VHF Single-Crystal Silicon Elliptic Bulk-Mode Capacitive Disk Resonators—Part I: Design and Modeling

Hao, Zhili; Pourkamali, Siavash; Ayazi, Farrokh

doi:10.1109/jmems.2004.838387

Cited by 99 publications

(65 citation statements)

References 16 publications

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“…Their frequencies f are determined by the following characteristic equations, 10,11,15,16 under the thin-plate approximation where the disk radius R is much greater than the disk thickness: Figure 1 shows images of a device from optical microscope and scanning electron microscope (SEM). As seen from the images, a pulley-shaped wrap-around waveguide is specially designed for light to couple into and out of the disk resonator.…”

mentioning

confidence: 99%

High-Q silicon optomechanical microdisk resonators at gigahertz frequencies

Sun

Zhang

Tang

2012

Applied Physics Letters

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mentioning

confidence: 99%

High-Q silicon optomechanical microdisk resonators at gigahertz frequencies

Sun

Zhang

Tang

2012

Applied Physics Letters

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“…Lastly, the parameters q 1 (t) and q 2 (t) in Equations (1a) and (1b) are the generalized coordinates of modes 1 and 2, respectively, that determine the gyroscope's modal displacements in combination with the mode-shape functions 12 . Figure 2 shows the simulated modal deformations of the second-elliptical (n = 3) in-plane degenerate modes of an SD-BAW gyro that was created in a 40-μm-thick (100) SCS silicon-on-insulator (SOI) wafer with a radius of 420 μm.…”

Section: Design and Simulationmentioning

confidence: 99%

“…These effects translate into a frequency split that affects the overall performance of the gyro 14 . Additionally, these non-idealities tend to generate mode-to-mode coupling terms (k 12 Although q 2stiffness (t) is detrimental to gyro performance, the fact that its phase is 90°with respect to q 2coriolis (t) makes it easy to identify and correct, particularly when using coherent synchronous demodulation 15 . To compensate for this frequency split and the ZRO errors caused by the described anisoelasticity and anisoinertia, electrostatic spring softening can be used.…”

Section: Compensation Of Anisoinertia and Anisoelasticitymentioning

confidence: 99%

Substrate-decoupled, bulk-acoustic wave gyroscopes: Design and evaluation of next-generation environmentally robust devices

Serrano¹,

Zaman²,

Rahafrooz³

et al. 2016

Microsyst Nanoeng

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This paper reports on a new type of high-frequency mode-matched gyroscope with significantly reduced dependencies on environmental stimuli such as temperature, vibration, and shock. A novel stress-isolation system is used to effectively decouple an axis-symmetric bulk-acoustic wave (BAW) vibratory gyro from its substrate, minimizing the effect that external sources of error have on the offset and scale factor of the device. Substrate-decoupled (SD) BAW gyros with a resonance frequency of 4.3 MHz and Q values near 60 000 were implemented using the high aspect ratio poly and single-crystal silicon (HARPSS) process to achieve ultra-narrow capacitive gaps. Wafer-level packaged sensors were interfaced with a customized application-specific integrated circuit (ASIC) to achieve low variations in the offset across temperature (±26°s − 1 from − 40 to 85°C), supreme random-vibration immunity (0.012°s − 1 g RMS − 1 ) and excellent shock rejection. With a scale factor of 800 μV (°s, the SD-BAW gyro system attains a large full-scale range (±1250°s) with a non-linearity of less than 0.07%. A measured angle-random walk (ARW) of 0.39°/√h and a bias instability of 10.5°h − 1 are dominated by the thermal and flicker noise of the integrated circuit (IC), respectively. Additional measurements using external electronics show bias-instability values as low as 3.5°h INTRODUCTIONMicromachined gyroscopes have enabled a myriad of applications that range from basic motion detection for gaming to safety control systems in automobiles 1 . More recently, an increased interest in the use of microelectromechanical system inertial sensors for dead reckoning and pedestrian navigation in handheld electronics has placed stringent requirements on the die size, power consumption, and overall performance of this type of device. To date, most commercially available rate sensors have been designed as low-frequency flexural tuning-fork gyroscopes (TFGs), which are typically sensitive to random vibrations and prone to linear accelerations, such as those experienced under shock. These limitations complicate the use of TFG technology in large-volume, high-end applications, particularly in personal navigation, for which dependencies on fluctuations in the environment translate into long-term drift in the output of the system. Additionally, in recent months, concerns about the high sensitivity of consumer-grade gyroscopes in response to lowfrequency pressure signals that can be used to recover audio have increased as a potential threat for eavesdropping 2 , justifying the need for more environmentally robust rotation sensors.Acceleration suppression mechanisms can be implemented in TFGs to alleviate part of this problem using redundant proof masses that reject shock and vibration as common-mode signals 3 .

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“…Moreover, it is assumed that the ring resonator is made of single crystal silicon. Therefore, the equation governing the in-plane vibration of an annular ring, ignoring body force and internal heat source, can be given by [15,16]:…”

Section: Basic Assumptionsmentioning

confidence: 99%

Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators

2012

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Abstract:A distributed modeling approach has been developed to describe the dynamic behavior of ring resonators. The model includes the effect of large amplitudes around primary resonance frequencies, material and electrostatic nonlinearities. Through a combination of geometric and material nonlinearities, closed-form expression for third-order nonlinearity in mechanical stiffness of bulk-mode ring resonators is obtained. Moreover, to avoid dynamic pull-in instability, the choices of the quality factor, ac-drive and DC-bias voltages of the ring resonators, with a given geometry are limited by a resonant pull-in condition. Using the perturbation technique and the method of harmonic balance, the expressions for describing the effect of nonlinearities on the resonance frequency and displacement are derived. The results are discussed in detail, showing the effect of varying operating conditions and the quality factor on the harmonic distortions and third-order intermodulation distortion. The detailed nonlinear modeling and distortion analysis are applied as appropriate tools to design bulk-mode ring resonators with low motional resistance and high linearity.

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VHF Single-Crystal Silicon Elliptic Bulk-Mode Capacitive Disk Resonators—Part I: Design and Modeling

Cited by 99 publications

References 16 publications

High-Q silicon optomechanical microdisk resonators at gigahertz frequencies

High-Q silicon optomechanical microdisk resonators at gigahertz frequencies

Substrate-decoupled, bulk-acoustic wave gyroscopes: Design and evaluation of next-generation environmentally robust devices

Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators

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