Dans le cadre de la discrétion acoustique des navires militaires, cette thèse contribue à la modélisation de structures amorties par des matériaux viscoélastiques, sous forme de couches contraintes. Afin de pouvoir optimiser et dimensionner la structure et le matériau amortissant, il est souhaitable de disposer d'un outil numérique prédictif et efficace. Dans un premier temps, une stratégie de caractérisation et de modélisation du comportement de matériaux viscoélastiques est proposée. Elle inclue une méthode de recalage de résultats de mesures par DMA basée sur le respect des relations de Kramers-Kronig, permettant ainsi de construire des courbes maîtresses du matériau en accord avec le principe de causalité. Dans un deuxième temps, un code de calcul par éléments finis est développé, puis des essais de vibration sur structures sandwich sont réalisés afin de valider la modélisation par éléments finis de structures munies de matériaux viscoélastiques. Dans le cas d'une fine couche viscoélastique insérée dans une structure maillée par des éléments volumiques, deux éléments d'interface sont développés : ils permettent de tester simplement plusieurs configurations. Enfin, dans un troisième temps, deux catégories de méthodes de réduction adaptées au calcul de la réponse fréquentielle de structures fortement amorties par des matériaux viscoélastiques sont étudiées : les méthodes de projection sur bases modales et la méthode de reconstruction par approximants de Padé. Dans le cadre d'études paramétriques pour l'optimisation des performances acoustiques des traitements viscoélastiques contraints, les avantages des méthodes développées sont mis avant à travers deux cas d'application.

We give a rather self-contained introduction to the rare pion to dielectron decay which in nontrivial leading order is given by a QED triangle loop. We work within the dispersive framework where the imaginary part of the amplitude is obtained via the Cutkosky rules. We derive these rules in detail. Using the twofold Mellin-Barnes representation for the pion transition form factor, we derive a simple expression for the branching ratio B(π0 <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Crightarrow" /> e+e-) which we then test for various models. In particular a more recent form factor derived from a Lagrangian for light pseudoscalars and vector mesons inspired by effective field theories. Comparison with the KTeV experiment at Fermilab is made and we find that we are more than 3σ below the KTeV experiment for some of the form factors. This is in agreement with other theoretical models, such as the Vector Meson Dominance model and the quark-loop model within the constituent-quark framework. But we also find that we can be in agreement with KTeV if we explore some freedom of the form factor not fixed by the low-energy Lagrangian.

[ES] La difusión de la luz es un fenómeno ubicuo con implicaciones significativas en gran variedad de disciplinas. Mientras que la mayoría de los estudios de difusión se centran en la extinción u otras mediciones relacionadas con la amplitud, la fase de la onda difusa contiene información importante que puede ser aprovechada para múltiples propósitos. Aunque pocas técnicas de caracterización son adecuadas para esta tarea, la espectroscopía de terahercios (THz) es una técnica coherente que permite esto en un amplio rango de frecuencias con propiedades cuasi ópticas. Para lograrlo, estudiaremos y mejoraremos la metodología existente de pulsos de THz aumentando la velocidad de adquisición de espectros de alta resolución mediante la combinación de diversas técnicas para el muestreo de retardo. Esta tesis aborda la investigación de luz difusa con tecnología de THz para dos desarrollos principales. El primero es un método de caracterización del tamaño de partículas resuelto espectralmente utilizando medidas de extinción y de índice de refracción (IR). Al resolver el problema inverso de luz difusa, se puede obtener una gran información de las propiedades geométricas y químicas de las partículas. Este método tradicionalmente ha empleado solo de datos de extinción del medio heterogéneo. Demostramos que se puede lograr una mejora neta en la reconstrucción de la distribución del tamaño de partícula al combinar datos de extinción con datos de IR. Dado que las mediciones se encuentran en un rango de frecuencia limitado, obtener el IR a partir de relaciones de Kramers-Kronig (KK) no puede sustituir su medición directa utilizando técnicas coherentes. Una razón adicional por la cual las relaciones de KK pueden no ser útiles es que, en el caso de una partícula con una densidad óptica menor que el fondo, el IR efectivo complejo no sigue relaciones de dispersión convencionales. El estudio de este fenómeno y la interpretación de las implicaciones causales que surgen son el foco de la última parte de esta tesis, junto con su posible aplicación para el diseño de ondas con contenido espectral arbitrario. Finalmente, se discuten las conclusiones y las líneas futuras de trabajo derivadas de nuestros hallazgos. / [CA] La difusió de la llum és un fenomen ubic amb implicacions significatives en una gran varietat de disciplines. Mentre que la majoria dels estudis de difusió se centren en l'extinció o altres mesures relacionades amb l'amplitud, la fase de l'ona difusa conté informació important que es pot aprofitar per a múltiples propòsits. Encara que poques tècniques de caracterització són adequades per a aquesta tasca, l'espectroscòpia de teraherços (THz) és una tècnica coherent que permet això en un ampli rang de freqüències amb propietats quasi òptiques. Per a aconseguir-ho, estudiarem i millorem la metodologia existent de polsos de THz augmentant la velocitat d'adquisició d'espectres d'alta resolució mitjançant la combinació de diverses tècniques per al mostreig de retard. Aquesta tesi aborda la investigació de la llum difusa amb tecnologia de THz per a dos desenvolupaments principals. El primer és un mètode de caracterització de la mida de partícules resolt espectralment utilitzant mesures d'extinció i d'índex de refracció (IR). En resoldre el problema invers de llum difusa, es pot obtenir una gran informació sobre les propietats geomètriques i químiques de les partícules. Aquest mètode tradicionalment ha emprat només dades d'extinció del medi heterogeni. Demostrem que es pot aconseguir una millora neta en la reconstrucció de la distribució de la mida de partícula en combinar dades d'extinció amb dades d'IR. Donat que les mesures es troben en un rang de freqüència limitat, obtenir l'IR a partir de relacions de Kramers-Kronig (KK) no pot substituir la seua mesura directa utilitzant tècniques coherents. Una raó addicional per la qual les relacions de KK poden no ser útils és que, en el cas d'una partícula amb una densitat òptica menor que el fons, l'IR efectiu complex no segueix relacions de dispersió convencionals. L'estudi d'aquest fenomen i la interpretació de les implicacions causals que sorgeixen són el focus de la darrera part d'aquesta tesi, juntament amb la seua possible aplicació per al disseny d'ones amb contingut espectral arbitrari. Finalment, es discuteixen les conclusions i les línies futures de treball derivades dels nostres descobriments. / [EN] Light scattering is a ubiquitous