Enhancement of micromechanical resonator manufacturing precision via mechanically-coupled arraying

Yang, Lin; Li, Wei‐Chang; Kim, Bongsang; Lin, Yuqing; Ren, Zeying; Nguyen, C.T.-C.

doi:10.1109/freq.2009.5168142

Cited by 18 publications

(10 citation statements)

References 11 publications

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“…That the new negative capacitance equivalent circuit model introduced perfectly predicts this phenomenon, while also aiding circuit visualization, bodes well for its continued use in future resonator circuits for which tailored electrical stiffness strengths are desired. Indeed, the demonstrated stability enhancing attributes of mechanically-coupled arrays that make them less vulnerable to dc-bias voltage noise, dielectric charging, and external vibrations, together with already demonstrated arrayderived reductions in the standard deviation of array resonance frequency [26], present strong cases for a more prevalent use of arrays in next generation MEMS-based frequency reference devices.…”

Section: Resultsmentioning

confidence: 99%

Micromechanical Disk Array for Enhanced Frequency Stability Against Bias Voltage Fluctuations

Wu¹

2014

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. Copyright © 2014, by the author(s).All rights reserved.Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission. High-Q capacitive-gap transduced micromechanical resonators constructed via MEMS technology have recently taken center-stage among potential next generation timing and frequency reference devices that might satisfy present and future applications. Notably, oscillators referenced to very high Q capacitive-gap transduced MEMS resonators have already made inroads into the low-end timing market, and research devices have been reported to satisfy GSM phase noise requirements while only consuming less than 80 µW of power. Meanwhile, such devices have also posted some impressively low acceleration sensitivities, with measured sensitivity vectors less than 0.5 ppb/g. Interestingly, theory predicts that the acceleration sensitivity of these devices should be even better than this, if not for frequency instability due to electrical stiffness. Indeed, electrical stiffness is predicted to set lower limits on not only short-term stability, but longterm as well, especially when one considers frequency variations due to charging or temperature-induced geometric shifts. Micromechanical Disk Array for Enhanced Frequency Stability Against BiasPursuant to circumventing electrical stiffness-based instability, this work introduces a more circuit design-friendly equivalent circuit model that uses negative capacitance to capture the influence of electrical stiffness on device and circuit behavior. This new circuit model reveals that capacitive-gap transduced micromechanical resonators can offer better stability against electrical-stiffness-based frequency instability when used in large mechanically-coupled arrays. Measurements confirm that a 215-MHz 50-resonator disk array achieves a 3.5× enhancement in frequency stability against dc-bias voltage variation over a stand-alone single d...

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Section: Resultsmentioning

confidence: 99%

Micromechanical Disk Array for Enhanced Frequency Stability Against Bias Voltage Fluctuations

Wu¹

2014

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“…Some of these variations may be mitigated by mechanically coupling these resonators which has been shown to improve the feed-through, suppress spurious modes, and improve gain at resonance with the tradeoff of a larger overall footprint [19,20].…”

Section: Fabrication Variations and Yieldmentioning

confidence: 99%

Resonant body transistors in standard CMOS technology

Marathe

Wang

Mahmood

et al. 2012

2012 IEEE International Ultrasonics Symposium

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“…(9) For a single MEMS resonator, increasing the sensing capacitance is also one of the methods to reduce the motional impedance, for example, increasing the thickness of a disk fabricated by deep reactive-ion eching (DRIE), (10,11) or decreasing the electrode-to-resonator gap. (12) However, the motional impedance increases linearly with increasing frequency, (13) and when the frequency is in the ultrahigh frequency (UHF) range, the method of only increasing the thickness or reducing the gap is generally insufficient if a 50 Ω matching impedance is desired.…”

Section: Introductionmentioning

confidence: 99%

Inclination Effects on Voltage-controlled Tuning of MEMS Disk Resonator Array Composite Fabricated by Deep Reactive Ion Etching Process

Yan¹,

Bao²,

Quan³

et al. 2018

Sensors and Materials

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Capacitive micro-electromechanical system (MEMS) disk resonators fabricated by deep reactive-ion etching (DRIE) have large sensitive capacitances and low motional resistances. However, for the MEMS disk structure with a high aspect ratio, the cross section takes on a trapezoidal profile, which will affect the performance of the resonator. In this study, we firstly analyzed the electrostatic tuning mechanism of electrical stiffness produced by the electrostatic force, and the dependence of resonance frequency variation on the inclination angle and dc bias voltage is obtained and the electromechanical coupling strength was changed owing to the inclination angle. Secondly, after analyzing the feasibility of overcoming the inclination effect by introducing a tuning disk array, the optimal tuning voltage of the inclined disk resonator array and the scale of the array with a small motional resistance can be obtained. The results show that, for an array with the same inclination angle of 0.1° and biased at 10 V, when the tuning voltage is 20 V, the relative error of the resonance frequency can be reduced to 12.4 ppm. In addition, the optimal tuning voltage increases as the inclination angle increases, and when the inclination angle is 0.3°, the optimal tuning voltages are 28.68 and 57.35 V for the dc bias voltages of 10 and 30 V, respectively. If the motional resistance needs be reduced to 50 Ω, the integrated number of disk resonators will increase to 1048, and the optimal tuning voltage can reach 37.5 V. These results can provide some theoretical basis for the large-scale integration of the disk resonator array in the future.

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Enhancement of micromechanical resonator manufacturing precision via mechanically-coupled arraying

Cited by 18 publications

References 11 publications

Micromechanical Disk Array for Enhanced Frequency Stability Against Bias Voltage Fluctuations

Micromechanical Disk Array for Enhanced Frequency Stability Against Bias Voltage Fluctuations

Resonant body transistors in standard CMOS technology

Inclination Effects on Voltage-controlled Tuning of MEMS Disk Resonator Array Composite Fabricated by Deep Reactive Ion Etching Process

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