Cette thèse est décomposée en deux parties. La première est consacrée à l'étude de la restauration d'image et la seconde partie est consacrée à l'étude d'un modèle de Frenkel-Kontorova par des méthodes issues du calcul variationnel et des équations aux dérivées partielles. Au chapitre 1, nous présentons les questions essentielles que nous traiterons dans cette thèse, puis on fait des rappels sur les définitions et quelques propriétés d'espace des fonctions à variations bornées BV , l'espace d'Orlicz et le modèle de Frenkel-Kontorova. Au chapitre 2, nous montrons que les problèmes de minimisation non convexe (restauration d'image) contenant des termes de régularisation sous-linéaires sont mal posés. Au chapitre 3, nous étudions un modèle de restauration avec un terme de régularisation à croissance non standard, proposé par Blomgren et al. : le module du gradient est élevé a une puissance qui dépend elle même du gradient. On montre qu'elle est semi-continue inférieurement pour la topologie faible d'un certain espace d'Orlicz-Sobolev qui lui est associé, ce qui permet un résultat d'existence de la solution. Au chapitre 4, nous étudions un modèle de Frenkel-Kontorova, dont on montre l'existence d'au moins une solution de type travelling wave, u. / This thesis is divided into two parts. The first is devoted to the study of image restorationand the second part is devoted to the study of a Frenkel-Kontorova model using methodsfrom the calculus of variations and partial differential equations. In chapter 1, we presentthe key issues we will discuss in this thesis, and recal the denitions and some properties ofspaces of functions of bounded variations BV , Orlicz Sobolev spaces and Frenkel-Kontorovamodel results on image analysis. In chapter 2, we show that the non-convex minimizationproblems (restoration image) involving sublinear regularizing terms are ill-posed. In chapter3, we study a model of restoration with nonstandard increasing regularizing terms,proposedby Blomgren. We show that is lower semi-continuous in the weak topologie of some Sobolev-Orlicz space associated with it, which allows existence result of the solution. In Chaptre 4, we study a Frenkel-Kontorova model, that we show existence of at least a traveling wave type solution, u.

Ce travail se concentre sur l'étude de la dynamique des dislocations dans le réseau cristallin et il est découpé en deux parties : la première partie porte sur les mouvements horizontaux d'une chaîne d'atomes en interaction contenant une dislocation. Bien que, la deuxième partie traite de l'accumulation de dislocations formant ce qu'on appelle des murs de dislocations. Dans la première partie, nous considérons une généralisation complètement nonlinéaire des équations de diffusion de réaction discrète également appelée “modèles de Frenkel-Kontorova complètement amortis” qui décrivent la dynamique des défauts cristallins (dislocations) dans un réseau. Nous étudions à la fois : les non-linéarités bistable et monostable. Dans des conditions suffisantes, nous montrons l'existence et l'unicité des ondes progressives pour le cas de non-linéarité bistable. Pour le cas monostable, nous étudions l'existence de la branche des solutions d'ondes progressives pour une non-linéarité Lipschitz général. Nous montrons également que la vitesse minimale est positive et délimitée ci-dessous. Dans cette partie, nous étudions aussi la généralisation du modèle de Frenkel-Kontorova pour laquelle nous pouvons ajouter un paramètre de force motrice. Nous illustrons également, dans ce cas, la variation de la vitesse de propagation des ondes progressives en fonction du paramètre de force. Dans la deuxième partie, nous étudions l'accumulation des dislocations dans les murs de dislocations. Nous montrons en fait la convergence de plusieurs dislocations qui interagissent sur les murs de dislocations. Nous présentons aussi les résultats de quelques expériences numériques qui confirment les résultats théoriques que nous obtenons / This work focuses on the study of the dislocation dynamics in the crystal lattice and it is splitted into two parts : the first part is concerned with the horizontal motion of a chain of interacting atoms containing a dislocation. While, the second part deals with the accumulation of dislocations forming what is known as walls of dislocations. In the first part, we consider a fully nonlinear generalization of the discrete reaction diffusion equations “fully overdamped Frenkel-Kontorova models” that describe the dynamics of crystal defects (dislocations) in a lattice. We study both : the bistable and the monostable non-linearities. Under sufficient conditions, we show the existence and uniqueness of traveling wave solution for the bistable non-linearity case. For the monostable case, we study the existence of branch of traveling waves solutions for general Lipschitz non-linearity. We also prove that the minimal velocity is non-negative and bounded below. In this part, we as well study the generalization of Frenkel-Kontorova model for which we can add a driving force parameter. We also illustrate, in this case, the variation of the velocity of propagation of traveling waves in terms of the parameter force. In the second part, we study the accumulation of dislocations in walls of dislocations. We prove actually the convergence of several interacting dislocations to walls of dislocations. We also present results of some numerical experiments that confirm the theoretical results that we obtain

