Evidence of surface loss as ubiquitous limiting damping mechanism in SiN micro- and nanomechanical resonators

Silicon nitride (SiN) micro- and nanomechanical resonators have attracted a lot of attention in various research fields due to their exceptionally high quality factors ($Q$s). Despite their popularity, the origin of the limiting loss mechanisms in these structures has remained controversial. In this paper we propose an analytical model combining acoustic radiation loss with intrinsic loss. The model accurately predicts the resulting mode-dependent $Q$s of a low-stress silicon-rich and a high-stress stoichiometric SiN membrane. The large acoustic mismatch of the low-stress membrane to the substrate seems to minimize radiation loss and $Q$s of higher modes ($n \wedge m \geq 3$) are limited by intrinsic losses. The study of these intrinsic losses in low-stress membranes with varying lengths $L$ and thicknesses $h$ reveals an inverse linear dependence of the intrinsic loss with $h$ for thin resonators independent of $L$. This finding was confirmed by comparing the intrinsic dissipation of arbitrary (membranes, strings, and cantilevers) SiN resonators extracted from literature, suggesting surface loss as ubiquitous damping mechanism in thin SiN resonators with $Q_{surf} = \beta \cdot h$ and $\beta = 6\times10^{10} \pm4\times 10^{10}$~m$^{-1}$. Based on the intrinsic loss the maximal achievable $Q$s and $Q\cdot f$ products for SiN membranes and strings are outlined

Influence of clamp-widening on the quality factor of nanomechanical silicon nitride resonators

Nanomechanical resonators based on strained silicon nitride (Si$_3$N$_4$) have received a large amount of attention in fields such as sensing and quantum optomechanics due to their exceptionally high quality factors ($Q$s). Room-temperature $Q$s approaching 1 billion are now in reach by means of phononic crystals (soft-clamping) and strain engineering. Despite great progress in enhancing $Q$s, difficulties in fabrication of soft-clamped samples limits their implementation into actual devices. An alternative means of achieving ultra-high $Q$s was shown using trampoline resonators with engineered clamps, which serves to localize the stress to the center of the resonator, while minimizing stress at the clamping. The effectiveness of this approach has since come into question from recent studies employing string resonators with clamp-tapering. Here, we investigate this idea using nanomechanical string resonators with engineered clampings similar to those presented for trampolines. Importantly, the effect of orienting the strings diagonally or perpendicularly with respect to the silicon frame is investigated. It is found that increasing the clamp width for diagonal strings slightly increases the $Q$s of the fundamental out-of-plane mode at small radii, while perpendicular strings only deteriorate with increasing clamp width. Measured $Q$s agree well with finite element method simulations even for higher-order resonances. The small increase cannot account for previously reported $Q$s of trampoline resonators. Instead, we propose the effect to be intrinsic and related to surface and radiation losses.Comment: 7 pages, 4 figure

Position and Mode Dependent Optical Detection Back-Action in Cantilever Beam Resonators

Optical detection back-action in cantilever resonant or static detection presents a challenge when striving for state-of-the-art performance. The origin and possible routes for minimizing optical back-action have received little attention in literature. Here, we investigate the position and mode dependent optical back-action on cantilever beam resonators. A high power heating laser (100 {\mu}W) is scanned across a silicon nitride cantilever while its effect on the first three resonance modes is detected via a low-power readout laser (1 {\mu}W) positioned at the cantilever tip. We find that the measured effect of back-action is not only dependent on position but also the shape of the resonance mode. Relevant silicon nitride material parameters are extracted by fitting the temperature-dependent frequency response of the first three modes to finite element (FE) simulations. In a second round of simulations, using the extracted parameters, we successfully fit the FEM results with the measured mode and position dependent back-action. Finally, different routes for minimizing the effect of this optical detection back-action are described, allowing further improvements of cantilever-based sensing in general

Nanomechanical Photothermal Near Infrared Spectromicroscopy of Individual Nanorods

Understanding light-matter interaction at the nanoscale requires probing the optical properties of matter at the individual nano-absorber level. To this end, we have developed a nanomechanical photothermal sensing platform that can be used as a full spectromicroscopy tool for single molecule and single particle analysis. As a demonstration, the absorption cross-section of individual gold nanorods is resolved from the spectroscopic and polarization standpoint. By exploiting the capabilities of nanomechanical photothermal spectromicroscopy, the longitudinal localized surface plasmon resonance (LSPR) in the NIR range is unravelled and quantitatively characterized. The polarization features of the transversal surface plasmon resonance (TSPR) in the VIS range are also analyzed. The measurements are compared with the finite element method (FEM), elucidating the role played by electron-surface and bulk scattering in these plasmonic nanostructures, as well as the interaction between the nano-absorber and the nanoresonator, ultimately resulting in absorption strength modulation. Finally, a comprehensive comparison is conducted, evaluating the signal-to-noise ratio of nanomechanical photothermal spectromicroscopy against other cutting-edge single molecule and particle spectroscopy techniques. This analysis highlights the remarkable potential of nanomechanical photothermal spectromicroscopy due to its exceptional sensitivity

Thermal radiation dominated heat transfer in nanomechanical silicon nitride drum resonators

Nanomechanical silicon nitride (SiN) drum resonators are currently employed in various fields of applications that arise from their unprecedented frequency response to physical quantities. In the present study, we investigate the thermal transport in nanomechanical SiN drum resonators by analytical modelling, computational simulations, and experiments for a better understanding of the underlying heat transfer mechanism causing the thermal frequency response. Our analysis indicates that radiative heat loss is a non-negligible heat transfer mechanism in nanomechanical SiN resonators limiting their thermal responsivity and response time. This finding is important for optimal resonator designs for thermal sensing applications as well as cavity optomechanics.Comment: 8 pages, 4 figures in main text, 3 figures in supplementar