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Dissertations / Theses on the topic 'Non Equilibrium Green's Function'
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Gustafsson, Alexander. "Modeling of non-equilibrium scanning probe microscopy." Licentiate thesis, Linnéuniversitetet, Institutionen för fysik och elektroteknik (IFE), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-46448.
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The work in this thesis is basically divided into two related but separate investigations. The first part treats simple chemical reactions of adsorbate molecules on metallic surfaces, induced by means of a scanning tunneling probe (STM). The investigation serves as a parameter free extension to existing theories. The theoretical framework is based on a combination of density functional theory (DFT) and non-equilibrium Green's functions (NEGF). Tunneling electrons that pass the adsorbate molecule are assumed to heat up the molecule, and excite vibrations that directly correspond to the reaction coordinate. The theory is demonstrated for an OD molecule adsorbed on a bridge site on a Cu(110) surface, and critically compared to the corresponding experimental results. Both reaction rates and pathways are deduced, opening up the understanding of energy transfer between different configurational geometries, and suggests a deeper insight, and ultimately a higher control of the behaviour of adsorbate molecules on surfaces. The second part describes a method to calculate STM images in the low bias regime in order to overcome the limitations of localized orbital DFT in the weak coupling limit, i.e., for large vacuum gaps between a tip and the adsorbate molecule. The theory is based on Bardeen's approach to tunneling, where the orbitals computed by DFT are used together with the single-particle Green's function formalism, to accurately describe the orbitals far away from the surface/tip. In particular, the theory successfully reproduces the experimentally well-observed characteristic dip in the tunneling current for a carbon monoxide (CO) molecule adsorbed on a Cu(111) surface. Constant height/current STM images provide direct comparisons to experiments, and from the developed method further insights into elastic tunneling are gained.
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Covito, Fabio [Verfasser], and Angel [Akademischer Betreuer] Rubio. "An efficient ab-initio non-equilibrium Green's function approach to carrier dynamics in many-body interacting systems / Fabio Covito ; Betreuer: Angel Rubio." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2020. http://d-nb.info/1218688459/34.
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Kruglyak, Yu A. "Non-Equilibrium Green’s Function Method in Matrix Representation and Model Transport Problems of Nanoelectronics." Thesis, Sumy State University, 2013. http://essuir.sumdu.edu.ua/handle/123456789/35352.
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Non-equilibrium Green’s functions method in matrix representation is presented and applied to model transport problems for 1D and 2D conductors using a nearest neighbor orthogonal tight-binding model in the frame of the «bottom-up» approach of modern nanoelectronics. Simple methods to account for electric contacts in Schrödinger equation to solve quantum electron transport problems are given.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/35352
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Fonseca, James Ernest. "Accurate treatment of interface roughness in nanoscale double-gate metal oxide semiconductor field effect transistors using non-equilibrium Green's functions." Ohio : Ohio University, 2004. http://www.ohiolink.edu/etd/view.cgi?ohiou1176318345.
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Odell, Anders. "Quantum transport in photoswitching molecules : An investigation based on ab initio calculations and Non Equilibrium Green Function theory." Licentiate thesis, KTH, Materials Science and Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4790.
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Molecular electronics is envisioned as a possible next step in device miniaturization. It is usually taken to mean the design and manufacturing of electronic devices and applications where organic molecules work as the fundamental functioning unit. It involves the easurement and manipulation of electronic response and transport in molecules attached to conducting leads. Organic molecules have the advantages over conventional solid state electronics of inherent small sizes, endless chemical diversity and ambient temperature low cost manufacturing.
In this thesis we investigate the switching and conducting properties of photochromic dithienylethene derivatives. Such molecules change their conformation in solution when acted upon by light. Photochromic molecules are attractive candidates for use in molecular electronics because of the switching between different states with different conducting properties. The possibility of optically controlling the conductance of the molecule attached to leads may lead to new device implementations.
The switching reaction is investigated with potential energy calculations for different values of the reaction coordinate between the closed and the open isomer. The electronic and atomic structure calculations are performed with density functional theory (DFT). It is concluded that there is a large potential energy barrier separating the open and closed isomer and that switching between open and closed forms must involve excited states.
