An overview on the vise of microelectromechanical systems (MEMS) technologies for timing and frequency control is presented. In particular, micromechanical RF filters and reference oscillators based on recently demonstrated vibrating on-chip micromechanical resonators with Q's > 10,000 at 1.5 GHz are described as an attractive solution to the increasing count of RF components (e.g., filters) expected to be needed by future multiband, multimode wireless devices. With Q's this high in on-chip abundance, such devices might also enable a paradigm shift in the design of timing and frequency control functions, where the advantages of high-Q are emphasized, rather than suppressed (e.g., due to size and cost reasons), resulting in enhanced robustness and power savings. Indeed, as vibrating RF MEMS devices are perceived more as circuit building blocks than as stand-alone devices, and as the frequency processing circuits they enable become larger and more complex, the makings of an integrated micromechanical circuit technology begin to take shape, perhaps with a functional breadth not unlike that of integrated transistor circuits. With even more aggressive three-dimensional MEMS technologies, even higher on-chip Q's are possible, such as already achieved via chip-scale atomic physics packages, which so far have achieved Q's > 107 using atomic cells measuring only 10 mm3 in volume and consuming just 5 mW of power, all while still allowing atomic clock Allan deviations down to 10-11 at one hour

/pdf/mems-technology-for-timing-and-frequency-control-4x49gry32c.pdf

MEMS technology for timing and frequency control

MEMS-based oscillators are an emerging class of highly miniaturized, batch manufacturable timing devices that can rival the electrical performance of well-established quartz-based oscillators. In this review, a description is given of the key properties of a MEMS resonator that determine the overall performance of a MEMS oscillator. Piezoelectric, capacitive and active resonator transduction methods are compared and their impact on oscillator noise and power dissipation is explained. An overview is given of the performance of MEMS resonators and MEMS-based oscillators that have been demonstrated to date. Mechanisms that affect the frequency stability of the resonator, such as temperature-induced frequency drift, are explained and an overview is given of methods that have been demonstrated to improve the frequency stability. The aforementioned performance indicators of MEMS-based oscillators are benchmarked against established quartz and CMOS technologies.

https://iopscience.iop.org/article/10.1088/0960-1317/22/1/013001/pdf

A review of MEMS oscillators for frequency reference and timing applications

Series-resonant vibrating micromechanical resonator oscillators are demonstrated using a custom-designed single-stage zero-phase-shift sustaining amplifier together with planar-processed micromechanical resonator variants with quality factors Q in the thousands that differ mainly in their power-handling capacities. The resonator variants include two 40-/spl mu/m-long 10-MHz clamped-clamped-beam (CC-beam) resonators, one of them much wider than the other so as to allow larger power-handling capacity, and a 64-/spl mu/m-diameter 60-MHz disk resonator that maximizes both Q and power handling among the resonators tested. Tradeoffs between Q and power handling are seen to be most important in setting the close-to-carrier and far-from-carrier phase noise behavior of each oscillator, although such parameters as resonant frequency and motional resistance are also important. With a 10/spl times/ higher power handling capability than the wide-width CC-beam resonator, a comparable series motional resistance, and a 45/spl times/ higher Q of 48 000, the 60-MHz wine glass resonator reference oscillator exhibits a measured phase noise of -110 dBc/Hz at 1-kHz offset, and -132 dBc/Hz at far-from-carrier offsets. Dividing down to 10 MHz for fair comparison with a common conventional standard, this oscillator achieves a phase noise of -125 dBc/Hz at 1-kHz offset, and -147 dBc/Hz at far-from-carrier offsets.

Series-resonant VHF micromechanical resonator reference oscillators

A new fabrication methodology that allows self-alignment of a micromechanical structure to its anchor(s) has been used to achieve vibrating radial-contour mode polysilicon micromechanical disk resonators with resonance frequencies up to 1.156 GHz and measured Q's at this frequency >2,650 in both vacuum and air. In addition, a 734.6-MHz version has been demonstrated with Q's of 7,890 and 5,160 in vacuum and air, respectively. For these resonators, self-alignment of the stem to exactly the center of the disk it supports allows balancing of the resonator far superior to that achieved by previous versions (in which separate masks were used to define the disk and stem), allowing the present devices to retain high Q while achieving frequencies in the gigahertz range for the first time. In addition to providing details on the fabrication process, testing techniques, and experimental results, this paper formulates an equivalent electrical circuit model that accurately predicts the performance of these disk resonators.

1.156-GHz self-aligned vibrating micromechanical disk resonator

This review provides a summary of the work completed to date on the nonlinear dynamics of resonant micro- and nanoelectromechanical systems (MEMS/NEMS). This research area, which has been active for approximately a decade, involves the study of nonlinear behaviors arising in small scale, vibratory, mechanical devices that are typically integrated with electronics for use in signal processing, actuation, and sensing applications. The inherent nature of these devices, which includes low damping, desired resonant operation, and the presence of nonlinear potential fields, sets an ideal stage for the appearance of nonlinear behavior, and this allows engineers to beneficially leverage nonlinear dynamics in the course of device design. This work provides an overview of the fundamental research on nonlinear behaviors arising in micro/nanoresonators, including direct and parametric resonances, parametric amplification, impacts, selfexcited oscillations, and collective behaviors, such as localization and synchronization, which arise in coupled resonator arrays. In addition, the work describes the active exploitation of nonlinear dynamics in the development of resonant mass sensors, inertial sensors, and electromechanical signal processing systems. The paper closes with some brief remarks about important ongoing developments in the field.

