Search

Our previous report based on a 10 g (gravity) silicon-based inertial micro-switch showed that the contact effect between the two electrodes can be improved by squeeze-film damping. As an extended study toward its potential applications, the switch with a large proof mass suspended by four flexible serpentine springs was redesigned to achieve 5 g threshold value and enhanced threshold accuracy. The impact of the squeeze-film damping on the threshold value was theoretically studied. The theoretical results show that the threshold variation from the designed value due to fabrication errors can be reduced by optimizing the device thickness (the thickness of the proof mass and springs) and then establishing a tradeoff between the damping and elastic forces, thus improving the threshold accuracy. The design strategy was verified by FEM (finite-element-method) simulation and an experimental test. The simulation results show that the maximum threshold deviation was only 0.15 g, when the device thickness variation range was 16&ndash, 24 &mu, m, which is an adequately wide latitude for the current bulk silicon micromachining technology. The measured threshold values were 4.9&ndash, 5.8 g and the device thicknesses were 18.2&ndash, 22.5 &mu, m, agreeing well with the simulation results. The measured contact time was 50 &mu, s which is also in good agreement with our previous work.

High resolution and high throughput imaging are typically mutually exclusive. While there is a wide range of techniques to image features beyond the diffraction limit of light, they all have their own benefits and drawbacks, but they are often very slow compared to optical systems. As such, extending the performance of optical microscopes remains. Examples of high resolution optical concepts are metamaterials nano-antennas, superoscillatory lenses and hyperlenses. These concepts require precise and high speed positioning of the optical element at lens-to-sample separations measured in tens of nanometers. We present a design and process for a MEMS nanopositioning stage capable of sub-nm positioning of a metamaterials optical lens with very high bandwidth. Laser vibrometer measurements on the first batch of fully fabricated devices showed that the first eigenfrequency is at 500±25 kHz, somewhat below the 660 kHz obtained by FEM simulations. Due to squeeze film damping, the quality factor is relatively low (approximately 2-2.5), which is advantageous for reaching high positioning bandwidth when the device is used in a near-field optical imaging microscope.

Contact time is one of the most important properties for inertial micro-switches. However, it is usually less than 20 μs for the switch with rigid electrode, which is difficult for the external circuit to recognize. This issue is traditionally addressed by designing the switch with a keep-close function or flexible electrode. However, the switch with keep-close function requires an additional operation to re-open itself, causing inconvenience for some applications wherein repeated monitoring is needed. The switch with a flexible electrode is usually fabricated by electroplating technology, and it is difficult to realize low-g switches (

High resolution and high throughput imaging are typically mutually exclusive. While there is a wide range of techniques to image features beyond the diffraction limit of light, they all have their own benefits and drawbacks, but they are often very slow compared to optical systems. As such, extending the performance of optical microscopes remains. Examples of high resolution optical concepts are metamaterials nano-antennas, superoscillatory lenses and hyperlenses. These concepts require precise and high speed positioning of the optical element at lens-to-sample separations measured in tens of nanometers. We present a design and process for a MEMS nanopositioning stage capable of sub-nm positioning of a metamaterials optical lens with very high bandwidth. Laser vibrometer measurements on the first batch of fully fabricated devices showed that the first eigenfrequency is at 500±25 kHz, somewhat below the 660 kHz obtained by FEM simulations. Due to squeeze film damping, the quality factor is relatively low (approximately 2-2.5), which is advantageous for reaching high positioning bandwidth when the device is used in a near-field optical imaging microscope.

In a variety of MEMS applications, the thin film of fluid responsible of squeeze-film damping results to be rarefied and, thus, not suitable to be modeled though the classical Navier-Stokes equation. The simplest way to consider fluid rarefaction is the introduction of a slight modification into its ordinary formulation, by substituting the standard fluid viscosity with an effective viscosity term. In the present paper, some squeeze-film damping problems of both parallel and torsion plates at decreasing pressure are studied by numerical solving a full 3D Navier-Stokes equation, where the effective viscosity is computed according to proper expressions already included in the literature. Furthermore, the same expressions for the effective viscosity are implemented within known analytical models, still derived from the Navier-Stokes equation. In all the considered cases, the numerical results are shown to be very promising, providing comparable or even better agreement with the experimental data than the corresponding analytical results, even at low air pressure. Thus, unlike what is usually agreed in the literature, the effective viscosity approach can be efficiently applied at low pressure regimes, especially when this is combined with a finite element analysis (FEA

The experimental evaluation of damping-improved parallel-plate geometries is reported in this paper. An improved damper geometry with air channels was developed to address contradictory design constraints: large sensing parallel-plate area is desirable for a significant readout capacitance as well as reduced damping coefficient. Damping coefficients were measured at different gaps in conventional parallel-plates MEMS and in parallel-plates with air channels. The inertial masses of the fabricated structures were pulled-in and released. From the return to rest position trajectory, the damping coefficients, at each point, were extracted. Results show a significant damping decrease in parallel-plates with air channels without visible reduction in the capacitance value., Fundação para a Ciência e a Tecnologia (FCT)