Estudamos o comportamento de modelos para sistemas modulados magnéticos e estruturais. A primeira parte deste trabalho e dedicada ao modelo de Ising com interações competitivas numa rede de Bethe, no limite de coordenação infinita, num campo magnético. Focalizamos nossa atenção no comportamento das fases comensuráveis na presença de campo. Obtivemos vários diagramas T H utilizando algoritmos numéricos muito mais eficientes do que a simples iteração do mapeamento associado ao modelo. Na segunda parte estudamos o modelo de FrenkelKontorova com primeiro e segundo harmônicos no potencial externo. Encontramos e investigamos transições de segunda ordem no interior das fases comensuráveis de período ímpar. Essas transições, denominadas simétricaassimétricas, estão associadas à quebra da simetria por reflexão que ocorre para potenciais suficientemente fortes. / We studied the behavior of models for magnetically and structurally modulated systems. The first part of this work is dedicated to the study of the Ising model with competing interactions on a Bethe lattice, in the infinite coordination limit, in a magnetic field. We focused our attention on the behavior of the commensurate phases in the presence of a field. We obtained various T H phase diagrams using numerical methods far more efficient than simple iteration of the mapping associated to the model. In the second part we studied the FrenkelKontorova model with first and second harmonics in the external potential. We found and investigated the second order transitions within the commensurate phases of odd periodicity. These transitions, called symmetricasymmetric transitions, are related to the breaking of reflection symmetry which occurs at high potentials.

Estudamos o comportamento de modelos para sistemas modulados magnéticos e estruturais. A primeira parte deste trabalho e dedicada ao modelo de Ising com interações competitivas numa rede de Bethe, no limite de coordenação infinita, num campo magnético. Focalizamos nossa atenção no comportamento das fases comensuráveis na presença de campo. Obtivemos vários diagramas T H utilizando algoritmos numéricos muito mais eficientes do que a simples iteração do mapeamento associado ao modelo. Na segunda parte estudamos o modelo de FrenkelKontorova com primeiro e segundo harmônicos no potencial externo. Encontramos e investigamos transições de segunda ordem no interior das fases comensuráveis de período ímpar. Essas transições, denominadas simétricaassimétricas, estão associadas à quebra da simetria por reflexão que ocorre para potenciais suficientemente fortes. / We studied the behavior of models for magnetically and structurally modulated systems. The first part of this work is dedicated to the study of the Ising model with competing interactions on a Bethe lattice, in the infinite coordination limit, in a magnetic field. We focused our attention on the behavior of the commensurate phases in the presence of a field. We obtained various T H phase diagrams using numerical methods far more efficient than simple iteration of the mapping associated to the model. In the second part we studied the FrenkelKontorova model with first and second harmonics in the external potential. We found and investigated the second order transitions within the commensurate phases of odd periodicity. These transitions, called symmetricasymmetric transitions, are related to the breaking of reflection symmetry which occurs at high potentials.

The scaling of integrated circuits requires the use of alternative dielectric materials as the replacement for silicon dioxide in the submicron devices. The scaling limit for silicon dioxide used in MOSFETs is 1.2nm and the Oxide Nitride Oxide (ONO) stack used in flash memory applications is 13.0nm. The use of alternative dielectrics with high- κ value will alleviate the problem of charge retention and also would help to decrease the programming voltage in case of flash memory cells. Many alternative high- κ dielectric materials such as TaO2, TiO2, Al2O3 etc., have been examined for this purpose previously. Recently the metal oxides such as ZrO2 and HfO2 have been found to be viable replacements for the existing oxide. The high- κ value along with high bandgap motivates this replacement. A complete modeling of the reactively sputtered HfO2 films in the thickness range of 294Å to 480Å is attempted using the data obtained by one of the group members at the Sharp Laboratories of America, Inc. The IV and CV data is used to characterize the material properties and conduction mechanism in HfO2 films used as a control dielectric. The slope of the Poole-Frenkel plot is close to the theoretical value in the intermediate region however it starts to deviate at high field regions. Temperature dependent data also suggests that there are two types of vii traps active in the intermediate and high field regions. However the origin of these traps is not known. Temperature dependent data indicates that there is a rapid increase in the leakage current at elevated temperatures in the high field region further suggesting that the charge retention capability of the device would be adversely affected under such conditions.

