Numerical and compact modelling of squeeze-film damping in RF MEMS resonators

• Published in: 2008 Symposium on Design, Test, Integration and Packaging of MEMS/MOEMS pp. 222 - 228
• Main Authors: Veijola, T., Lehtovuori, A.
• Format: Conference Proceeding
• Language: English
• Published: Grenoble IEEE 01.04.2008; EDA publishing
• Subjects: Acoustic waves; Applied sciences; Circuit properties; Damping; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Fluid flow; Micro- and nanoelectromechanical devices (mems/nems); Navier-Stokes equations; Numerical models; Oscillators, resonators, synthetizers; Radiofrequency microelectromechanical systems; Resonance; Resonant frequency; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Shock absorbers; Springs; Damping; Resonator; Acoustic wave; Theoretical study; Compact design; Numerical method; Modeling; BioMEMS; Finite element method; Frequency shift; Frequency band; Wide band; Gas flow; Navier Stokes equation; Resonance frequency; Air gap; Reynolds equation; Microelectromechanical device
• ISBN: 2355000069; 9782355000065
• DOI: 10.1109/DTIP.2008.4752988

Oscillatory gas flow in squeeze-film dampers is studied up to frequencies where the length of the acoustic wave is comparable with the dimensions of the air gap. Damping and spring forces are calculated both numerically and analytically from the linearized 2D Navier-Stokes equations. In addition to the low frequency region of inertialess gas, where the use of the Reynolds equation is limited, the new model considers several additional phenomena. These are the inertia of the gas, the transition from isothermal to adiabatic conditions, and the gap resonances at frequencies where the acoustic wavelength is comparable to the air gap height. Velocity and temperature slip conditions are considered to make the model valid in micromechanical structures where the air gap heights are of the order of a micrometer. An approximate compact model is derived combining the low frequency model and the gap resonance model. The accuracy of the compact model is studied by comparing its response to the numerical results calculated with the finite element method. The agreement is very good in a wide frequency band when the ratio of the damper width and the gap height is greater than 10. The numerical study and the compact model are directly applicable in predicting the damping and the resonance frequency shift due to air in RF MEMS resonators having narrow air gap widths and operating at frequencies where the wavelengths become comparable to the flow channel dimensions.