Comparing the performance of single and multifrequency Kelvin probe force microscopy techniques in air and water

In this paper, we derive and present quantitative expressions governing the performance of single and multifrequency Kelvin probe force microscopy (KPFM) techniques in both air and water. Metrics such as minimum detectable contact potential difference, minimum required AC bias, and signal-to-noise ratio are compared and contrasted both off resonance and utilizing the first two eigenmodes of the cantilever. These comparisons allow the reader to quickly and quantitatively identify the parameters for the best performance for a given KPFM-based experiment in a given environment. Furthermore, we apply these performance metrics in the identification of KPFM-based modes that are most suitable for operation in liquid environments where bias application can lead to unwanted electrochemical reactions. We conclude that open-loop multifrequency KPFM modes operated with the first harmonic of the electrostatic response on the first eigenmode offer the best performance in liquid environments whilst needing the smallest AC bias for operation.