An analytical model for the resonance frequency of square perforated Lamé-mode resonators

Luschi, Luca; Pieri, Francesco

doi:10.1016/j.snb.2015.07.085

Cited by 19 publications

(8 citation statements)

References 31 publications

(55 reference statements)

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“…A model for the temperature coefficient of thin perforated Lamé resonators can be derived from the resonance frequency model already presented in [32], where holes are taken into account through a cellular material approach [33]. For the purpose of this work, cellular materials are microstructured solids obtained by periodic repetition of a unit cell.…”

Section: Model Derivationmentioning

confidence: 99%

“…Accurate expressions for Ep,eq, νp,eq and ρeq are given in [32] as a function of the fill factor α, i.e. the ratio of the distance between holes ts to the pitch ls (Fig.…”

Section: Model Derivationmentioning

confidence: 99%

“…where Ep, νp are the SCS Young's modulus and Poisson's ratio along directions parallel to the sides of the resonator, respectively, and ρ is the SCS density. The used optimum values of k were determined using the approach in [32] and were 2.85 for [100] SCS (all dopings and temperatures), 3.45 for [110] SCS (all dopings and temperatures). These expressions were obtained assuming a plane stress hypothesis in the unit cell.…”

Section: Model Derivationmentioning

confidence: 99%

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Temperature Compensation of Silicon Lamé Resonators Using Etch Holes: Theory and Design Methodology

Luschi

Iannaccone

Pieri

2017

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

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We present a new approach to the temperature compensation of MEMS Lamé resonators, based on the combined effect of the doping concentration and of the geometry of etch holes on the equivalent temperature coefficients of silicon. To this purpose, we develop and validate an analytical model which describes the effect of etch holes on the temperature stability of Lamé resonators through comparison with experiments available in the literature and finite-element method (FEM) simulations. We show that two interesting regions of the design space for Lamé resonators exist, where a cancellation of the first-order temperature coefficient of the resonance frequency is possible: [100]-oriented silicon with n-doping of 2.5 ·10 cm , and [110]-oriented silicon with p-doping higher than 1.4 ·10 cm .

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Section: Model Derivationmentioning

confidence: 99%

“…Accurate expressions for Ep,eq, νp,eq and ρeq are given in [32] as a function of the fill factor α, i.e. the ratio of the distance between holes ts to the pitch ls (Fig.…”

Section: Model Derivationmentioning

confidence: 99%

Section: Model Derivationmentioning

confidence: 99%

See 1 more Smart Citation

Temperature Compensation of Silicon Lamé Resonators Using Etch Holes: Theory and Design Methodology

Luschi

Iannaccone

Pieri

2017

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

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“…The actual number of holes along 𝑦 in the holed segment does not influence the PnC behavior, as long as it is large enough that the equivalent material hypothesis holds. Having a large number of holes along 𝑦 increases the surface to volume ratio, a property linked to an increase in sensitivity in resonant mass sensors [10,[21][22][23].…”

Section: Modelmentioning

confidence: 99%

“…The values of 𝛺 𝑛0 and 𝐼 𝑃,𝛺𝛺 can be determined by equating ( 14) and (22) in the homogeneous (𝛿𝛼 = 0) case: (28)…”

Section: Appendix Bmentioning

confidence: 99%

A Simple Method for the Design of 1-D MEMS Flexural Phononic Crystals

Luschi

Pieri

Iannaccone

2016

IEEE Trans. Electron Devices

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We present a simple and computationally inexpensive method to design 1-D MEMS flexural phononic crystals (PnCs) with assigned width and central frequency of the acoustic bandgap based on the analysis of the characteristic polynomial of the acoustic transmission matrix of the crystal elementary cell. Our analysis shows that a high acoustic contrast does not necessarily lead to wide bandgaps, unless the modulation of the mechanical properties is properly chosen. We also demonstrate that the acoustic attenuation inside the bandgap, which is an important design target, is essentially predetermined once that the bandgap width and center have been chosen. The method can be valuable for fast design of PnC devices with applications spanning from sensors to filters and resonators

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