In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to \documentclass[12pt]{minimal}\begin{document}$2.5 \times 10^{-15}\,{\rm m}/\sqrt{\rm Hz}$\end{document}2.5×10−15m/ Hz ), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few μm.

In recent years, an increasing number of devices and experiments are shown to be limited by mechanical thermal noise. In particular, subhertz laser frequency stabilization and gravitational wave detectors that are able to measure fluctuations of ${10}^{$-${}18}\text{ }\text{ }\mathrm{m}/\sqrt{\mathrm{Hz}}$ or less are being limited by thermal noise in the dielectric coatings deposited on mirrors. In this paper, we present a new measurement of thermal noise in low absorption dielectric coatings deposited on microcantilevers, and we compare it with the results obtained from the mechanical loss measurements. The coating thermal noise is measured on the widest range of frequencies with the highest signal-to-noise ratio ever achieved. In addition, we present a novel technique to deduce the coating mechanical losses from the measurement of the mechanical quality factor which does not rely on the knowledge of the coating and substrate Young's moduli. The dielectric coatings are deposited by ion beam sputtering. The results presented here give a frequency-independent loss angle of $(4.7\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{$-${}4}$ with a Young's modulus of 118 GPa for annealed tantala from 10 Hz to 20 kHz. For as-deposited silica, a weak frequency dependence ($$\propto${}{f}^{$-${}0.025}$) is observed in this frequency range, with a Young's modulus of 70 GPa and an internal damping of $(6.0\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{$-${}4}$ at 16 kHz, but this value decreases by one order of magnitude after annealing, and the frequency dependence disappears.

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 1000 °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.

When heated, micro-resonators present a shift of their resonance frequencies. We study specifically silicon cantilevers heated locally by laser absorption and evaluate theoretically and experimentally their temperature profile and its interplay with the mechanical resonances. We present an enhanced version of our earlier model [Sandoval et al., J. Appl. Phys. 117, 234503 (2015)], including both elasticity and geometry temperature dependency, showing that the latter can account for 20% of the observed shift for the first flexural mode. The temperature profile description takes into account thermal clamping conditions, radiation at high temperature, and lower conductivity than bulk silicon due to phonon confinement. Thanks to space–power equivalence in the heat equation, scanning the heating point along the cantilever directly reveals the temperature profile. Finally, frequency shift measurement can be used to infer the temperature field with a few percent precision.

An interferometric method is implemented in order to accurately assess the thermal fluctuations of a micro-cantilever sensor in liquid environments. The power spectrum density (PSD) of thermal fluctuations together with Sader’s model of the cantilever allow for the indirect measurement of the liquid viscosity with good accuracy. The good quality of the deflection signal and the characteristic low noise of the instrument allow for the detection and corrections of drawbacks due to both the cantilever shape irregularities and the uncertainties on the position of the laser spot at the fluctuating end of the cantilever. Variation of viscosity below 0.03 mPa·s was detected with the alternative to achieve measurements with a volume as low as 50 µL.