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.

Investigation of the nuclear matter density distributions of the exotic 12 Be, 14 Be and 8 B nuclei by elastic proton scattering in inverse kinematics

The proton-nucleus elastic scattering at intermediate energies is a well-established method for the investigation of the nuclear matter distribution in stable nuclei and was recently applied also for the investigation of radioactive nuclei using the method of inverse kinematics. In the current experiment, the differential cross sections for proton elastic scattering on the isotopes $^{7,9,10,11,12,14}$Be and $^8$B were measured. The experiment was performed using the fragment separator at GSI, Darmstadt to produce the radioactive beams. The main part of the experimental setup was the time projection ionization chamber IKAR which was simultaneously used as hydrogen target and a detector for the recoil protons. Auxiliary detectors for projectile tracking and isotope identification were also installed. As results from the experiment, the absolute differential cross sections d$sigma$/d$t$ as a function of the four momentum transfer $t$ were obtained. In this work the differential cross sections for elastic p-$^{12}$Be, p-$^{14}$Be and p-$^{8}$B scattering at low $t$ ($t leq$~0.05~(GeV/c)$^2$) are presented. The measured cross sections were analyzed within the Glauber multiple-scattering theory using different density parameterizations, and the nuclear matter density distributions and radii of the investigated isotopes were determined. The analysis of the differential cross section for the isotope $^{14}$Be shows that a good description of the experimental data is obtained when density distributions consisting of separate core and halo components are used. The determined {it rms} matter radius is $3.11 pm 0.04 pm 0.13$~fm. In the case of the $^{12}$Be nucleus the results showed an extended matter distribution as well. For this nucleus a matter radius of $2.82 pm 0.03 pm 0.12$~fm was determined. An interesting result is that the free $^{12}$Be nucleus behaves differently from the core of $^{14}$Be and is much more extended than it. The data were also compared with theoretical densities calculated within the FMD and the few-body models. In the case of $^{14}$Be, the calculated cross sections describe the experimental data well while, in the case of $^{12}$Be there are discrepancies in the region of high momentum transfer. Preliminary experimental results for the isotope $^8$B are also presented. An extended matter distribution was obtained (though much more compact as compared to the neutron halos). A proton halo structure was observed for the first time with the proton elastic scattering method. The deduced matter radius is $2.60pm 0.02pm 0.26$~fm. The data were compared with microscopic calculations in the frame of the FMD model and reasonable agreement was observed. The results obtained in the present analysis are in most cases consistent with the previous experimental studies of the same isotopes with different experimental methods (total interaction and reaction cross section measurements, momentum distribution measurements). For future investigation of the structure of exotic nuclei a universal detector system EXL is being developed. It will be installed at the NESR at the future FAIR facility where higher intensity beams of radioactive ions are expected. The usage of storage ring techniques provides high luminosity and low background experimental conditions. Results from the feasibility studies of the EXL detector setup, performed at the present ESR storage ring, are presented.

Influence of ice crystal habit and cirrus spatial inhomogeneities on the retrieval of cirrus optical thickness and effective radius

Diese Dissertation untersucht den Einfluss von Eiskristallform und räumlicher Inhomogenität von Zirren auf das Retrieval von optischer Wolkendicke und effektivem Eispartikelradius. Zu diesem Zweck werden flugzeuggetragene spektrale Messungen solarer Strahlung sowie solare und langwellige Strahlungstransfersimulationen durchgeführt. Flugzeuggetragene spektrale aufwärtsgerichtete Radianzen (Strahldichten) sind mit dem SMART-Albedometer (Spectral Modular Airborne Radiation measurement sysTem) während des CIRCLE-2 (CIRrus CLoud Experiment-2) Feldexperiments im Mai 2007 gemessen worden. Basierend auf diesen Radianzdaten werden mittels eines Wolkenretrievalalgorithmus optische Wolkendicken und effektive Eispartikelradien anhand von eindimensionalen Strahlungstransferrechnungen bestimmt. Die Auswirkung der Annahme unterschiedlicher Eiskristallformen auf die retrievten Parameter wird durch Variation der Einfachstreueigenschaften der Eispartikel untersucht. Darüber hinaus wird mittels Strahlungstransferrechnungen auch der Einfluss der Eiskristallform auf den Strahlungsantrieb von Eiswolken ermittelt. Die Frage nach dem relativen Einfluss von räumlicher Wolkeninhomogenität und Eiskristallform wird anhand von dreidimensionalen und independent pixel approximation (IPA) Strahlungssimulationen untersucht. Die Analyse basiert auf einer Modelleiswolke, die aus Daten des NASA (National Aeronautics and Space Administration) TC4 (Tropical Composition, Cloud, and Climate Coupling) Feldexperiments im Sommer 2007 in Costa Rica erzeugt wurde. Lokal gesehen können beide Effekte - Eiskristallform und räumliche Eiswolkeninhomogenität - die gleiche Grössenordnung haben und zu einer Unter- bzw. Überschätzung der retrievten Parameter um 40 – 60% führen. Gemittelt über die ganze Wolke ist jedoch der Einfluss der Eiskristallform viel bedeutender als der von räumlichen Inhomogenitäten.

