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Scattering operators for the spherical harmonics expansion of the Boltzmann transport equation
Diese Arbeit behandelt die Beschreibung von Streuprozessen im Rahmen der Boltzmann Transport Gleichung, welche nach Kugelflächenfunktionen (sog. Spherical Harmonics) entwickelt wird. Dabei wird auf die Arbeit von Karl Rupp aufgebaut, insbesondere wird der von ihm entwickelte Simulator "ViennaSHE" verwendet. Der Fokus wird dabei auf einen der kompliziertesten Streumechansimen gelegt, die Elektronen-Elektronen Streuung, welche zum ersten Mal in dieser Form beschrieben wird.Zu Beginn werden die mathematischen und physikalischen Grundlagen der Halbleiterphysik ausgearbeitet. Dabei werden die grundlegenden Halbleiter-Gleichungen, namentlich die Schrödinger Gleichung, die Boltzmann Transport Gleichung und die zugehörigen Momentengleichungen beschrieben. Letztere sollen die Vorteile der Kugelflächenfunktionsentwicklung hervorstreichen. Anschließend folgt ein Abschnitt, in dem detailliert die Entwicklung der Boltzmann Transport Gleichung nach Kugelflächenfunktionen ausgeführt wird. Des Weiteren wird der Übergang von der quantenmechanischen zur semi-klassischen Beschreibung des Elektrons beschrieben. In der semi-klassichen Beschreibung werden die Elektronen als klassische Teilchen angesehen, die Streuprozesse hingegen quantenmechanisch berücksichtigt. Basierend auf der Goldenen Regel von Fermi wird eine allgemeine Beschreibung der Streutheorie dargestellt. Die theoretischen Konzepte werden schließlich angewendet, um systematisch Ausdrücke für die Streuung an ionisierten Störstellen, die Streuung an akustischen und optischen Phonen innerhalb eines Leitungsbandtales und die Elektron-Elektron Streuung zu entwickeln.Im letzten Teil der Arbeit werden die Implementierungen für die Streuung an ionisierten Störstellen, sowie für Elektron-Elektron Streuung besprochen. Dabei wird auf die für die Elektron-Elektron Streuung vorgenommenen Vereinfachungen detailliert eingegangen. Zusätzlich werden numerische Untersuchungen des Streuoperators durchgeführt. Abschließend werden ausgewählte Simulationsresultate für einen Metall-Oxid-Halbleiter-Feldeffekttransistor (MOSFET) präsentiert.This thesis deals with the description of scattering in the framework of the Spherical Harmonics Expansion (SHE) of the Boltzmann Transport Equation (BTE). The focus is on one of the most complicated scattering mechanism, electron-electron scattering, which is described for the first time in this context. It is based on the pioneering work of Karl Rupp, who developed the Spherical Harmonics Boltzmann Solver "ViennaSHE". The mathematical and physical foundation, starting with the basic semiconductor equations, is presented in detail. Here, the advantages of the SHE approach are emphasized by comparison with the widely used balance equation methods (e.g. drift diffusion), which are also based on the BTE. The expansion of the BTE including the scattering operator is derived rigorously. In the following, the transition from the quantum mechanical description of the electron to the semi-classical description, where the motion of electrons is described classically and scattering is described quantum mechanically is discussed. Consequently, a general approach for describing scattering mechanisms is developed.This includes an elaboration of Fermi's Golden Rule, which is the foundation of the scattering theory.The theoretical concepts are applied to describe ionized impurity, acoustic and optical intra-valley phonon and electron-electron scattering. Afterwards, the implementation of ionized impurity and electron-electron scattering is described. For electron-electron scattering, a simplified model for the scattering operator is presented.This is necessary in order to reduce the complexity of the implementation. Finally, the applicability of the implementation is demonstrated by numerical simulation results for a metalâEUR"oxideâEUR"semiconductor field-effect transistor (MOSFET)
Physics and Characterization of the Gate Stack in Gallium Nitride based MIS-HEMTs
