A Method to Reconstruct Charge Density Distribution on Dielectric Surfaces Using Kelvin Probe Force Microscopy

Reliable and accurate measurement of the quantity and density distribution of surface charges on dielectric materials is critically important across numerous fields. However, due to its inherent measurement principles, the widely adopted KPFM technique faces significant challenges in accurately deriving surface charge density from surface potential measurements on dielectric surfaces. To address this issue, this paper establishes both a theoretical model and a two-dimensional simulation model to mimic the actual surface potential measurement of KPFM on dielectric surfaces. The validity of the simulation model is partially supported by both the KPFM measurements and the theoretical analysis. Theoretical analysis and numerical calculations reveal that the theoretical formula based on the parallel-plate capacitor model is only valid for quantifying the relationship between the surface potential and charge density on uniformly charged, infinitely extended dielectric surfaces. For finite charged surfaces, the measured potential is strongly influenced by factors including the lateral size of the charged region, probe height, sample thickness, relative permittivity, and nearby surface charges. By fitting simulation results, we derive an analytical expression for the measured potential distribution above a point charge. Based on this expression, we propose a method to reconstruct the surface charge density distribution from measured potential data.