Dynamics of a beam-based micro-electromechanical resonator is investigated theoretically and experimentally. The resonant structure comprises a micro-beam and two electrostatic comb-drives, one for exciting the vibration, and the other for detecting the response. Two identical resonators of this type can form a double-ended tuning fork. An analytical linear model of these resonators is developed by assuming the beam to obey the thin beam theory subjected to an axial force. The comb-drives are initially treated as a point mass. The point mass is free to be placed anywhere along the beam span. The exact natural frequencies and mode shapes of vibration are obtained. Further, the mass is considered to have rotary inertia. The influence of the rotary inertia on the natural frequencies and mode shapes of vibration are investigated. Subsequently, the model of a beam with a guided mass is studied to determine the upper limit of the natural frequencies of the resonator. The advantage of this model over the previous ones is in providing detailed insight into the dynamics of the resonator, particularly when the comb-drives are placed at locations other than the mid-point of the beam. It has been shown that the mode shapes of vibration of these resonators are not orthogonal to each other under its classic definition. The orthogonality condition of the mode shapes of the beam-lumped mass system is introduced, and used for studying the forced vibration response. The nonlinear vibration of the system due to stretching is considered for the case of free vibration and the primary resonance. The nonlinear model is used to investigate the effect of damping on the resonator response. The interaction of the electrostatic governing equations and the mechanical model is studied. This model is employed for designing the experiment circuits for testing fabricated resonators. The fabrication processes used are explained, and the design parameters of each resonator are provided. The experimental results are reported, and used to find the axial force and stress of the resonant beams. The model and results of this dissertation can be used in the design of beam-based micromachined resonators for different applications.

Dynamics of a beam-based micro-electromechanical resonator is investigated theoretically and experimentally. The resonant structure comprises a micro-beam and two electrostatic comb-drives, one for exciting the vibration, and the other for detecting the response. Two identical resonators of this type can form a double-ended tuning fork. An analytical linear model of these resonators is developed by assuming the beam to obey the thin beam theory subjected to an axial force. The comb-drives are initially treated as a point mass. The point mass is free to be placed anywhere along the beam span. The exact natural frequencies and mode shapes of vibration are obtained. Further, the mass is considered to have rotary inertia. The influence of the rotary inertia on the natural frequencies and mode shapes of vibration are investigated. Subsequently, the model of a beam with a guided mass is studied to determine the upper limit of the natural frequencies of the resonator. The advantage of this model over the previous ones is in providing detailed insight into the dynamics of the resonator, particularly when the comb-drives are placed at locations other than the mid-point of the beam. It has been shown that the mode shapes of vibration of these resonators are not orthogonal to each other under its classic definition. The orthogonality condition of the mode shapes of the beam-lumped mass system is introduced, and used for studying the forced vibration response. The nonlinear vibration of the system due to stretching is considered for the case of free vibration and the primary resonance. The nonlinear model is used to investigate the effect of damping on the resonator response. The interaction of the electrostatic governing equations and the mechanical model is studied. This model is employed for designing the experiment circuits for testing fabricated resonators. The fabrication processes used are explained, and the design parameters of each resonator are provided. The experimental results are reported, and used to find the axial force and stress of the resonant beams. The model and results of this dissertation can be used in the design of beam-based micromachined resonators for different applications.

Hydrogen sensors have obtained increased interest with the widened application of hydrogen energy in recent years. Among them, various chemiresistor based hydrogen sensors have been studied due to their relatively simple structure and well-established detection mechanism. The recent progress in micro/nanotechnology has accelerated the development of small-scale chemical sensors. In this work, MEMS (Micro-Electro-Mechanical Systems) sensor platforms with interdigitated electrodes have been designed and fabricated. Integrating indium doped tin dioxide nanoparticles, these hydrogen sensors showed improved sensor characteristics such as sensitivity, response and selectivity at room temperature. Design parameters of interdigitated electrodes have been studied in association with sensor characteristics. It was observed that these parameters (gap between the electrodes, width and length of the fingers, and the number of the fingers) imposed different impacts on the sensor performance. In order to achieve small, robust, low cost and fast hydrogen micro/nano sensors with high sensitivity and selectivity, the modeling and process optimization was performed. The effect of humidity and the influence of the applied voltage were also studied. The sensor could be tuned to have high sensitivity (105), fast response time (10 seconds) and low energy consumption (19 nW). Finally, a portable hydrogen instrument integrated with a micro sensor, display, sound warning system, and measurement circuitry was fabricated based on the calibration data of the sensor.

