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Kelvin probe force microscopy (KPFM) is a powerful tool for studying contactelectrification at the nanoscale, but converting KPFM voltage maps to chargedensity maps is non-trivial due to long-range forces and complex systemgeometry. Here we present a strategy using finite element method (FEM)simulations to determine the Green's function of the KPFMprobe/insulator/ground system, which allows us to quantitatively extractsurface charge. Testing our approach with synthetic data, we find thataccounting for the AFM tip, cone and cantilever are necessary to recover aknown input, and that commonly applied heuristics and approximations lead togross miscalculation. Applying it to experimental data, we demonstrate itscapacity to extract realistic surface charge densities and fine details fromcontact charged surfaces. Our method gives a straightforward recipe to convertqualitative KPFM voltage data into quantitative charge data over a range ofexperimental conditions, enabling quantitative contact electrificationexperiments at the nanoscale.

Quantifying nanoscale charge density features of contact-charged surfaces with an FEM/KPFM-hybrid approach