Numerical Study of the Impact of Vibration Localization on the Motional Resistance of Weakly Coupled MEMS Resonators

Abstract

This paper presents a numerical study of the impact of process-induced variations on the achievable motional resistance Rx of one-dimensional, two-dimensional, cyclic and cross-coupled architectures of weakly coupled, electrostatically transduced MEMS resonators operating in the 250 kHz range. We use modal analysis to find the Rx of such coupled arrays and express it as a function of the eigenvectors of the specific mode of vibration. Monte Carlo numerical simulations, which accounted for up to 0.75% variation in critical resonator feature sizes, were initiated for different array sizes and coupling strengths, for the four distinct coupling architectures. Improvements in the mean and standard deviation of the generated Rx distributions are reported when the resonators are implemented in a cross-coupled scheme, as opposed to the traditional one-dimensional chain. The two-dimensional coupling scheme proves to be a practical and scalable alternative to weakly coupled one-dimensional chains to improve the immunity to process variations. It is shown that a 75% reduction in both the mean and standard deviation of the Rx is achieved as compared to the traditional one-dimensional chain for a normalized internal coupling κ > 10 −2 .

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

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Acoustic mode confinement using coupled cavity structures in UHF unreleased MEMS resonators

“…Just as in the case of weakly coupled released resonators, perturbations induced in the structurally symmetry can significantly affect the vibration dynamics and energy distribution within the system (Erbes et al 2015).…”

Nonlinear size-dependent modeling and dynamics of nanocrystalline arc resonators

“…At the macro-scale, Lacarbonara et al (Lacarbonara et al 2005) investigated the veering phenomena numerically by introducing imperfection to the initially curved beam by considering linear and torsional springs at the boundaries. In MEMS and NEMS, the veering phenomenon was associated mostly with the mode-localization phenomenon arising in weakly coupled systems (Wang et al 2012;Erbes et al 2014). Most recent, veering for internally coupled modes in micromachined systems was reported for arc and V-shaped resonators with high stiffness tuning (Hajjaj et al 2017a, b;Alcheikh et al 2020;Ouakad et al 2021).…”