The primary objective of this thesis was to gain a deeper understanding of acoustic wave propagation in phononic crystals, particularly those that include materials whose properties can be varied periodically in time. This research was accomplished in three ways. First, a 2D phononic crystal was designed, created, and characterized. Its properties closely matched those determined through simulation. The crystal demonstrated band gaps, dispersion, and negative refraction. It served as a means of elucidating the practicalities of phononic crystal design and construction and as a physical verification of their more interesting properties. Next, the transmission matrix method for analyzing 1D phononic crystals was extended to include the effects of time-varying material parameters. The method was then used to provide a closed-form solution for the case of periodically time-varying material parameters. Some intriguing results from the use of the extended method include dramatically altered transmission properties and parametric amplification. New insights can be gained from the governing equations and have helped to identify the conditions that lead to parametric amplification in these structures. Finally, 2D multiple scattering theory was modified to analyze scatterers with time-varying material parameters. It is shown to be highly compatible with existing multiple scattering theories. It allows the total scattered field from a 2D time-varying phononic crystal to be determined. It was shown that time-varying material parameters significantly affect the phononic crystal transmission spectrum, and this was used to switch an incident monochromatic wave. Parametric amplification can occur under certain circumstances, and this effect was investigated using the closed-form solutions provided by the new 1D method. The complexity of the extended methods grows logarithmically as opposed linearly with existing methods, resulting in superior computational complexity for large numbers of scatterers. Also, since both extended methods provide analytic solutions, they may give further insights into the factors that govern the behaviour of time-varying phononic crystals. These extended methods may now be used to design an active phononic crystal that could demonstrate new or enhanced properties.

The development and fabrication of silicon-based phononic band gap crystals has been gaining interest since phononic band gap crystals have implications in fundamental science and display the potential for application in engineering by providing a relatively new platform for the realization of sensors and signal processing elements. The seminal study of phononic band gap phenomenon for classical elastic wave localization in structures with periodicity in two- or three-physical dimensions occurred in the early 1990’s. Micro-integration of silicon devices that leverage this phenomenon followed from the mid-2000’s until the present. The reported micro-integration relies on exotic piezoelectric transduction, phononic band gap crystals that are etched into semi-infinite or finite-thickness slabs which support surface or slab waves, phononic band gap crystals of numerous lattice constants in dimension and phononic band gap crystal truncation by homogeneous mediums or piezoelectric transducers. The thesis reports, to the best of the author's knowledge, for the first time, the theory, design methodology and experiment of an electrostatically actuated silicon-plate phononic band gap quasi-crystal architecture, which may serve as a platform for the development of a new generation of silicon-integrated sensors, signal processing elements and improved mechanical systems. Electrostatic actuation mitigates the utilization of piezoelectric transducers and provides action at a distance type forces so that the phononic band gap quasi-crystal edges may be free standing for potentially reduced anchor and substrate mode loss and improved energy confinement compared with traditional surface and slab wave phononic band gap crystals. The proposed phononic band gap quasi-crystal architecture is physically scaled for fabrication as MEMS in a silicon-on-insulator process. Reasonable experimental verification of the model of the electrostatically actuated phononic band gap quasi-crystal architecture is obtained through extensive dynamic harmonic analysis and mode shape topography measurements utilizing optical non-destructive laser-Doppler velocimetry. We have utilized our devices to obtain fundamental information regarding novel transduction mechanisms and behavioral characteristics of the phononic band gap quasi-crystal architecture. Applicability of the phononic band gap quasi-crystal architecture to physical temperature sensors is demonstrated experimentally. Vibration stabilized resonators are demonstrated numerically.

