An open-source framework for quantitative electrostatic simulations in Kelvin probe force microscopy

Abstract

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.