Centimeter-scale nanomechanical resonators with low dissipation

Nat. Commun. 15, 4255 (2024) · DOI: 10.1038/s41467-024-48183-7

License: CC BY 4.0.

Abstract

High-aspect-ratio mechanical resonators are pivotal in precision sensing, from macroscopic gravitational wave detectors to nanoscale acoustics. However, fabrication challenges and high computational costs have limited the length-to-thickness ratio of these devices, leaving a largely unexplored regime in nano-engineering. We present nanomechanical resonators that extend centimeters in length yet retain nanometer thickness. We explore this expanded design space using an optimization approach which judiciously employs fast millimeter-scale simulations to steer the more computationally intensive centimeter-scale design optimization. By employing delicate nanofabrication techniques, our approach ensures high-yield realization, experimentally confirming room-temperature quality factors close to theoretical predictions. The synergy between nanofabrication, design optimization guided by machine learning, and precision engineering opens a solid-state path to room-temperature quality factors approaching 10 billion at kilohertz mechanical frequencies – comparable to the performance of leading cryogenic resonators and levitated nanospheres, even under significantly less stringent temperature and vacuum conditions.

Figures

9 panels with data across 3 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

• panel (c): Quality factor against aspect ratio $L/h$ for a Si$_3$N$_4$ string: measured state-of-the-art devices of panel (a) by symbol (blue), the predicted design of this work (red star), the bending-loss and clamping-loss lines and the intrinsic level (grey). The shaded and hatched regions of the print are not drawn. data.csv
• panel (d): Thickness $h$ ($\mu$m) against length $L$ (mm) of the nanoscale resonators of panel (a) (blue, by symbol), the LIGO suspensions of panel (b) (teal) and the design of this work (red star), with the dotted line of its aspect ratio. The drawn strings, the shaded groupings and the duplicate symbols beside them are not reproduced. data.csv

Fig. 2

• panel (a): Histograms (probability density) of $\log_{10}$ of the simulated quality factor for 25 random designs at the two lengths, $Q^{3\,\mathrm{mm}}$ (green) and $Q^{3\,\mathrm{cm}}$ (blue), each with its normal fit (black). The print labels the axis in powers of ten ($10^6$ to $10^{10}$). data.csv
• panel (b): Histogram (probability density) of $\log_{10}$ of the ratio $Q^{3\,\mathrm{cm}}/Q^{3\,\mathrm{mm}}$ over the 25 random designs, with its normal fit (black). The print labels the axis 10, 100, 1000. data.csv
• panel (d): Best quality factor found so far ($\times 10^9$) against iteration $\times$ cost for the transformed MFBO (red) and regular single-fidelity BO (black). The dashed line marks the end of the random initial designs, which the print shows as a change of background shading. data.csv
• panel (e): Simulated quality factor ($\times 10^9$) of each design evaluated during the transformed MFBO against iteration $\times$ cost: 3 cm high-fidelity (blue, 122 points) and 3 mm low-fidelity (green, 226 points) simulations. The print breaks its linear axis between 0.1 and 1; here one continuous log axis is used. data.csv
• panel (f): Distance in design-parameter space from the best design so far to the design evaluated at each iteration, against iteration $\times$ cost (black line); red markers flag the iterations where a higher quality factor was found. The dashed line marks the end of the random initial designs (Random and Bayesian optimization regions in the print). data.csv

Fig. 3

Illustrative figure, no extractable data. Shown in the paper PDF. Page 5 of the PDF.

Fig. 4

• panel (d): Ringdown of the optimized 3 cm nanoresonator excited at 214 kHz: peak power (dBm) against time (h) (blue points) with the linear fit (black line). The print also carries the label box $Q = 6.6 \cdot 10^9$, $f = 214$ kHz. data.csv
• panel (e): Thermomechanical noise spectrum of the nanoresonator: power (dBm) against frequency $f$ (kHz), from 65 to 350 kHz. data.csv

Cite

Andrea Cupertino, Dongil Shin, Leo Guo, Peter G. Steeneken, Miguel A. Bessa, Richard A. Norte. Centimeter-scale nanomechanical resonators with low dissipation. Nat. Commun. 15, 4255 (2024). https://doi.org/10.1038/s41467-024-48183-7

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