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

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MEMS technology for timing and frequency control

Photoplethysmography and its application in clinical physiological measurement

The paper presents an overview and reports the recent progress of research on squeeze film air damping in MEMS. The review starts with the governing equations of squeeze film air damping: the nonlinear isothermal Reynolds equation and various reduced forms of the equation for different conditions. After the basic effects of squeeze film damping on the dynamic performances of micro-structures are discussed based on the analytical solutions to parallel plate problems, recent research on various aspects of squeeze film air damping are reviewed, including the squeeze film air damping of perforated and slotted plate, the squeeze film air damping in rarefied air and the squeeze film air damping of torsion mirrors. Finally, the simulation of squeeze film air damping is reviewed. For quick reference, important equations and curves are included.

Squeeze film air damping in MEMS

Recently, remarkable advances have been made in coupling a number of high-Q modes of nano-mechanical systems to high-finesse optical cavities, with the goal of reaching regimes in which quantum behavior can be observed and leveraged toward new applications. To reach this regime, the coupling between these systems and their thermal environments must be minimized. Here we propose a novel approach to this problem, in which optically levitating a nano-mechanical system can greatly reduce its thermal contact, while simultaneously eliminating dissipation arising from clamping. Through the long coherence times allowed, this approach potentially opens the door to ground-state cooling and coherent manipulation of a single mesoscopic mechanical system or entanglement generation between spatially separate systems, even in room-temperature environments. As an example, we show that these goals should be achievable when the mechanical mode consists of the center-of-mass motion of a levitated nanosphere.

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Cavity opto-mechanics using an optically levitated nanosphere

This paper is an overview of current gyroscopes and their roles based on their applications. The considered gyroscopes include mechanical gyroscopes and optical gyroscopes at macro- and micro-scale. Particularly, gyroscope technologies commercially available, such as Mechanical Gyroscopes, silicon MEMS Gyroscopes, Ring Laser Gyroscopes (RLGs) and Fiber-Optic Gyroscopes (FOGs), are discussed. The main features of these gyroscopes and their technologies are linked to their performance.

Gyroscope Technology and Applications: A Review in the Industrial Perspective

This paper presents an analytical model for support loss in clamped–free (C–F) and clamped–clamped (C–C) micromachined beam resonators with in-plane flexural vibrations. In this model, the flexural vibration of a beam resonator is described using the beam theory. An elastic wave excited by the shear stress of the beam resonator and propagating in the support structure is described through the 2D elastic wave theory, with the assumption that the beam thickness (h) is much smaller than the transverse elastic wavelength (λT). Through the combination of these two theories and the Fourier transform, closed-form expressions for support loss in C–F and C–C beam resonators are obtained. Specifically, closed-form expression for the support loss in a C–C beam resonator is derived for the first time. The model suggests lower support quality factor (Qsupport) for higher order resonant modes compared to the fundamental mode of a beam resonator. Through comparison with experimental data, the validity of the presented analytical model is demonstrated. © 2003 Elsevier B.V. All rights reserved.

An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations

In this paper, we report on the design, fabrication, and characterization of an in-plane mode-matched tuning-fork gyroscope (M2-TFG). The M2-TFG uses two high-quality-factor (Q) resonant flexural modes of a single crystalline silicon mi- crostructure to detect angular rate about the normal axis. Operating the device under mode-matched condition, i.e., zero-hertz frequency split between drive and sense modes, enables a Q -factor mechanical amplification in the rate sensitivity and also improves the overall noise floor and bias stability of the device. The M2 -TFG is fabricated on a silicon-on-insulator substrate using a combination of device and handle-layer silicon etching that precludes the need for any release openings on the proof-mass, thereby maximizing the mass per unit area. Experimental data indicate subdegree-per-hour Brownian noise floor with a measured Allan deviation bias instability of 0.15deg /hr for a 60-mum-thick 1.5 mm X 1.7 mm footprint M2-TFG prototype. The gyroscope exhibits an open-loop rate sensitivity of approximately 83 mV/deg/s in vacuum. [2007-0100].

A Mode-Matched Silicon-Yaw Tuning-Fork Gyroscope With Subdegree-Per-Hour Allan Deviation Bias Instability

This work, the second of two parts, reports on the implementation and characterization of high-quality factor (Q) side-supported single crystal silicon (SCS) disk resonators. The resonators are fabricated on SOI substrates using a HARPSS-based fabrication process and are 3 to 18 /spl mu/m thick. They consist of a single crystal silicon resonant disk structure and trench-refilled polysilicon drive and sense electrodes. The fabricated resonators have self-aligned, ultra-narrow capacitive gaps in the order of 100 nm. Quality factors of up to 46 000 in 100 mTorr vacuum and 26000 at atmospheric pressure are exhibited by 18 /spl mu/m thick SCS disk resonators of 30 /spl mu/m in diameter, operating in their elliptical bulk-mode at /spl sim/150 MHz. Motional resistance as low as 43.3 k/spl Omega/ was measured for an 18-/spl mu/m-thick resonator with 160 nm capacitive gaps at 149.3 MHz. The measured electrostatic frequency tuning of a 3-/spl mu/m-thick device with 120 nm capacitive gaps shows a tuning slope of -2.6 ppm/V. The temperature coefficient of frequency for this resonator is also measured to be -26 ppm//spl deg/C in the temperature range from 20 to 150/spl deg/C. The measurement results coincide with the electromechanical modeling presented in Part I.

VHF single crystal silicon capacitive elliptic bulk-mode disk resonators-part II: implementation and characterization

This work, the first of two parts, presents the design and modeling of VHF single-crystal silicon (SCS) capacitive disk resonators operating in their elliptical bulk resonant mode. The disk resonators are modeled as circular thin-plates with free edge. A comprehensive derivation of the mode shapes and resonant frequencies of the in-plane vibrations of the disk structures is described using the two-dimensional (2-D) elastic theory. An equivalent mechanical model is extracted from the elliptic bulk-mode shape to predict the dynamic behavior of the disk resonators. Based on the mechanical model, the electromechanical coupling and equivalent electrical circuit parameters of the disk resonators are derived. Several considerations regarding the operation, performance, and temperature coefficient of frequency of these devices are further discussed. This model is verified in part II of this paper, which describes the implementation and characterization of the SCS capacitive disk resonators.

VHF single-crystal silicon elliptic bulk-mode capacitive disk resonators-part I: design and modeling

This paper presents a comprehensive analysis of support loss, the dominant loss mechanism, in center-supported micromechanical disk resonators operating in their radial bulk-modes. Through separation and coupling between the three components (disk, support beam, and support structure) of a disk resonator, support loss is evaluated quantitatively and the closed-form expression is obtained for support quality factor ( Q support ) of a center-supported disk resonator. The comparison between theoretical analysis and experimental data shows good agreement. This work provides significant insights into the geometrical design and choice of materials in high- Q center-supported disk resonant structures. To minimize support loss, a quarter wavelength rule exists for the height of the support beam in a center-supported disk resonator, similar to the length of torsion support beams of a free–free flexural beam resonator.

Zhili Hao

Papers

An analytical model for support loss in micromachined beam resonators with in-plane flexural vibrations

A Mode-Matched Silicon-Yaw Tuning-Fork Gyroscope With Subdegree-Per-Hour Allan Deviation Bias Instability

VHF single crystal silicon capacitive elliptic bulk-mode disk resonators-part II: implementation and characterization

VHF single-crystal silicon elliptic bulk-mode capacitive disk resonators-part I: design and modeling

Support loss in the radial bulk-mode vibrations of center-supported micromechanical disk resonators