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Squeeze film effects on dynamic performance of MEMS μ-mirrors-consideration of gas rarefaction and surface roughness

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Abstract

The squeeze film behavior of MEMS torsion mirrors is modeled, analyzed and discussed. Effects of gas rarefaction (first-order slip-flow model with non-symmetric accommodation coefficients, ACs) and surface roughness are considered simultaneously by using the average Reynolds type equation (ARTE). Based on the operating conditions with small variations in film thickness and pressure, the ARTE is linearized. A coordinate transformation, by stretching or contracting the axes by referring to the roughness flow factors, is proposed to transform the linearized ARTE into a diffusion type modal equation. The dynamic coefficients (stiffness and damping coefficients) are then derived and expressed in analytical form. The results show that the tilting frequency (or Γ0 squeeze number), roughness parameters (γ Peklenik numbers, σ standard deviation of composite roughness) and gas rarefaction parameters (D inverse Knudsen number, \(\alpha_{1}, \alpha_{2}:\) ACs) are all important parameters on analyzing the dynamic performance of MEMS torsion mirrors.

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Acknowledgments

Te authors would like to thank for the financial support from National Science Council, Taiwan, contract number: NSC94-2622-E-151-004-CC3.

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  1. Institute of Nanotechnology and Microsystems Engineering, National Cheng Kung University, No.1 University Road, Tainan City, 701, Taiwan

    Wang-Long Li

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  1. Wang-Long Li
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Correspondence to Wang-Long Li.

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Li, WL. Squeeze film effects on dynamic performance of MEMS μ-mirrors-consideration of gas rarefaction and surface roughness. Microsyst Technol 14, 315–324 (2008). https://doi.org/10.1007/s00542-007-0479-x

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