La synthèse d’images réalistes repose sur des modèles physiques décrivant les interactions entre la lumière et les matériaux attachés aux objets dans une scène tridimensionnelle. Ces modèles mathématiques sont complexes et, dans le cas général, n’admettent pas de solution analytique. Pour cette raison, l’utilisation de méthodes numériques robustes et efficaces est nécessaire. Les méthodes de Monte Carlo ou techniques alternatives comme l’utilisation de développement par fonction de base sont appropriées pour résoudre ce type de problème. Dans cette thèse par articles, nous présentons deux nouvelles techniques permettant l’in- tégration numérique efficace de matériaux complexes. En premier lieu, nous introduisons une nouvelle méthode permettant d’intégrer simultanément plusieurs dimensions définies dans le domaine angulaire et spatiale. Avoir une technique efficace est essentiel pour intégrer des matériaux avec des normales variant rapidement sous différentes conditions d’éclairage. Notre technique utilise une nouvelle formulation basée sur un histogramme sphérique définie de façon directionnelle et spatial. Ce dernier nous permet d’utiliser des harmoniques sphé- riques pour intégrer les différentes dimensions rapidement, réduisant le temps de calcul d’un facteur approximatif de 30× par rapport aux méthodes de l’état de l’art. Dans notre second travail, nous introduisons une nouvelle stratégie d’échantillonnage pour estimer le transport de lumière à l’intérieur de matériaux multicouches. En identifiant les meilleures stratégies d’échantillonnage, nous proposons une technique efficace et non biaisée pour construire des chemins de lumière à l’intérieur de ce type de matériau. Notre nouvelle approche permet d’obtenir un estimateur de Monte Carlo efficace et de faible variance dans des matériaux contenant un nombre arbitraire de couches. / Realistic computer generated images and simulations require physically-based models to properly capture and reproduce light-material interactions. The underlying mathematical formulations are complex and mandate the use of efficient numerical methods, since analytic solutions are not available. Monte Carlo integration is one such commonly used numerical method, although, alternative approaches leveraging, e.g., basis expansions, may be suitable to solve these challenging problems. In this thesis by articles, we present two works where we efficiently devise numerical integration strategies for the rendering of complex materials. First, we propose a method to compute a spatial-angular multi-dimensional integration problem present when rendering materials with high-frequency normal variation under large, angularly varying illumination. By computing and manipulating a novel spherical histogram data representation, we are able to use spherical harmonics to efficiently solve the integral, outperforming the state-of-the-art by a factor of roughly 30×. Our second work describes a high-performance Monte Carlo integration strategy for rendering layered materials. By identifying the best path sampling strategies in the micro-scale light transport context, we are able to tailor an unbiased and efficient path construction method to evaluate high throughput, low variance paths through an arbitrary number of layers.

In this bachelor thesis we report on our numerical investigations into the optimal design of protective multi-layer coatings subject to an external force of Hertzian form. In view of mechanical reliablity and durability of the substrate and the coating we aim to find the best composition of given materials with the least computational effort. Numerical studies are carried out using the simulation software ELASTICA being the first non-FEM approach for the computation of stress fields within multi-layer coated, elastic materials. We thereby made use of the massive parallel computer CLiC (Chemnitzer Linux Cluster) where we ran our Windows based application in a Wine Environment. The outcome of the optimization is in general very sensitive towards the input parameters(i.e., material properties) which are not always available in the desired accuracy. However, the scheme outlined in this work is shown to produce very good results and could contribute a great deal to find optimal solutions for real applications. / Diese Bachelorarbeit befasst sich mit numerischen Untersuchungen zum optimalen Design von schützenden Mehrschichtbeschichtungen, die einer externen, Hertzschen Last ausgesetzt sind. Hinsichtlich der mechanischen Zuverlässigkeit und Haltbarkeit von Substrat und Beschichtung, versuchen wir die beste Zusammensetzung von gegebenen Materialien mit möglichst geringem Rechenaufwand zu finden. Die numerischen Berechungen wurden mit der Simulationssoftware ELASTICA durchgeführt, welches das erste kommerzielle, nicht-FEM-basierte Programm zur Berechnung von Stressfeldern innerhalb mehrfach beschichteter, elastischer Materialien darstellt. Dafür benutzten wir auf dem massiven Parrallelrechner CLiC (Chemnitzer Linux Cluster) unsere Windows basierte Anwendung unter der Emulationssoftware Wine. Das Ergebnis der Optimierung hängt im allgemeinen sehr stark von der Qualität der Eingangsparameter (z.B. Materialeigenschaften) ab, welche nicht immer in der erwünschten Genauigkeit vorliegen. Es wird gezeigt, dass die in dieser Arbeit vorgestellte Vorgehensweise sehr gute Resultate liefert und für reale Anwendungen einen äusserst ressourcenschonenden Lösungsweg darstellt.

