Frequency dependence of viscous and viscoelastic dissipation in coated micro-cantilevers from noise measurement

TL;DR

This study investigates how coatings affect the frequency-dependent viscous and viscoelastic energy dissipation in micro-cantilevers by measuring their thermal noise spectrum over a wide frequency range.

Contribution

It introduces a combined experimental and modeling approach to distinguish viscous and viscoelastic damping effects in coated micro-cantilevers using noise measurements.

Findings

Coated cantilevers exhibit a 1/f noise trend, unlike uncoated ones.

Viscoelastic damping follows a power-law frequency dependence.

Viscous damping aligns with the Sader model.

Abstract

We measure the mechanical thermal noise of soft silicon atomic force microscopy cantilevers. Using an interferometric setup, we have a resolution down to 1E-14 m/rtHz on a wide spectral range (3 Hz to 1E5 Hz). The low frequency behavior depends dramatically on the presence of a reflective coating: almost flat spectrums for uncoated cantilevers versus 1/f like trend for coated ones. The addition of a viscoelastic term in models of the mechanical system can account for this observation. Use of Kramers-Kronig relations validate this approach with a complete determination of the response of the cantilever: a power law with a small coefficient is found for the frequency dependence of viscoelasticity due to the coating, whereas the viscous damping due to the surrounding atmosphere is accurately described by the Sader model.