HCl gas gettering of 3d transition metals for crystalline silicon solar cell concepts

In order to reduce the costs of crystalline silicon solar cells, low-cost silicon materials like upgraded metallurgical grade (UMG) silicon are investigated for the application in the photovoltaic (PV) industry. Conventional high-purity silicon is made by cost-intensive methods, based on the so-called Siemens process, which uses the reaction to form chlorosilanes and subsequent several distillation steps before the deposition of high-purity silicon on slim high-purity silicon rods. UMG silicon in contrast is gained from metallurgical silicon by a rather inexpensive physicochemical purification (e.g., acid leaching and/or segregation). However, this type of silicon usually contains much higher concentrations of impurities, especially 3d transition metals like Ti, Fe, and Cu. These metals are extremely detrimental in the electrically active part of silicon solar cells, as they form recombination centers for charge carriers in the silicon band gap. This is why simple purification techniques like gettering, which can be applied between or during solar cell process steps, will play an important role for such low-cost silicon materials. Gettering in general describes a process, whereby impurities are moved to a place or turned into a state, where they are less detrimental to the solar cell. Hydrogen chloride (HCl) gas gettering in particular is a promising simple and cheap gettering technique, which is based on the reaction of HCl gas with transition metals to form volatile metal chloride species at high temperatures.rnThe aim of this thesis was to find the optimum process parameters for HCl gas gettering of 3d transition metals in low-cost silicon to improve the cell efficiency of solar cells for two different cell concepts, the standard wafer cell concept and the epitaxial wafer equivalent (EpiWE) cell concept. Whereas the former is based on a wafer which is the electrically active part of the solar cell, the latter uses an electrically inactive low-cost silicon substrate with an active layer of epitaxially grown silicon on top. Low-cost silicon materials with different impurity grades were used for HCl gas gettering experiments with the variation of process parameters like the temperature, the gettering time, and the HCl gas concentration. Subsequently, the multicrystalline silicon neighboring wafers with and without gettering were compared by element analysis techniques like neutron activation analysis (NAA). It was demonstrated that HCl gas gettering is an effective purification technique for silicon wafers, which is able to reduce some 3d transition metal concentrations by over 90%. Solar cells were processed for both concepts which could demonstrate a significant increase of the solar cell efficiency by HCl gas gettering. The efficiency of EpiWE cells could be increased by HCl gas gettering by approximately 25% relative to cells without gettering. First process simulations were performed based on a simple model for HCl gas gettering processes, which could be used to make qualitative predictions.

Random lattice models

This thesis deals with three different physical models, where each model involves a random component which is linked to a cubic lattice. First, a model is studied, which is used in numerical calculations of Quantum Chromodynamics.In these calculations random gauge-fields are distributed on the bonds of the lattice. The formulation of the model is fitted into the mathematical framework of ergodic operator families. We prove, that for small coupling constants, the ergodicity of the underlying probability measure is indeed ensured and that the integrated density of states of the Wilson-Dirac operator exists. The physical situations treated in the next two chapters are more similar to one another. In both cases the principle idea is to study a fermion system in a cubic crystal with impurities, that are modeled by a random potential located at the lattice sites. In the second model we apply the Hartree-Fock approximation to such a system. For the case of reduced Hartree-Fock theory at positive temperatures and a fixed chemical potential we consider the limit of an infinite system. In that case we show the existence and uniqueness of minimizers of the Hartree-Fock functional. In the third model we formulate the fermion system algebraically via C*-algebras. The question imposed here is to calculate the heat production of the system under the influence of an outer electromagnetic field. We show that the heat production corresponds exactly to what is empirically predicted by Joule's law in the regime of linear response.

