Compact models for squeezed-film dampers with inertial and rarefied gas effects

Veijola, Timo

doi:10.1088/0960-1317/14/7/034

Cited by 112 publications

(135 citation statements)

References 15 publications

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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%

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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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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Implications of Rarefied Gas Damping for RF MEMS Reliability

Alexeenko¹,

Chigullapalli²

2011

AIP Conference Proceedings

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“…For damping flow in slip regime (0.001<K n<0.1), analytical solutions can be obtained from Reynolds equation with slip and trivial pressure boundary conditions [3]. As the Knudsen number increases, non-trivial pressure need to be taken into account.…”

Section: Compact Gas Damping Modelmentioning

confidence: 99%

“…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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“…[1][2][3][4][5][6][7][8] Subcontinuum transport in gases has been studied comprehensively, particularly for high-altitude aerothermodynamics. 9 With the advent of microelectromechanical systems ͑MEMS͒, the area of rarefied gas dynamics has attracted new attention in microchannel flow and heat transfer, [10][11][12][13] squeeze film damping, 14,15 heat transfer from microcantilevers to substrates, [16][17][18] and in microthrusters, 19 among other areas.…”

Section: Introductionmentioning

confidence: 99%

Modeling of subcontinuum thermal transport across semiconductor-gas interfaces

Singh

Guo²,

Alexeenko³

et al. 2009

Journal of Applied Physics

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A physically rigorous computational algorithm is developed and applied to calculate subcontinuum thermal transport in structures containing semiconductor-gas interfaces. The solution is based on a finite volume discretization of the Boltzmann equation for gas molecules ͑in the gas phase͒ and phonons ͑in the semiconductor͒. A partial equilibrium is assumed between gas molecules and phonons at the interface of the two media, and the degree of this equilibrium is determined by the accommodation coefficients of gas molecules and phonons on either side of the interface. Energy balance is imposed to obtain a value of the interface temperature. The classic problem of temperature drop across a solid-gas interface is investigated with a simultaneous treatment of solid and gas phase properties for the first time. A range of transport regimes is studied, varying from ballistic phonon transport and free molecular flow to continuum heat transfer in both gas and solid. A reduced-order model is developed that captures the thermal resistance of the gas-solid interface. The formulation is then applied to the problem of combined gas-solid heat transfer in a two-dimensional nanoporous bed and the overall thermal resistance of the bed is characterized in terms of the governing parameters. These two examples exemplify the broad utility of the model in practical nanoscale heat transfer applications.

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Compact models for squeezed-film dampers with inertial and rarefied gas effects

Cited by 112 publications

References 15 publications

Implications of Rarefied Gas Damping for RF MEMS Reliability

Implications of Rarefied Gas Damping for RF MEMS Reliability

Uncertainty quantification models for micro‐scale squeeze‐film damping

Modeling of subcontinuum thermal transport across semiconductor-gas interfaces

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