There are various energy dissipation mechanisms that affect the dynamic response of microstructures used in MEMS devices. A cumulative effect of such losses is captured by an important characteristic of the structure called Quality factor or Q-factor. Estimating Q-factor at the design stage is crucial in all applications that use dynamics as their principle mode of operation. A high Q-factor indicates sharp resonance that, in turn, can indicate a broad flat response region of the structure. In addition, a high Q-factor typically indicates a high sensitivity. Microstructures used in MEMS are generally required to have much higher Q-factors than their macro counterparts. However some damping mechanisms present in microstructures can reduce the Q-factor of the structure significantly. In the present work, we investigate the dependence of Q-factor on the squeeze film damping an energy dissipation mechanism that dominates by a couple of orders of magnitude over other losses when a fluid (e.g., air) is squeezed through gaps due to vibrations of a microstructure. In particular, we show the effect of nonlinear terms in the analysis of squeeze film damping on the Q-factor of a structure. We also show the effect of rarefaction, surface roughness along with their coupled effect and with different boundary conditions such as open border effect, blocked boundary effect on the squeeze film damping. Finally, we develop similitude laws for calculating squeeze film damping force in up-scaled structures. We illustrate the effects by studying various type of microstructures including parallel plates, beams, plate and beam assemblies such as MEMS microphone, vibratory gyroscope etc. We view the contributions of this work as a significant in investigating and integrating all important effects altogether on the squeeze film damping, which is a significant factor in the design and analysis of MEMS devices.

Ce travail de thèse porte sur l’étude et la réalisation de micro-capteurs dédiés à la mesure de vitesse angulaire par des principes basés sur des échanges thermiques. Deux types de gyromètres ont été développés dont la principale différence est liée au principe qui permet la mise en mouvement du gaz : convection forcée pour l’un et expansion thermique pour l’autre. Le principe est basé sur la modification par la force de Coriolis des échanges thermiques dans un fluide chauffé localement lorsque le dispositif est soumis à une vitesse de rotation. L’utilisation d’un fluide comme masse sismique est en rupture avec les concepts de gyromètres dits traditionnels. Cet avantage a pour conséquence la possibilité d’une utilisation dans des conditions environnementales sévères telles que de fortes accélérations (> 10 000 g) et de fortes vibrations. Les objectifs de ce travail consistent à étudier, à développer et à caractériser ces deux types de gyromètres. Pour cela, des études numériques ont été menées afin de mieux appréhender les phénomènes physiques et thermiques mis en jeu dans la cavité. On a pu aussi étudier l’effet des paramètres thermo-physiques du fluide, des différentes dimensions géométriques et de la vitesse d’écoulement du gaz sur la sensibilité et l’étendue de mesure. Par ailleurs, des prototypes des deux types de gyromètres ont été réalisés puis caractérisés. Les résultats sont très encourageants et les principes validés, mais leur confrontation avec ceux de la simulation montre que des améliorations sont à apporter sur le modèle numérique. / This PhD thesis deals with both study and fabrication of micro-sensors dedicated to the measurement of angular velocity, these devices are based on heat exchanges. Two types of gyroscopes have been developed, one using a jet of gas being deflected by the rotation, the other one using thermal expansion of a gas. Under rotation, heat transfers in a locally heated fluid is modified by the Coriolis force and induces a change in temperature distribution. Using a fluid as seismic mass enhances performances in terms shock (> 10 000g) and vibration resistances compared with standard mechanical gyroscopes.The aim of this work has been to study, develop and characterize these two gyroscopes. For this purpose, numerical studies have been carried out in order to improve our understanding of physical and thermal phenomena involved in the device. Effects of thermo-physical parameters, sensor size and gas flow velocity on both sensitivity and measuring range were analyzed.On the other hand, prototypes of both gyroscopes were manufactured and characterized. The proof of concept has been validated and encouraging results have been found. Comparison of measure and simulation have shown that improvements have to be made on the numerical model.

