Surface potential modeling and reconstruction in Kelvin probe force microscopy.

Kelvin probe force microscopy (KPFM) measurement has been extensively applied in metallic, semiconductor and organic electronic or photovoltaic devices, to characterize the local contact potential difference or surface potential of the samples at the nanoscale. Here, a comprehensive modeling of surface potential in KPFM is established, from the well-known single capacitance model to a precise electrodynamic model, considering the long range property of the electrostatic force in KPFM. The limitations and relations of different models are also discussed. Besides, the feedback condition of the KPFM system is reconsidered and modified, showing that the influence of the cantilever has been overestimated by about 20% in previous reports. Afterwards, the surface potential of charged Si-nanocrystals is reconstructed based on the electrodynamic model, and the calculated surface charge density is very consistent with the macroscopic capacitance-voltage (C-V) measurement. A deep understanding and correct reconstruction of surface potential is crucial to the quantitative analysis of KPFM results.