Poursuivant l'essor des méta-matériaux micro-ondes et photoniques, les cristaux phononiques, organisations périodiques de matériaux acoustiquement différents présentant notamment des bandes d'arrêt, c'est-à-dire de plages de fréquences pour lesquelles aucun mode ne se propage dans la structure, laissent entrevoir des applications acoustiques hors de portée des technologies existantes. Dans cette thèse, nous visons des réalisations aux fréquences RF afin de viser des applications complémentaires des résonateurs ou des filtres acoustiques largement employés dans le domaine des transmissions sans fil. Nous avons tout d'abord développé un procédé de fabrication simple permettant de réaliser des cristaux phononiques à deux dimensions à l'échelle micrométrique sur membrane piézoélectrique, afin de rendre ces systèmes compatibles avec les composants à ondes de Lamb développés au CEA-LETI pour des applications de filtrage de canal dans des architectures de transmission sans fil faible consommation. Ce procédé a été utilisé pour réaliser des cristaux phononiques, ainsi que des résonateurs à ondes de Lamb, ou à ondes de volume et des structures plus complexes comme par exemple des filtres passe-bande. Une étude paramétrique des composants à ondes de Lamb nous a permis d'affiner notre maîtrise de ces dispositifs, ce qui nous a été utile pour la mise au point des lignes à retard permettant de caractériser les propriétés de transmission acoustique des cristaux phononiques. Du point de vue théorique, un modèle de simulation par éléments finis a été mis en place, dans un premier temps pour dimensionner les structures réalisées et prendre en compte les modifications apportées par la réalisation technologique. Nous avons ensuite réalisé des cristaux phononiques que nous avons caractérisés électriquement et optiquement, en collaboration avec l'Institut FEMTO-ST. Les mesures confirment la présence de bandes d'arrêt, aux fréquences attendues, mais d'une largeur a priori bien supérieure à celle prévue par la simulation. Une étude détaillée des diagrammes de bandes attribue ce phénomène à la présence de bandes sourdes dans le cristal ne pouvant être excitées par les transducteurs utilisés. Cet aspect est d'une importance critique dans le dimensionnement de cristaux phononiques en vue d'une utilisation dans des applications pratiques. / In the straight line of photonic and microwave meta-materials, phononic crystals are foreseen to enable novel acoustic applications that existing technologies cannot reach. These phononic crystals are periodic organisation of acoustically different materials exhibiting, for example, qtop bands, which means frequency ranges in which no wave can propagate in the structure. In this thesis we target RF frequencies in order to investigate applications complementary to the conventional resonators or filters widely used in mobile telecommunication systems. We developed a simple process flow to realise micrometric two-dimensional phononic crystals on a piezoelectric membrane. These structures are fabricated along with Lamb wave devices studied in CEA-LETI for channel filtering in low consumption wireless transmission architectures, and with bulk wave resonators or more complex structures like band-pass filters. A parametric study of Lamb wave resonators sharpens our knowledge on these devices, which allow us to design and fabricate delay lines to characterise acoustic transmission properties of phononic crystals. From a theoretical point of view we set up a simulation model using finite element method. This model was used to design the phononic crystal we realised, and to take into account the effects of the modifications brought by the technological realisation. We then fabricated phononic crystals, and electrically and optically characterised them, in collaboration with FEMTO-ST institute. Measurements confirmed the presence of band gaps at the targeted frequency, but over a wider frequency range than predicted by calculation. A detailed study of band diagrams is attributing this phenomenon to the presence of deaf bands, which cannot be excited by interdigitated fingers. This shows that the determination of these deaf bands is of critical importance in designing phononic crystals for practical applications.