Conjugated Polymers have attracted a great deal of research interest in recent years due to their optoelectronic properties which makes them suitable for applications in organic light-emitting devices (OLEDs) and organic photovoltaics. Their properties are strongly dependent on the electron-electron and electron-nuclear interactions as well as the disorder which is present in almost all systems at finite temperatures. In this thesis the optical properties of electronically neutral conjugated polymers will be investigated. The results obtained are general and applicable to a wide range of parameters. In order to compare these to experiment the optical properties of poly( paraphenylene), poly(para-phenylene vinylene), and derivatives have been calculated. In these polymers the primary photoexcitations are Frenkel excitons which can be described by the Frenkel-Holstein Hamiltonian, which explicitly takes into account the exciton-nuclear coupling. Disorder can be introduced into this model both as diagonal and off-diagonal disorder within the Hamiltonian. First the optical transitions in ordered, linear conjugated polymers are investigated. It is found that the length of the polymer has a direct spectroscopic signature in the emission spectrum. When off-diagonal disorder is introduced the excitons localise on portions of the chain and the length of these portions, the conjugation length, then shows a clear emission signature. As such, a disordered polymer can be described theoretically as a chain of shorter segments, which define chromophores in a polymer context. Following from these calculations the role of conformation was investigated and effects were observed that greatly determine the optical properties of non-linear polymers. Most notable the Herzberg-Teller effect, which renders symmetrically forbidden transitions weakly allowed and greatly affects the absorption and emission spectra. The signatures observed in these spectra allow the determination of the (coarse grained) conformation of the polymer, something that has been difficult to measure directly.

A defect band is formed in hydrogenated amorphous silicon nitride (a-SiNx:H) due to current stressing of the material. This gives rise to an increase in conductivity, referred to as current induced conductivity. This thesis investigates the current transport mechanisms that occur in the induced defect band, by comparing the temperature dependence of the conductivity of several sets of a-SiNx:H thin film diodes. These sets were systematically current stressed to different levels with one set remaining unstressed. Samples with energy gaps of 2.06 eV and 2.28 eV were considered. We show that around room temperature a modified Poole-Frenkel description of conduction (i.e. field enhanced hopping of carriers via charged defect states) provides a good fit to the data. Using this model the activation energy of current transport was calculated and shown to depend on the material band gap. Data fitting to the Poole-Frenkel model provided further support for the field-assisted hopping mechanism. Previous investigations had suggested that the defect band resides in the lower half of the band gap, so that current transport through the defect band was then expected to be due to the movement of holes, in a manner consistent with Poole-Frenkel conduction. By considering samples grown on p-type and n-type substrates, we demonstrated that transport was indeed the result of the movement of holes through the defect states within the induced defect band. At lower temperatures the experimental data is poorly described by a modified Poole-Frenkel type process, so further mechanisms were considered, including variable-range hopping and nearest-neighbour hopping. Due to the similar nature and slight temperature dependence of each process, differentiating between the two mechanisms proved difficult. However, other factors such as the temperature range and defect density favoured variable-range hopping transport. By assuming this form of low temperature hopping transport, conduction through the defect-band of the a-SiNx:H, could then be convincingly explained over the entire temperature range from 320 K to 20 K in terms of two dominant transport mechanisms, Poole-Frenkel conduction and variable-range hopping.

A new understanding of the damage formation mechanisms in Si is developed and investigated over an extended range of ion energy, dose, and irradiation temperature. A simple model for dealing with ion-induced damage is proposed, which is shown to be applicable over the range of implantation conditions. In particular the concept of defect "excesses" will be discussed. An excess exists in the lattice when there is a local surplus of one particular type of defect, such as an interstitial, over its complimentary defect (i.e., a vacancy). Mechanisms for producing such excesses by implantation will be discussed. The basis of this model specifies that accumulation of stable lattice damage during implantation depends upon the excess defects and not the total number of defects. The excess defect model is validated by fundamental damage studies involving ion implantation over a range of conditions. Confirmation of the model is provided by comparing damage profiles after implantation with computer simulation results. It will be shown that transport of ions in matter (TRIM) can be used effectively to model the ion-induced damage profile, i.e. excess defect distributions, by a simple subtraction process in which the spatially correlated defects are removed, thereby simulating recombination. Classic defect studies illuminate defect interactions from concomitant implantation of high- and medium-energy Si+-self ions. Also, the predictive quality of the excess defect model was tested by applying the model to develop several experiments to engineer excess defect concentrations to substantially change the nature and distribution of the defects. Not only are the excess defects shown to play a dominant role in defect-related processing issues, but their manipulation is demonstrated to be a powerful tool in tailoring the implantation process to achieve design goals. Pre-amorphization and dual implantation of different energetic ions are two primary investigative tools used in this work. Various analyses, including XTEM, RBS/channeling, PAS, and SIMS, provided experimental verification of the excess defect model disseminated within this dissertation.

