Finite-element discretization of 3D energy-transport equations for semiconductors

In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and demonstrated in detail. We compare these new iterations with a standard method that is complemented by a feature to fit in the current context. A further innovation is the computation of solutions in three-dimensional domains, which are still rare. Special attention is paid to applicability of the 3D simulation tools. The programs are designed to have justifiable working complexity. The simulation results of some models of contemporary semiconductor devices are shown and detailed comments on the results are given. Eventually, we make a prospect on future development and enhancements of the models and of the algorithms that we used.

Supernova detection in a future extension of the IceCube neutrino telescope

Marking the final explosive burning stage of massive stars, supernovae are onernthe of most energetic celestial events. Apart from their enormous optical brightnessrnthey are also known to be associated with strong emission of MeV neutrinos—up tornnow the only proven source of extrasolar neutrinos.rnAlthough being designed for the detection of high energy neutrinos, the recentlyrncompleted IceCube neutrino telescope in the antarctic ice will have the highestrnsensitivity of all current experiments to measure the shape of the neutrino lightrncurve, which is in the MeV range. This measurement is crucial for the understandingrnof supernova dynamics.rnIn this thesis, the development of a Monte Carlo simulation for a future low energyrnextension of IceCube, called PINGU, is described that investigates the response ofrnPINGU to a supernova. Using this simulation, various detector configurations arernanalysed and optimised for supernova detection. The prospects of extracting notrnonly the total light curve, but also the direction of the supernova and the meanrnneutrino energy from the data are discussed. Finally the performance of PINGU isrncompared to the current capabilities of IceCube.

Feasibility studies for accessing nucleon structure observables with the PANDA experiment at the future FAIR facility

The availability of a high-intensity antiproton beam with momentum up to 15,GeV/c at the future FAIR will open a unique opportunity to investigate wide areas of nuclear physics with the $overline{P}$ANDA (anti{$overline{P}$}roton ANnihilations at DArmstadt) detector. Part of these investigations concern the Electromagnetic Form Factors of the proton in the time-like region and the study of the Transition Distribution Amplitudes, for which feasibility studies have been performed in this Thesis. rnMoreover, simulations to study the efficiency and the energy resolution of the backward endcap of the electromagnetic calorimeter of $overline{P}$ANDA are presented. This detector is crucial especially for the reconstruction of processes like $bar pprightarrow e^+ e^- pi^0$, investigated in this work. Different arrangements of dead material were studied. The results show that both, the efficiency and the energy resolution of the backward endcap of the electromagnetic calorimeter fullfill the requirements for the detection of backward particles, and that this detector is necessary for the reconstruction of the channels of interest. rnrnThe study of the annihilation channel $bar pprightarrow e^+ e^-$ will improve the knowledge of the Electromagnetic Form Factors in the time-like region, and will help to understand their connection with the Electromagnetic Form Factors in the space-like region. In this Thesis the feasibility of a measurement of the $bar pprightarrow e^+ e^-$ cross section with $overline{P}$ANDA is studied using Monte-Carlo simulations. The major background channel $bar pprightarrow pi^+ pi^-$ is taken into account. The results show a $10^9$ background suppression factor, which assure a sufficiently clean signal with less than 0.1% background contamination. The signal can be measured with an efficiency greater than 30% up to $s=14$,(GeV/c)$^2$. The Electromagnetic Form Factors are extracted from the reconstructed signal and corrected angular distribution. Above this $s$ limit, the low cross section will not allow the direct extraction of the Electromagnetic Form Factors. However, the total cross section can still be measured and an extraction of the Electromagnetic Form Factors is possible considering certain assumptions on the ratio between the electric and magnetic contributions.rnrnThe Transition Distribution Amplitudes are new non-perturbative objects describing the transition between a baryon and a meson. They are accessible in hard exclusive processes like $bar pprightarrow e^+ e^- pi^0$. The study of this process with $overline{P}$ANDA will test the Transition Distribution Amplitudes approach. This work includes a feasibility study for measuring this channel with $overline{P}$ANDA. The main background reaction is here $bar pprightarrow pi^+ pi^- pi^0$. A background suppression factor of $10^8$ has been achieved while keeping a signal efficiency above 20%.rnrnrnPart of this work has been published in the European Physics Journal A 44, 373-384 (2010).rn

