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Micro-electrometer Based on Mode-Localization Effect

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Micro and Nano Machined Electrometers

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Abstract

Resonant micro-electrometers have been the research interest to many groups around the world. Conventionally, the resonant electrometers rely on a frequency-shift based readout. In this chapter, a new type of resonant micro-electrometer based on mode-localization effect is introduced and discussed. This new electrometer implementation is one subset of a broader family of sensors termed as “mode-localized sensors”. The readout metric of this category of sensors is essentially based on amplitude modulation, which is a key identifier of this approach. In addition to the sensing paradigm shift, the mode-localized sensors have a distinguishable topology to the convention based on a single resonator: that is, typically more than one resonators are intentionally coupled to each other through a coupling element, to allow spatial energy extension. Due the advantages that accompany the unique configurations, such as higher sensitivity and common mode rejection capabilities, the new sensing scheme has quickly attracted researchers’ attention. And naturally it has been adapted for electrometer applications. Currently, the resolution that can be achieved by an electrometer utilizing this approach can be less than 10 e/Hz\(^{1/2}\). Future directions to further enhance the sensor performance are also discussed.

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Notes

  1. 1.

    Here, the subscript \(i=1, 2\) denotes the number of the resonator.

  2. 2.

    Since the amplitude ratio is a dimensionless value, to fairly compare the two scale factors, it is necessary to normalize the scale factor [20].

  3. 3.

    This is generally true for a force input, as the stiffness change induced by the axial stress is generally much larger than that caused by strain variations.

  4. 4.

    The approximation is valid when \(\frac{qd}{\varepsilon _{0}A}<V_{0}\), which is true for small charge injections.

  5. 5.

    The unstable region in the frequency response of the resonators, above the critical linear amplitude.

  6. 6.

    Also, the slope of derivative of phase with respect to frequency, \(\mathrm {d}\phi /\mathrm {d}f\).

  7. 7.

    In this study [45], resonator 1 and 2 are defined as the resonator being directly driven by an AC drive voltage, and the resonator being driven through coupling, respectively.

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Authors and Affiliations

  1. Centre for Gravitational Experiments, Huazhong University of Science and Technology, Wuhan, China

    Chun Zhao, Huafeng Liu, Peiyi Song & Fangjing Hu

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  1. Chun Zhao
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  2. Huafeng Liu
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Correspondence to Chun Zhao .

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  1. School of Engineering and Built Environment, Griffith University, Gold Coast Campus, Southport, QLD, Australia

    Yong Zhu

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Zhao, C., Liu, H., Song, P., Hu, F. (2020). Micro-electrometer Based on Mode-Localization Effect. In: Zhu, Y. (eds) Micro and Nano Machined Electrometers. Springer, Singapore. https://doi.org/10.1007/978-981-13-3247-0_2

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  • DOI: https://doi.org/10.1007/978-981-13-3247-0_2

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