phenomenon with significant implications across various disciplines. While most scattering studies focus on extinction or other amplitude-related measurements, the phase of the scattered wave holds important information that can be harnessed for a multitude of purposes. However, while few characterization techniques are suited for this task, terahertz (THz) spectroscopy is a coherent technique that permits this across a wide range of frequencies with quasi-optical properties. To accomplish this, we will study and improve the existing methodology of pulsed THz by increasing the speed of acquisition of high-resolution spectra with a combination of existing delay sampling techniques. This thesis approaches light scattering research with THz technology for two main developments. The first one is a spectrally resolved particle size characterization method using extinction and refractive index (RI) measurement. By solving the inverse scattering problem, great insight into the geometric and chemical properties of the particles can be gained. This method has traditionally relied only on extinction data from the heterogeneous medium. We demonstrate that a net improvement in the reconstruction of the particle size distribution can be made by combining extinction with RI datasets. Since the measurements are in a limited frequency range, obtaining the RI from Kramers-Kronig (KK) relations cannot substitute for its direct measurement using coherent techniques. One additional reason why KK relations may not be of use is that, for the case of a particle with lower optical density than the background, the measured complex effective RI does not follow conventional dispersion relations. The study of this phenomenon and the interpretation of the causal implications that arise are the subject of the last part of this thesis, along with its possible application to the arbitrary shaping of spectral wave features. Ultimately, the conclusions and future lines of work derived from our findings are discussed. / This thesis has been developed under grant FPI ACIF-2018-163 by GVA, project PID2019-111339GBI00 and project PDC2021-121597-I00 by MCIN/AEI / Báez Chorro, MÁ. (2024). Study of the Complex Spectral Response of Scattering Media with Terahertz Spectroscopy [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/205586

Im Hinblick auf das immense Potential von Diamant als Material für die Mikroelektronik wurden im Rahmen dieser Arbeit undotierte und dotierte Diamantfilme mittels chemischer Gasphasenabscheidung auf Silizium präpariert und anschließend auf ihre elektronischen Eigenschaften hin untersucht. Für Letzteres wurde hauptsächlich die Elektronen-Energieverlustspektroskopie in Transmission verwendet. In situ Gasphasendotierung oder Ionenimplantation wurde zur Dotierung der Filme mit Bor, Lithium oder Phosphor eingesetzt. Bei der Ionenimplantation wurde aufgrund der Erzeugung von Strahlenschäden generell eine Erhöhung des sp2-Anteils beobachtet: Letzterer konnte jedoch im Falle der Bordotierung durch eine, den Implantationsprozeß folgende, Hochtemperaturtemperung wieder deutlich vermindert werden. Für die in situ Dotierung mit Bor wurde eine Verringerung des sp2-Gehaltes mit steigender Dotierkonzentration gefunden. Für den Film mit der höchsten Borkonzentration konnte auch die B1s Absorptionskante untersucht werden. Sie gibt Hinweise auf den überwiegenden Einbau der Boratome in einer tetragonalen Orientierung. Das hiermit verbundene Vorhandensein von Akzeptoren führt zu elektronischen Anregungen im Energiebereich der Bandlücke, welche mittels Infrarotspektroskopie und EELS nachgewiesen werden konnten. Aus den EELS Messungen lassen sich Akzeptorkonzentrationen berechnen, welche wiederum den hohen Anteil an tetraedrisch eingebauten Boratomen bestätigen. Desweiteren untersucht wurden, als interessante Materialklasse mit weitreichendem technologischem Potential, undotierte und stickstoffdotierte, diamantartige amorphe Kohlenstoffilme und hierbei insbesondere die Abhängigkeit der elektronischen und optischen Eigenschaften von der Ionenenergie und dem Stickstoffpartialdruck während der Filmpräparation. Die Plasmonenergien, Massendichten, sp3-Anteile und die optischen Bandlücken der Filme wurden quantitativ bestimmt, wobei das jeweilige Maximum bei einer Ionenenergie von 100 eV gefunden wurde. Alle eben genannten Größen verringern sich kontinuierlich mit zunehmendem Stickstoffanteil. Eine Kramers-Kronig Analyse der Verlustspektren gibt Zugriff auf den Real- und Imaginärteil der dielektrischen Funktion und damit auf das Spektrum der Einteilchenanregungen. Die Hybridisierung der Kohlenstoff- und der Stickstoffatome wurde detailliert aus den jeweiligen 1s Absorptionskanten bestimmt. Weiterhin wurde Diamant als Modellsystem eines Festkörpers mit rein kovalenten Bindungen untersucht, insbesondere die Verlustfunktion von Diamant entlang mehrerer Hochsymmetriekristallrichtungen über einen großen Energie- und Impulsbereich. Aus den EELS Messungen erschließt sich unmittelbar die stark anisotrope Plasmonendispersion von Diamant. Aus dem Vergleich der experimentellen Spektren mit ab initio LDA Rechnungen, die sowohl Kristallokalfeldeffekte als auch Austausch- und Korrelationseffekte beinhalten, lassen sich direkt Rückschlüsse auf den Einfluß der verschiedenen Effekte ziehen. Schon im optischen Limit, aber umso mehr mit steigendem Impulsübertrag q, wird eine Überlagerung der kollektiven Plasmonanregung mit Einteilchenanregungen im Energiebereich des Plasmons beobachtet, woraus eine Kopplung zwischen beiden Arten von Anregungen resultiert. Abgesehen vom deutlichen Einfluß der Bandstruktur auf die Plasmonendispersion läßt die überaus inhomogene Elektronenverteilung von Diamant auf nicht zuvernachlässigende Kristallokalfeldeffekte schließen. Der Vergleich zwischen experimentellen und berechneten Spektren zeigt deutlich, wie die Kristallokalfeldeffekte in der Tat mit steigendem Impulsübertrag an Gewicht zunehmen und die Struktur der Verlustfunktion mitbestimmen. / In the context of the immense potential of diamond as a material for use in the microelectronics industry, in this thesis pristine and doped diamond films have been deposited on silicon using chemical vapour deposition. Subsequently their electronic properties have been investigated using mainly electron energy-loss spectroscopy. Doping of the films with boron, lithium or phosphorous was carried out either via in-situ gas phase doping during film growth or using ion implantation. Upon ion implantation an increase of the carbon content with sp2 hybridisation has generally been found due to ion beam induced damage. In the case of boron doping it was possible to significantly reduce this sp2-contribution using a high temperature anneal. For the in-situ doping with boron, upon increasing doping concentration a decrease of the sp2-contribution was found. For the sample with the highest boron content the boron 1s absorption edge could also be investigated, providing evidence for the preferential incorporation of the boron atoms into tetrahedrally co-ordinated sites. This boron incorporation leads to the existence of electronic excitations in the energy range of the band gap, which could be observed using both infrared and electron energy-loss spectroscopy. From the