Generating vegetation-spectra as a basis for global monitoring of annual vegetation cycles using DOAS satellite observations

Vegetation-cycles are of general interest for many applications. Be it for harvest-predictions, global monitoring of climate-change or as input to atmospheric models.rnrnCommon Vegetation Indices use the fact that for vegetation the difference between Red and Near Infrared reflection is higher than in any other material on Earth’s surface. This gives a very high degree of confidence for vegetation-detection.rnrnThe spectrally resolving data from the GOME and SCIAMACHY satellite-instrumentsrnprovide the chance to analyse finer spectral features throughout the Red and Near Infrared spectrum using Differential Optical Absorption Spectroscopy (DOAS). Although originally developed to retrieve information on atmospheric trace gases, we use it to gain information on vegetation. Another advantage is that this method automatically corrects for changes in the atmosphere. This renders the vegetation-information easily comparable over long time-spans.rnThe first results using previously available reference spectra were encouraging, but also indicated substantial limitations of the available reflectance spectra of vegetation. This was the motivation to create new and more suitable vegetation reference spectra within this thesis.rnThe set of reference spectra obtained is unique in its extent and also with respect to its spectral resolution and the quality of the spectral calibration. For the first time, this allowed a comprehensive investigation of the high-frequency spectral structures of vegetation reflectance and of their dependence on the viewing geometry.rnrnThe results indicate that high-frequency reflectance from vegetation is very complex and highly variable. While this is an interesting finding in itself, it also complicates the application of the obtained reference spectra to the spectral analysis of satellite observations.rnrnThe new set of vegetation reference spectra created in this thesis opens new perspectives for research. Besides refined satellite analyses, these spectra might also be used for applications on other platforms such as aircraft. First promising studies have been presented in this thesis, but the full potential for the remote sensing of vegetation from satellite (or aircraft) could bernfurther exploited in future studies.

Microscopic and spectroscopic analysis of biogenic aerosols

Aerosol particles are important actors in the Earth’s atmosphere and climate system. They scatter and absorb sunlight, serve as nuclei for water droplets and ice crystals in clouds and precipitation, and are a subject of concern for public health. Atmospheric aerosols originate from both natural and anthropogenic sources, and emissions resulting from human activities have the potential to influence the hydrological cycle and climate. An assessment of the extent and impacts of this human force requires a sound understanding of the natural aerosol background. This dissertation addresses the composition, properties, and atmospheric cycling of biogenic aerosol particles, which represent a major fraction of the natural aerosol burden. The main focal points are: (i) Studies of the autofluo-rescence of primary biological aerosol particles (PBAP) and its application in ambient measure-ments, and (ii) X-ray microscopic and spectroscopic investigations of biogenic secondary organic aerosols (SOA) from the Amazonian rainforest.rnAutofluorescence of biological material has received increasing attention in atmospheric science because it allows real-time monitoring of PBAP in ambient air, however it is associated with high uncertainty. This work aims at reducing the uncertainty through a comprehensive characterization of the autofluorescence properties of relevant biological materials. Fluorescence spectroscopy and microscopy were applied to analyze the fluorescence signatures of pure biological fluorophores, potential non-biological interferences, and various types of reference PBAP. Characteristic features and fingerprint patterns were found and provide support for the operation, interpretation, and further development of PBAP autofluorescence measurements. Online fluorescence detection and offline fluorescence microscopy were jointly applied in a comprehensive bioaerosol field measurement campaign that provided unprecedented insights into PBAP-linked biosphere-atmosphere interactions in a North-American semi-arid forest environment. Rain showers were found to trigger massive bursts of PBAP, including high concentrations of biological ice nucleators that may promote further precipitation and can be regarded as part of a bioprecipitation feedback cycle in the climate system. rnIn the pristine tropical rainforest air of the Amazon, most cloud and fog droplets form on bio-genic SOA particles, but the composition, morphology, mixing state and origin of these particles is hardly known. X-ray microscopy and spectroscopy (STXM-NEXAFS) revealed distinctly different types of secondary organic matter (carboxyl- vs. hydroxy-rich) with internal structures that indicate a strong influence of phase segregation, cloud and fog processing on SOA formation, and aging. In addition, nanometer-sized potassium-rich particles emitted by microorganisms and vegetation were found to act as seeds for the condensation of SOA. Thus, the influence of forest biota on the atmospheric abundance of cloud condensation nuclei appears to be more direct than previously assumed. Overall, the results of this dissertation suggest that biogenic aerosols, clouds and precipitation are indeed tightly coupled through a bioprecipitation cycle, and that advanced microscopic and spectroscopic techniques can provide detailed insights into these mechanisms.rn

