Diese Arbeit stellt einen Beitrag zur Modellierung der gerichteten Erstarrung von Silizium für die Photovoltaik dar. Es wurde basierend auf einem industriellen Prozesses ein Modellaufbau der Schmelze mit zwei Induktoren nach der Ähnlichkeitstheorie abgeleitet. Dieser ermöglicht, durch die Verwendung von niedrig schmelzenden Metallen, eine umfassende Messung der Strömungsgeschwindigkeiten mit Ultraschall-Velocimetrie. Basierend auf den experimen- tellen Daten wurde ein numerisches Modell zur Berechnung der Schmelzströmung unter Magnetfeldeinfluss validiert. Es wurden detaillierte Untersuchungen zu Strömungsstrukturen und beeinflussende Parameter durchgeführt, eine Methode zur Klassifizierung entwickelt und die Rotationskennzahl Ro eingeführt, mit welcher man in Abhängigkeit vom Magnetfeld und der Schmelzgeometrie die horizontale Rotation der Schmelzströmung in einem breiten Gültigkeitsbereich vorhersagen kann. Das validierte numerische Modell wurde zur Prozessoptimierung auf die Schmelzströmung des industriellen Prozesses angewendet.

CHAMP (CHAllenging Minisatellite Payload) is a German small satellite mission to study the earth's gravity field, magnetic field and upper atmosphere. Thanks to the good condition of the satellite so far, the planned 5 years mission is extended to year 2009. The satellite provides continuously a large quantity of measurement data for the purpose of Earth study. The measurements of the magnetic field are undertaken by two Fluxgate Magnetometers (vector magnetometer) and one Overhauser Magnetometer (scalar magnetometer) flown on CHAMP. In order to ensure the quality of the data during the whole mission, the calibration of the magnetometers has to be performed routinely in orbit. The scalar magnetometer serves as the magnetic reference and its readings are compared with the readings of the vector magnetometer. The readings of the vector magnetometer are corrected by the parameters that are derived from this comparison, which is called the scalar calibration. In the routine processing, these calibration parameters are updated every 15 days by means of scalar calibration. There are also magnetic effects coming from the satellite which disturb the measurements. Most of them have been characterized during tests before launch. Among them are the remanent magnetization of the spacecraft and fields generated by currents. They are all considered to be constant over the mission life. The 8 years of operation experience allow us to investigate the long-term behaviors of the magnetometers and the satellite systems. According to the investigation, it was found that for example the scale factors of the FGM show obvious long-term changes which can be described by logarithmic functions. The other parameters (offsets and angles between the three components) can be considered constant. If these continuous parameters are applied for the FGM data processing, the disagreement between the OVM and the FGM readings is limited to pm1nT over the whole mission. This demonstrates, the magnetometers on CHAMP exhibit a very good stability. However, the daily correction of the parameter Z component offset of the FGM improves the agreement between the magnetometers markedly. The Z component offset plays a very important role for the data quality. It exhibits a linear relationship with the standard deviation of the disagreement between the OVM and the FGM readings. After Z offset correction, the errors are limited to pm0.5nT (equivalent to a standard deviation of 0.2nT). We improved the corrections of the spacecraft field which are not taken into account in the routine processing. Such disturbance field, e.g. from the power supply system of the satellite, show some systematic errors in the FGM data and are misinterpreted in 9-parameter calibration, which brings false local time related variation of the calibration parameters. These corrections are made by applying a mathematical model to the measured currents. This non-linear model is derived from an inversion technique. If the disturbance field of the satellite body are fully corrected, the standard deviation of scalar error triangle B remains about 0.1nT. Additionally, in order to keep the OVM readings a reliable standard, the imperfect coefficients of the torquer current correction for the OVM are redetermined by solving a minimization problem. The temporal variation of the spacecraft remanent field is investigated. It was found that the average magnetic moment of the magneto-torquers reflects well the moment of the satellite. This allows for a continuous correction of the spacecraft field. The reasons for the possible unknown systemic error are discussed in this thesis. Particularly, both temperature uncertainties and time errors have influence on the FGM data. Based on the results of this thesis the data processing of future magnetic missions can be designed in an improved way. In particular, the upcoming ESA mission Swarm can take advantage of our findings and provide all the auxiliary measurements needed for a proper recovery of the ambient magnetic field. / CHAMP (CHAllenging Minisatellite Payload) ist eine deutsche Kleinsatellitenmission für die Forschung und Anwendung in Bereich der Geowissenschaften und Atmosphärenphysik. Das Projekt wird vom GFZ geleitet. Mit seinen hochgenauen, multifunktionalen, sich ergänzenden Nutzlastelementen (Magnetometer, Akzelerometer, Sternsensor, GPS-Empfänger, Laser-Retroreflektor, Ionendriftmeter) liefert CHAMP erstmalig gleichzeitig hochgenaue Schwere- und Magnetfeldmessungen (seit Mitte 2000). Dank des bisherigen guten Zustandes des Satelliten ist die auf 5 Jahre ausgelegte Mission bis 2009 verlängert geworden. An Board befinden sich ein skalares Overhauser-Magnetometer(OVM) für Kalibrierungszwecke sowie zwei Fluxgate-Magnetometer(FGM) zur Messung des magnetischen Feldvektors. Die Messungen vom FGM werden immer verglichen mit denen vom OVM und korregiert im Fall von Widersprüche, das ist die sog. Skalar-Kalibrierung. Um eine zuverlässige Datenqualität während der 8 jährigen Mission zu garantieren, ist die Nachkalibrierung implementiert. Im Rahmen der standard mäßigen Datenverarbeitung werden die Instrumentenparameter des FGM alle 15 Tage neu bestimmt. Das Ziel der vorliegenden Arbeit ist es, eine Verbesserung der Vektormagnetfelddaten zu erzielen durch eine neue Methode der Kalibrierung, die die Eigenschaften der Sensoren und Störung vom Raumfahrzeug mit berücksichtigt. Die Erfahrung aus den zurückliegenden Jahren hat gezeigt, dass sich die Skalenfaktoren des FGM stark mit der Zeit ändern. Dieser Verlauf lässt sich gut durch eine Logarithmuskurve anpassen. Andere Parameter wie die Winkel und die Offsets scheinen stabil zu sein. Eine Ausnahme macht der Offset der Z-Komponent. Dieser bedarf einer regelmäßigen Korrektur. Während die Standardverarbeitung eine undifferenzierte Bestimmung aller 9 FGM Parameter durch nicht-lineare Inversion der skalar Daten vornimmt, beziehen wir jetzt die langzeitlichen Eigenschaften der Parameter in die Bestimmung mit ein. Eine weitere Verbesserung der CHAMP-Magnetfelddaten konnte erreicht werden durch geeignete Berücksichtigung von Störung vom Raumfahrzeug. Die verbleibenden Unsicherheiten konnten durch diese Maßnahmen auf eine Standardabweichung von 0.1nT reduziert werden.

