The development of materials with tailored functionalities and with continuously shrinking linear dimensions towards (and below) the nanoscale is not only going to revolutionize state of the art fabrication technologies, but also the computational methodologies used to model the materials properties. Specifically, atomistic methodologies are becoming increasingly relevant in the field of materials science as a fundamental tool in gaining understanding on as well as for pre-designing (in silico material design) the behavior of nanoscale materials in response to external stimuli. The major long-term goal of atomistic modelling is to obtain structure-function relationships at the nanoscale, i.e. to correlate a definite response of a given physical system with its specific atomic conformation and ultimately, with its chemical composition and electronic structure. This has clearly its pendant in the development of bottom-up fabrication technologies, which also require a detailed control and fine tuning of physical and chemical properties at sub-nanometer and nanometer length scales. The current work provides an overview of different applications of atomistic approaches to the study of nanoscale materials. We illustrate how the use of first-principle based electronic structure methodologies, quantum mechanical based molecular dynamics, and appropriate methods to model the electrical and thermal response of nanoscale materials, provides a solid starting point to shed light on the way such systems can be manipulated to control their electrical, mechanical, or thermal behavior. Thus, some typical topics addressed here include the interplay between mechanical and electronic degrees of freedom in carbon based nanoscale materials with potential relevance for designing nanoscale switches, thermoelectric properties at the single-molecule level and their control via specific chemical functionalization, and electrical and spin-dependent properties in biomaterials. We will further show how phenomenological models can be efficiently applied to get a first insight in the behavior of complex nanoscale systems, for which first principle electronic structure calculations become computationally expensive. This will become especially clear in the case of biomolecular systems and organic semiconductors.

The development of materials with tailored functionalities and with continuously shrinking linear dimensions towards (and below) the nanoscale is not only going to revolutionize state of the art fabrication technologies, but also the computational methodologies used to model the materials properties. Specifically, atomistic methodologies are becoming increasingly relevant in the field of materials science as a fundamental tool in gaining understanding on as well as for pre-designing (in silico material design) the behavior of nanoscale materials in response to external stimuli. The major long-term goal of atomistic modelling is to obtain structure-function relationships at the nanoscale, i.e. to correlate a definite response of a given physical system with its specific atomic conformation and ultimately, with its chemical composition and electronic structure. This has clearly its pendant in the development of bottom-up fabrication technologies, which also require a detailed control and fine tuning of physical and chemical properties at sub-nanometer and nanometer length scales. The current work provides an overview of different applications of atomistic approaches to the study of nanoscale materials. We illustrate how the use of first-principle based electronic structure methodologies, quantum mechanical based molecular dynamics, and appropriate methods to model the electrical and thermal response of nanoscale materials, provides a solid starting point to shed light on the way such systems can be manipulated to control their electrical, mechanical, or thermal behavior. Thus, some typical topics addressed here include the interplay between mechanical and electronic degrees of freedom in carbon based nanoscale materials with potential relevance for designing nanoscale switches, thermoelectric properties at the single-molecule level and their control via specific chemical functionalization, and electrical and spin-dependent properties in biomaterials. We will further show how phenomenological models can be efficiently applied to get a first insight in the behavior of complex nanoscale systems, for which first principle electronic structure calculations become computationally expensive. This will become especially clear in the case of biomolecular systems and organic semiconductors.

Zur vollständigen Beschreibung eines monochromatischen Wellenfeldes ist die Kenntnis über die Amplituden- und Phasenverteilung unabdingbar. Während sich die messtechnische Erfassung der Amplitudenverteilung durch lichtempfindliche Sensoren recht einfach realisieren lässt, gestaltet sich die Bestimmung der Phasenverteilung weitaus schwieriger. Die Phasenverteilung eines optischen Wellenfeldes kann nur über indirekte Verfahren gewonnen werden. Es ergibt sich ein sogenanntes phase retrieval Problem. Zur Lösung dieses Problems bieten sich verschiedene Verfahren aus dem Bereich der berührungslosen und zerstörungsfreien optische Messtechnik an. In dieser Arbeit wird ein deterministisches Verfahren zur Phasenrekonstruktion mit Hilfe Greenscher Funktionen vorgestellt. Die erste Greensche Identität dient als Grundlage zur Entwicklung einer Gleichung, welche in der Lage ist, bei der Rekonstruktion einer Phasenverteilung spezifische Randbedingungen zu berücksichtigen. Dies ermöglicht unter anderem eine genaue Charakterisierung von Phasenobjekten bzw. ihren optischen Eigenschaften, wie beispielsweise der Brechzahlverteilung. Das vorgestellte Verfahren zur Phasenrekonstruktion basiert einerseits auf schnellen Algorithmen, welche die Leistung von parallelen Prozessoren ausnutzen und andererseits auf geschickten experimentellen Aufbauten, mit welchen die notwendigen Eingangsdaten zur Lösung der Gleichung simultan gewonnen werden können. Es ergibt sich damit die Möglichkeit, die Amplituden- und Phasenverteilung eines Wellenfeldes in Echtzeit zu bestimmen und daraus folgend ein Mittel zur quantitativen Bewertungen und Analyse von dynamischen Prozessen sowohl in der Industrie als auch im Bereich der Life Sciences. / In order to describe a monochromatic wave field entirely, knowledge about the amplitude and phase distribution is elementary. While it is easy to measure the amplitude distribution of an optical wave field by the use of photosensitive detectors, the determination of the phase distribution is by far more difficult. Due to the fact, that the phase distribution can not be measured directly, a problem of phase retrieval is presented. This problem may be solved by applying a non-contacting and non-destructive optical metrology technique. In this thesis a deterministic method for phase retrieval based on Green''s functions will be introduced. Green''s first identity serves as a starting point to derive an equation for phase retrieval considering different boundary conditions. Among others, this allows an exact characterization of phase objects, or their optical properties, as for example the refractive index distribution. On the one hand, the presented phase retrieval technique is based on fast algorithms which take advantage of the performance of parallel processors. On the other hand, skilful experimental setups allow the simultaneous acquisition of the input data, which are necessary to solve the phase retrieval equation. It follows that the presented technique is able to determine the amplitude and phase distribution of a wave field in real-time. Hence this technique enables the quantitative evaluation and analysis of dynamic processes in industry as well as in the area of life sciences.

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