Hadronic matrix elements in lattice QCD

The lattice formulation of Quantum ChromoDynamics (QCD) has become a reliable tool providing an ab initio calculation of low-energy quantities. Despite numerous successes, systematic uncertainties, such as discretisation effects, finite-size effects, and contaminations from excited states, are inherent in any lattice calculation. Simulations with controlled systematic uncertainties and close to the physical pion mass have become state-of-the-art. We present such a calculation for various hadronic matrix elements using non-perturbatively O(a)-improved Wilson fermions with two dynamical light quark flavours. The main topics covered in this thesis are the axial charge of the nucleon, the electro-magnetic form factors of the nucleon, and the leading hadronic contributions to the anomalous magnetic moment of the muon. Lattice simulations typically tend to underestimate the axial charge of the nucleon by 5 − 10%. We show that including excited state contaminations using the summed operator insertion method leads to agreement with the experimentally determined value. Further studies of systematic uncertainties reveal only small discretisation effects. For the electro-magnetic form factors of the nucleon, we see a similar contamination from excited states as for the axial charge. The electro-magnetic radii, extracted from a dipole fit to the momentum dependence of the form factors, show no indication of finite-size or cutoff effects. If we include excited states using the summed operator insertion method, we achieve better agreement with the radii from phenomenology. The anomalous magnetic moment of the muon can be measured and predicted to very high precision. The theoretical prediction of the anomalous magnetic moment receives contribution from strong, weak, and electro-magnetic interactions, where the hadronic contributions dominate the uncertainties. A persistent 3σ tension between the experimental determination and the theoretical calculation is found, which is considered to be an indication for physics beyond the Standard Model. We present a calculation of the connected part of the hadronic vacuum polarisation using lattice QCD. Partially twisted boundary conditions lead to a significant improvement of the vacuum polarisation in the region of small momentum transfer, which is crucial in the extraction of the hadronic vacuum polarisation.

Volatile organic compounds at the air-sea interface : gas exchange rates, oceanic emissions and the effect of ocean acidification

Oceans are key sources and sinks in the global budgets of significant atmospheric trace gases, termed Volatile Organic Compounds (VOCs). Despite their low concentrations, these species have an important role in the atmosphere, influencing ozone photochemistry and aerosol physics. Surprisingly, little work has been done on assessing their emissions or transport mechanisms and rates between ocean and atmosphere, all of which are important when modelling the atmosphere accurately.rnA new Needle Trap Device (NTD) - GC-MS method was developed for the effective sampling and analysis of VOCs in seawater. Good repeatability (RSDs <16 %), linearity (R2 = 0.96 - 0.99) and limits of detection in the range of pM were obtained for DMS, isoprene, benzene, toluene, p-xylene, (+)-α-pinene and (-)-α-pinene. Laboratory evaluation and subsequent field application indicated that the proposed method can be used successfully in place of the more usually applied extraction techniques (P&T, SPME) to extend the suite of species typically measured in the ocean and improve detection limits. rnDuring a mesocosm CO2 enrichment study, DMS, isoprene and α-pinene were identified and quantified in seawater samples, using the above mentioned method. Based on correlations with available biological datasets, the effects of ocean acidification as well as possible ocean biological sources were investigated for all examined compounds. Future ocean's acidity was shown to decrease oceanic DMS production, possibly impact isoprene emissions but not affect the production of α-pinene. rnIn a separate activity, ocean - atmosphere interactions were simulated in a large scale wind-wave canal facility, in order to investigate the gas exchange process and its controlling mechanisms. Air-water exchange rates of 14 chemical species (of which 11 VOCs) spanning a wide range of solubility (dimensionless solubility, α = 0:4 to 5470) and diffusivity (Schmidt number in water, Scw = 594 to 1194) were obtained under various turbulent (wind speed at ten meters height, u10 = 0:8 to 15ms-1) and surfactant modulated (two different sized Triton X-100 layers) surface conditions. Reliable and reproducible total gas transfer velocities were obtained and the derived values and trends were comparable to previous investigations. Through this study, a much better and more comprehensive understanding of the gas exchange process was accomplished. The role of friction velocity, uw* and mean square slope, σs2 in defining phenomena such as waves and wave breaking, near surface turbulence, bubbles and surface films was recognized as very significant. uw* was determined as the ideal turbulent parameter while σs2 described best the related surface conditions. A combination of both uw* and σs2 variables, was found to reproduce faithfully the air-water gas exchange process. rnA Total Transfer Velocity (TTV) model provided by a compilation of 14 tracers and a combination of both uw* and σs2 parameters, is proposed for the first time. Through the proposed TTV parameterization, a new physical perspective is presented which provides an accurate TTV for any tracer within the examined solubility range. rnThe development of such a comprehensive air-sea gas exchange parameterization represents a highly useful tool for regional and global models, providing accurate total transfer velocity estimations for any tracer and any sea-surface status, simplifying the calculation process and eliminating inevitable calculation uncertainty connected with the selection or combination of different parameterizations.rnrn