Die Arbeit befasst sich mit der Herstellung massiver Halbleitereinkristalle nach der Vertical Gradient Freeze (VGF) – Technologie unter dem Einfluss eines kombinierten magnetischen Gleich- und Wechselfeldes. Konkret wurden ein axial statisches und ein wanderndes Magnetfeld eingesetzt, um eine maßgeschneiderte Strömung in der Halbleiterschmelze zu erzeugen. Die Eigenschaften der Strömung wurden anhand von isothermalen Modellexperimenten detailliert untersucht. Des Weiteren wurden numerische Modelle der experimentellen Anordnungen entwickelt und umfangreiche Simulationen zu den auftretenden Magnet-, Strömungs-, Temperatur- und Spannungsfeldern durchgeführt. Der Arbeitsschwerpunkt lag auf der Optimierung der Kristalleigenschaften bei der Züchtung von GaAs- und Ge-Einkristallen. Durch den Einsatz der kombinierten Magnetfelder konnte eine signifikante Verringerung der Durchbiegung der Phasengrenze Schmelze/Kristall und der damit verbundenen thermischen Spannungen im Kristall gezeigt werden. Gleichzeitig wurde eine sehr homogene makroskopische Dotierstoffverteilung ohne auftretende Mikrosegregation erreicht.

Graphene, the two-dimensional lattice of sp2-hybridized carbon atoms, has a great potential for future electronics, in particular for opto-electronic devices. The carrier relaxation dynamics, which is of key importance for such applications, is in the main focus of this thesis. Besides a short introduction into the most prominent material properties of graphene and the experimental techniques, this thesis is divided into three main parts. The investigation of the carrier relaxation dynamics in the absence of a magnetic field is presented in Chapter 3. In the first experiment, the anisotropy of the carrier excitation and relaxation in momentum space was investigated by pump-probe measurements in the near-infrared range. While this anisotropy was not considered in all previous experiments, our measurements with a temporal resolution of less than 50 fs revealed the polarization dependence of the carrier excitation and the subsequent relaxation. About 150 fs after the electrons are excited, the carrier distribution in momentum space gets isotropic, caused by electron-phonon scattering. In a second set of two-color pump-probe experiments, the temperature of the hot carrier distribution, which was obtained within the duration of the pump pulse (about 200 fs), could be estimated. Furthermore, a change in sign of the pump-probe signal can be used as an indicator for the Fermi energy of different graphene layers. Pump-probe experiments in the far-infrared range in reflection and transmission geometry were performed at high pump power. A strong saturation of the pump-induced transmission was found in previous experiments, which was attributed to the pump-induced change in absorption. Our investigation shows the strong influence of pump-induced reflection at long wavelengths, as well as a lot smaller influence of the saturation of the pump-induced change in absorption. At a high pump power, the increase of the reflection exceeds the change in absorption strongly, which leads to negative pump-probe signals in transmission geometry. In Chapter 4, investigations of the carrier dynamics of graphene in magnetic fields of up to 7T are presented. Even though the optical properties of Landau-quantized graphene are very interesting, the carrier dynamics were nearly unexplored. A low photon energy of 14meV allows the investigation of the intraband Landau-level (LL) transitions. These experiments revealed two main findings: Firstly, the Landau quantization strongly suppresses the carrier relaxation via optical-phonon scattering, resulting in an increased relaxation time. Secondly, a change in sign of the pump-probe signal can be observed when the magnetic field is varied. This change in sign indicates a hot carrier distribution shortly after the pump pulse, which means that carrier-carrier scattering remains very strong in magnetic fields. In a second set of pump-probe measurements, carried out at a photon energy of 75meV, the relaxation dynamics of interband LL transitions was investigated. In particular, experiments on the two energetically degenerate LL transitions LL(−1)->LL(0) and LL(0)->LL(1) showed the influence of extremely strong Auger processes. An ultrafast and extremely broadband terahertz detector, based on a graphene flake, is presented in the last chapter of this thesis. To couple the radiation efficiently to the small flake, the inner part of a logarithmic periodic antenna is connected to it. With a rise time of about 50 ps in a wavelength range of 9 μm to 500 μm, this detector is very interesting to obtain the temporal overlap in two-color pump-probe experiments with the free-electron laser FELBE. Furthermore, the importance of the substrate material, in particular for the high-speed performance, is discussed.

