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

TL;DR

This paper introduces a hybrid FEM/KPFM approach to accurately convert KPFM voltage maps into quantitative nanoscale surface charge density maps, overcoming previous limitations due to complex geometries and long-range forces.

Contribution

It presents a novel FEM-based method to extract quantitative charge densities from KPFM data, accounting for detailed probe geometry and system effects.

Findings

Accurate charge density extraction requires modeling AFM tip, cone, and cantilever.

Common heuristics lead to significant errors in charge estimation.

The method successfully reveals realistic surface charge distributions from experimental data.

Abstract

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