Fuer anorganische Kristalle werden die chemischen Bindungen durch kovalente oder ionische Beitraege dominiert. Im Gegensatz dazu stehen organische Molekuelkristalle, in denen in jedem der Molekuele starke kovalente Bindungen vorherrschen, waehrend die Molekuele untereinander nur relativ schwache Wechselwirkung zeigen. Daher sind die Veraenderungen zwischen den Spektren freier Molekuele und den entsprechenden Kristallen wesentlich geringer als die zwischen einem freien Atom und einem anorganischen Kristall. In einem organischen Kristall kann eine optisch erzeugte elektronische Anregung zwischen verschiedenen Molekuelen transferiert werden. Fuer das Modellsystem PTCDA (3,4,9,10-Perylentetracarbonsaeuredianhydrid) wurden die elektronischen und vibronischen Spektren analysiert und die aus dem Transfer der Anregung resultierende exzitonische Bandstruktur untersucht. Die optische Absorption erzeugt ein Frenkel-Exziton am Dispersionsmaximum in der Naehe des Gamma-Punktes in der Brillouin-Zone. Durch inelastische Streuvorgaenge relaxiert dieses Exziton zum Dispersionsminimum am Rand der Brillouin-Zone. Die Photolumineszenz bei tiefen Temperaturen entsteht daraus durch vertikale Rekombination, wobei der Endzustand eine vibronische Anregung mit endlichem Quasi-Impuls enthaelt. Die berechnete strahlende Rekombinationsrate und die Linienform der Photolumineszenzbande stimmen dabei gut mit den experimentellen Ergebnissen ueberein. Das Modell des Exzitonentransfers im Volumenmaterial kann auf Filme endlicher Dicke verallgemeinert werden, so dass sich die veraenderten optischen Eigenschaften duenner Filme beschreiben lassen. Durch die endliche Zahl der molekularen Monolagen in einem solchen Film ist das energetische Spektrum diskret, wobei die Einhuellenden der exzitonischen Wellenfunktionen entlang der Quantisierungsrichtung an die Zustaende in einem Quantentrog mit unendlich hohen Barrieren erinnern. Das Zusammenspiel von geometrischer Randbedingung und energetischer Lage des molekularen uebergangs in der Randschicht kann sowohl zu einer Rot- als auch zu einer Blauverschiebung der optischen Antwort fuehren.

Plants and bacteria both have specialized light-harvesting pigment-protein complexes, composed of a network of chromophores encompassed by a protein scaffold, that are involved in photosynthesis. While chromophore, as well as protein, composition and arrangement vary in these light-harvesting complexes, chromophores transfer energy as molecular excitation energy through their complex multi-chromophoric network with near perfect efficiency. Understanding the efficiency of this excitation energy transfer process has been the focus of many interdisciplinary studies. By elucidating the mechanisms involved in efficient excitation energy transfer in biological systems, we are able to guide the design of novel organic materials for their application in photovoltaic systems. Interdisciplinary studies of light-harvesting biological systems leverage advanced spectroscopic techniques and theoretical models to help explain the interaction be- tween excited electronic states. Difficulties in assigning the origin of spectral features in spectroscopy experiments arise from both homogeneous and inhomogeneous effects. Various computational studies have been able to provide theoretical models that help disentangle these effects and provide insight into the origin of some these spectral features. In this work, we present a computational approach that is used to calculate an ensemble of model Hamiltonians for a light-harvesting pigment-protein complex found in algae. To verify the reliability of our model, we compare various computed spec- tra with experimental measurements. Next, we extend our computational approach for parameterizing an ensemble of Hamiltonians for two configurationally unique or- ganic dimers. Finally, we examine the error of some of the approximations made while partitioning “system” and “bath” degrees of freedom when computing molecu- lar properties. Using these methods we are able to provide mechanistic interpretations and explanations of spectral signatures observed in various linear and nonlinear ex- perimental spectra.