Darmstadt, Techn. Universiẗat, Diss., 2007.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1996. / Includes bibliographical references (p. 147-149) and index.

Nürnberg, University, Diss., 2004--Erlangen.

Graphene, the two-dimensional lattice of sp2-hybridized carbon atoms, has a great potential for future electronics, in particular for opto-electronic devices. The carrier relaxation dynamics, which is of key importance for such applications, is in the main focus of this thesis. Besides a short introduction into the most prominent material properties of graphene and the experimental techniques, this thesis is divided into three main parts. The investigation of the carrier relaxation dynamics in the absence of a magnetic field is presented in Chapter 3. In the first experiment, the anisotropy of the carrier excitation and relaxation in momentum space was investigated by pump-probe measurements in the near-infrared range. While this anisotropy was not considered in all previous experiments, our measurements with a temporal resolution of less than 50 fs revealed the polarization dependence of the carrier excitation and the subsequent relaxation. About 150 fs after the electrons are excited, the carrier distribution in momentum space gets isotropic, caused by electron-phonon scattering. In a second set of two-color pump-probe experiments, the temperature of the hot carrier distribution, which was obtained within the duration of the pump pulse (about 200 fs), could be estimated. Furthermore, a change in sign of the pump-probe signal can be used as an indicator for the Fermi energy of different graphene layers. Pump-probe experiments in the far-infrared range in reflection and transmission geometry were performed at high pump power. A strong saturation of the pump-induced transmission was found in previous experiments, which was attributed to the pump-induced change in absorption. Our investigation shows the strong influence of pump-induced reflection at long wavelengths, as well as a lot smaller influence of the saturation of the pump-induced change in absorption. At a high pump power, the increase of the reflection exceeds the change in absorption strongly, which leads to negative pump-probe signals in transmission geometry. In Chapter 4, investigations of the carrier dynamics of graphene in magnetic fields of up to 7T are presented. Even though the optical properties of Landau-quantized graphene are very interesting, the carrier dynamics were nearly unexplored. A low photon energy of 14meV allows the investigation of the intraband Landau-level (LL) transitions. These experiments revealed two main findings: Firstly, the Landau quantization strongly suppresses the carrier relaxation via optical-phonon scattering, resulting in an increased relaxation time. Secondly, a change in sign of the pump-probe signal can be observed when the magnetic field is varied. This change in sign indicates a hot carrier distribution shortly after the pump pulse, which means that carrier-carrier scattering remains very strong in magnetic fields. In a second set of pump-probe measurements, carried out at a photon energy of 75meV, the relaxation dynamics of interband LL transitions was investigated. In particular, experiments on the two energetically degenerate LL transitions LL(−1)->LL(0) and LL(0)->LL(1) showed the influence of extremely strong Auger processes. An ultrafast and extremely broadband terahertz detector, based on a graphene flake, is presented in the last chapter of this thesis. To couple the radiation efficiently to the small flake, the inner part of a logarithmic periodic antenna is connected to it. With a rise time of about 50 ps in a wavelength range of 9 μm to 500 μm, this detector is very interesting to obtain the temporal overlap in two-color pump-probe experiments with the free-electron laser FELBE. Furthermore, the importance of the substrate material, in particular for the high-speed performance, is discussed.

