An electrostatic actuator driven by conventional voltage control and charge control requires high actuation voltage and suffers from the pull-in phenomenon that limits its operation range, much less than its entire gap. To provide effective solutions to these problems, we present complete analytical and numerical models of various electrostatic actuators coupled with resonant drive circuits that are able to drive electrostatic actuators at much lower input voltage than that of conventional actuation methods and to extend their operation range beyond their conventional pull-in points in the presence of high parasitic capacitance. Moreover, in order to validate the analytical and numerical models of various electrostatic actuators coupled with the resonant drive circuits, we perform the experiment on the microplate and the micromirror coupled with the resonant drive circuit. For instance, using a high voltage amplifier, we manage to rotate the micromirror with sidewall electrodes by 6 ° at 180 V. However, using the resonant drive circuit, we are able to rotate the same micromirror by 6 ° at much lower input voltage, 8.5 V. In addition, the presented work also facilitates the stability analysis of electrostatic actuators coupled with the resonant drive circuits and provides how the effect of the parasitic capacitance can be minimized. For example, the resonant drive circuit placed within a positive feedback loop of a variable gain amplifier is able to extend the operation range much further even in the presence of very high parasitic capacitance. The resonant drive circuit with the proposed feedback controllers is also able to minimize the detrimental effects of the parasitic capacitance and to displace a parallel-plate actuator over its entire gap without the saddle-node bifurcation. Finally, we present a new displacement measurement method of electrostatic actuators coupled with the resonant drive circuits by sensing the phase delay of an actuation voltage with respect to an input voltage. This new measurement method allows us to easily implement feedback control into existent systems employing an electrostatic actuator without any modification or alteration to the electrostatic actuator itself. Hence, this research work presents the feasibility of electrostatic actuators coupled with the resonant drive circuit in various industrial and medical applications, in which the advantages of miniaturization, low supply voltage, and low power consumption are greatly appreciated.

This thesis presents development of microwave lumped elements for a specific surface-micromachining based technology, a self-contained mechanical characterization of fixed-fixed type beams and realization of a shunt, capacitive-contact RF MEMS switch for millimeter-wave applications. Interdigital capacitor, planar spiral inductor and microstrip patch lumped elements developed in this thesis are tailored for a surface-micromachining technology incorporating a single metallization layer, which allows an easy and low-cost fabrication process while permitting mass production. Utilizing these elements, a bandpass filter is fabricated monolithically with success, which exhibits a measured in-band return loss better than -20 dB and insertion loss of 1.2 dB, a pass-band located in S-band and a stop-band extending up to 20 GHz. Analytical derivations for deflection profile and spring constant of fixed-fixed beams are derived for constant distributed loads while taking axial effects into account. Having built experience with the mechanical domain, next, Finite Difference solution schemes are established for pre-pull-in and post-pull-in electrostatic actuation problems. Using the developed numerical tools / pull-in, release and zipping phenomena are investigated. In particular, semi-empirical expressions are developed for the pull-in voltage with associated errors not exceeding 3.7 % of FEA (Finite Element Analysis) results for typical configurations. The shunt, capacitive-contact RF MEMS switch is designed in electromagnetic and mechanical domains for Ka-band operation. Switches fabricated in the first process run could not meet the design specifications. After identifying sources of relevant discrepancies, a design modification is attempted and re-fabricated devices are operated successfully. In particular, measured OFF-state return and insertion losses better than -16.4 dB and 0.27 dB are attained in 1-40 GHz. By applying a 20-25V actuation, ON-state resonances are tuned precisely to 35 GHz with an optimum isolation level of 39 dB.

An electrostatic actuator driven by conventional voltage control and charge control requires high actuation voltage and suffers from the pull-in phenomenon that limits its operation range, much less than its entire gap. To provide effective solutions to these problems, we present complete analytical and numerical models of various electrostatic actuators coupled with resonant drive circuits that are able to drive electrostatic actuators at much lower input voltage than that of conventional actuation methods and to extend their operation range beyond their conventional pull-in points in the presence of high parasitic capacitance. Moreover, in order to validate the analytical and numerical models of various electrostatic actuators coupled with the resonant drive circuits, we perform the experiment on the microplate and the micromirror coupled with the resonant drive circuit. For instance, using a high voltage amplifier, we manage to rotate the micromirror with sidewall electrodes by 6 ° at 180 V. However, using the resonant drive circuit, we are able to rotate the same micromirror by 6 ° at much lower input voltage, 8.5 V. In addition, the presented work also facilitates the stability analysis of electrostatic actuators coupled with the resonant drive circuits and provides how the effect of the parasitic capacitance can be minimized. For example, the resonant drive circuit placed within a positive feedback loop of a variable gain amplifier is able to extend the operation range much further even in the presence of very high parasitic capacitance. The resonant drive circuit with the proposed feedback controllers is also able to minimize the detrimental effects of the parasitic capacitance and to displace a parallel-plate actuator over its entire gap without the saddle-node bifurcation. Finally, we present a new displacement measurement method of electrostatic actuators coupled with the resonant drive circuits by sensing the phase delay of an actuation voltage with respect to an input voltage. This new measurement method allows us to easily implement feedback control into existent systems employing an electrostatic actuator without any modification or alteration to the electrostatic actuator itself. Hence, this research work presents the feasibility of electrostatic actuators coupled with the resonant drive circuit in various industrial and medical applications, in which the advantages of miniaturization, low supply voltage, and low power consumption are greatly appreciated.