electron energy-loss measurements it was possible to calculate acceptor concentrations which were consistent with the large amount of tetrahedrally co-ordinated boron atoms. A second theme in this thesis involved the study of pristine and nitrogen doped diamond-like amorphous carbon films, which are an interesting material class with far-reaching technological potential. Here the focus of the research concerned the dependency of the electronic and optical properties of the films upon the ion energy and the nitrogen partial pressure applied during the film preparation. The plasmon energies, mass densities, sp3 contribution and the optical band gaps of the samples were determined quantitatively, whereby the maximum in all these quantities was found to occur for ion energies of 100 eV. Furthermore, all of these characteristics were found to decrease continually with increasing nitrogen content. A Kramers-Kronig analysis of the loss spectra enabled the derivation of the real and imaginary parts of the dielectric function and with this of the complete spectrum of single particle excitations. The hybridization between the carbon and nitrogen atoms was also studied in detail from the analysis of the respective 1s absorption edges. Furthermore this thesis deals with the investigation of diamond as a model system for solids with pure covalent bonds. In particular, the loss function of diamond was measured along different high symmetry directions over a wide range of energy and momentum. Firstly, the EELS measurements showed directly the strongly anisotropic nature of the plasmon dispersion in diamond. Secondly, by the comparison of the experimental spectra with ab initio LDA-based calculations that include crystal local field effects as well as exchange and correlation contributions, conclusions can be drawn as to the influence of these quantities. In the optical limit, but even more so with increasing momentum transfer q, a superposition of the collective plasmon excitation and the single particle excitations in the energy range of the plasmon is observed. This energetic proximity results in a coupling between both types of excitations. Apart from the distinct influence of the bandstructure on the plasmon dispersion, the considerably inhomogeneous electron distribution of diamond would lead one to expect significant crystal local field effects in this system. The comparison between the experimental and the calculated spectra shows explicitly that the crystal local field effects increase with increasing momentum transfer and play an important role in defining the structure of the loss function.

A rich variety of discs are found orbiting massive bodies in the universe. These could be accretion discs composed of gas around stellar mass compact objects fueling micro-quasar activity; protoplanetary discs, mainly composed of dust and gas, are the progenitors for planet formation; accretion discs composed of stars and gas around super-massive black holes at the centers of galaxies fueling the active galactic nuclei activity; discs in spiral galaxies; and many more. Structural and kinematic properties of these discs in several astrophysical systems are correlated to the global properties; for example, over a sample of thousands of galaxies, a correlation has been found between lopsidedness, black hole growth, and the presence of young stellar populations in the centers of galaxies. Galaxy formation and evolution of the central BH are some of the contexts in which such correlations become important. Studying the dynamics of these discs helps to explain their structural properties and is thus of paramount importance. In most astrophysical discs(a notable exception being the stellar discs in spiral galaxies),the dynamics are usually dominated by the gravity of the central object, and is thus nearly Keplerian. However, there is a small contribution to the total force experienced by the disc due to the disc material. Discs mentioned above differ from each other due to different underlying force that dominates the non-Keplerian dynamics of these discs. Two important numbers which are useful in describing physical properties of any disc structure in astrophysics are: (1) Mach number M , and(2) Toomre Q parameter. If thermal pressure gradient and/or random motion dominate the non-Keplerian forces, then M « Q, and in the case when the self-gravity of the disc is more important then Particles constituting the disc orbit under Keplerian potential due to central object, plus the small contribution from the non-Keplerian potential due to disc self-gravity, or the thermal pressure gradient. For a Keplerian potential, the radial and azimuthal frequencies are in 1 : 1 ratio w.r.t. each other and hence there is no precession in the orbits. In case of nearly Keplerian potential(when non-Keplerian contributions are small), the orbits precess at a rate proportional to the non-Keplerian forces. It is this non-zero but small precession that allows the existence of modes whose frequencies are proportional to the precession rate. These modes are referred to as slow modes (Tremaine 2001). Such modes are likely to be the only large-scale or long-wavelength modes. The damping they suffer due to viscosity, collisions, Landau damping, or other dissipative processes is also relatively less. Hence, these modes can dominate the overall appearance of discs. In this thesis we intend to study slow modes for nearly Keplerian discs. Slow modes innear-Kepleriandiscscantobethereasonforvariousnon-axisymmetricfeatures observed in many systems: 1 Galactic discs: Of the few galaxies for which the observations of galactic nuclei exist, two galaxies: NGC4486B(an elliptical galaxy) andM31(spiral galaxy), show an unusual double-peak distribution of stars at their centers. In order to explain such distributions, Tremaine in 1995 proposed an eccentric disc model for M31; this model was then further explored by many authors. In addition, lopsidedness is observed in many galaxies on larger scales, and such asymmetries need to be explained via robust modeling of galactic discs. 2 Debris disc: Many of the observed discs show non-axisymmetric structures, such as lopsided distribution in brightness of scattered light, warp, and clumps in the disc around β Pictoris; spiral structure inHD141569A,etc. Most of these features have been attributed to the presence of planets, and in some cases planets have also been detected. However, Jalali & Tremaine(2012)proposed that most of these structures can be formed also due to slow (m =1 or 2) modes. 