Mathematical extraction of mechanical characteristics from electrical signals from an electrically driven quartz tuning fork in vacuum, air, and liquid environments

A quartz tuning fork is an electromechanical resonator with self-actuating and self-sensing capabilities and is widely used as a force sensor in atomic force microscopy and spectroscopy. While the electrical response of a tuning fork is affected by the two prongs’ mechanical motion and stray capacitive current, a purely mechanical motion signal of the tuning fork is required for a quantitative analysis. Here, we demonstrate the extraction of a mechanical motion signal from the electrical signal of an electrically driven quartz tuning fork in various environments, including vacuum, air, and liquid. We show that the extraction formalism is well implemented in vacuum and air, but it does not work in liquid due to the largely enhanced damping and ions present in liquids. Furthermore, using the mechanical signal extracted from the electrical signal, we determine the interaction force exerted on the tip of the tuning fork in ambient air. The present extraction method enables versatile use of electrically driven tuning forks for force, mass, and environmental sensing, in which true mechanical motion signals should be used for accurate and quantitative analysis.