Interpretation of atomic force microscope (AFM) signals from surface charge on insulators

The surface of an insulator can accumulate charge by a variety of means. There is a need for good experimental procedures to measure these surface charge densities. The most promising new method is to use an atomic force microscope (AFM). The vastly improved resolution compared with the previous methods, coupled with use in the ambient atmosphere, mean that this method will become widely used. The observed signals show a spatial spreading and a temporal decay. In this paper we show how these measurements can be related to the physical mechanisms causing charge motion on the surface and within the bulk of the sample. A patch of charge having a radius a of about 100 nm is deposited on the surface of a dielectric. It is then monitored by an AFM probe which is scanned across the charged zone at a height h, also of order 100 nm. Either the force gradient or the force can be obtained, but we consider only the force in this paper. This force is due to the vertical electric field of the charge patch, which we need to calculate. A typical sample thickness of 25 μm is much larger than the size of the patch of charge, so the grounded surroundings are effectively at infinity. This view is confirmed by the elementary calculation of Stern et al. (1988), which agrees with experiment