Research Article

Improving mechanical sensor performance through larger damping

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Science  15 Jun 2018:
Vol. 360, Issue 6394, eaar5220
DOI: 10.1126/science.aar5220

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Reconsidering resonator sensing

Changes in the frequency of a nanoscale mechanical resonator can be used for many sensing applications, provided that there is an adequate signal-to-noise ratio. Normally, this ratio is improved by creating resonators with higher quality factors that “ring” for longer times. Taking a cue from the approaches used in atomic force microscopy, Roy et al. show that if the thermomechanical noise of the resonator is well defined, the signal-to-noise ratio of the frequency shift can improve by lowering the quality factor. They used this approach to demonstrate temperature sensing with a double-clamped silicon beam resonator, which performed better at ambient pressures than in a vacuum.

Science, this issue p. eaar5220

Structured Abstract


Nano-optomechanical systems (NOMS) are very small resonating mechanical devices that have extraordinary sensitivity. The coupling of mechanical motion to an optical cavity allows the motion to be tracked with femtometer precision. When using NOMS (or their electrical cousin, nanoelectromechanical systems) as a stable frequency reference, tiny force and mass changes can be distinguished by small frequency shifts. This is useful in atomic force microscopy and ultrasensitive mass measurement. For example, improvements in mass sensitivity have enabled the resolution of single molecules and have launched a prospective new paradigm of mechanical mass spectrometry. Any method to improve stability improves the performance of these sensors. If stability could remain the same or improve with more damping, NOMS ultrasensitivity could be deployed in a damping medium, like air or liquid, greatly enhancing their utility for use as biosensors or gas sensors or in the environment. Better stability could also benefit oscillator clock electronics, which could ultimately improve technologies such as GPS.


The quality factor (Q) is the inverse of the damping and indicates how sharp the resonance is in frequency. Q has been used as a proxy metric for frequency stability. However, Q only provides half the contribution; the other half comes from how large the resonance signal is compared to noise [the signal-to-noise ratio (SNR)]. This relationship is known as Robins’ model. Although traditionally Q and SNR have been assumed to be correlated, we noted that when the resonance conditions are limited only by intrinsic factors, the SNR should be inversely proportional to Q. In this case, stability should be independent of Q, and stable performance should be maintained in a variety of damping conditions.


We measured intrinsic resonator stability in NOMS while decreasing Q by increasing the air pressure around the device. We found that SNR behaved inversely to Q as hypothesized; however, stability unexpectedly improved with decreasing Q. This improved performance with damping is diametrically opposed to conventional expectations that had been established for decades. We revisited Robins’ model to find that it was based on a high-Q approximation. Rederiving the model without approximation gave rise to a new flatband regime for large damping (low Q). In this new regime, stability tracked to SNR only and, correspondingly, improved with damping, explaining the measured data. We confirmed the improved performance at higher damping by monitoring temperature fluctuations at different pressures and found that the best stability occurred at highest SNR, consistent with the new model. Finally, there is a noise source called dephasing that is known to prevent mechanical resonators from reaching their stability limits. We confirmed that this extra noise source correlated with Q and therefore was mitigated at large damping and removed completely at atmospheric pressure.


Our measurements confirm that Q and SNR behave inversely for intrinsically limited resonators, refuting long-standing assumptions about Q as a stability proxy. More notably, we found stability improved with damping. A low-Q approach was further shown to elegantly solve a vexing stability limitation caused by dephasing. We rederived Robins’ model to find a new flatband regime in which stability is linked only to SNR and found the new model to be consistent with the measured data. The flatband model displayed intriguing properties (in addition to stability behaving inversely to Q), including moderation of the trade-off between low noise and bandwidth and a route to frequency-scaling enhancement. The results offer a new paradigm for thinking about stability in mechanical resonators and suggest new pathways to improve stability in resonant sensors and crystal clock oscillators.

Higher SNR leads to better stability.

A mechanical resonator operating near intrinsic limits (e.g., limited only by thermomechanical noise and driven to the end of its linear regime) has a higher SNR in a low-Q state. SNR correlates to stability; frequency fluctuations are higher in the high-Q case. The surprising result is that low-Q devices can make better sensors and oscillators. (Inset) Cartoon of a NOMS chip with a waveguide bus (top), racetrack optical resonator (middle), and mechanical resonant doubly clamped beam (bottom). Beam motion is monitored with high precision through evanescent field interaction with and amplification by the optical cavity.


Mechanical resonances are used in a wide variety of devices, from smartphone accelerometers to computer clocks and from wireless filters to atomic force microscopes. Frequency stability, a critical performance metric, is generally assumed to be tantamount to resonance quality factor (the inverse of the linewidth and of the damping). We show that the frequency stability of resonant nanomechanical sensors can be improved by lowering the quality factor. At high bandwidths, quality-factor reduction is completely mitigated by increases in signal-to-noise ratio. At low bandwidths, notably, increased damping leads to better stability and sensor resolution, with improvement proportional to damping. We confirm the findings by demonstrating temperature resolution of 60 microkelvin at 300-hertz bandwidth. These results open the door to high-performance ultrasensitive resonators in gaseous or liquid environments, single-cell nanocalorimetry, nanoscale gas chromatography, atmospheric-pressure nanoscale mass spectrometry, and new approaches in crystal oscillator stability.

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