Modal characteristics of coupled MEMS resonator array under the effect of residual stress

Peng, Bo; Hu, Kai-Ming; Fang, Xiao-Yong; Li, Xiuyuan; Zhang, Wenming

doi:10.1016/j.sna.2021.113236

Cited by 12 publications

(6 citation statements)

References 32 publications

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“…Electrostatic micro-electron-mechanical-systems (MEMS) devices with parallel plates have achieved considerable performance levels thanks to the increasingly consolidated synergy between advanced analytical-numerical modeling and technology (Liu et al, 2023;Li et al, 2023;Eidi, 2023;Azrak et al, 2023;Niekiel et al, 2023). This highlights correspondences between the mechanical stresses of the deformable microplate (from now on, d-microplate) and the intended use of the device (Zhang et al, 2022;Peng et al, 2022;Hosseini-Pishrobat et al, 2023), reducing the causes of excessive deformation of the d-microplate, such as fringing field, E ff (Krakover et al, 2022;Kumar et al, 2023;Tausiff et al, 2020;Ouakad, 2018), which depends on the ratio between the length of the device and its width, which proves the bending of the lines strength of the electric field, E, inside the device, which gradually becomes more intense near the edges (Boloni et al, 2010;García-Moreno and Bandala-S anchez, 2016;Hosseini-Pishrobat et al, 2023).…”

Section: Introductionmentioning

confidence: 89%

Galerkin-FEM approach for dynamic recovering of the plate profile in electrostatic MEMS with fringing field

Versaci,

Angiulli,

Fattorusso

et al. 2024

COMPEL

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Purpose Based on previous results of the existence, uniqueness, and regularity conditions for a continuous dynamic model for a parallel-plate electrostatic micro-electron-mechanical-systems with the fringing field, the purpose of this paper concerns a Galerkin-FEM procedure for deformable element deflection recovery. The deflection profiles are reconstructed by assigning the dielectric properties of the moving element. Furthermore, the device’s use conditions and the deformable element’s mechanical stresses are presented and discussed. Design/methodology/approach The Galerkin-FEM approach is based on weighted residuals, where the integrals appearing in the solution equation have been solved using the Crank–Nicolson algorithm. Findings Based on the connection between the fringing field and the electrostatic force, the proposed approach reconstructs the deflection of the deformable element, satisfying the conditions of existence, uniqueness and regularity. The influence of the electromechanical properties of the deformable plate on the method has also been considered and evaluated. Research limitations/implications The developed analytical model focused on a rectangular geometry. Practical implications The device studied is suitable for industrial and biomedical applications. Originality/value This paper proposed numerical approach characterized by low CPU time enables the creation of virtual prototypes that can be analyzed with significant cost reduction and increased productivity.

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Section: Introductionmentioning

confidence: 89%

Galerkin-FEM approach for dynamic recovering of the plate profile in electrostatic MEMS with fringing field

Versaci,

Angiulli,

Fattorusso

et al. 2024

COMPEL

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“…After cooling down to room temperature (or cooler), the packaged MEMS resonant accelerometer of dissimilar materials will experience large thermo-mechanical stress, since the CTE of the silicon MEMS die (2.6 ppm/ • C) is much lower than that of the ceramic substrate and the solder layers (6.5~25 ppm/ • C). Then, the stress is inevitably transmitted into the resonant beam through the fixing anchors, and consequently results in the frequency drift [8].…”

Section: Analysis Of Thermally Induced Packaging Effectsmentioning

confidence: 99%

“…However, thermally induced frequency drift is an inevitable practical issue that impacts the scale factor and zero-bias stability of a MEMS resonant accelerometer [ 4 , 5 ]. The thermal effects on the frequency drift of MEMS resonant accelerometers mainly include changes in the structural dimensions of the resonant beam and the Young’s modulus of monocrystalline silicon, caused by temperature variation [ 3 , 6 ]; temperature-dependent intrinsic residual stress within the resonant beam, produced during the manufacturing process [ 7 , 8 ]; and thermo-mechanical stress generated during the packaging process, due to the thermal mismatch between dissimilar materials [ 9 , 10 ]. Therefore, how to reduce the thermally induced frequency drift is the crucial problem to be solved urgently.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Thermally Induced Packaging Effects on the Frequency Drift of Micro-Electromechanical System Resonant Accelerometer