Graphene, the two-dimensional lattice of sp2-hybridized carbon atoms, has a great potential for future electronics, in particular for opto-electronic devices. The carrier relaxation dynamics, which is of key importance for such applications, is in the main focus of this thesis. Besides a short introduction into the most prominent material properties of graphene and the experimental techniques, this thesis is divided into three main parts. The investigation of the carrier relaxation dynamics in the absence of a magnetic field is presented in Chapter 3. In the first experiment, the anisotropy of the carrier excitation and relaxation in momentum space was investigated by pump-probe measurements in the near-infrared range. While this anisotropy was not considered in all previous experiments, our measurements with a temporal resolution of less than 50 fs revealed the polarization dependence of the carrier excitation and the subsequent relaxation. About 150 fs after the electrons are excited, the carrier distribution in momentum space gets isotropic, caused by electron-phonon scattering. In a second set of two-color pump-probe experiments, the temperature of the hot carrier distribution, which was obtained within the duration of the pump pulse (about 200 fs), could be estimated. Furthermore, a change in sign of the pump-probe signal can be used as an indicator for the Fermi energy of different graphene layers. Pump-probe experiments in the far-infrared range in reflection and transmission geometry were performed at high pump power. A strong saturation of the pump-induced transmission was found in previous experiments, which was attributed to the pump-induced change in absorption. Our investigation shows the strong influence of pump-induced reflection at long wavelengths, as well as a lot smaller influence of the saturation of the pump-induced change in absorption. At a high pump power, the increase of the reflection exceeds the change in absorption strongly, which leads to negative pump-probe signals in transmission geometry. In Chapter 4, investigations of the carrier dynamics of graphene in magnetic fields of up to 7T are presented. Even though the optical properties of Landau-quantized graphene are very interesting, the carrier dynamics were nearly unexplored. A low photon energy of 14meV allows the investigation of the intraband Landau-level (LL) transitions. These experiments revealed two main findings: Firstly, the Landau quantization strongly suppresses the carrier relaxation via optical-phonon scattering, resulting in an increased relaxation time. Secondly, a change in sign of the pump-probe signal can be observed when the magnetic field is varied. This change in sign indicates a hot carrier distribution shortly after the pump pulse, which means that carrier-carrier scattering remains very strong in magnetic fields. In a second set of pump-probe measurements, carried out at a photon energy of 75meV, the relaxation dynamics of interband LL transitions was investigated. In particular, experiments on the two energetically degenerate LL transitions LL(−1)->LL(0) and LL(0)->LL(1) showed the influence of extremely strong Auger processes. An ultrafast and extremely broadband terahertz detector, based on a graphene flake, is presented in the last chapter of this thesis. To couple the radiation efficiently to the small flake, the inner part of a logarithmic periodic antenna is connected to it. With a rise time of about 50 ps in a wavelength range of 9 μm to 500 μm, this detector is very interesting to obtain the temporal overlap in two-color pump-probe experiments with the free-electron laser FELBE. Furthermore, the importance of the substrate material, in particular for the high-speed performance, is discussed.

Melt flow plays an important role in directional solidification of multicrystalline silicon influencing the temperature field and the crystallization interface as well as the transport of impurities. This work investigates the potential of a traveling magnetic field (TMF) for an active control of the melt flow. A system of 3D numerical models was developed and adapted based on open-source software for calculations of Lorentz force, melt flow, and related phenomena. Isothermal and non-isothermal model experiments with a square GaInSn melt were used to validate the numerical models by direct velocity measurements. Several new 3D flow structures of turbulent TMF flows were observed for different melt heights. Further numerical parameter studies carried out for silicon melts showed that already a weak TMF-induced Lorentz force can stir impurities near to the complete mixing limit. Simultaneously, the deformed temperature field leads to an increase of the deflection of crystallization interface, which may exhibit a distinct asymmetry. The numerical results of this work were implemented in a research-scale silicon crystallization furnace. Scaling laws for various phenomena were derived allowing a limited transfer of the results to the industrial scale.