Investigations on asymptotic safety of metric, tetrad and Einstein-Cartan gravity

Among the different approaches for a construction of a fundamental quantum theory of gravity the Asymptotic Safety scenario conjectures that quantum gravity can be defined within the framework of conventional quantum field theory, but only non-perturbatively. In this case its high energy behavior is controlled by a non-Gaussian fixed point of the renormalization group flow, such that its infinite cutoff limit can be taken in a well defined way. A theory of this kind is referred to as non-perturbatively renormalizable. In the last decade a considerable amount of evidence has been collected that in four dimensional metric gravity such a fixed point, suitable for the Asymptotic Safety construction, indeed exists. This thesis extends the Asymptotic Safety program of quantum gravity by three independent studies that differ in the fundamental field variables the investigated quantum theory is based on, but all exhibit a gauge group of equivalent semi-direct product structure. It allows for the first time for a direct comparison of three asymptotically safe theories of gravity constructed from different field variables. The first study investigates metric gravity coupled to SU(N) Yang-Mills theory. In particular the gravitational effects to the running of the gauge coupling are analyzed and its implications for QED and the Standard Model are discussed. The second analysis amounts to the first investigation on an asymptotically safe theory of gravity in a pure tetrad formulation. Its renormalization group flow is compared to the corresponding approximation of the metric theory and the influence of its enlarged gauge group on the UV behavior of the theory is analyzed. The third study explores Asymptotic Safety of gravity in the Einstein-Cartan setting. Here, besides the tetrad, the spin connection is considered a second fundamental field. The larger number of independent field components and the enlarged gauge group render any RG analysis of this system much more difficult than the analog metric analysis. In order to reduce the complexity of this task a novel functional renormalization group equation is proposed, that allows for an evaluation of the flow in a purely algebraic manner. As a first example of its suitability it is applied to a three dimensional truncation of the form of the Holst action, with the Newton constant, the cosmological constant and the Immirzi parameter as its running couplings. A detailed comparison of the resulting renormalization group flow to a previous study of the same system demonstrates the reliability of the new equation and suggests its use for future studies of extended truncations in this framework.

Stacked searches for high-energy neutrinos from blazars with IceCube

In the year 2013, the detection of a diffuse astrophysical neutrino flux with the IceCube neutrino telescope – constructed at the geographic South Pole – was announced by the IceCube collaboration. However, the origin of these neutrinos is still unknown as no sources have been identified to this day. Promising neutrino source candidates are blazars, which are a subclass of active galactic nuclei with radio jets pointing towards the Earth. In this thesis, the neutrino flux from blazars is tested with a maximum likelihood stacking approach, analyzing the combined emission from uniform groups of objects. The stacking enhances the sensitivity w.r.t. the still unsuccessful single source searches. The analysis utilizes four years of IceCube data including one year from the completed detector. As all results presented in this work are compatible with background, upper limits on the neutrino flux are given. It is shown that, under certain conditions, some hadronic blazar models can be challenged or even rejected. Moreover, the sensitivity of this analysis – and any other future IceCube point source search – was enhanced by the development of a new angular reconstruction method. It is based on a detailed simulation of the photon propagation in the Antarctic ice. The median resolution for muon tracks, induced by high-energy neutrinos, is improved for all neutrino energies above IceCube’s lower threshold at 0.1TeV. By reprocessing the detector data and simulation from the year 2010, it is shown that the new method improves IceCube’s discovery potential by 20% to 30% depending on the declination.

Chemical exfoliation of graphene and its application in organic electronics and energy storage devices