3 Accretion Discs around stellar mass binaries have also been found to be asymmetric. One plausible reason for this asymmetry can be m =1slowmodes in these systems. Slow modes are studied in detail in this thesis. The main approaches that we have used, and the major conclusions from this work are as follows: Slow pressure modes in thin accretion disc Earlier work on slow modes assumed that the self-gravity of the disc dominates the pressure gradient in the discs. However, this assumption is not valid for thin and hot accretion discs around stellar mass compact objects. We begin our study of slow modes with the analysis of modes in thin accretion discs around stellar mass compact objects. First, the WKB analysis is used to prove the existence of these modes. Next, we formulate the eigenvalue equation for the slow modes, which turns out to be in the Sturm-Liouville form; thus all the eigenvalues are real. Real eigenvalues imply that the disc is stable to these perturbations. We also discuss the possible excitation mechanisms for these modes; for instance, excitation due to the stream of matter from the secondary star that feeds the accretion disc, or through the action of viscous forces. Slow modes in self-gravitating, zero-pressure fluid disc We next generalize the study of slow m = 1 modes for a single self-gravitating disc of Tremaine(2001) to a system of two self-gravitating counter–rotating, zero-pressure fluid discs, where the disc particles interact via softened-gravity. Counter– rotating streams of matter are susceptible to various instabilities. In particular, Touma(2002)found unstable modes in counter–rotating ,nearly Keplerian systems. These modes were calculated analytically for a two-ring system, and numerically for discs modeled assuming a multiple–ring system. Motivated by this, the corresponding problem for continuous discs was studied by Sridhar & Saini(2010),who proposed a simple model, with dynamics that could be studied largely analytically in the local WKB approximation. Their work, however, had certain limitations; they could construct eigenmodes only for η =0&12, where η is the mass fraction in the retrograde disc. They could only calculate eigenvalues but not the eigen functions. To overcome the above mentioned limitations, we formulate and analyze the full eigenvalue problem to understand the systematic behaviour of such systems. Our general conclusions are as follows 1 The system is stable for m = 1 perturbations in the case of no-counter rotation. 2. For other values of mass fraction , the eigenvalues are generally complex, and the discs are unstable. For η =12,theeigenvalues are imaginary, giving purely growing modes. 2 The pattern speed appears to be non-negative for all values of , with the growth(or damping) rate being larger for larger values of pattern speed. 3 Perturbed surface density profile is generally lopsided, with an overall rotation of the patterns as they evolve in time, with the pattern speed given by the real part of the eigenvalue. Local WKB analysis for Keplerian stellar disc We next urn to stellar discs, whose dynamics is richer than softened gravity discs. Jalali & Tremaine(2012)derived the dispersion relation for short wavelength slow modes for a single disc with Schwarzschild distribution function. In contrast to the softened gravity discs(which have slow modes only for m = 1), stellar discs permit slow modes for m 1. The dispersion relation derived by Jalali & Tremaine makes it evident that all m 1 slow modes are neutrally stable. We study slow modes for the case of two counter–rotating discs, each described by Schwarzschild distribution function, and derive the dispersion relation for slow m 1 modes in the local WKB limit and study the nature of the instabilities. One of the important applications of the dispersion relation derived in this chapter is the stability analysis of the modes. For fluid discs, it is well known that the stability of m = 0 modes guarantees the stability of higher m modes; and the stability criterion for such discs is the well known Toomre stability criterion. However, this is not the case for collisionless discs. Even if the discs are stable for axisymmetric modes, they can still be unstable for non-axisymmetric modes. The stability of axisymmetric modes is governed by the Toomre stability criterion The non-axisymmetric perturbations were found to be unstable if the mass in the retrograde component of the disc is non-zero. We next solve the dispersion relation using the Bohr-Sommerfeld quantization condition to obtain the eigen-spectrum for a given unperturbed surface density profile and velocity dispersion. We could obtain only the eigenvalues for no counter– rotation η = 0, where η is the mass fraction in the retrograde disc and equal counter–rotation(η =12). All the eigenvalues obtained were real for no counter– rotation, and purely growing/damping for equal counter–rotation. The eigenvalue trends that we get favour detection of high ω and low m modes observationally. We also make a detailed comparison between the eigenvalues for m = 1 modes that we obtain with those obtained after solving the integral eigenvalue problem for the softened gravity discs for no counter–rotation and equal counter–rotation. The match between the eigenvalues are quite good, confirming the assertion that softened gravity discs can be reasonable surrogates for collisionless disc for m =1 modes. Non-local WKB theory for eigenmodes One major limitation of the above method is that eigenfunctions cannot be obtained as directly as in quantum mechanics because the dispersion relation is transcendental in radial wave number . We overcome this difficulty by dropping the assumption of locality of the relationship between perturbed self-gravity and surface density. Using the standard WKB analysis and epicyclic theory, together with the logarithmic-spiral decomposition of surface density and gravitational potential, we formulate an integral equation for determining both WKB eigenvalues and eigenfunctions. The application of integral equation derived is not only restricted to Keplerian disc; it could be used to study eigenmodes in galactic discs where the motion of stars is not dominated by the potential due to a central black hole (however we have not pursued the potential application in this thesis). We first verify that the integral equation derived reduces to the well known WKB dispersion relation under the local approximation. We next specialize to slow modes in Keplerian discs. The following are some of the general conclusions of this work 1 We find that the integral equation for slow modes reduces to a symmetric eigenvalue problem, implying that the eigenvalues are all real, and hence the disc is stable. 2 All the non-singular eigenmodes we obtain are prograde, which implies that the density waves generated will have the same sense of rotation as the disc, albeit with a speed which is compared to the the rotation speed of the disc. 3 Eigenvalue ω decreases as we go from m =1 to 2. In addition, for a given , the number of nodes for m =1 are larger than those for m =2. 4 The fastest pattern speed is a decreasing function of the heat in the disc. Asymmetric features in various types of discs could be due to the presence of slow m =1 or 2 modes. In the case of debris discs, these asymmetric features could also be due to the presence of planets. Features due to the presence of slow modes or due to planets can be distinguished from each other if the observations are made for a long enough time. The double peak nucleus observed in galaxies like M31 and NGC4486B differ from each other: stellar distribution in NGC4486B is symmetric w.r.t. its photocenter in contrast to a lopsided distribution seen in M31. It is more likely that the double peak nucleus in NGC4486B is due to m = 2 mode, rather than m = 1 mode as is the case for M31. NGC4486B being an elliptical galaxy, it is possible that the excitation probability for m =2 mode is higher.

