Abstract
The dynamic performance of a micro-resonator depends on its energy loss mechanism which is quantified by Q-factor (Quality factor). This paper presents numerical and analytical modelling techniques to understand the air damping on energy loss and Q-factor in enclosed micro-resonators. A complete finite element based numerical model is presented that can recreate a vacuum packaged MEMS resonators operating condition and capture its Q-factor for various design and pressure conditions. The finite element model was then compared with analytical models available in the literature. In this work, various vacuum regions relevant to encapsulated MEMS resonators are investigated using analytical and finite element approaches for pressure ranges of < 1 Pa, 1–10 Pa, and 10–100 Pa. When the pressure decreases, the Q factor from finite element analysis and the analytical model exponentially increases until it levels off in intrinsic damping. The modelling techniques described in this paper are compared with previously reported experimental work showing good qualitative agreement of the change in Q-factor with pressure. Air damping is divided into squeeze film damping and slide film damping to further explore damping effects and squeeze film damping is found to be the dominant energy loss mechanism in the studied device. In a gap-closing structure, the air gaps between moving structure and fixed fingers create squeeze film damping and cause energy loss while the smaller air gaps between them generate large forces, increasing the damping. The modelling techniques presented in this paper can be applied generically to MEMS resonators to mitigate air damping losses.
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Authors would like to thank MITACS and Teledyne Micralyne for financial supports. The authors also thank CMC Microsystems for CAD tools support.
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Wang, A., Sahandabadi, S., Harrison, T. et al. Modelling of air damping effect on the performance of encapsulated MEMS resonators. Microsyst Technol 28, 2529–2539 (2022). https://doi.org/10.1007/s00542-022-05385-7
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DOI: https://doi.org/10.1007/s00542-022-05385-7