Recently, high-κ materials have become the focus of research and been extensively utilized as the gate dielectric layer in aggressive scaled complementary metal-oxide-semiconductor (CMOS) technology. Hafnium dioxide (HfO2) is the most promising high-κ material because of its excellent chemical, thermal, mechanical and dielectric properties and also possesses good thermodynamic stability and better band offsets with silicon. Hence, HfO2 has already been used as gate dielectric in modern CMOS devices. For future technologies, it is very difficult to scale the silicon transistor gate length, so it is a necessary requirement of replacing the channel material from silicon to some high mobility material. Two-dimensional layered materials such as graphene and molybdenum disulfide (MoS2) are potential candidates to replace silicon. Due to its planar structure and atomically thin nature, they suit well with the conventional MOSFET technology and are very stable mechanically as well as chemically. HfO2 plays a vital role as a gate dielectric, not only in silicon CMOS technology but also in future nano-electronic devices such as graphene/MoS2 based devices, since high-κ media is expected to screen the charged impurities located in the vicinity of channel material, which results in enhancement of carrier mobility. So, for sustenance and enhancement of new technology, extensive study of the functional materials and its processing is required. In the present work, optimization of HfO2 thin films for gate dielectric applications in Nano-electronic devices using electron beam evaporation is discussed. HfO2 thin films have been optimized in two different thickness regimes, (i) about 35 nm physical thicknesses for back gate oxide graphene/MoS2 transistors and (ii) about 5 nm physical thickness to get Equivalent Oxide Thickness (EOT) less than 1 nm for top gate applications. Optical, chemical, compositional, structural and electrical characterizations of these films have been done using Ellipsometry, X-ray Photoelectron Spectroscopy (XPS), Rutherford Back Scattering (RBS), X-ray Diffraction (XRD), Capacitance-Voltage and Current-Voltage characterization techniques. The amount of O2 flow rate, during evaporation is optimized for 35 nm thick HfO2 films, to achieve the best optical, chemical and electrical properties. It has been observed that with increasing oxygen flow rate, thickness of the films increased and refractive index decreased due to increase in porosity resulting from the scattering of the evaporant. The films deposited at low O2 flow rates (1 and 3 SCCM) show better optical and compositional properties. The effects of post deposition annealing (PDA) and post metallization annealing (PMA) in forming gas ambient (FGA) on the optical and electrical properties of the films have been analyzed. The film deposited at 3 SCCM O2 flow rate shows the best properties as measured on MOS capacitors. A high density film (ρ=8.2 gram/cm3, 85% of bulk density) with high dielectric constant of κ=19 and leakage current density of J=2.0×10-6 A/cm2 at -1 MV/cm has been achieved at optimized deposition conditions. Bilayer graphene on HfO2/Si substrate has been successfully identified and also transistor has been fabricated with HfO2 (35 nm) as a back gate. High transconductance compared to other back gated devices such as SiO2/Si and Al2O3/Si and high mobility have been achieved. The performance of back gated bilayer graphene transistors on HfO2 films deposited at two O2 flow rates of 3 SCCM and 20 SCCM has been evaluated. It is found that the device on the film deposited at 3 SCCM O2 flow rate shows better properties. This suggests that an optimum oxygen pressure is necessary to get good quality films for high performance devices. MoS2 layers on the optimized HfO2/Si substrate have been successfully identified and transistor has been fabricated with HfO2 (32 nm) as a back gate. The device is switching at lower voltages compared to SiO2 back gated devices with high ION/IOFF ratio (>106). The effect of film thickness on optical, structural, compositional and electrical properties for top gate applications has been studied. Also the effect of gate electrode material and its processing on electrical properties of MOS capacitors have been studied. EOT of 1.2 nm with leakage current density of 1×10-4 A/cm2 at -1V has been achieved.