Modeling nanoscale charge measurements
Phys. Rev. B 108, 085420 – Published 15 August, 2023
DOI: https://doi.org/10.1103/PhysRevB.108.085420
Abstract
The quantitative measurement of charges at the nanoscale yields important insights into fundamental physical, chemical, or biological processes. In principle, charges can be probed by the sharp tip of a dynamic atomic force microscope, however, quantitative measurements are still a challenge as a large number of parameters and effects contribute to the measured signal. Here, we introduce the fundamental framework for charge force microscopy (CFM) and investigate charges located in, on, or above the surface of a dielectric substrate supported by a metal electrode. We present a comprehensive analysis of CFM signal generation and, in particular, unravel the dependency of the CFM signal on the probe oscillation amplitude, on system parameters such as the substrate dielectric constant or the tip geometry, and on the vertical and lateral position of charges. Most importantly, we untangle the influence from nearby charges when quantifying the magnitude of a central charge of interest in presence of many surrounding charges. We find that charge quantification from regular imaging bears many ambiguities, while mapping the CFM signal perpendicular to the sample surface allows to untangle many signal contributions. Thus, by accounting for measurement parameters and nonlocal influences, quantitative measurements are possible with CFM.
