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

Kelvin probe force microscopy (KPFM) is a powerful tool for studying contact electrification (CE) at the nanoscale, but converting KPFM voltage maps to charge density nontrivial due long-range forces and complex system geometry. Here we present strategy using finite-element method (FEM) simulations determine Green's function of probe/insulator/ground system, which allows us quantitatively extract surface charge. Testing our approach with synthetic data, find that accounting atomic microscope (AFM) tip, cone, cantilever necessary recover known input existing methods lead gross miscalculation or even incorrect sign underlying Applying it experimental demonstrate its capacity realistic densities fine details from contact-charged surfaces. Our gives straightforward recipe convert qualitative data into quantitative over range conditions, enabling CE nanoscale.