Resonance frequency shift of strongly heated micro-cantilevers

TL;DR

This paper investigates how increasing optical power heats micro-cantilevers, causing measurable shifts in their resonance frequencies, with an analytical model explaining the temperature-dependent frequency changes and experimental validation in vacuum and air.

Contribution

It introduces an analytical model linking temperature profiles to resonance frequency shifts and demonstrates significant heating effects at moderate light intensities.

Findings

Resonance frequency shifts correlate with temperature rise.

Heating up to 1000°C with only 10 mW of light.

Different behaviors observed in vacuum versus air.

Abstract

In optical detection setups to measure the deflection of micro-cantilevers, part of the sensing light is absorbed, heating the mechanical probe. We present experimental evidences of a frequency shift of the resonant modes of a cantilever when the light power of the optical measurement set-up is increased. This frequency shift is a signature of the temperature rise, and presents a dependence on the mode number. An analytical model is derived to take into account the temperature profile along the cantilever, it shows that the frequency shifts are given by an average of the profile weighted by the local curvature for each resonant mode. We apply this framework to measurements in vacuum and demonstrate that huge temperatures can be reached with moderate light intensities: a thousand {\textdegree}C with little more than 10 mW. We finally present some insight into the physical phenomena when the cantilever is in air instead of vacuum.