Die Bedeutung von Elektrizität nimmt zu und dadurch auch die Rolle von Halbleiterbauelementen zur elektrischen Leistungswandlung. Galliumnitrid und verwandte Verbundmaterialien bieten überragende Materialeigenschaften die eine weitere signifikante Verbesserung der elektrischen Eigenschaften dieser Bauelemente ermöglichen. Das in diesem Zusammenhang favorisierte Bauelementekonzept basiert auf einem Aluminumgalliumnitrid/Galliumnitrid Heterostrukturübergang. Ein auf der Aluminiumgalliumnitrid-Barriere abgeschiedenes Dielektrikum wird überlicherweise verwendet um die Gate-Leckströme zu minimieren. Dabei allerdings ist die Dichte an elektrischen Defekten an der Grenzfläche zur Barriere so hoch, dass dies zu extremen Driften der Einsatzspannung führt. In dieser Arbeit wird eine Methode präsentiert, die einen quantitativen Vergleich verschiedener Gate-Strukturen ermöglicht. Im Gegensatz dazu, haben sich die meisten etablierten Methoden zur Charakterisierung der Grenzflächendefektdichte als ungeignet zum Vergleich verschiedene Prozess- und Designvariationen herausgestellt. Die Verfügbarkeit einer solchen Methode ist der Schlüssel zur technologischen Optimierung der Grenzflächeneigenschaften. Der Ansatz basiert auf einer zeitaufgelösten Messung der Relaxation der Einsatzspannungsdriften nach de nierten positiven Stresspulsen am Gate-Kontakt des Bauelements mit varrierender Stressspanung und Stresszeit. Eine systematische Untersuchung unterschiedlicher Dielektrika und Schichtstrukturen hat gezeigt, dass die Stress- und Relaxationszeitkonstanten eine logarithmische Verteilung aufweisen, welche messtechnisch im Bereich von s bis Ms untersucht werden. Es wird dargelegt, warum die Defektprozesse sich nicht mit dem einfachen Bild von Defekten mit diskreten Energieleveln beschreiben lassen. Darüberhinaus wird gezeigt, dass die dielektrische Konstante einen starken Einfluss auf das Driftverhalten hat, wobei die extrahierten Defektdichten direkt mit der dielektrischen Kapazität skalieren, wenn die Gate-Spannung gröer als die kritischen Spannung zur Akkumulation von Elektronen am dielektrischen Interface ist. Daraus wird die Schlussfolgerung gezogen, dass die eigentliche Defektdichte viel höher sein muss und die Messung durch die dielektrische Durchbruchsfestigkeit begrenzt wird.The importance of electricity is increasing and hence the role of power semiconductor devices for improving the eciency of electrical power conversion systems. Gallium nitride and its compounds oer superior material properties for a further signi cant improvement of these devices. The favored device structure is based on an aluminum gallium nitride/gallium nitride heterojunction. An insulated gate contact on top of the aluminum gallium nitride barrier layer would be much desired to suppress parasitic gate leakage currents. But the high density of interface states between the barrier and the deposited dielectric causes tremendous threshold voltage drifts. In this work, a measurement setup for a time-resolved measurement of the recovery curves of the threshold voltage drift after forward bias gate stress pulses of varying magnitude and duration is developed. This setup enables a quantitative comparison of dierent test samples, whereas most of the established interface characterization methods are not suitable for this purpose. The availability of such a method is of key importance for the technological improvement of the interface quality. This setup is used to perform a systematic study of threshold voltage drift dependency on gate stress bias and time with stress times ranging from 100 ns to 10 ks and recovery times ranging from 1 s and 1 Ms. The typical stress biases are below 10 V. Dierent test samples with dierent dielectric materials, varying dielectric layer thickness and barrier layer thickness are compared. Moreover, the impact of repetitive stress pulses is investigated. The experimental data show a broad distribution of characteristic stress/recovery time constants of threshold voltage drift Vth, as well as an increase with the stress bias. It is concluded that the observed stress/recovery behavior cannot be explained by rst-order defect kinetics. Furthermore, a Coulomb charging of the interface is proposed. In these experiments no saturation of Vth with increasing stress bias and time is found. For small stress bias and short stress times the barrier layer is proposed to be a rate limiter for electron capture processes at the dielectric/III-N interface. Moreover, it is suggested that under spill-over conditions, i.e. accumulation of a second electron channel at the dielectric/III-N interface, the density of trapped electrons under stress scales with the dielectric capacitance. It is argued that the number of defect states at the interface is larger than what can be electrically measured
Going Beyond Counting First Authors in Author Co-citation Analysis
The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Enhancement of Vth Drift for Repetitive Gate Stress Pulses due to Charge Feedback Effect in GaN MIS-HEMTs
Variations on the Author
“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
We provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Inclusion of Carrier-Carrier-Scattering Into Arbitrary-Order Spherical Harmonics Expansions of the Boltzmann Transport Equation
Dispelling the Myths Behind First-author Citation Counts
We conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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