Effects of electrostatic fields and Casimir force on cantilever vibrations

TL;DR

This paper investigates how electrostatic and Casimir forces influence cantilever vibrations, revealing their impact on frequency shifts and damping, with implications for nanoscale diagnostics and force measurements.

Contribution

It provides a combined analysis of electrostatic and Casimir effects on cantilever dynamics, including geometry-dependent frequency shifts and damping mechanisms.

Findings

Electrostatic forces cause frequency shifts and damping related to substrate properties.

Casimir forces induce measurable frequency shifts consistent with recent experiments.

Geometry of the cantilever tip significantly affects vibrational characteristics.

Abstract

The effect of an external bias voltage and fluctuating electromagnetic fields on both the fundamental frequency and damping of cantilever vibrations is considered. An external voltage induces surface charges causing cantilever-sample electrostatic attraction. A similar effect arises from charged defects in dielectrics that cause spatial fluctuations of electrostatic fields. The cantilever motion results in charge displacements giving rise to Joule losses and damping. It is shown that the dissipation increases with decreasing conductivity and thickness of the substrate, a result that is potentially useful for sample diagnostics. Fluctuating electromagnetic fields between the two surfaces also induce attractive (Casimir) forces. It is shown that the shift in the cantilever fundamental frequency due to the Casimir force is close to the shift observed in recent experiments of Stipe et al. Both the electrostatic and Casimir forces have a strong effect on the cantilever eigenfrequencies, and both effects depend on the geometry of the cantilever tip. We consider cylindrical, spherical, and ellipsoidal tips moving parallel to a flat sample surface. The dependence of the cantilever effective mass and vibrational frequencies on the geometry of the tip is studied both numerically and analytically.