The conducting properties of the molecule inserted between gold leads is calculated within the Non Equilibrium Green Function theory. The transmission function is calculated for the two isomers with different basis sizes for the gold contacts, as well as the electrostatic potential, for finite applied bias voltages. We conclude that a Au 6s basis give qualitatively the same result as a Au spd basis close to the Fermi level. The transmission coefficient at the Fermi energy is around 10 times larger in the closed molecule compared to the open. This will result in a large difference in conductivity. It is also found that the large difference in conductivity will remain for small applied bias voltages. The results are consistent with earlier work.
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Monturet, Serge. "Inelastic effects in electronic currents at the nanometer scale." Phd thesis, Université Paul Sabatier - Toulouse III, 2008. http://tel.archives-ouvertes.fr/tel-00469906.
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This thesis deals with inelastic effects in electronic currents. We developed a time-dependent technique and show that this approach gives rich insight into electron-phonon coupling during transport. We compare our results with a time-independent technique and analyse the validity of our model. Finally, the results of a quantum chemistry calculation are presented in the framework of scanning tunneling miscroscopy (STM). We study the chemisorption of a tetrathiafulvalene molecule on a gold surface by performing the calculation of the charge transfer, the induced dipole, and the STM images using the density functional theory.
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MOTTA, CARLO. "First-principles study of electronic transport in organic molecular junctions." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/40094.
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This thesis focuses on the theoretical description of coherent electronic transport in organic molecular junctions.
The ab-initio theoretical methods and the theory of quantum transport in nanoscale systems are presented. The Landauer theory of transport formulated in terms of Green's function is analyzed by means of the embedding theory for a simplified model in which electrons are considered as moving in a one-dimensional modulated potential introduced to simulate resonant tunneling junctions.
Following the introductory section, relevant systems of interest from both basic and technology points of view are investigated.
The transport properties of two-dimensional graphene/graphene-nanoribbon (GNR) heterojunctions are shown to critically depend upon the geometrical features of the GNR.
Diarylethene junctions with graphene electrodes are comprehensively analyzed, with emphasis on the photoswitching properties of the system. The use of graphene electrodes can improve the performance of such switching junctions as compared with the use of other substrates.
A full characterization of a platinum/pyrazine bistable junction studied in a recent experiment is then established. The switching mechanism has been determined as a result of a molecule-lead configurational rearrangement.
A final section is devoted to the description of a new methodology to calculate the elastic lifetimes of electronic states of adsorbates on surfaces. The method has been applied to dye molecules on TiO2 substrates, which are relevant for photovoltaics applications. The effects of modification of the spacers between the acceptor and donor part of the dyes are analyzed.
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Barr, Joshua. "Transport in Interacting Nanostructures." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/301551.
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Transport through nanostructures is studied at the many-body level using exact diagonalization and nonequilibrium Green's functions. Organic molecular junctions are a particular focus because of their technological promise. Work is presented regarding: (1) A π-electron model of organic molecular junctions developed using effective field theory; (2) series transmission and transmission node structure in interacting systems; (3) the effect of interactions on quantum interference and thermoelectricity in polycyclic junctions; and (4) nanoscale transport calculations using self-consistent statistical ensembles.
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Edirisinghe, Pathirannehelage Neranjan S. "Charge Transfer in Deoxyribonucleic Acid (DNA): Static Disorder, Dynamic Fluctuations and Complex Kinetic." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/phy_astr_diss/45.
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The fact that loosely bonded DNA bases could tolerate large structural fluctuations, form a dissipative environment for a charge traveling through the DNA. Nonlinear stochastic nature of structural fluctuations facilitates rich charge dynamics in DNA. We study the complex charge dynamics by solving a nonlinear, stochastic, coupled system of differential equations. Charge transfer between donor and acceptor in DNA occurs via different mechanisms depending on the distance between donor and acceptor. It changes from tunneling regime to a polaron assisted hopping regime depending on the donor-acceptor separation. Also we found that charge transport strongly depends on the feasibility of polaron formation. Hence it has complex dependence on temperature and charge-vibrations coupling strength. Mismatched base pairs, such as different conformations of the G・A mispair, cause only minor structural changes in the host DNA molecule, thereby making mispair recognition an arduous task. Electron transport in DNA that depends strongly on the hopping transfer integrals between the nearest base pairs, which in turn are affected by the presence of a mispair, might be an attractive approach in this regard. I report here on our investigations, via the I –V characteristics, of the effect of a mispair on the electrical properties of homogeneous and generic DNA molecules. The I –V characteristics of DNA were studied numerically within the double-stranded tight-binding model. The parameters of the tight-binding model, such as the transfer integrals and on-site energies, are determined from first-principles calculations. The changes in electrical current through the DNA chain due to the presence of a mispair depend on the conformation of the G・A mispair and are appreciable for DNA consisting of up to 90 base pairs. For homogeneous DNA sequences the current through DNA is suppressed and the strongest suppression is realized for the G(anti)・A(syn) conformation of the G・A mispair. For inhomogeneous (generic) DNA molecules, the mispair result can be either suppression or an enhancement of the current, depending on the type of mispairs and actual DNA sequence.
