An Improved Reynolds-Equation Model for Gas Damping of Microbeam Motion

Gallis, Michail A.; Torczynski, J. R.

doi:10.1109/jmems.2004.832194

Cited by 67 publications

(80 citation statements)

References 12 publications

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“…Substrate-dependent slip can then have a leading-order effect on drag (as illustrated by figure 9c, d). For a cantilever very close to a substrate in air, the present model may lose its validity both through high values of slip and through discrete molecular effects (treated by Gallis & Torczynski 2004). The drag results presented here must therefore be interpreted with considerable caution in some circumstances, although the present results provide a foundation on which to base further studies.…”

Section: Discussionmentioning

confidence: 80%

The drag on a microcantilever oscillating near a wall

et al. 2005

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Motivated by devices such as the atomic force microscope, we compute the drag experienced by a cylindrical body of circular or rectangular cross-section oscillating at small amplitude near a plane wall. The body lies parallel to the wall and oscillates normally to it; the body is assumed to be long enough for the dominant flow to be two-dimensional. The flow is parameterized by a frequency parameter γ 2 (a Strouhal number) and the wall-body separation ∆ (scaled on body radius). Numerical solutions of the unsteady Stokes equations obtained using finite-difference computations in bipolar coordinates (for circular cross-sections) and boundary-element computations (for rectangular cross-sections) are used to determine the drag on the body. Numerical results are validated and extended using asymptotic predictions (for circular cylinders) obtained at all extremes of (γ, ∆)-parameter space. Regions in parameter space for which the wall has a significant effect on drag are identified.

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Section: Discussionmentioning

confidence: 80%

The drag on a microcantilever oscillating near a wall

et al. 2005

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“…Here we compare three models: (i) a model based on unsteady Reynolds equation [7]; (ii) a model based on a modified Reynolds equation with the first-order slip boundary conditions formulated from DSMC simulations [8] (iii) compact model based on Boltzmann-ESBGK simulations [9]. As shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…In this paper, we analyze rarefied flow effects on the gas-damping behavior of typical capacitive switches. Several damping models based on Reynolds equation [7,8] and on Boltzmann kinetic equation [9,6] are applied to quantify the effects of uncertainties in fabrication and operating conditions on the impact velocity of switch contact surfaces for various switch configurations. Implications of rarefied flow effects in the gas damping for design and analysis of RF MEMS devices are discussed.…”

Section: Introductionmentioning

confidence: 99%

Implications of Rarefied Gas Damping for RF MEMS Reliability

Alexeenko¹,

Chigullapalli²

2011

AIP Conference Proceedings

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Abstract.Capacitive and ohmic RF MEMS switches are based on micron-sized structures moving under electrostatic force in a gaseous environment. Recent experimental measurements [4,5] point to a critical role of gas-phase effects on the lifetime of RF MEMS switches. In this paper, we analyze rarefied flow effects on the gas-damping behavior of typical capacitive switches. Several damping models based on Reynolds equation [7,8] and on Boltzmann kinetic equation [9,6] are applied to quantify the effects of uncertainties in fabrication and operating conditions on the impact velocity of switch contact surfaces for various switch configurations. Implications of rarefied flow effects in the gas damping for design and analysis of RF MEMS devices are discussed. It has been demonstrated that although all damping models considered predict a similar damping quality factor and agree well for predictions of closing time, the models differ by a factor of two and more in predicting the impact velocity and acceleration at contact. Implications of parameter uncertainties on the key reliability-related parameters such as the pull-in voltage, closing time and impact velocity are also discussed.

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“…Gas damping in micro-electro-mechanical systems (MEMS) has attracted a lot of interest in the past two decades [1][2][3][4][5][6]. Better understanding of gas damping effects on micro-structure dynamics gPC can be highly accurate and efficient.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty quantification models for micro‐scale squeeze‐film damping

Guo

Xiu

et al. 2010

Numerical Meth Engineering

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SUMMARYTwo squeeze-film gas damping models are proposed to quantify uncertainties associated with the gap size and the ambient pressure. Modeling of gas damping has become a subject of increased interest in recent years due to its importance in micro-electro-mechanical systems (MEMS). In addition to the need for gas damping models for design of MEMS with movable micro-structures, knowledge of parameter dependence in gas damping contributes to the understanding of device-level reliability. In this work, two damping models quantifying the uncertainty in parameters are generated based on rarefied flow simulations. One is a generalized polynomial chaos (gPC) model, which is a general strategy for uncertainty quantification, and the other is a compact model developed specifically for this problem in an early work. Convergence and statistical analysis have been conducted to verify both models. By taking the gap size and ambient pressure as random fields with known probability distribution functions (PDF), the output PDF for the damping coefficient can be obtained. The first four central moments are used in comparisons of the resulting non-parametric distributions. A good agreement has been found, within 1%, for the relative difference for damping coefficient mean values. In study of geometric uncertainty, it is found that the average damping coefficient can deviate up to 13% from the damping coefficient corresponding to the average gap size. The difference is significant at the nonlinear region where the flow is in slip or transitional rarefied regimes.

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An Improved Reynolds-Equation Model for Gas Damping of Microbeam Motion

Cited by 67 publications

References 12 publications

The drag on a microcantilever oscillating near a wall

The drag on a microcantilever oscillating near a wall

Implications of Rarefied Gas Damping for RF MEMS Reliability

Uncertainty quantification models for micro‐scale squeeze‐film damping

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