Les matériaux piézoélectriques, comme le titanate-zirconate de plomb Pb(ZrxTi1-x)O3 (PZT), l’oxyde de zinc ZnO, ainsi que la solution solide de Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), sont actuellement l’objet d’études de plus en plus nombreuses à cause de leurs applications innovantes dans les systèmes micro-électromécaniques (MEMS). Afin de les intégrer sur substrat de silicium, certaines précautions doivent être prises en compte concernant par exemple des couches tampon, les électrodes inférieures. Dans cette thèse, des films piézoélectriques (PZT et PMN-PT) ont été épitaxiés avec succès sous forme de monocristaux sur silicium et SOI (silicon-on-insulator) par procédé sol-gel. En effet, des études récentes ont montré que les films piézoélectriques monocristallins semblent posséder des propriétés supérieures à celles des films polycristallins, permettant ainsi une augmentation de la performance des dispositifs MEMS. Le premier objectif de cette thèse était de réaliser l'épitaxie de film monocristallin de matériaux piézoélectriques sur silicium. L'utilisation d’une couche tampon d'oxyde de gadolinium (Gd2O3) ou de titanate de strontium (SrTiO3 ou STO) déposés par la technique d’épitaxie par jets moléculaires (EJM) a été explorée en détail pour favoriser l’épitaxie du PZT et PMN-PT sur silicium. Sur le système Gd2O3/Si(111), l’étude par diffraction des rayons X (XRD) de la croissance du film PZT montre que le film est polyphasé avec la présence de la phase parasite pyrochlore non ferroélectrique. Cependant, le film PZT déposé sur le système STO/Si(001) est parfaitement épitaxié sous forme d’un film monocristallin. Afin de mesurer ses propriétés électriques, une couche de ruthenate de strontium conducteur SrRuO3 (SRO) déposée par ablation laser pulsé (PLD) a été utilisée comme l'électrode inférieure à cause de son excellente conductibilité et de sa structure cristalline pérovskite similaire à celle du PZT. Les caractérisations électriques sur des condensateurs Ru/PZT/SRO démontrent de très bonnes propriétés ferroélectriques avec présence de cycles d'hystérésis. Par ailleurs, le matériau relaxeur PMN-PT a aussi été épitaxié sur STO/Si comme l’a confirmé la diffraction des rayons X ainsi que la microscopie électronique en transmission (TEM). Ce film monocristallin est de la phase de perovskite sans présence de pyrochlore. En outre, une étude en transmission du rayonnement infrarouge au synchrotron a prouvé une transition de phase diffuse sur une large gamme de température, comme attendue dans le cas d’un relaxeur. L'autre intérêt d'avoir des films PZT monocristallins déposés sur silicium et SOI est de pouvoir utiliser les méthodes de structuration du silicium bien standardisées maintenant pour fabriquer les dispositifs MEMS. La mise au point d’un procédé de micro-structuration en salle blanche a permis de réaliser des cantilevers et des membranes afin de caractériser mécaniquement les couches piézoélectriques. Des déplacements par l'application d'une tension électrique ont ainsi pu être détectés par interférométrie. Finalement, cette caractérisation par interférométrie a été combinée avec une modélisation basée sur la méthode des éléments finis. Dans le futur, il sera nécessaire d’optimiser le procédé de microfabrication du dispositif MEMS afin d’en améliorer les performances électromécaniques. Enfin, des caractérisations au niveau du dispositif MEMS lui-même devront être développées en vue de leur utilisation dans de futures applications. / Recently, piezoelectric materials, like lead titanate zirconate Pb(ZrxTi1-x)O3 (PZT), zinc oxide ZnO, and the solid solution Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), increasingly receive intensive studies because of their innovative applications in the microelectromechanical systems (MEMS). In order to integrate them on silicon substrate, several preliminaries must be taken into considerations, e.g. buffer layer, bottom electrode. In this thesis, piezoelectric films (PZT and PMN-PT) have been successfully epitaxially grown on silicon and SOI (silicon-on-insulator) in the form of single crystal by sol-gel process. In fact, recent studies show that single crystalline films seem to possess the superior properties than that of polycrystalline films, leading to an increase of the performance of MEMS devices. The first objective of this thesis was to realize the epitaxial growth of single crystalline film of piezoelectric materials on silicon. The use of a buffer layer of gadolinium oxide(Gd2O3) or strontium titanate (SrTiO3 or STO) deposited by molecular beam epitaxy (MBE) has been studied in detail to integrate epitaxial PZT and PMN-PT films on silicon. For Gd2O3/Si(111) system, the study of X-ray diffraction (XRD) on the growth of PZT film shows that the film is polycrystalline