/pdf/nonlinear-dynamics-and-its-applications-in-micro-and-2d8rp19sh4.pdf

Nonlinear Dynamics and Its Applications in Micro- and Nanoresonators

Substantial reductions in vibrating micromechanical resonator series motional resistance Rx have been attained by mechanically coupling and exciting a parallel array of corner-coupled polysilicon square plate resonators. Using this technique with seven resonators, an effective Rx of 480 Omega has been attained at 70 MHz, which is more than 5.9X smaller than the 2.82 kOmega exhibited by a stand-alone transverse-mode corner-supported square resonator, and all this achieved while still maintaining an effective Q>9000. This method for Rx-reduction is superior to methods based on brute force scaling of electrode-to-resonator gaps or dc-bias increases, because it allows a reduction in Rx without sacrificing linearity, and thereby breaks the Rx versus dynamic range tradeoff often seen when scaling. This paper also compares two types of anchoring schemes for transverse-mode square micromechanical resonators and models the effect of support beam parameters on resonance frequency

Mechanically Corner-Coupled Square Microresonator Array for Reduced Series Motional Resistance

Polysilicon wine-glass mode micromechanical disk resonators using a stemless, non-intrusive suspension structure have been demonstrated in both vacuum and atmospheric pressure at frequencies around 73.4 MHz with Q's as high as 98,000 in vacuum, and 8,600 in atmosphere-the highest ever reported Q's at this frequency range and in these environments for any on-chip micro-scale resonator. The Q of 98,000 in vacuum for this wine-glass mode resonator is more than 10X higher than measured on radial contour mode counterparts, and more than 8X higher than exhibited by published free-free beams at 70 MHz.

Stemless wine-glass-mode disk micromechanical resonators

Substantial reductions in vibrating micromechanical resonator series motional resistance R/sub x/ have been attained by mechanically coupling and exciting a parallel array of corner-coupled polysilicon square plate resonators. Using this technique with five resonators, an effective R/sub x/ of 4.4 k/spl Omega/ has been attained at 64 MHz, which is more than 4.8 X smaller than the 21.3 k/spl Omega/ exhibited by a stand-alone transverse-mode square resonator, and all this achieved while still maintaining an effective Q>9,000. This method for R/sub x/-reduction is superior to methods based on brute force scaling of electrode-to-resonator gaps or DC-bias increases, because it allows a reduction in R/sub x/ without sacrificing linearity, and thereby breaks the R/sub x/ versus dynamic range trade-off often seen when scaling.

http://people.eecs.berkeley.edu/~ctnguyen/Research/IEEEJournalPubs/SquareResArray.jmems.Dec06.mdemirci.ctnguyen.04020264.pdf

Mechanically corner-coupled square microresonator array for reduced series motional resistance

The mechanism behind third order intermodulation distortion (IM/sub 3/) in capacitively driven clamped-clamped beam micromechanical ("CC-beam /spl mu/mechanical") resonators is shown to arise mainly from nonlinear interactions between applied off-resonance electrical signals and the mechanical displacements they induce. Analytical formulations for the third-order input intercept point (IIP/sub 3/) are then presented, first with simplifications that allow a closed form expression, then with additional complexities to account for second-order effects, such as beam bending due to an applied dc-bias voltage. Using this analytical formulation, predicted voltage IIP/sub 3/'s of 1.8 V and 6.5 V for 9.2 MHz and 17.4 MHz /spl mu/mechanical resonators, respectively, closely match measured values of 1.8 V and 6.3 V. Extensive data on the dependence of IIP/sub 3/ on dc-bias voltage, resonator Q, and resonator center frequency, are also included to lend further insight into the trade-offs involved when designing for a specific linearity requirement.

/pdf/third-order-intermodulation-distortion-in-capacitively-4fotxbrl1a.pdf

Third-order intermodulation distortion in capacitively-driven CC-beam micromechanical resonators

Polysilicon free-free beam micromechanical resonators based on MEMS technology operating in second and third-mode flexural vibrations have been demonstrated at frequencies as high as 102 MHz with Q's on the order of 11,500. Via strategic placement of electrodes, and careful determination of the exact support beam attachment locations that minimize anchor loss, these new resonators actually exhibit higher Q in the second mode than in the fundamental at the same frequency. Experiments to gauge the effect of variations in support beam dimensions and attachment locations on free-free beam microresonator performance show that an offset of only 0.6 /spl mu/m in the support beam attachment location results in a 7X degradation in the Q. In addition, measured temperature coefficients for second-mode free-free beam /spl mu/resonators are on the order of -13.1 ppm//spl deg/C, which is on par with that for fundamental mode resonance.

Higher-mode free-free beam micromechanical resonators

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