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Dans cette thèse, différentes techniques de microscopie électronique à transmission et à balayage (STEM : scanning transmission electron microscopy) ont été améliorées et appliquées à plusieurs structures essentiellement à base de semiconducteurs. La création de nouveaux matériaux et dispositifs a été à l'origine du développement des civilisations et des méthodes de caractérisation expérimentales sont nécessaires pour étudier les nouvelles structures afin de les comprendre et de les améliorer. Avec le développement des nanotechnologies, la microscopie électronique est devenu un outil indispensable du fait de sa grande résolution spatiale et de la pléthore d'information qu'elle permet d'obtenir.Dans la première partie de cette thèse, les nombreux développements réalisés sont présentés. Plusieurs sous-techniques du STEM ont été améliorés : création de moirés obtenus par balayage (SMF : scanning moiré fringes), nano-diffraction électronique en mode précession (NPED : nano-beam precession diffraction) et haute résolution en STEM (HR-STEM). Ces développements permettent d'obtenir des cartographies quantitatives sur les déformations et les champs électriques et indirectement des informations chimiques.Dans la deuxième partie, les techniques développés sont utilisés pour étudier différentes structures et les résultats sont comparés à ceux d'autres techniques comme l'holographie et le contraste de phase différentielle (DPC : differentail phase contrast). Dans une structure photovoltaïque à base de matériaux II-VI, une accumulation d'un matériau II a été détectée aux interfaces grâce aux mesures des déformations. Des champs de déformations très faibles capitaux pour le fonctionnement des isolants topologiques à base de HgTe ont été mesurés. Des cartographies de déformation très précises ont été obtenues dans des transistors SiGe. Dans des couches AlN/GaN des cartographies de déformation et de champs électriques ont pu être réalisés simultanément révélant l'importance des dislocations. Des domaines d'inversion coeur-coquille ont été mis en évidence pour la première fois. Ils ont été observés dans de nombreux fils de GaN élaborés par épitaxie par jet moléculaires. Les positions des atomes dans un domaine d'inversion ont pu être mesurés à quelques picomètres près et comparés à des calculs ab-initio. / In this work, different scanning transmission electron microscopy (STEM) techniques have been developed and applied to several material systems. The creation of novel materials and devices has been a backbone of society’s development and characterization methods are needed to investigate these materials in order to understand and improve them. With the advent of nanotechnology, electron microscopy has become an invaluable tool, as it is able to visualize the atomic structure of thin samples and produces a plethora of quantifiable signals.In a first part, the numerous developments realized in this thesis are presented. Several STEM based techniques have been improved: scanning moiré fringes (SMF), nano-beam precession diffraction (NPED) and high-resolution STEM (HR-STEM). These developments allow for more accurate strain measurements, the quantitative mapping of electric fields and to realize accurate chemical profiles.In a second part, the developed methods are applied to different material systems and compared to more classical techniques, like holography and differential phase contrast (DPC). In a II/VI solar cell structure the interface chemistry is determined from strain with atomic resolution. Very faint strain gradients that are vital for the topological insulator properties of HgTe are measured. Accurate two-dimensional strain maps are obtained of a SiGe transistor. Simultaneous strain and electric field maps of m-plane AlN/GaN reveal the influence of dislocations in the material. Core-shell type inversion domains are described for the first time in GaN nanowires. They were found in many samples grown by molecular beam epitaxy. Thanks to quantitative analysis the exact atomic structure of inversion domains in GaN is described and compared to simulations.