La transduction électrostatique est utilisée depuis plusieurs décennies dans les fréquences du domaine audible, principalement sous la forme de microphones membranaires. La transposition du même principe de transduction, mais dans un domaine de fréquence au-dessus du MHz, et par l’utilisation de dispositifs micro-usinés, c'est-à-dire produits à l’aide de technologies de photolithographie, a été proposée à partir de la fin des années 1990. Ces transducteurs, désignés sous l’acronyme cMUT (capacitive micromachine ultrasonic transducers), se composent d’un assemblage de transducteurs élémentaires, chacun possédant une partie mobile conventionnellement appelée diaphragme ou membrane, actionnée par la pression électrostatique. Cette thèse s’inscrit dans le développement de transducteurs de ce type destinés au domaine de l’imagerie médicale ultrasonore. Ce secteur d’application utilise actuellement des transducteurs basés sur des céramiques (ou, dans certains cas précis, des polymères) piézoélectriques. Le cMUT est intéressant dans certains sous-domaines d’application des ultrasons médicaux en raison de sa bonne adaptation à une production en grande série, de son intégration plus facile avec des éléments électroniques, de son faible échauffement et de l’absence de matériaux toxiques dans son processus de fabrication. La partie théorique de cette thèse repose sur une approche de modélisation par différences finies. Un modèle basé sur la théorie des plaques minces est développé pour prendre en compte la mécanique du transducteur élémentaire cMUT (c'est-à-dire d’un seul diaphragme). Ce modèle est ensuite complété par l’intégration de l’effet d’un chargement acoustique par un fluide. De façon à modéliser un transducteur entier, il est nécessaire de prendre en compte le couplage acoustique existant entre les différentes membranes. Pour rendre cela possible, un circuit équivalent, permettant de réduire chaque membrane à un système à un seul degré de liberté, est développé. Il est validé en le comparant au modèle de différences finies dans des cas où celui-ci peut être utilisé. Les travaux expérimentaux ont fait appel principalement aux deux techniques de caractérisation suivantes : les mesures d’impédance électrique, et les mesures de déplacement effectuées par interférométrie laser. Ces mesures ont été utilisées dans une double optique. D’une part, dans un objectif de caractérisation, ils ont permis de vérifier la fonctionnalité des dispositifs fabriqués et d’évaluer leurs performances. D’autre part, en comparant différentes configurations entre elles, ils ont rendu possible une validation expérimentale du modèle qui a été mis au point. / Electro-acoustic transduction based on electrostatic force has a long history in the range of audible frequencies, mainly as membrane-based microphones. Starting in the late 1990’s, it has been proposed to use the same principle in the multi-MHz frequency domain, thanks to micro-machined devices – meaning they’re produced through lithography technology. Such transducers, known as cMUT for capacitive micromachine ultrasonic transducers, are made of an assembly of elementary vertically mobile cells, usually designated as membranes, driven by electrostatic force. This PhD work is part of the development of this kind of transducers designed for medical imaging applications. This area currently uses transducers based on piezoelectric ceramics (or piezoelectric polymers for some peculiar cases). CMUT is an interesting alternative for some subdomains of medical ultrasound applications, due to its volume production ability, its easier integration with electronic elements, its low heat dissipation and the absence of toxic materials.

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.

La complexité des microsystèmes, leur multidisciplinarité, l’hétérogénéité des matériaux utilisés et les interfaces avec l’environnement extérieur rendent difficiles l’évaluation et la maîtrise de leur fiabilité indispensables pour l’exploitation des nombreuses possibilités innovantes qu’ils offrent.L’approche que nous avons proposée dans ce travail, afin de prédire la fiabilité des microsystèmes, se fonde sur l’usage intensif de la modélisation et de la simulation, dans les conditions d’usage du microsystème (profil de mission), en associant donc l’évaluation de la fiabilité à la démarche de conception : avant d’entreprendre une modélisation fonctionnelle de type VHDL-AMS, les objectifs de fiabilité sont exprimés explicitement dans le cahier des charges du microsystème, au même titre que les objectifs plus habituels de performances.Afin de supporter nos travaux, nous avons appliqué cette démarche de prédiction de la fiabilité sur deux types de microsystèmes :- des micro-actionneurs électrothermiques. - des commutateurs RF capacitifs à actionnement électrostatique / The complexity of microsystems, their multidisciplinarity, the heterogeneity of materials and interfaces with the external environment makes difficult the assessment and control of reliability, which is indispensable for the exploitation of the several innovative opportunities that they offer. The approach we proposed, in this work, to predict the reliability of microsystems is based on the intensive use of modelling and simulation, in the use and environmental conditions of micro-system (mission profile), thus by combining the reliability evaluation in the design process: before undertaking any type of functional modelling VHDL-AMS, reliability objectives are expressed explicitly in the specification of the micro-system, as well as the most common performance goals.To support our work, we applied this approach for predicting the reliability for two types of microsystems:- Electro-thermal micro-actuators.- Capacitive RF MEMS switches