Ab initioinvestigation of noncontact atomic force microscopy tip-surface instability in InAs(110) surface

Abstract

In the present work we report ab initio pseudopotential calculations based on density functional theory to investigate the noncontact atomic force microscopy (NC-AFM) image contrast on the InAs(110) $(1\ifmmode\times\else\texttimes\fi{}1)$ surface. The foremost tip structure is modeled by a $\mathrm{Si}{\mathrm{H}}_{3}$ tip. The effect of the tip-induced surface relaxations on the calculated forces was investigated for the tip above As and In atoms. The force curves corresponding to these vertical scans show an hysteretic behavior and this effect causes an energy dissipation of 0.3 (tip on top of As) and $1.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ (tip on top of In), respectively. The presence of this hysteresis suggests that stable NC-AFM images can be obtained for tip-sample distances before this instability. In this stable regime the force curves obtained for perturbed (due to tip-sample interaction) and unperturbed InAs(110) surface exhibit the same qualitative behavior. From the calculated forces for the unperturbed InAs(110) surface on a large number of grid points in real space we obtained maps of constant frequency shifts. The influence of long-range van der Waals forces on the simulated AFM images due to the macroscopic part of the tip was taken into account by an empirical model. The overall structure and the corrugation of the simulated NC-AFM images are in good agreement with the experimental results and allow us to explain the experimentally observed features of the image contrast mechanism on the basis of the calculated short-range chemical tip-sample interaction forces.