[pt] Neste trabalho foi feito o estudo do espalhamento da luz realizado por partículas esféricas dielétricas, pelo uso do método dos elementos finitos, através do software COMSOL Multiphysics 5.6, sendo considerado o comportamento da luz tanto como onda quanto como partícula. Este estudo visa, no futuro, a compreensão do laser aleatório em sistemas com centros espalhadores de diferentes geometrias. Considerando o comportamento ondulatório da luz, foi estudada a teoria sobre as séries de Mie. Esta, por sua vez, é uma solução que, dado o campo de incidência, pode-se calcular os campos espalhados e absorvidos por partículas esféricas. Foram calculados os valores da seção de choque de espalhamento e a média do cosseno do ângulo de espalhamento para uma partícula de raio (r) maior que um décimo do comprimento de onda (Comprimento de onda) da luz (raio maior que um décimo do comprimento de onda) e uma com (raio menor que um décimo do comprimento de onda). Neste último caso, também foi estudada a variação da intensidade da luz espalhada em função do ângulo de espalhamento. Os resultados das partículas pequenas corresponderam ao regime de Rayleigh. As partículas esféricas consideradas foram a rutila, TiO2, e a alumina, Al2O3. Foi estudado também o espalhamento de luz realizado por duas partículas idênticas. Para esse caso, obteve-se uma luz espalhada mais intensa na região entre as partículas em comparação a outras regiões. Ademais, ao comparar com o espalhamento feito por uma única partícula, foi notado que a luz espalhada por duas partículas, na região entre as duas, também era mais intenso. Além disso, ao estudar o confinamento de luz entre duas e três partículas de r = 230 nm, viu-se que o espectro do campo espalhado apresentava mais de um pico, como há em lasers aleatórios coerentes. No que concerne ao comportamento corpuscular da luz, foi considerada a equação de difusão de fótons, onde o espectro de emissão da fluorescência de R6G incidindo em uma concentração da ordem de 1010 cm−3 partículas foi simulado e, posteriormente, comparou-se o resultado obtido com o comportamento de um sistema de laser aleatório incoerente. / [en] In this work, the study of light scattering performed by dielectric spherical particles was carried out, using the finite element method, through the COMSOL Multiphysics 5.6 software, considering the behavior of light both as a wave and as a particle. This study aims, in the future, to understand the random laser in systems with scatter centers with different geometries. Considering the wave behavior of light, the theory of the Mie series was studied. This is a solution that, given the incidence field, makes it possible to calculate the fields scattered and absorbed by the spherical particles. The values of the scattering cross section and the mean of the cosine of the scattering angle were calculated for a particle with radius (r) bigger than one tenth of the light wavelength (wave length) (radius greater than one tenth of the wave length) and one with (radius less than one tenth of the wave length). In the latter case, the variation of the scattered light intensity as a function of the scattering angle was also studied. The small particle results corresponded to the Rayleigh regime. The spherical particles considered were rutile, TiO2, and aluminium oxide, Al2O3. The scattering of light performed by two identical particles was also studied. For this case, a more intense scattered light was obtained in the region between the particles compared to other regions. Furthermore, when comparing with the scattering done by a single particle, it was noticed that the light scattered by two particles, in the region between the two, was also more intense. Furthermore, when studying the confinement of light between two and three particles with r = 230 nm, it was seen that the spectrum of the scattered field showed more than one peak, as one has in coherent random lasers. Concerning the corpuscular behavior of light, the photon diffusion equation was considered, where the emission spectrum of the fluorescence of R6G incident on a concentration of the order of 1010 cm−3 particles was simulated and, later, the result obtained was compared with the behavior of an incoherent random laser system.