Effects of uncertainties in gas damping models, geometry and mechanical properties on the dynamics of micro-electro-mechanical systems (MEMS) capacitive switch are studied. A sample of typical capacitive switches has been fabricated and characterized at Purdue University. High-fidelity simulations of gas damping on planar microbeams are developed and verified under relevant conditions. This and other gas damping models are then applied to study the dynamics of a single closing event for switches with experimentally measured properties. It has been demonstrated that although all damping models considered predict 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 discussed. A notable effect of uncertainty is that the nominal switch, i.e. the switch with the average properties, does not actuate at the mean actuation voltage. Additionally, the device-to-device variability leads to significant differences in dynamics. For example, the mean impact velocity for switches actuated under the 90%-actuation voltage (about 150V), i.e. the voltage required to actuate 90% of the sample, is about 129 cm/s and increases to 173 cm/s for the 99%-actuation voltage (of about 173 V). Response surfaces of impact velocity and closing time to five input variables were constructed using the Smolyak sparse grid algorithm. The sensitivity analysis showed that impact velocity is most sensitive to the damping coefficient whereas the closing time is most affected by the geometric parameters such as gap and beam thickness. (C) 2011 Elsevier Ltd. All rights reserved.

Closed-loop pull-in time operated devices are a good alternative for high sensitivity accelerometers. This paper proposes the use of time measurement as the transduction mechanism for the realization of a high-precision accelerometer. The key feature is the existence of a metastable region that dominates pull-in behavior, thus making pull-in time very sensitive to external accelerations. The main design challenges for a pull-in time parallel-plate capacitive Microelectromechanical system (MEMS) accelerometer are related to the damping and the associated tradeoff between sensitivity and noise is discussed. Parallel-plate MEMS structures designed and fabricated in a 25 um-thick SOI micromachining process (SOIMUMPS) are used to demonstrate the accelerometer time-based approach and experimental results demonstrate a sensitivityof 0.25 us/ ug., Fundação para a Ciência e a Tecnologia (FCT), ADI - Agência de Inovação

Two 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. Copyright © 2010 John Wiley & Sons, Ltd.

Correct modelling of damping is essential to capture the dynamic behaviour of a MEMS device. Our interest is squeeze-film damping which models the behaviour of a fluid in small gaps between a fixed surface and a structure moving perpendicular to this surface . The lateral dimensions of the surfaces are large compared to the gap and the system is considered isothermal. Squeeze film damping is then governed by the Reynolds equation [1].

International audience; Reduced-order modelling of the Reynolds equation for flexible structures

The first objective of this dissertation is to present hybrid numerical-analytical approaches and reduced-order models to simulate microelectromechanical systems (MEMS) in multi-physics fields. These include electric actuation (AC and DC), squeeze-film damping, thermoelastic damping, and structural forces. The second objective is to investigate MEMS phenomena, such as squeeze-film damping and dynamic pull-in, and use the latter to design a novel RF-MEMS switch. In the first part of the dissertation, we introduce a new approach to the modeling and simulation of flexible microstructures under the coupled effects of squeeze-film damping, electrostatic actuation, and mechanical forces. The new approach utilizes the compressible Reynolds equation coupled with the equation governing the plate deflection. The model accounts for the slip condition of the flow at very low pressures. Perturbation methods are used to derive an analytical expression for the pressure distribution in terms of the structural mode shapes. This expression is substituted into the plate equation, which is solved in turn using a finite-element method for the structural mode shapes, the pressure distributions, the natural frequencies, and the quality factors. We apply the new approach to a variety of rectangular and circular plates and present the final expressions for the pressure distributions and quality factors. We extend the approach to microplates actuated by large electrostatic forces. For this case, we present a low-order model, which reduces significantly the cost of simulation. The model utilizes the nonlinear Euler-Bernoulli beam equation, the von K´arm´an plate equations, and the compressible Reynolds equation. The second topic of the dissertation is thermoelastic damping. We present a model and analytical expressions for thermoelastic damping in microplates. We solve the heat equation for the thermal flux across the microplate, in terms of the structural mode shapes, and hence decouple the thermal equation from the plate equation. We utilize a perturbation method to derive an analytical expression for the quality factor of a microplate with general boundary conditions under electrostatic loading and residual stresses in terms of its structural mode shapes. We present results for microplates with various boundary conditions. In the final part of the dissertation, we present a dynamic analysis and simulation of MEMS resonators and novel RF MEMS switches employing resonant microbeams. We first study microbeams excited near their fundamental natural frequencies (primary-resonance excitation). We investigate the dynamic pull-in instability and formulate safety criteria for the design of MEMS sensors and RF filters. We also utilize this phenomenon to design a low-voltage RF MEMS switch actuated with a combined DC and AC loading. Then, we simulate the dynamics of microbeams excited near half their fundamental natural frequencies (superharmonic excitation) and twice their fundamental natural frequencies (subharmonic excitation). For the superharmonic case, we present results showing the effect of varying the DC bias, the damping, and the AC excitation amplitude on the frequency-response curves. For the subharmonic case, we show that if the magnitude of the AC forcing exceeds the threshold activating the subharmonic resonance, all frequency-response curves will reach pull-in. Ph. D.

International audience; Correct modelling of damping is essentiel to capture the dynamic behaviour of a NEMS device. Our interest is squeeze-film damping which models the behaviour of a fluid in small gaps between a fixed surface and a structure moving perpendicular to this surface. The lateral dimensions of the surfaces are large compared to the gap and the system is considered isothermal. Squeeze film damping is then governed by the Reynolds equation.