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We developed an open-source numerical code for calculating electrostatic interactions between a hyperbolic metallic tip and a conducting surface under Kelvin probe force microscopy (KPFM)-relevant conditions. The code solves the electrostatic potential in the tip-sample vacuum gap under an applied bias by imposing Dirichlet boundary conditions on the tip and sample surfaces, and evaluates electrostatic force observables from the calculated potential. In addition to laterally homogeneous samples, the full three-dimensional implementation treats spatially inhomogeneous surfaces and reproduces contact potential difference profiles. Quantitative comparison with experiments is achieved without arbitrary scale factors or other ad hoc proportionality constants. The method provides a practical framework for experimental-parameter extraction, quantitative KPFM data analysis, and future investigations of contrast formation and other measurement aspects in KPFM.

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  This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Nobuyuki Ishida; An open-source framework for quantitative electrostatic simulations in Kelvin probe force microscopy. J. Appl. Phys. 14 July 2026; 140 (2): 024301 and may be found at https://doi.org/10.1063/5.0336722.

Keyword: Kelvin probe force microscopy, Electrostatic force, Numerical calculation, METALTIP

Date published: 2026-07-14

Publisher: AIP Publishing

Journal:

• Journal of Applied Physics (ISSN: 00218979) vol. 140 issue. 2 024301

Funding:

• Japan Society for the Promotion of Science JP17K06366
• Japan Society for the Promotion of Science JP21H01818
• Japan Society for the Promotion of Science JP24K01367

Manuscript type: Author's version (Accepted manuscript)

MDR DOI: https://doi.org/10.48505/nims.6417

First published URL: https://doi.org/10.1063/5.0336722

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Updated at: 2026-07-21 13:30:01 +0900

Published on MDR: 2026-07-21 16:30:32 +0900