Measurements and modeling of ozone fluxes in and above Norway spruce canopies

Ozon (O3) ist ein wichtiges Oxidierungs- und Treibhausgas in der Erdatmosphäre. Es hat Einfluss auf das Klima, die Luftqualität sowie auf die menschliche Gesundheit und die Vegetation. Ökosysteme, wie beispielsweise Wälder, sind Senken für troposphärisches Ozon und werden in Zukunft, bedingt durch Stürme, Pflanzenschädlinge und Änderungen in der Landnutzung, heterogener sein. Es ist anzunehmen, dass diese Heterogenitäten die Aufnahme von Treibhausgasen verringern und signifikante Rückkopplungen auf das Klimasystem bewirken werden. Beeinflusst wird der Atmosphären-Biosphären-Austausch von Ozon durch stomatäre Aufnahme, Deposition auf Pflanzenoberflächen und Böden sowie chemische Umwandlungen. Diese Prozesse zu verstehen und den Ozonaustausch für verschiedene Ökosysteme zu quantifizieren sind Voraussetzungen, um von lokalen Messungen auf regionale Ozonflüsse zu schließen.rnFür die Messung von vertikalen turbulenten Ozonflüssen wird die Eddy Kovarianz Methode genutzt. Die Verwendung von Eddy Kovarianz Systemen mit geschlossenem Pfad, basierend auf schnellen Chemilumineszenz-Ozonsensoren, kann zu Fehlern in der Flussmessung führen. Ein direkter Vergleich von nebeneinander angebrachten Ozonsensoren ermöglichte es einen Einblick in die Faktoren zu erhalten, die die Genauigkeit der Messungen beeinflussen. Systematische Unterschiede zwischen einzelnen Sensoren und der Einfluss von unterschiedlichen Längen des Einlassschlauches wurden untersucht, indem Frequenzspektren analysiert und Korrekturfaktoren für die Ozonflüsse bestimmt wurden. Die experimentell bestimmten Korrekturfaktoren zeigten keinen signifikanten Unterschied zu Korrekturfaktoren, die mithilfe von theoretischen Transferfunktionen bestimmt wurden, wodurch die Anwendbarkeit der theoretisch ermittelten Faktoren zur Korrektur von Ozonflüssen bestätigt wurde.rnIm Sommer 2011 wurden im Rahmen des EGER (ExchanGE processes in mountainous Regions) Projektes Messungen durchgeführt, um zu einem besseren Verständnis des Atmosphären-Biosphären Ozonaustauschs in gestörten Ökosystemen beizutragen. Ozonflüsse wurden auf beiden Seiten einer Waldkante gemessen, die einen Fichtenwald und einen Windwurf trennt. Auf der straßenähnlichen Freifläche, die durch den Sturm "Kyrill" (2007) entstand, entwickelte sich eine Sekundärvegetation, die sich in ihrer Phänologie und Blattphysiologie vom ursprünglich vorherrschenden Fichtenwald unterschied. Der mittlere nächtliche Fluss über dem Fichtenwald war -6 bis -7 nmol m2 s-1 und nahm auf -13 nmol m2 s-1 um die Mittagszeit ab. Die Ozonflüsse zeigten eine deutliche Beziehung zur Pflanzenverdunstung und CO2 Aufnahme, was darauf hinwies, dass während des Tages der Großteil des Ozons von den Pflanzenstomata aufgenommen wurde. Die relativ hohe nächtliche Deposition wurde durch nicht-stomatäre Prozesse verursacht. Die Deposition über dem Wald war im gesamten Tagesverlauf in etwa doppelt so hoch wie über der Freifläche. Dieses Verhältnis stimmte mit dem Verhältnis des Pflanzenflächenindex (PAI) überein. Die Störung des Ökosystems verringerte somit die Fähigkeit des Bewuchses, als Senke für troposphärisches Ozon zu fungieren. Der deutliche Unterschied der Ozonflüsse der beiden Bewuchsarten verdeutlichte die Herausforderung bei der Regionalisierung von Ozonflüssen in heterogen bewaldeten Gebieten.rnDie gemessenen Flüsse wurden darüber hinaus mit Simulationen verglichen, die mit dem Chemiemodell MLC-CHEM durchgeführt wurden. Um das Modell bezüglich der Berechnung von Ozonflüssen zu evaluieren, wurden gemessene und modellierte Flüsse von zwei Positionen im EGER-Gebiet verwendet. Obwohl die Größenordnung der Flüsse übereinstimmte, zeigten die Ergebnisse eine signifikante Differenz zwischen gemessenen und modellierten Flüssen. Zudem gab es eine klare Abhängigkeit der Differenz von der relativen Feuchte, mit abnehmender Differenz bei zunehmender Feuchte, was zeigte, dass das Modell vor einer Verwendung für umfangreiche Studien des Ozonflusses weiterer Verbesserungen bedarf.rn