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RESEARCH PRODUCT

Insights into Kelvin probe force microscopy data of insulator-supported molecules

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We present a detailed analysis and understanding of Kelvin probe force microscopy (KPFM) data for a system of point charges in a vacuum-dielectric tip-sample system. Explicit formulae describing the KPFM signal $\ensuremath{\Delta}V$ are derived for the two KPFM operation modes, namely amplitude modulation and frequency modulation (FM). The formulae allow for a physical interpretation of the resulting KPFM signal, reveal contributing parameters, and especially disclose an additive behavior. We numerically evaluate these equations and show exemplary KPFM slice data for a single point charge. The theoretical analysis is complemented by two-dimensional FM-KPFM maps obtained experimentally on 2,5-dihydrobenzoic acid on calcite $(1\phantom{\rule{0.59998pt}{0ex}}0\phantom{\rule{0.59998pt}{0ex}}.\phantom{\rule{0.59998pt}{0ex}}4)$. The molecules assemble in two coexisting phases understood as protonated and deprotonated molecules. The two-dimensional maps reveal a convex shape of the KPFM signal $\ensuremath{\Delta}V$ across the islands and a clear difference between the two phases is revealed. Furthermore, we apply the theoretically suggested difference strategy to extract the molecular component from the measured total KPFM signal.