Influence of the macroscopic shape of the tip on the contrast in scanning polarization forcemicroscopy images

Abstract

We demonstrate that a quantitative analysis of the contrast obtained in electrostatic forcemicroscopy images that probe the dielectric response of the sample (scanning polarizationforce microscopy (SPFM)) requires numerical simulations that take into account both themacroscopic shape of the tip and the nanoscopic tip apex. To simulate the SPFMcontrast, we have used the generalized image charge method (GICM), which isable to accurately deal with distances between a few nanometers and severalmicrons, thus involving more than three orders of magnitude. Our numericalsimulations show that the macroscopic shape of the tip accounts for most of the SPFMcontrast. Moreover, we find a quasi-linear relation between the working tip–sampledistance and the contrast for tip radii between 50 and 200 nm. Our calculations arecompared with experimental measurements of the contrast between a thermallygrown silicon oxide sample and a few-layer graphene film transferred onto it.