with coexistence of the nonferroelectric parasite phase, i.e. pyrochlore phase. On the other hand, the PZT film deposited on STO/Si(001) substrate is successfully epitaxially grown in the form of single crystalline film. In order to measure the electrical properties, a layer of strontium ruthenate (SrRuO3 or SRO) deposited by pulsed laser deposition (PLD) has been employed for bottom electrode due to its excellent conductivity and perovskite crystalline structure similar to that of PZT. The electrical characterization on Ru/PZT/SRO capacitors demonstrates good ferroelectric properties with the presence of hysteresis loop. Besides, the relaxor ferroelectric PMN-PT has been also epitaxially grown on STO/Si and confirmed by XRD and transmission electrical microscopy (TEM). This single crystalline film has the perovskite phase without the appearance of pyrochlore. Moreover, the study of infrared transmission using synchrotron radiation has proven a diffused phase transition over a large range of temperature, indicating a typical relaxor ferroelectric material. The other interesting in the single crystalline PZT films deposited on silicon and SOI is to employ them in the application of MEMS devices, where the standard silicon techniques are used. The microfabrication process performed in the cleanroom has permitted to realize cantilevers and membranes in order to mechanically characterize the piezoelectric layers. Mechanical deflection under the application of an electric voltage could be detected by interferometry. Eventually, this characterization by interferometry has been studied using the modeling based on finite element method and analytic method. In the future, it will be necessary to optimize the microfabrication process of MEMS devices based on single crystalline piezoelectric films in order to ameliorate the electromechanical performance. Finally, the characterizations at MEMS device level must be developed for their utilization in the future applications.

Cette thèse est consacrée à l’étude théorique et numérique de plusieurs équations aux dérivées partielles non linéaires qui apparaissent dans la modélisation de la séparation de phase et des micro-systèmes électro-mécaniques (MSEM). Dans la première partie, nous étudions des modèles d’ordre élevé en séparation de phase pour lesquels nous obtenons le caractère bien posé et la dissipativité, ainsi que l’existence de l’attracteur global et, dans certains cas, des simulations numériques. De manière plus précise, nous considérons dans cette première partie des modèles de type Allen-Cahn et Cahn-Hilliard d’ordre élevé avec un potentiel régulier et des modèles de type Allen-Cahn d’ordre élevé avec un potentiel logarithmique. En outre, nous étudions des modèles anisotropes d’ordre élevé et des généralisations d’ordre élevé de l’équation de Cahn-Hilliard avec des applications en biologie, traitement d’images, etc. Nous étudions également la relaxation hyperbolique d’équations de Cahn-Hilliard anisotropes d’ordre élevé. Dans la seconde partie, nous proposons des schémas semi-discrets semi-implicites et implicites et totalement discrétisés afin de résoudre l’équation aux dérivées partielles non linéaire décrivant à la fois les effets élastiques et électrostatiques de condensateurs MSEM. Nous faisons une analyse théorique de ces schémas et de la convergence sous certaines conditions. De plus, plusieurs simulations numériques illustrent et appuient les résultats théoriques. / This thesis is devoted to the theoretical and numerical study of several nonlinear partial differential equations, which occur in the mathematical modeling of phase separation and micro-electromechanical system (MEMS). In the first part, we study higher-order phase separation models for which we obtain well-posedness and dissipativity results, together with the existence of global attractors and, in certain cases, numerical simulations. More precisely, we consider in this first part higher-order Allen-Cahn and Cahn-Hilliard equations with a regular potential and higher-order Allen-Cahn equation with a logarithmic potential. Moreover, we study higher-order anisotropic models and higher-order generalized Cahn-Hilliard equations, which have applications in biology, image processing, etc. We also consider the hyperbolic relaxation of higher-order anisotropic Cahn-Hilliard equations. In the second part, we develop semi-implicit and implicit semi-discrete, as well as fully discrete, schemes for solving the nonlinear partial differential equation, which describes both the elastic and electrostatic effects in an idealized MEMS capacitor. We analyze theoretically the stability of these schemes and the convergence under certain assumptions. Furthermore, several numerical simulations illustrate and support the theoretical results.