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Nadimi, Ebrahim. "Quantum Mechanical and Atomic Level ab initio Calculation of Electron Transport through Ultrathin Gate Dielectrics of Metal-Oxide-Semiconductor Field Effect Transistors." Doctoral thesis, Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800477.
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The low dimensions of the state-of-the-art nanoscale transistors exhibit increasing quantum mechanical effects, which are no longer negligible. Gate tunneling current is one of such effects, that is responsible for high power consumption and high working temperature in microprocessors. This in turn put limits on further down scaling of devices. Therefore modeling and calculation of tunneling current is of a great interest. This work provides a review of existing models for the calculation of the gate tunneling current in MOSFETs. The quantum mechanical effects are studied with a model, based on a self-consistent solution of the Schrödinger and Poisson equations within the effective mass approximation. The calculation of the tunneling current is focused on models based on the calculation of carrier’s lifetime on quasi-bound states (QBSs). A new method for the determination of carrier’s lifetime is suggested and then the tunneling current is calculated for different samples and compared to measurements. The model is also applied to the extraction of the “tunneling effective mass” of electrons in ultrathin oxynitride gate dielectrics. Ultrathin gate dielectrics (tox<2 nm) consist of only few atomic layers. Therefore, atomic scale deformations at interfaces and within the dielectric could have great influences on the performance of the dielectric layer and consequently on the tunneling current. On the other hand the specific material parameters would be changed due to atomic level deformations at interfaces. A combination of DFT and NEGF formalisms has been applied to the tunneling problem in the second part of this work. Such atomic level ab initio models take atomic level distortions automatically into account. An atomic scale model interface for the Si/SiO2 interface has been constructed and the tunneling currents through Si/SiO2/Si stack structures are calculated. The influence of single and double oxygen vacancies on the tunneling current is investigated. Atomic level distortions caused by a tensile or compression strains on SiO2 layer as well as their influence on the tunneling current are also investigatedDie vorliegende Arbeit beschäftigt sich mit der Berechnung von Tunnelströmen in MOSFETs (Metal-Oxide-Semiconductor Field Effect Transistors). Zu diesem Zweck wurde ein quantenmechanisches Modell, das auf der selbstkonsistenten Lösung der Schrödinger- und Poisson-Gleichungen basiert, entwickelt. Die Gleichungen sind im Rahmen der EMA gelöst worden. Die Lösung der Schrödinger-Gleichung unter offenen Randbedingungen führt zur Berechnung von Ladungsverteilung und Lebensdauer der Ladungsträger in den QBSs. Der Tunnelstrom wurde dann aus diesen Informationen ermittelt. Der Tunnelstrom wurde in verschiedenen Proben mit unterschiedlichen Oxynitrid Gatedielektrika berechnet und mit gemessenen Daten verglichen. Der Vergleich zeigte, dass die effektive Masse sich sowohl mit der Schichtdicke als auch mit dem Stickstoffgehalt ändert. Im zweiten Teil der vorliegenden Arbeit wurde ein atomistisches Modell zur Berechnung des Tunnelstroms verwendet, welche auf der DFT und NEGF basiert. Zuerst wurde ein atomistisches Modell für ein Si/SiO2-Schichtsystem konstruiert. Dann wurde der Tunnelstrom für verschiedene Si/SiO2/Si-Schichtsysteme berechnet. Das Modell ermöglicht die Untersuchung atom-skaliger Verzerrungen und ihren Einfluss auf den Tunnelstrom. Außerdem wurde der Einfluss einer einzelnen und zwei unterschiedlich positionierter neutraler Sauerstoffleerstellen auf den Tunnelstrom berechnet. Zug- und Druckspannungen auf SiO2 führen zur Deformationen in den chemischen Bindungen und ändern den Tunnelstrom. Auch solche Einflüsse sind anhand des atomistischen Modells berechnet worden
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Visciarelli, Michele. "Modeling transport properties of molecular devices by a novel computational approach." Doctoral thesis, Scuola Normale Superiore, 2014. http://hdl.handle.net/11384/85807.