In dieser Arbeit wird das lokal aufgelöste Deformationsfeld einzelner (In,Ga)N/GaN Drähte mit Hilfe nanofokussierter Röntgenbeugung und der Methode der Finiten Elemente untersucht. Hiermit soll ein Beitrag zum grundlegenden Verständis der optischen Eigenschaften geleistet werden, die durch das Deformationsfeld maßgeblich beeinflusst werden. Zunächst wird die Abhängigkeit der vertikalen Normalkomponente, epsilon_zz, des elastischen Dehnungstensors von der Geometrie eines axialen (In,Ga)N/GaN Nanodrahtes diskutiert. Dabei wird ein signifikant negativer epsilon_zz-Wert beobachtet, sobald das Verhältnis von Nanodrahtradius und (In,Ga)N-Segmentlänge gegen eins strebt. Auffallend große Scherkomponenten und eine konvexe Verformung der äußeren Oberfläche begleiten das Auftreten des negativen epsilon_zz- Wertes und sind die Ursache dieses Effekts. Durch eine Ummantelung von GaN-Nanodrähten mit einer (In,Ga)N-Schale lässt sich die aktive Fläche und somit die potentielle Lichtausbeute pro Fläche im Vergleich zu planaren Strukturen deutlich erhöhen. Es wurde jedoch festgestellt, dass das entlang der Drahthöhe emittierte Licht rotverschoben ist. Um den Ursprung dieses Phänomens zu beleuchten, wird das lokale Deformationsfeld mit Hilfe nanofokussierter Röntgenbeugung vermessen. Durch die gute räumliche Auflösung ist es möglich, das Deformationsfeld innerhalb einzelner Seitenfacetten zu untersuchen, wobei ein deutlicher Gradient festgestellt wird. Basierend auf dem mit der Methode der Finiten Elemente simulierten Deformationsfeld und kinematischen Streusimulationen, ist es möglich, den Deformationszustand in einen In-Gehalt zu übersetzen. Wenn neben dem Deformationsfeld auch der strukturelle Aufbau in der Simulation berücksichtigt wird, kann der In-Gehalt mit noch größerer Genauigkeit bestimmt werden. / In this thesis, nanofocus x-ray diffraction and the finite element method are applied to analyze the local strain field in (In,Ga)N/GaN nanowires and micro-rods which are discussed as candidates for a plethora of future optoelectronic applications. However, to improve and tailor their properties, a fundamental understanding on the level of individual objects is essential. In this spirit, the dependence of the vertical normal component, epsilon_zz, of the elastic strain tensor on the geometry of an axial (In,Ga)N/GaN nanowire is systematically analyzed using the finite element method. Hereby, it is found that if the ratio of nanowire radius and (In,Ga)N segment length approaches unity, a significantly negative epsilon_zz value is observed. This stands in stark contrast to naive expectations and shows that the common knowledge about planar systems where epsilon_zz would always be greater or equal zero cannot easily be translated to nanowires with an equivalent material sequence. As the origin of this effect significant shear strains are discussed which go along with a convex deformation of the outer surface resulting in a highly complex strain distribution. The increased active area of core-shell (In,Ga)N/GaN micro-rods makes them promising candidates for next-generation light emitting diodes. However, it is found that the emission wavelength is significantly red-shifted along the rod height. To shed light on the origin of this phenomenon, nanofocus x-ray diffraction is applied to analyze the local strain field. Due to the high spatial resolution it is possible to investigate the strain field within individual side-facets and to detect a significant gradient along the rod height. Based on the deformation field simulated using the finite element method and subsequent kinematic scattering simulations it is possible to translate the strain state into an In content.

The analysis of wide-angle cellular light scattering patterns is a challenging problem. Small changes to the organization, orientation, shape, and optical properties of scatterers and scattering populations can significantly alter their complex two-dimensional scattering signatures. Because of this, it is difficult to find methods that can identify medically relevant cellular properties while remaining robust to experimental noise and sample-to-sample differences. It is an important problem. Recent work has shown that changes to the internal structure of cells---specifically, the distribution and aggregation of organelles---can indicate the progression of a number of common disorders, ranging from cancer to neurodegenerative disease, and can also predict a patient's response to treatments like chemotherapy. However, there is no direct analytical solution to the inverse wide-angle cellular light scattering problem, and available simulation and interpretation methods either rely on restrictive cell models, or are too computationally demanding for routine use. This dissertation addresses these challenges from a computational vantage point. First, it explores the theoretical limits and optical basis for wide-angle scattering pattern analysis. The result is a rapid new simulation method to generate realistic organelle scattering patterns without the need for computationally challenging or restrictive routines. Pattern analysis, image segmentation, machine learning, and iterative pattern classification methods are then used to identify novel relationships between wide-angle scattering patterns and the distribution of organelles (in this case mitochondria) within a cell. Importantly, this work shows that by parameterizing a scattering image it is possible to extract vital information about cell structure while remaining robust to changes in organelle concentration, effective size, and random placement. The result is a powerful collection of methods to simulate and interpret experimental light scattering signatures. This gives new insight into the theoretical basis for wide-angle cellular light scattering, and facilitates advances in real-time patient care, cell structure prediction, and cell morphology research.

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