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

A powerful tool for studying contact electrification is Kelvin Probe Force Microscopy (KPFM), where electrical signals from an AFM tip allow one to spatially map a voltage above a surface that is caused by the presence of charge. However, a fundamental challenge from KPFM is to convert the voltage map to a surface charge density map. Without a method to convert voltage to charge, the signal from KPFM remains qualitative.

We have developed a method to convert KPFM voltage maps to surface charge density maps. Due to superposition, the measured KPFM voltage at any location is the summed contribution from the point-charge KPFM voltage of each carrier on the surface. We take advantage of this and do finite element simulations to determine the Green’s function for the tip-sample-ground system. Using the Green's function as a kernel, we deconvolve the KPFM map and extract the charge distribution. We test our approach by creating artificial charge maps, generating KPFM data from these, and then using our algorithm to recover the known input. We find that simulating the whole AFM tip and cantilever is necessary to obtain high-fidelity copies of the original input. Moving forward, we are using this approach to precisely extract surface charge densities from experimental data of charge transfer with soft materials. This will help us to gain information about CE at the nanoscale, thus bringing KPFM from qualitative to quantitative.