Im Hinblick auf das immense Potential von Diamant als Material für die Mikroelektronik wurden im Rahmen dieser Arbeit undotierte und dotierte Diamantfilme mittels chemischer Gasphasenabscheidung auf Silizium präpariert und anschließend auf ihre elektronischen Eigenschaften hin untersucht. Für Letzteres wurde hauptsächlich die Elektronen-Energieverlustspektroskopie in Transmission verwendet. In situ Gasphasendotierung oder Ionenimplantation wurde zur Dotierung der Filme mit Bor, Lithium oder Phosphor eingesetzt. Bei der Ionenimplantation wurde aufgrund der Erzeugung von Strahlenschäden generell eine Erhöhung des sp2-Anteils beobachtet: Letzterer konnte jedoch im Falle der Bordotierung durch eine, den Implantationsprozeß folgende, Hochtemperaturtemperung wieder deutlich vermindert werden. Für die in situ Dotierung mit Bor wurde eine Verringerung des sp2-Gehaltes mit steigender Dotierkonzentration gefunden. Für den Film mit der höchsten Borkonzentration konnte auch die B1s Absorptionskante untersucht werden. Sie gibt Hinweise auf den überwiegenden Einbau der Boratome in einer tetragonalen Orientierung. Das hiermit verbundene Vorhandensein von Akzeptoren führt zu elektronischen Anregungen im Energiebereich der Bandlücke, welche mittels Infrarotspektroskopie und EELS nachgewiesen werden konnten. Aus den EELS Messungen lassen sich Akzeptorkonzentrationen berechnen, welche wiederum den hohen Anteil an tetraedrisch eingebauten Boratomen bestätigen. Desweiteren untersucht wurden, als interessante Materialklasse mit weitreichendem technologischem Potential, undotierte und stickstoffdotierte, diamantartige amorphe Kohlenstoffilme und hierbei insbesondere die Abhängigkeit der elektronischen und optischen Eigenschaften von der Ionenenergie und dem Stickstoffpartialdruck während der Filmpräparation. Die Plasmonenergien, Massendichten, sp3-Anteile und die optischen Bandlücken der Filme wurden quantitativ bestimmt, wobei das jeweilige Maximum bei einer Ionenenergie von 100 eV gefunden wurde. Alle eben genannten Größen verringern sich kontinuierlich mit zunehmendem Stickstoffanteil. Eine Kramers-Kronig Analyse der Verlustspektren gibt Zugriff auf den Real- und Imaginärteil der dielektrischen Funktion und damit auf das Spektrum der Einteilchenanregungen. Die Hybridisierung der Kohlenstoff- und der Stickstoffatome wurde detailliert aus den jeweiligen 1s Absorptionskanten bestimmt. Weiterhin wurde Diamant als Modellsystem eines Festkörpers mit rein kovalenten Bindungen untersucht, insbesondere die Verlustfunktion von Diamant entlang mehrerer Hochsymmetriekristallrichtungen über einen großen Energie- und Impulsbereich. Aus den EELS Messungen erschließt sich unmittelbar die stark anisotrope Plasmonendispersion von Diamant. Aus dem Vergleich der experimentellen Spektren mit ab initio LDA Rechnungen, die sowohl Kristallokalfeldeffekte als auch Austausch- und Korrelationseffekte beinhalten, lassen sich direkt Rückschlüsse auf den Einfluß der verschiedenen Effekte ziehen. Schon im optischen Limit, aber umso mehr mit steigendem Impulsübertrag q, wird eine Überlagerung der kollektiven Plasmonanregung mit Einteilchenanregungen im Energiebereich des Plasmons beobachtet, woraus eine Kopplung zwischen beiden Arten von Anregungen resultiert. Abgesehen vom deutlichen Einfluß der Bandstruktur auf die Plasmonendispersion läßt die überaus inhomogene Elektronenverteilung von Diamant auf nicht zuvernachlässigende Kristallokalfeldeffekte schließen. Der Vergleich zwischen experimentellen und berechneten Spektren zeigt deutlich, wie die Kristallokalfeldeffekte in der Tat mit steigendem Impulsübertrag an Gewicht zunehmen und die Struktur der Verlustfunktion mitbestimmen. / In the context of the immense potential of diamond as a material for use in the microelectronics industry, in this thesis pristine and doped diamond films have been deposited on silicon using chemical vapour deposition. Subsequently their electronic properties have been investigated using mainly electron energy-loss spectroscopy. Doping of the films with boron, lithium or phosphorous was carried out either via in-situ gas phase doping during film growth or using ion implantation. Upon ion implantation an increase of the carbon content with sp2 hybridisation has generally been found due to ion beam induced damage. In the case of boron doping it was possible to significantly reduce this sp2-contribution using a high temperature anneal. For the in-situ doping with boron, upon increasing doping concentration a decrease of the sp2-contribution was found. For the sample with the highest boron content the boron 1s absorption edge could also be investigated, providing evidence for the preferential incorporation of the boron atoms into tetrahedrally co-ordinated sites. This boron incorporation leads to the existence of electronic excitations in the energy range of the band gap, which could be observed using both infrared and electron energy-loss spectroscopy. From the electron energy-loss measurements it was possible to calculate acceptor concentrations which were consistent with the large amount of tetrahedrally co-ordinated boron atoms. A second theme in this thesis involved the study of pristine and nitrogen doped diamond-like amorphous carbon films, which are an interesting material class with far-reaching technological potential. Here the focus of the research concerned the dependency of the electronic and optical properties of the films upon the ion energy and the nitrogen partial pressure applied during the film preparation. The plasmon energies, mass densities, sp3 contribution and the optical band gaps of the samples were determined quantitatively, whereby the maximum in all these quantities was found to occur for ion energies of 100 eV. Furthermore, all of these characteristics were found to decrease continually with increasing nitrogen content. A Kramers-Kronig analysis of the loss spectra enabled the derivation of the real and imaginary parts of the dielectric function and with this of the complete spectrum of single particle excitations. The hybridization between the carbon and nitrogen atoms was also studied in detail from the analysis of the respective 1s absorption edges. Furthermore this thesis deals with the investigation of diamond as a model system for solids with pure covalent bonds. In particular, the loss function of diamond was measured along different high symmetry directions over a wide range of energy and momentum. Firstly, the EELS measurements showed directly the strongly anisotropic nature of the plasmon dispersion in diamond. Secondly, by the comparison of the experimental spectra with ab initio LDA-based calculations that include crystal local field effects as well as exchange and correlation contributions, conclusions can be drawn as to the influence of these quantities. In the optical limit, but even more so with increasing momentum transfer q, a superposition of the collective plasmon excitation and the single particle excitations in the energy range of the plasmon is observed. This energetic proximity results in a coupling between both types of excitations. Apart from the distinct influence of the bandstructure on the plasmon dispersion, the considerably inhomogeneous electron distribution of diamond would lead one to expect significant crystal local field effects in this system. The comparison between the experimental and the calculated spectra shows explicitly that the crystal local field effects increase with increasing momentum transfer and play an important role in defining the structure of the loss function.

