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In the last two decades, nano-mechanical resonators have risen as highly promising devices for mass sensing due to their ultrahigh sensitivity. They can be used to measure the mass and stiffness of single particles like small pollution particles, viruses, bacteria, or even proteins. These capabilities of the nano-mechanical resonators have allowed the birth of a new type of mass spectrometry with no need of fragmentation or ionization of the sample and therefore ideal to measure big masses, where conventional mass spectrometers have important problems. The shape and modes of vibration of a nano-mechanical resonator can be very different and the advantages and drawbacks of one respect to another is still a hot topic. A unified theoretical framework to describe the effect of particle adsorption on a mechanical resonator is fundamental but still lacks in the literature. In this work, we present such a framework and examine the particular case of a rod-like particle adsorbed on a cantilever beam for flexural and torsional vibrations as well as on a disk resonator for radial breathing vibrations and compare the results with finite element simulations ; This work was supported by the European Union's Horizon 2020 Research and Innovation Program under Grant Agreement No. 731868—VIRUSCAN. REFERENCES ; No

Ultrasensitive physical, chemical and biological sensors have emerged in the last decade based on the measurement of the eigenfrequencies of micro- and nanosized cantilever plates. Surface stress is omnipresent in these devices due to a variety of factors such as the fabrication process, temperature variations and analyte adsorption. How surface stress influences on the eigenfrequencies of cantilever plates has remained as an unsolved question in physics that has raised a long debate since first experiments in 1975. Recent theoretical models have shed light on the role of the net surface stress. Still, there exists a discrepancy between theory and some experimental reports, affecting to the capability for quantification of these sensors. In this Letter, we present a theoretical framework that demonstrates that the cantilever bending due to differential surface stress between opposite faces of the cantilever, a neglected effect in classical beam theory, plays a relevant role in the stiffness and eigenfrequencies of cantilevers. We develop a new theoretical framework that provides analytical equations that accurately describe the effect of surface stress on the first three vibration modes of cantilevers. Our findings provide the final piece of the puzzle for solving this long-standing problem in physics ; This study has been supported by European Union' s Horizon 2020 research and innovation programme under grant agreement No 731868 – VIRUSCAN and European Research Council grant 681275 – LIQUIDMASS- ERC- CoG-2015; by Spanish Ministry of Economy and Competitiveness (grant MAT2015-66904-R). PMK acknowledges financial support by Fundación General CSIC (ComFuturo Program) ; Peer reviewed

Free-standing dielectric structures with a substrate underneath, as the SiN microdrums studied here, are the basis of optomechanical devices. Optimization of the optomechanical coupling is demanding in order to enhance the performance of these devices. The optomechanical coupling in the case of drum resonators critically depends on the thickness of the drum, the surface stress, the cavity length and the wavelength. Here, we develop a methodology that combines spatially multiplexed microspectrophotometry, optical modelling of the cavity and finite element method simulation of the mechanical eigenmodes that enables obtaining the properties of the optomechanical cavity and predicting the wavelength that optimizes the optomechanical coupling. By choosing this illumination wavelength we are able to spatially resolve the thermal motion of the microdrums up to the fourth mechanical mode ~ 20 MHz. The presented study opens the door for further optimization pathways for optomechanical detection and actuation. ; This work was supported by the Spanish Science Ministry (MINECO) through project MAT2015-66904-R and by the European Union's Horizon 2020 research and innovation program under grant agreement No 731868–VIRUSCAN. D.R. acknowledges the RyC fellowship supported by MINECO. ; Peer reviewed