et al. 2023

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Due to the working principle of MEMS resonant accelerometers, their thermally induced frequency drift is an inevitable practical issue for their extensive application. This paper is focused on reducing the thermally induced packaging effects on the frequency drift. A leadless ceramic chip carrier package with a stress-buffering layer was proposed for a MEMS resonant accelerometer, and the influences of packaging structure parameters on the frequency drift were investigated through finite element simulations and verified experimentally. Because of the thermal mismatch between dissimilar materials, the thermo-mechanical stress within the resonant beam leads to a change in the effective stiffness and causes the frequency drift to decrease linearly with increasing temperature. Furthermore, our investigations reveal that increasing the stress-buffering layer thickness and reducing the solder layer thickness can significantly minimize the thermo-mechanical stress within the resonant beam. As the neutral plane approaches the horizontal symmetry plane of the resonant beam when optimizing the packaging structure, the effects of the compressive and tensile stresses on the effective stiffness of the resonant beam will cancel each other out, which can dramatically reduce the frequency drift. These findings provide guidelines for packaging design through which to improve the temperature stability of MEMS resonant accelerometers.

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“…The coupling resonance of MEMS has become one of the hot topics in research. The nonlinear coupling and energy transfers between multiple modes in micro/nanomechanical resonators were studied on intermodal coupling, internal resonance and synchronization [19][20][21][22][23]. Multimode nonlinear coupling was achieved by (1:2) internal resonance and parametric excitation with efficient coherent energy transfer [20].…”

Section: Introductionmentioning

confidence: 99%

“…Multimode nonlinear coupling was achieved by (1:2) internal resonance and parametric excitation with efficient coherent energy transfer [20]. The influence of residual stress on the modal characteristics of MEMS resonator array was analyzed with the laser Doppler method [21]. Asadi et al investigated experimentally and analytically the 1:2 and 2:1 internal resonance in a clamped-clamped beam resonator to provide insights into the detailed mechanism of internal resonance [22].…”

Section: Introductionmentioning

confidence: 99%

Internal Resonance of the Coupling Electromechanical Systems Based on Josephson Junction Effects

Liu

Zhang

2022

Micromachines

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The internal resonances of the coupling vibration among electro-dynamic modes of an NEMS are studied for the coupling resonators connected on a Josephson junction. The methodology adopted involves coupling a resonator connected on a Josephson junction. The mathematical model of the coupled system is then obtained by considering the regulatory nonlinear effect of the phase difference of that Josephson junction. The resulting dynamic differential equation is deduced by considering the nonlinear terms of the Josephson junction and the nanobeam. The multi-scale method is then used to obtain the 1:1:1 resonant amplitude–frequency response equation of the coupled electromechanical system. The influence of the phase difference of the Josephson junction, magnetic field, external excitation and other factors are analyzed based on the internal resonant amplitude of the coupled system. The simulation results illustrate that the changes in the values of the magnetic field, excitation amplitude and divided resistances can lead to a remarkable change in the values of the nanobeam frequency and amplitude. The internal resonance principle is used to generate a mutual conversion and amplification among electrical signals and mechanical signals. This research provides a theoretical framework and a numerical approach for improving the sensitivity of magnetic quality detection.

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Modal characteristics of coupled MEMS resonator array under the effect of residual stress

Cited by 12 publications

References 32 publications

Galerkin-FEM approach for dynamic recovering of the plate profile in electrostatic MEMS with fringing field

Galerkin-FEM approach for dynamic recovering of the plate profile in electrostatic MEMS with fringing field

Analysis of the Thermally Induced Packaging Effects on the Frequency Drift of Micro-Electromechanical System Resonant Accelerometer

Internal Resonance of the Coupling Electromechanical Systems Based on Josephson Junction Effects

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