Imaging and modeling of pore scale processes in porous media using X-ray computed tomography and lattice Boltzmann solver

In der Erdöl– und Gasindustrie sind bildgebende Verfahren und Simulationen auf der Porenskala im Begriff Routineanwendungen zu werden. Ihr weiteres Potential lässt sich im Umweltbereich anwenden, wie z.B. für den Transport und Verbleib von Schadstoffen im Untergrund, die Speicherung von Kohlendioxid und dem natürlichen Abbau von Schadstoffen in Böden. Mit der Röntgen-Computertomografie (XCT) steht ein zerstörungsfreies 3D bildgebendes Verfahren zur Verfügung, das auch häufig für die Untersuchung der internen Struktur geologischer Proben herangezogen wird. Das erste Ziel dieser Dissertation war die Implementierung einer Bildverarbeitungstechnik, die die Strahlenaufhärtung der Röntgen-Computertomografie beseitigt und den Segmentierungsprozess dessen Daten vereinfacht. Das zweite Ziel dieser Arbeit untersuchte die kombinierten Effekte von Porenraumcharakteristika, Porentortuosität, sowie die Strömungssimulation und Transportmodellierung in Porenräumen mit der Gitter-Boltzmann-Methode. In einer zylindrischen geologischen Probe war die Position jeder Phase auf Grundlage der Beobachtung durch das Vorhandensein der Strahlenaufhärtung in den rekonstruierten Bildern, das eine radiale Funktion vom Probenrand zum Zentrum darstellt, extrahierbar und die unterschiedlichen Phasen ließen sich automatisch segmentieren. Weiterhin wurden Strahlungsaufhärtungeffekte von beliebig geformten Objekten durch einen Oberflächenanpassungsalgorithmus korrigiert. Die Methode der „least square support vector machine” (LSSVM) ist durch einen modularen Aufbau charakterisiert und ist sehr gut für die Erkennung und Klassifizierung von Mustern geeignet. Aus diesem Grund wurde die Methode der LSSVM als pixelbasierte Klassifikationsmethode implementiert. Dieser Algorithmus ist in der Lage komplexe geologische Proben korrekt zu klassifizieren, benötigt für den Fall aber längere Rechenzeiten, so dass mehrdimensionale Trainingsdatensätze verwendet werden müssen. Die Dynamik von den unmischbaren Phasen Luft und Wasser wird durch eine Kombination von Porenmorphologie und Gitter Boltzmann Methode für Drainage und Imbibition Prozessen in 3D Datensätzen von Böden, die durch synchrotron-basierte XCT gewonnen wurden, untersucht. Obwohl die Porenmorphologie eine einfache Methode ist Kugeln in den verfügbaren Porenraum einzupassen, kann sie dennoch die komplexe kapillare Hysterese als eine Funktion der Wassersättigung erklären. Eine Hysterese ist für den Kapillardruck und die hydraulische Leitfähigkeit beobachtet worden, welche durch die hauptsächlich verbundenen Porennetzwerke und der verfügbaren Porenraumgrößenverteilung verursacht sind. Die hydraulische Konduktivität ist eine Funktion des Wassersättigungslevels und wird mit einer makroskopischen Berechnung empirischer Modelle verglichen. Die Daten stimmen vor allem für hohe Wassersättigungen gut überein. Um die Gegenwart von Krankheitserregern im Grundwasser und Abwässern vorhersagen zu können, wurde in einem Bodenaggregat der Einfluss von Korngröße, Porengeometrie und Fluidflussgeschwindigkeit z.B. mit dem Mikroorganismus Escherichia coli studiert. Die asymmetrischen und langschweifigen Durchbruchskurven, besonders bei höheren Wassersättigungen, wurden durch dispersiven Transport aufgrund des verbundenen Porennetzwerks und durch die Heterogenität des Strömungsfeldes verursacht. Es wurde beobachtet, dass die biokolloidale Verweilzeit eine Funktion des Druckgradienten als auch der Kolloidgröße ist. Unsere Modellierungsergebnisse stimmen sehr gut mit den bereits veröffentlichten Daten überein.

