Nonlinear mechanical effects in silicon longitudinal mode beam resonators

Kaajakari, V.; Mattila, T.; Lipsanen, Antti; Oja, Aarne

doi:10.1016/j.sna.2004.11.010

Cited by 88 publications

(50 citation statements)

References 9 publications

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“…The response of a fabricated 3-GHz resonator was measured for different values of the input available power. The maximum value of available input power before bifurcation [16] occurs (Fig. 11) was estimated to be approximately 5 dBm.…”

Section: A Shf 2-port Cmrsmentioning

confidence: 99%

Super-high-frequency two-port AlN contour-mode resonators for RF applications

Rinaldi

Zuniga

Zuo

et al. 2010

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

213

102

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This paper reports on the design and experimental verification of a new class of thin-film (250 nm) superhighfrequency laterally-vibrating piezoelectric microelectromechanical (MEMS) resonators suitable for the fabrication of narrow-band MEMS filters operating at frequencies above 3 GHz. The device dimensions have been opportunely scaled both in the lateral and vertical dimensions to excite a contourextensional mode of vibration in nanofeatures of an ultra-thin (250 nm) AlN film. In this first demonstration, 2-port resonators vibrating up to 4.5 GHz have been fabricated on the same die and attained electromechanical coupling, kt^2, in excess of 1.5%. These devices are employed to synthesize the highest frequency MEMS filter (3.7 GHz) based on AlN contour-mode resonator technology ever reported. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This journal article is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/522 0885-3010/$25.00 © 2010 IEEE 38 IEEE TransacTIons on UlTrasonIcs, FErroElEcTrIcs, and FrEqUEncy conTrol, vol. 57, no. 1, JanUary 2010Abstract-This paper reports on the design and experimental verification of a new class of thin-film (250 nm) superhigh-frequency laterally-vibrating piezoelectric microelectromechanical (MEMS) resonators suitable for the fabrication of narrow-band MEMS filters operating at frequencies above 3 GHz. The device dimensions have been opportunely scaled both in the lateral and vertical dimensions to excite a contourextensional mode of vibration in nanofeatures of an ultra-thin (250 nm) AlN film. In this first demonstration, 2-port resonators vibrating up to 4.5 GHz have been fabricated on the same die and attained electromechanical coupling, k t 2 , in excess of 1.5%. These devices are employed to synthesize the highest frequency MEMS filter (3.7 GHz) based on AlN contour-mode resonator technology ever reported.

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Section: A Shf 2-port Cmrsmentioning

confidence: 99%

Super-high-frequency two-port AlN contour-mode resonators for RF applications

Rinaldi

Zuniga

Zuo

et al. 2010

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

213

102

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“…Nonlinearities play an increasingly dominant role in the dynamics of small scale applications [5,9,10], such as periodic metamaterials with micro-or nanoscale unit cells. Precise design at these scales relies on a complete understanding of how nonlinearities affect operation and performance.…”

Section: Introductionmentioning

confidence: 99%

Multiple scales analysis of wave–wave interactions in a cubically nonlinear monoatomic chain

2010

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The interaction of waves in nonlinear media is of practical interest in the design of acoustic devices such as waveguides and filters. This investigation of the monoatomic mass-spring chain with a cubic nonlinearity demonstrates that the interaction of two waves results in different amplitude and frequency dependent dispersion branches for each wave, as opposed to a single amplitude-dependent branch when only a single wave is present. A theoretical development utilizing multiple time scales results in a set of evolution equations which are validated by numerical simulation. For the specific case where the wavenumber and frequency ratios are both close to 1:3 as in the long wavelength limit, the evolution equations suggest that small amplitude and frequency modulations may be present. Predictable dispersion behavior for weakly nonlinear materials provides additional latitude in tunable metamaterial design. The general results developed herein may be extended to three or more wavewave interaction problems.

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“…As shown in Figure 4, the geometric nonlinearities caused by large radial displacements in infinitesimal element could be addressed as follows: (23) where Moreover, the large displacement develops internal stresses inside the structure of the resonator, and therefore, nonlinear elastic behavior of silicon results in a nonlinear Young's modulus [18]:…”

Section: Modeling the Origins Of The Nonlinearitiesmentioning

confidence: 99%

“…The greatest vibration amplitude before hysteresis, called the critical vibration amplitude, X c , can be used to estimate the limit for power handling as given by E c = (K m X c 2 )/2 [18], where E c is the maximum stable energy stored in the resonator. Moreover, Figure 9 shows that the frequency stability limits the maximum allowable quality factor.…”

Section: Nonlinear Effects On Frequency Responsementioning

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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Nonlinear mechanical effects in silicon longitudinal mode beam resonators

Cited by 88 publications

References 9 publications

Super-high-frequency two-port AlN contour-mode resonators for RF applications

Super-high-frequency two-port AlN contour-mode resonators for RF applications

Multiple scales analysis of wave–wave interactions in a cubically nonlinear monoatomic chain

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

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