The topic of this thesis is a diffusion process on a potential landscape which is given by a smooth Hamiltonian function in the regime of small noise. The work provides a new proof of the Eyring-Kramers formula for the Poincaré inequality of the associated generator of the diffusion. The Poincaré inequality characterizes the spectral gap of the generator and establishes the exponential rate of convergence towards equilibrium in the L²-distance. This result was first obtained by Bovier et. al. in 2004 relying on potential theory. The presented approach in the thesis generalizes to obtain also asymptotic sharp estimates of the constant in the logarithmic Sobolev inequality. The optimal constant in the logarithmic Sobolev inequality characterizes the convergence rate to equilibrium with respect to the relative entropy, which is a stronger distance as the L²-distance and slightly weaker than the L¹-distance. The optimal constant has here no direct spectral representation. The proof makes use of the scale separation present in the dynamics. The Eyring-Kramers formula follows as a simple corollary from the two main results of the work: The first one shows that the associated Gibbs measure restricted to a basin of attraction has a good Poincaré and logarithmic Sobolev constants providing the fast convergence of the diffusion to metastable states. The second main ingredient is a mean-difference estimate. Here a weighted transportation distance is used. It contains the main contribution to the Poincaré and logarithmic Sobolev constant, resulting from exponential long waiting times of jumps between metastable states of the diffusion.

Die fortschreitenden Entwicklungen in der Mikro- und Nanotechnologie erfordern eine solide Unterstützung durch Simulationen. Numerische Bauelementesimulationen waren und sind dabei unerlässliche Werkzeuge, die jedoch zunehmend an ihre Grenzen kommen. So basieren sie auf Parametern, die für beliebige Atomanordnungen nicht verfügbar sind, und scheitern für stark verkleinerte Strukturen infolge zunehmender Relevanz von Quanteneffekten. Diese Arbeit behandelt den Transport in Siliziumnanodrähten sowie durch NiSi2-Si-Grenzflächen. Dichtefunktionaltheorie wird dabei verwendet, um die stabile Atomanordnung und alle für den elektronischen Transport relevanten quantenmechanischen Effekte zu beschreiben. Bei der Untersuchung der Nanodrähte liegt das Hauptaugenmerk auf der radialen Abhängigkeit der elektronischen Struktur sowie deren Änderung bei Variation des Durchmessers. Dabei zeigt sich, dass der Kern der Nanodrähte für den Ladungstransport bestimmend ist. Weiterhin kann ein Durchmesser von ungefähr 5 nm identifiziert werden, oberhalb dessen die Zustandsdichte im Nanodraht große Ähnlichkeiten mit jener des Silizium-Volumenkristalls aufweist und der Draht somit zunehmend mit Näherungen für den perfekt periodischen Kristall beschrieben werden kann. Der Fokus bei der Untersuchung der NiSi2-Si-Grenzflächen liegt auf der Symmetrie von Elektron- und Lochströmen im Tunnelregime, welche für die Entwicklung von rekonfigurierbaren Feldeffekttransistoren besondere Relevanz hat. Verschiedene NiSi2-Si-Grenzflächen und Verzerrungszustände werden dabei systematisch untersucht. Je nach Grenzfläche ist die Symmetrie dabei sehr unterschiedlich und zeigt auch ein sehr unterschiedliches Verhalten bei externer Verzerrung. Weiterhin werden grundlegende physikalische Größen mit Bezug zu NiSi2-Si-Grenzflächen betrachtet. So wird beispielsweise die Stabilität anhand von Grenzflächen-Energien ermittelt. Am stabilsten sind {111}-Grenzflächen, was deren bevorzugtes Auftreten in Experimenten erklärt. Weitere wichtige Größen, deren Verzerrungsabhängigkeit untersucht wird, sind die Schottky-Barrierenhöhe, die effektive Masse der Ladungsträger sowie die Austrittsarbeiten von NiSi2- und Si-Oberflächen. Ein Beitrag zur Modellentwicklung numerischer Bauelementesimulationen wird durch einen Vergleich zwischen den Ergebnissen von Dichtefunktionaltheorie-basierten Transportrechnungen und denen eines vereinfachten Models basierend auf der Wentzel-Kramers-Brillouin-Näherung geliefert. Diese Näherung ist Teil vieler numerischer Bauelementesimulatoren und erlaubt die Berechnung des Tunnelstroms basierend auf grundlegenden physikalischen Größen. Der Vergleich ermöglicht eine Evaluierung des vereinfachten Models, welches anschließend genutzt wird, um den Einfluss der grundlegenden physikalischen Größen auf den Tunneltransport zu untersuchen.:Index of Abbreviations 1. Introduction 2. Silicon Based Devices and Silicon Nanowires 2.1. Introduction 2.2. The Reconfigurable Field-effect Transistor 2.2.1. Design and Functionality 2.2.2. Fabrication 2.3. Overview Over Silicon Nanowires 2.3.1. Geometric Structure 2.3.2. Fabrication Techniques 2.3.3. Electronic Properties 3. Simulation Tools 3.1. Introduction 3.2. Electronic Structure Calculations 3.2.1. Introduction and Basis Functions 3.2.2. Density Functional Theory 3.2.3. Description of Exchange and Correlation Effects 3.2.4. Practical Aspects of Density Functional Theory 3.3. Electron Transport 3.3.1. Introduction 3.3.2. Scattering Theory 3.3.3. Wentzel-Kramers-Brillouin Approximation for a Triangular Barrier 3.3.4. Non-equilibrium Green’s Function Formalism A. Radially Resolved Electronic Structure and Charge Carrier Transport in Silicon Nanowires A.1. Introduction A.2. Model System A.3. Results and Discussion A.4. Summary and Conclusions A.5. Appendix A: Computational Details A.6. Appendix B: Supplementary Material A.6.1. Comparison of the Band Gap Between Relaxed and Unrelaxed SiNWs A.6.2. Band Structures for Some of the Calculated SiNWs A.6.3. Radially Resolved Density of States for Some of the Calculated SiNWs B. Electron Transport Through NiSi2-Si Contacts and Their Role in Reconfigurable Field-effect Transistors B.1. Introduction B.2. Model for Reconfigurable Field-effect Transistors B.2.1. Atomistic Quantum Transport Model to Describe Transport Across the Contact Interface B.2.2. Simplified Compact Model to Calculate the Device Characteristics B.3. Results and Discussion B.3.1. Characteristics of a Reconfigurable Field-effect Transistor B.3.2. Variation of the Crystal Orientations and Influence of the Schottky Barrier B.3.3. Comparison to Fabricated Reconfigurable Field-effect Transistors B.4. Summary and