Graphene, the thinnest two-dimensional material possible, is considered as a realistic candidate for the numerous applications in electronic, energy storage and conversion devices due to its unique properties, such as high optical transmittance, high conductivity, excellent chemical and thermal stability. However, the electronic and chemical properties of graphene are highly dependent on their preparation methods. Therefore, the development of novel chemical exfoliation process which aims at high yield synthesis of high quality graphene while maintaining good solution processability is of great concern. This thesis focuses on the solution production of high-quality graphene by wet-chemical exfoliation methods and addresses the applications of the chemically exfoliated graphene in organic electronics and energy storage devices.rnPlatinum is the most commonly used catalysts for fuel cells but they suffered from sluggish electron transfer kinetics. On the other hand, heteroatom doped graphene is known to enhance not only electrical conductivity but also long term operation stability. In this regard, a simple synthetic method is developed for the nitrogen doped graphene (NG) preparation. Moreover, iron (Fe) can be incorporated into the synthetic process. As-prepared NG with and without Fe shows excellent catalytic activity and stability compared to that of Pt based catalysts.rnHigh electrical conductivity is one of the most important requirements for the application of graphene in electronic devices. Therefore, for the fabrication of electrically conductive graphene films, a novel methane plasma assisted reduction of GO is developed. The high electrical conductivity of plasma reduced GO films revealed an excellent electrochemical performance in terms of high power and energy densities when used as an electrode in the micro-supercapacitors.rnAlthough, GO can be prepared in bulk scale, large amount of defect density and low electrical conductivity are major drawbacks. To overcome the intrinsic limitation of poor quality of GO and/or reduced GO, a novel protocol is extablished for mass production of high-quality graphene by means of electrochemical exfoliation of graphite. The prepared graphene shows high electrical conductivity, low defect density and good solution processability. Furthermore, when used as electrodes in organic field-effect transistors and/or in supercapacitors, the electrochemically exfoliated graphene shows excellent device performances. The low cost and environment friendly production of such high-quality graphene is of great importance for future generation electronics and energy storage devices. rn

Controllable assembly of graphene hybrid materials and their application in energy storage and conversion

Hybrid Elektrodenmaterialien (HEM) sind der Schlüssel zu grundlegenden Fortschritten in der Energiespeicherung und Systemen zur Energieumwandlung, einschließlich Lithium-Ionen-Batterien (LiBs), Superkondensatoren (SCs) und Brennstoffzellen (FCs). Die faszinierenden Eigenschaften von Graphen machen es zu einem guten Ausgangsmaterial für die Darstellung von HEM. Jedoch scheitern traditionelle Verfahren zur Herstellung von Graphen-HEM (GHEM) scheitern häufig an der fehlenden Kontrolle über die Morphologie und deren Einheitlichkeit, was zu unzureichenden Grenzflächenwechselwirkungen und einer mangelhaften Leistung des Materials führt. Diese Arbeit konzentriert sich auf die Herstellung von GHEM über kontrollierte Darstellungsmethoden und befasst sich mit der Nutzung von definierten GHEM für die Energiespeicherung und -umwandlung. Die große Volumenausdehnung bildet den Hauptnachteil der künftigen Lithium-Speicher-Materialien. Als erstes wird ein dreidimensionaler Graphen Schaumhybrid zur Stärkung der Grundstruktur und zur Verbesserung der elektrochemischen Leistung des Fe3O4 Anodenmaterials dargestellt. Der Einsatz von Graphenschalen und Graphennetzen realisiert dabei einen doppelten Schutz gegen die Volumenschwankung des Fe3O4 bei dem elektrochemischen Prozess. Die Leistung der SCs und der FCs hängt von der Porenstruktur und der zugänglichen Oberfläche, beziehungsweise den katalytischen Stellen der Elektrodenmaterialien ab. Wir zeigen, dass die Steuerung der Porosität über Graphen-basierte Kohlenstoffnanoschichten (HPCN) die zugängliche Oberfläche und den Ionentransport/Ladungsspeicher für SCs-Anwendungen erhöht. Desweiteren wurden Stickstoff dotierte Kohlenstoffnanoschichten (NDCN) für die kathodische Sauerstoffreduktion (ORR) hergestellt. Eine maßgeschnittene Mesoporosität verbunden mit Heteroatom Doping (Stickstoff) fördert die Exposition der aktiven Zentren und die ORR-Leistung der metallfreien Katalysatoren. Hochwertiges elektrochemisch exfoliiertes Graphen (EEG) ist ein vielversprechender Kandidat für die Darstellung von GHEM. Allerdings ist die kontrollierte Darstellung von EEG-Hybriden weiterhin eine große Herausforderung. Zu guter Letzt wird eine Bottom-up-Strategie für die Darstellung von EEG Schichten mit einer Reihe von funktionellen Nanopartikeln (Si, Fe3O4 und Pt NPs) vorgestellt. Diese Arbeit zeigt einen vielversprechenden Weg für die wirtschaftliche Synthese von EEG und EEG-basierten Materialien.