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Frequency fluctuations in silicon nanoresonators

Abstract

Frequency stability is key to the performance of nanoresonators. This stability is thought to reach a limit with the resonator's ability to resolve thermally induced vibrations. Although measurements and predictions of resonator stability usually disregard fluctuations in the mechanical frequency response, these fluctuations have recently attracted considerable theoretical interest. However, their existence is very difficult to demonstrate experimentally. Here, through a literature review, we show that all studies of frequency stability report values several orders of magnitude larger than the limit imposed by thermomechanical noise. We studied a monocrystalline silicon nanoresonator at room temperature and found a similar discrepancy. We propose a new method to show that this was due to the presence of frequency fluctuations, of unexpected level. The fluctuations were not due to the instrumentation system, or to any other of the known sources investigated. These results challenge our current understanding of frequency fluctuations and call for a change in practices.

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Figure 1: The frequency stability of resonators measured in the literature is on average 2.1 orders of magnitude greater than the thermomechanical noise-limited stability.
Figure 2: The frequency stability of our monocrystalline silicon nanomechanical resonators is limited by a source of noise exceeding thermal fluctuations.
Figure 3: Additive phase noise and frequency fluctuations show different features in the Allan deviation.
Figure 4: The limit in frequency stability of our silicon resonators is due to frequency fluctuations.
Figure 5: The limiting frequency fluctuations are not due to temperature fluctuations alone.
Figure 6: Known sources of frequency fluctuations.

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Acknowledgements

The authors acknowledge partial support from the LETI Carnot Institute NEMS-MS project, as well as from the European Union through the ERC Enlightened project (616251) and the Marie-Curie Eurotalents outgoing (S.H.) and incoming (M.S.) fellowships. The authors thank C. Marcoux and C. Dupré for their support with device fabrication. L.G.V. acknowledges financial support from the Swiss National Science Foundation (PP00P2-144695) and the European Commission (PCIG14-GA-2013-631801). A.K.N. acknowledges financial support from the Indian Institute of Science, Bangalore.

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M.S. performed all experiments and processed the data. M.S., G.J., A.K.N. and S.H. conceived and designed the experiments. L.G.V. and S.H. performed the literature review. M.G. fabricated the devices and performed all SEM observations. M.S., G.J. and S.H. co-wrote the paper. All authors commented on the manuscript.

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Correspondence to Sébastien Hentz.

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Sansa, M., Sage, E., Bullard, E. et al. Frequency fluctuations in silicon nanoresonators. Nature Nanotech 11, 552–558 (2016). https://doi.org/10.1038/nnano.2016.19

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