Interpretation of KPFM data with the weight function for charges

Abstract

The KPFM signal for systems containing local charges can be expressed as a weighted sum over all local charges. The weight function for charges quantifies the contribution of each charge, depending on its position. In this chapter, we evaluate the KPFM weight function for charges by analyzing several application-relevant model systems. The intention of this chapter is to provide insights into the KPFM contrast formation in order to facilitate the KPFM data interpretation. For this, we concentrate on three model systems: (A) a conductive sample in ultra-high vacuum, (B) a dielectric sample in ultra-high vacuum, and (C) a dielectric sample in water. We calculate the weight function for charges for each of these systems using a conductive sphere as a tip model. While the analysis substantiates a number of known experimental observations, it reveals surprising effects in some environments. For example, the sign of the FM-KPFM signal reflects the sign of the charges measured in the systems A and B, but in system C the sign of the KPFM signal is found to be tip-sample distance dependent. Additionally, we deduce the lateral KPFM resolution limits and finally discuss the lateral decay of the weight function to assess how charges contribute to the signal. Our discussion is accompanied by an interactive visualization available at www.pc1.uni-bielefeld.de/kpfm.