Conclusions B.5. Appendix: Supplementary Material B.5.1. Band Structure and Density of States of the Contact Metal B.5.2. Relaxation Procedure B.5.3. Total Transmission Through Multiple Barriers C. Formation and Crystallographic Orientation of NiSi2-Si Interfaces C.1. Introduction C.2. Fabrication and characterization methods C.3. Model System and Simulation Details C.4. Results and discussion C.4.1. Atomic structure of the interface C.4.2. Discussion of ways to modify the interface orientation C.5. Summary C.6. Appendix: Supplementary Material D. NiSi2-Si Interfaces Under Strain: From Bulk and Interface Properties to Tunneling Transport D.1. Introduction D.2. Model System and Simulation Approach D.3. Computational Details D.3.1. Electronic Structure Calculations (Geometry Relaxations) D.3.2. Electronic Structure Calculations (Electronic Structure) D.3.3. Device Calculations D.4. Tunneling Transport From First-principles Calculations D.4.1. Evaluation of the Current D.4.2. Isotropic Strain D.4.3. Anisotropic Strain D.5. Transport Related Properties and Effective Modeling Schemes D.5.1. Schottky Barrier Height D.5.2. Simplified Transport Model D.5.3. Models for the Schottky Barrier Height D.6. Summary and Conclusions D.7. Appendix: Supplementary Material D.7.1. Schottky Barriers of the {110} Interface Under Anisotropic Strain D.7.2. Silicon Band Structure, Electric Field, and Number of Transmission Channels D.7.3. k∥-resolved Material Properties D.7.4. Evaluation of the Work Functions and Electron Affinities D.7.5. Verification of the Work Function Calculation 4. Discussion 5. Ongoing Work and Possible Extensions 6. Summary Bibliography List of Figures List of Tables Acknowledgements Selbstständigkeitserklärung Curriculum Vitae Scientific Contributions / The ongoing developments in micro- and nanotechnologies require a profound support from simulations. Numerical device simulations were and still are essential tools to support the device development. However, they gradually reach their limits as they rely on parameters, which are not always available, and neglect quantum effects for small structures. This work addresses the transport in silicon nanowires and through NiSi2-Si interfaces. By using density functional theory, the atomic structure is considered, and all electron transport related quantum effects are taken into account. Silicon nanowires are investigated with special attention to their radially resolved electronic structure and the corresponding modifications when the silicon diameter is reduced. The charge transport occurs mostly in the nanowire core. A diameter of around 5 nm can be identified, above which the nanowire core exhibits a similar density of states as bulk silicon. Thus, bulk approximations become increasingly valid above this diameter. NiSi2-Si interfaces are studied with focus on the symmetry between electron and hole currents in the tunneling regime. The symmetry is especially relevant for the development of reconfigurable field-effect transistors. Different NiSi2-Si interfaces and strain states are studied systematically. The symmetry is found to be different between the interfaces. Changes of the symmetry upon external strain are also very interface dependent. Furthermore, fundamental physical properties related to NiSi2-Si interfaces are evaluated. The stability of the different interfaces is compared in terms of interface energies. {111} interfaces are most stable, which explains their preferred occurrence in experiments. Other properties, whose strain dependence is studied, include the Schottky barrier height, the effective mass of the carriers, and work functions. A contribution to the development of numerical device simulators will be given by comparing the results from density functional theory based transport calculations and a model based on the Wentzel-Kramers-Brillouin approximation. This approximation, which is often employed in numerical device simulators, offers a relation between interface properties and the tunneling transport. The comparison allows an evaluation of the simplified model, which is then used to investigate the relation between the fundamental physical properties and the tunneling transport.:Index of Abbreviations 1. Introduction 2. Silicon Based Devices and Silicon Nanowires 2.1. Introduction 2.2. The Reconfigurable Field-effect Transistor 2.2.1. Design and Functionality 2.2.2. Fabrication 2.3. Overview Over Silicon Nanowires 2.3.1. Geometric Structure 2.3.2. Fabrication Techniques 2.3.3. Electronic Properties 3. Simulation Tools 3.1. Introduction 3.2. Electronic Structure Calculations 3.2.1. Introduction and Basis Functions 3.2.2. Density Functional Theory 3.2.3. Description of Exchange and Correlation Effects 3.2.4. Practical Aspects of Density Functional Theory 3.3. Electron Transport 3.3.1. Introduction 3.3.2. Scattering Theory 3.3.3. Wentzel-Kramers-Brillouin Approximation for a Triangular Barrier 3.3.4. Non-equilibrium Green’s Function Formalism A. Radially Resolved Electronic Structure and Charge Carrier Transport in Silicon Nanowires A.1. Introduction A.2. Model System A.3. Results and Discussion A.4. Summary and Conclusions A.5. Appendix A: Computational Details A.6. Appendix B: Supplementary Material A.6.1. Comparison of the Band Gap Between Relaxed and Unrelaxed SiNWs A.6.2. Band Structures for Some of the Calculated SiNWs A.6.3. Radially Resolved Density of States for Some of the Calculated SiNWs B. Electron Transport Through NiSi2-Si Contacts and Their Role in Reconfigurable Field-effect Transistors B.1. Introduction B.2. Model for Reconfigurable Field-effect Transistors B.2.1. Atomistic Quantum Transport Model to Describe Transport Across the Contact Interface B.2.2. Simplified Compact Model to Calculate the Device Characteristics B.3. Results and Discussion B.3.1. Characteristics of a Reconfigurable Field-effect Transistor B.3.2. Variation of the Crystal Orientations and Influence of the Schottky Barrier B.3.3. Comparison to Fabricated Reconfigurable Field-effect Transistors B.4. Summary and Conclusions B.5. Appendix: Supplementary Material B.5.1. Band Structure and Density of States of the Contact Metal B.5.2. Relaxation Procedure B.5.3. Total Transmission Through Multiple Barriers C. Formation and Crystallographic Orientation of NiSi2-Si Interfaces C.1. Introduction