Inhomogeneous probe surface induced effect in Kelvin probe force microscopy

The probe in Kelvin probe force microscopy (KPFM) may have an inhomogeneous tip surface by artificial modification or by unexpected wearing or contamination. In the present work, the non-equipotential tip surface induced effect in KPFM with conducting samples was simulated by an analytical multiple-capacitances model and a numerical boundary element model, respectively. The capacitance model showed that the KPFM system satisfies the principle of superposition without couplings between the inhomogeneous tip and inhomogeneous sample induced signals. In addition, the more precise boundary element model demonstrated that the non-uniform tip surface would not change the KPFM resolution but will induce a signal shift depending on tip-sample distance, tip oscillation amplitude, and modulation mode. In the simulations, a cantilever calibration factor of 3/8 was proposed based on the Euler-Bernoulli beam theory. Our simulation result is in good agreement with a recent KPFM distance spectroscopy experiment on a silver sample, and the simulation method is also promising for the future discussion about dielectric samples.