employed can have a significant quantitative effect on calculated forces when the tip and surface are clearly separated.