Gas Damping in Capacitive MEMS Transducers in the Free Molecular Flow Regime.

Boris A Boom,Eric Hennes,Johannes F J Van Den Brand,Alessandro Bertolini

doi:10.3390/s21072566

Boris A Boom, Eric Hennes + Show 2 more

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https://doi.org/10.3390/s21072566

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Abstract

We present a novel analysis of gas damping in capacitive MEMS transducers that is based on a simple analytical model, assisted by Monte-Carlo simulations performed in Molflow+ to obtain an estimate for the geometry dependent gas diffusion time. This combination provides results with minimal computational expense and through freely available software, as well as insight into how the gas damping depends on the transducer geometry in the molecular flow regime. The results can be used to predict damping for arbitrary gas mixtures. The analysis was verified by experimental results for both air and helium atmospheres and matches these data to within 15% over a wide range of pressures.

Highlights

Accurate prediction of the gas damping in microelectromechanical systems (MEMS)structures is of vital importance for the design of various types of microsensors
The accuracy and resolution of MEMS gyroscopes is closely linked to the quality factor of the vibrating sensing elements, and the Brownian noise level in MEMS accelerometers is often dominated by squeezed-film damping in the narrow gaps in its capacitive transducers
We present an analysis that is based on relatively simple analytical models for both kinetic gas damping [8] and squeezed-film damping [9] in the free molecular flow regime

Summary

Introduction

Accurate prediction of the gas damping in microelectromechanical systems (MEMS)structures is of vital importance for the design of various types of microsensors. The accuracy and resolution of MEMS gyroscopes is closely linked to the quality factor of the vibrating sensing elements, and the Brownian noise level in MEMS accelerometers is often dominated by squeezed-film damping in the narrow gaps in its capacitive transducers. Because of the typically small feature sizes in these microsensors, the mean free path of the gas molecules inside these packages is often significantly larger than the relevant dimensions of the sensor, and the gas damping is fully determined by individual gas–wall collisions. There are two classes of models for gas damping in this free molecular flow regime, both with their own challenges. Several limiting assumptions were subsequently removed by Frangi et al [3], resulting in a deterministic 3D model for damping in the rarefied gas regime assuming fully diffuse gas–wall interactions

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