C.2. Fabrication and characterization methods C.3. Model System and Simulation Details C.4. Results and discussion C.4.1. Atomic structure of the interface C.4.2. Discussion of ways to modify the interface orientation C.5. Summary C.6. Appendix: Supplementary Material D. NiSi2-Si Interfaces Under Strain: From Bulk and Interface Properties to Tunneling Transport D.1. Introduction D.2. Model System and Simulation Approach D.3. Computational Details D.3.1. Electronic Structure Calculations (Geometry Relaxations) D.3.2. Electronic Structure Calculations (Electronic Structure) D.3.3. Device Calculations D.4. Tunneling Transport From First-principles Calculations D.4.1. Evaluation of the Current D.4.2. Isotropic Strain D.4.3. Anisotropic Strain D.5. Transport Related Properties and Effective Modeling Schemes D.5.1. Schottky Barrier Height D.5.2. Simplified Transport Model D.5.3. Models for the Schottky Barrier Height D.6. Summary and Conclusions D.7. Appendix: Supplementary Material D.7.1. Schottky Barriers of the {110} Interface Under Anisotropic Strain D.7.2. Silicon Band Structure, Electric Field, and Number of Transmission Channels D.7.3. k∥-resolved Material Properties D.7.4. Evaluation of the Work Functions and Electron Affinities D.7.5. Verification of the Work Function Calculation 4. Discussion 5. Ongoing Work and Possible Extensions 6. Summary Bibliography List of Figures List of Tables Acknowledgements Selbstständigkeitserklärung Curriculum Vitae Scientific Contributions

This mémoire presents my current research interests in micro and nano-mechanics in a comprehensive manuscript. Our experimental device is first presented: this atomic force microscope, designed and realized in the Laboratoire de Physique de l'ENS Lyon, is based on a quadrature phase differential interferometer. It features a very high resolution (down to 10 fm/rtHz) in the measurement of deflexion, down to low frequencies and on a huge input range. The dual output of the interferometer implies a specific handling to interface common scanning probe microscope controllers. We developed analog circuitries to tackle static (contact mode) and dynamic (tapping mode) operations, and we demonstrate their performance by imaging a simple calibration sample. As a first application, we used the high sensitivity of our interferometer to study the mechanical behavior of micro-cantilevers from their fluctuations. The keystone of the analysis is the Fluctuation-Dissipation Theorem (FDT), relating the thermal noise spectrum to the dissipative part of the response. We apply this strategy to confront Sader's model for viscous dissipation with measurements on raw silicon cantilevers in air, demonstrating an excellent agreement. When a gold coating is added, the thermal noise is strongly modified, presenting a 1/f like trend at low frequencies: we show that this behavior is due to a viscoelastic damping, and we provide a quantitative phenomenological model. We also characterize the mechanical properties of cantilevers (stiffness and Elastic Moduli) from a mapping of the thermal noise on their surface. This analysis validates the description of the system in term of its normal modes of oscillations in an Euler-Bernoulli framework for flexion and in Saint-Venant approach for torsion, but points toward a refined model for the dispersion relation of torsional modes. Finally, we present peeling experiments on a single wall carbon nanotube attached to the cantilever tip. It is pushed against a flat substrate, and we measure the quasi-static force as well as the dynamic stiffness using an analysis of the thermal noise during this process. The most striking feature of these two observables is a plateau curve for a large range of compression, the values of which are substrate dependent. We use the Elastica to describe the shape of the nanotube, and a simple energy of adhesion per unit length Ea to describe the interaction with the substrate. We analytically derive a complete description of the expected behavior in the limit of long nanotubes. The analysis of the experimental data within this simple framework naturally leads to every quantity of interest in the problem: the force plateau is a direct measurement of the energy of adhesion Ea for each substrate, and we easily determine the mechanical properties of the nanotube itself.

We have measured the optical properties of films of the organic semiconductors PTCDA (3,4:9,10-perylene-tetracarboxylic dianhydride) and HBC (peri-hexabenzocoronene), prepared by Organic Molecular Beam Expitaxy (OMBE), on different substrates by means of Differential Reflectance Spectroscopy (DRS). The optical setup enables us to directly follow the thickness dependent optical properties of the organic films, starting from submonolayer coverage up to thicker films on the order of 20 monolayers (ML) film thickness. Due to the different optical nature of the different substrates used, i.e., mica, glass, Au(111), and HOPG, the direct interpretation of the DRS signal is not feasible. Therefore, we have proposed a method by which the calculation of the optical constants n (index of refraction) and k (absorption index) of thin films on arbitrary substrates from just one spectral measurement (in our case the DRS) becomes possible. The results fulfill a priori a Kramers-Kronig consistency and no specific model is needed to express the spectral behavior of the optical constants. Based on our method, we have successfully calculated the optical constants, and therefore the absorption behavior, of films of different thickness of PTCDA on mica, glass, Au(111), and HOPG, as well as of HBC on mica, glass, and HOPG. Extrinsic effects due to island growth or the presence of a polarizable substrate (screening) have been accounted for. We have introduced a finite dipole model which considers the extended geometry and anisotropy of the organic molecules. The calculated absorption behavior is discussed in great detail in terms of spectral changes with varying film thickness, different growth modes, degree of ordering of the films, interactions with the substrates and oscillator strength. A direct observation of a monomer-dimer transition in solid films could be observed for the first time. Our results indicate an exciton delocalization over about 4 molecules for both molecules.