Orientador: Hugo Luis Fragnito / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin. / Made available in DSpace on 2018-08-12T16:20:28Z (GMT). No. of bitstreams: 1 Wiederhecker_GustavoSilva_D.pdf: 26845631 bytes, checksum: f23a4b48df09da35f76ca70361b0231d (MD5) Previous issue date: 2008 / Resumo: Neste trabalho são investigadas técnicas para controlar o confinamento de fótons e fônons em fibras ópticas de cristal fotônico (PCF). Utilizando métodos numéricos robustos para resolver as equações de Maxwell, um novo tipo de PCF com núcleo tubular é proposto. Simulações e experimentos demonstram que esta estrutura confina a luz em um buraco de ar com diâmetro de apenas 110 nm. A figura de mérito para efeitos não-lineares nesta pequena região é 10 bilhões de vezes maior do que no caso de um feixe gaussiano altamente focalizado e 100 vezes maior que o atual estado-da-arte em fibras de band-gap fotônico. Também é analisada teoricamente uma fibra PCF do tipo kagomé. Modelos que explicam suas complexas características de guiamento são investigados de forma analítica e numérica. No que diz respeito à fônons em PCFs, é investigado o espalhamento Brillouin copropagante e contra-propagante. Em particular, são demonstradas maneiras de reduzir a interação acusto-óptica nos casos de co- e retro-espalhamento. Também é demonstrada a presença de band-gaps fonônicos nestas estruturas. Finalmente, é investigado o controle óptico coerente de modos acústicos nestas fibras, mostra-se que é possível amplificar ou frear modos acústicos com freqüência de oscilação na faixa de GHz. / Abstract: Techniques that may allow control and tight confinement of photons and phonons in photonic crystal fibers (PCFs) are investigated in this thesis. By means of robust numerical methods to solve Maxwell equations, a new kind of PCF with a tubular core is proposed. Simulations and experimental results show that such structure is able to confine light tighly inside the 100 nm bore, the nonlinear figure of merir for such tiny bore is found to be 10 billion fold larger the focused Gaussian beam counterpart, it is also 100 times larger than the state-of-the-art hollow core photonic band-gap fibers. The guidance mechanism of kagomé structure hollow-core PCF is also investigated, simple models are proposed to explain most of the experimentally observed features and compared to full numerical simulations. In what concerns phonons, both forward and backward Brillouin scattering is investi-gated in PCFs. It is demonstrated how one may suppress both using such fibers. It is also shown the existence of complete band-gaps for in-plane propagation in the PCF cladding. Another set of experiments show that one can perform coherent optical control of the acoustic modes of such fibers, 100-fold amplification or almost complete suppression of GHz oscillations is achieved. / Doutorado / Física / Doutor em Ciências

In this thesis, the propagation of transient waves in heterogeneous media and the tuning of periodic elastic materials are studied. The behaviour of time harmonic waves in complex media is a well understood phenomenon. The primary aim of this text is to gain a deeper understanding into the propagation of transient waves in periodic media. The secondary aim is to explore the time harmonic behaviour of two dimensional pre-stressed elastic media and investigate the plausibility of band gap tuning. We begin this text by investigating the reflection of pulses from a semi-infinite set of point masses (we call 'beads') on a string. The reflected pulse is formulated using Fourier transforms which involve the harmonic reflection coefficient. We find that the reflected amplitude of a harmonic wave depends on its frequency. We then ask whether it is possible to find an effective reflection coefficient by assuming the beaded portion of the string is given by some effective homogeneous medium. An effective reflection coefficient is found by assuming the homogeneous medium has the wavenumber given by the infinite beaded string. This effective reflection coefficient is compared to the exact reflection coefficient found using the Wiener-Hopf technique. The results from studying the reflection problem gave inspiration to chapter 4, which focuses on the time dependent forcing of an infinite beaded string that is initially at rest. We again use the Fourier transform to find a time dependent solution. The z-transform is then used, after sampling the solution at the bead positions. We impose a sinusoidal loading which is switched on at a specified time. In doing this we are able to explore how the system behaves differently when excited in a stop band, a pass band and at a frequency on the edge between the two. An exact solution for the infinite beaded string is found at any point in time by expanding the branch points of the solution as a series of poles. We compare this exact solution to the long time asymptotics. The energy input into the system is studied with the results from the exact solution and long time approximation showing agreement. Interesting behaviour is discovered on the two edges between stop and pass bands. In chapter 5 the effect of a nonlinear elastic pre-stress on the wave band structure of a two dimensional phononic crystal is investigated. In this chapter we restrict ourselves to incompressible materials with the strain energy functions used being the neo-Hookean, Mooney-Rivlin and Fung. The method of small-on-large is used to derive the equation for incremental elastic waves and then the plane wave expansion method is used to find the band structure. Finally, chapter 6 focuses on the same geometry with a compressible elastic material. The strain energy function used is the one suggested by Levinson and Burgess. We use the theory of small-on-large to derive the incremental equations for coupled small amplitude pressure and shear waves in this material. In both compressible and incompressible materials we show how it is possible to control the stop bands in a material by applying a large elastic pre-stress.

