The study of thin-film materials is a subject of growing interest. Some of these materials are insulating due to the presence of disorder, which also produces localization of charges. Kelvin probe force microscopy (KPFM) is a unique tool to characterize these materials, but a full quantitative interpretation of the results is still lacking. To address this problem, we propose a simple and fast procedure based on the image charge method that represents an advance in this direction since it is not limited to any film thickness or the nature of the underlying substrate. Even more, it can be combined with fast Fourier transform algorithms to generate theoretical images from known charge distributions or to obtain charge distributions from the Kelvin voltage images. Within this framework, we analyze the problem of the lateral resolution of the technique, providing a criterion to estimate it. Finally, we address the problem of systems with hopping conductivity where multiple localized charges coexist. We demonstrate that even in these complex systems, the KPFM gives valuable information, allowing us to distinguish between noninteracting and interacting electronic systems. Furthermore, it is possible to calculate the charge density in the noninteracting case.

• Received 19 December 2019
• Revised 13 February 2020
• Accepted 14 February 2020

DOI:https://doi.org/10.1103/PhysRevB.101.075432