Hadronic correlation functions with quark-disconnected contributions in lattice QCD

One of the fundamental interactions in the Standard Model of particle physicsrnis the strong force, which can be formulated as a non-abelian gauge theoryrncalled Quantum Chromodynamics (QCD). rnIn the low-energy regime, where the QCD coupling becomes strong and quarksrnand gluons are confined to hadrons, a perturbativernexpansion in the coupling constant is not possible.rnHowever, the introduction of a four-dimensional Euclidean space-timernlattice allows for an textit{ab initio} treatment of QCD and provides arnpowerful tool to study the low-energy dynamics of hadrons.rnSome hadronic matrix elements of interest receive contributionsrnfrom diagrams including quark-disconnected loops, i.e. disconnected quarkrnlines from one lattice point back to the same point. The calculation of suchrnquark loops is computationally very demanding, because it requires knowledge ofrnthe all-to-all propagator. In this thesis we use stochastic sources and arnhopping parameter expansion to estimate such propagators.rnWe apply this technique to study two problems which relay crucially on therncalculation of quark-disconnected diagrams, namely the scalar form factor ofrnthe pion and the hadronic vacuum polarization contribution to the anomalousrnmagnet moment of the muon.rnThe scalar form factor of the pion describes the coupling of a charged pion torna scalar particle. We calculate the connected and the disconnected contributionrnto the scalar form factor for three different momentum transfers. The scalarrnradius of the pion is extracted from the momentum dependence of the form factor.rnThe use ofrnseveral different pion masses and lattice spacings allows for an extrapolationrnto the physical point. The chiral extrapolation is done using chiralrnperturbation theory ($chi$PT). We find that our pion mass dependence of thernscalar radius is consistent with $chi$PT at next-to-leading order.rnAdditionally, we are able to extract the low energy constant $ell_4$ from thernextrapolation, and ourrnresult is in agreement with results from other lattice determinations.rnFurthermore, our result for the scalar pion radius at the physical point isrnconsistent with a value that was extracted from $pipi$-scattering data. rnThe hadronic vacuum polarization (HVP) is the leading-order hadronicrncontribution to the anomalous magnetic moment $a_mu$ of the muon. The HVP canrnbe estimated from the correlation of two vector currents in the time-momentumrnrepresentation. We explicitly calculate the corresponding disconnectedrncontribution to the vector correlator. We find that the disconnectedrncontribution is consistent with zero within its statistical errors. This resultrncan be converted into an upper limit for the maximum contribution of therndisconnected diagram to $a_mu$ by using the expected time-dependence of therncorrelator and comparing it to the corresponding connected contribution. Wernfind the disconnected contribution to be smaller than $approx5%$ of thernconnected one. This value can be used as an estimate for a systematic errorrnthat arises from neglecting the disconnected contribution.rn