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<p>With the emergence of 5G/mm-Wave communication, there is a growing need for novel front-end electromechanical devices in filtering and carrier generation applications. CMOS-MEMS resonators fabricated using state-of-the-art Integrated Circuit (IC) manufacturing processes provide a significant advantage for power, area and cost savings. In this work, a comprehensive physics-based compact model capable of capturing the non-linear behaviour and other non-idealities has been developed for MEMS resonators seamlessly integrated in CMOS. As the first large signal model for CMOS-embedded resonators, it enables holistic design of MEMS components with advanced CMOS circuits as well as system-level performance evaluation within the framework of modern IC design tools. Global Foundries 14nm FinFET (GF14LPP) Resonant Body Transistors (fRBT) operating at 11.8 GHz are demonstrated and benchmarked against this large-signal electromechanical model. </p> <p><br></p> <p>Additionally, there is a growing interest in CMOS-integrable ferroelectric materials such as Hafnium Dioxide (HfO2) and Aluminum Scandium Nitride (AlScN) for next-generation memory and computation, as well as electromechanical transduction in CMOS-MEMS devices. This work also explores the performance of 700 MHz Ferroelectric Capacitor-based resonators in the Texas Instruments HPE035 process under high-power operating conditions. Identification of previously unreported characteristics, together with the first nonlinear large signal model for integrated ferroelectric resonators, provides insights on the design of frequency references and acoustic filters using ferroelectric transducers. </p> <p><br></p> <p>Extending the range of unreleased CMOS-MEMS resonators to lower frequency using novel design, we also investigate embedded transducers in chip-scale devices for physical sensing. We have simulated and modeled the transducer coupling for low-frequency propagating modes and benchmarked their projected performance against state-of-the-art conventional MEMS sensors. A new approach to phononic crystal (PnC) Interdigitated Transducers (IDTs) is presented emulating the acoustic dispersion in conventional ICs. Unloaded quality factors up to 15,000 have been measured in $\sim$80 MHz resonators, demonstrating their capacity for resonant rotation sensing. We present a unique methodology to amplify and collimate acoustic waves using CMOS-design-rule-compliant Graded Index (GRIN) Phononic IDTs. Ultimately, the CMOS-MEMS techniques presented in this work for both RF applications and physical sensing can facilitate additional functionality in standard CMOS and emerging 3D heterogeneously integrated (3DHI) ICs with minor or no modifications to manufacturing and packaging. This enables new paradigms in next-generation communications, internet of things (IoT), and hardware security.</p>

Acoustic properties of periodic elastic structures have been a subject of active research for more than a century. Here, I derived and analyzed the dispersion equation for sound waves propagating in a periodic layered heterogeneous structure containing at least one viscous fluid as a constituent. The derivation of the dispersion equation is based on the Navier-Stokes equation for sound wave and the boundary conditions of continuity of fluid displacement and stresses at the interfaces with Bloch periodic boundary condition. The obtained dispersion equation is very general, it is valid for different combinations of elastic layers, any direction of propagation, and frequency of sound. In the case of superlattice consisting of narrow layers with high viscosity fluid and layers of ideal fluid, an acoustic analog of the Borrmann effect is predicted. In the other part of my dissertation, I study the nonreciprocal wave propagation in phononic crystals induced by viscosity. Using Fourier-transformed wave equation, I proved analytically that for an infinite phononic crystal with broken PT-symmetry dispersion relation remains the same switching the direction of the wave propagation, while Fourier components of velocity are nonreciprocal. I optimized shape of the scatterer to reach the highest value of the nonreciprocity in a two-dimensional finite phononic crystal. Sound propagation through crystals with various unit cells is numerically simulated with COMSOL Multiphysics to create a dataset of transmission values. For each introduced parameter the optimized scatterer's geometries are obtained utilizing machine learning techniques. I found parameters of the crystal, which may serve as a linear non-resonant passive acoustic diode.