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Baniahmad, Ata. "QUANTUM MECHANICAL Study and Modelling of MOLECULAR ELECTRONIC DEVICES." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13193/.
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Molecular electronics pursues the use of molecules as fundamental electronic components. The inherent properties of molecules such as nano-size, low cost, scalability, and self-assembly are seen by many as a perfect complement to conventional silicon electronics. Molecule based electronics has captured the attention of a broad cross section of the scientific community.
In molecular electronic devices, the possibility of having channels that are just one atomic layer thick, is perhaps the most attractive feature that takes the attention to graphene.The conductivity, stability, uniformity, composition, and 2D nature of graphene make it an excellent material for electronic devices.
In this thesis we focused on Zigzag Graphene NanoRibbon(ZGNR) as a transmission channel. Due to the importance of an accurate description of the quantum effects in the operation of graphene devices, a full-quantum transport model has been adopted: the electron dynamics has been described by Density Functional Theory(DFT) and transport has been solved within the formalism of Non-Equilibrium Green’s Functions (NEGF). Using DFT and NEGF methods, the transport properties of ZGNR and ZGNR doped with Si are studied by systematically computing the transmission spectrum. It is observed that Si barrier destroyed the electronic transport properties of ZGNR, an energy gap appeared for ZGNR, and variations from conductor to semiconductor are displayed. Its followed by a ZGNR grown on a SiO2 crystal substrate, while substituting the Graphene electrodes with the Gold ones, and its effect on transmission properties have been studied. Improvement in transmission properties observed due to the formation of C-O bonds between ZGNR and substrate that make the ZGNR corrugated. Finally, we modeled a nano-scale Field Effect Transistor by implementing a gate under SiO2 substrate. A very good I-ON/I-OFF ratio has been observed although the device thickness.
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Fransson, Jonas. "Non-Orthogonality and Electron Correlations in Nanotransport : Spin- and Time-Dependent Currents." Doctoral thesis, Uppsala University, Department of Physics, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-2687.
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The concept of the transfer Hamiltonian formalism has been reconsidered and generalized to include the non-orthogonality between the electron states in an interacting region, e.g. quantum dot (QD), and the states in the conduction bands in the attached contacts. The electron correlations in the QD are described by means of a diagram technique for Hubbard operator Green functions for non-equilibrium states.
It is shown that the non-orthogonality between the electrons states in the contacts and the QD is reflected in the anti-commutation relations for the field operators of the subsystems. The derived forumla for the current contains corrections from the overlap of the same order as the widely used conventional tunneling coefficients.
It is also shown that kinematic interactions between the QD states and the electrons in the contacts, renormalizes the QD energies in a spin-dependent fashion. The structure of the renormalization provides an opportunity to include a spin splitting of the QD levels by polarizing the conduction bands in the contacts and/or imposing different hybridizations between the states in the contacts and the QD for the two spin channels. This leads to a substantial amplification of the spin polarization in the current, suggesting applications in magnetic sensors and spin-filters.
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Kaur, Tejinder. "Electronic Transport in Non-equilibrium Nanoscale Systems." Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1373318228.
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Chou, Yen-Liang. "Relaxation phenomena during non-equilibrium growth." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/28574.
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The surface width, a global quantity that depends on time, is used to characterize the temporal evolution of growing surfaces. One of the most successful concepts for describing the property of the surface width is the famous Family-Vicsek scaling relation. We discuss an extended scaling relation that yields a complete description for various growth models.
For two linear Langevin equations, namely the Edwards-Wilkinson equation and the Mullins-Herring equation, we furthermore study analytically the behavior of global quantities related to the surface width or to a quantity which is conjugated to the diffusion constant. The global quantities depend in a non-trivial way on two different times. We discuss the dynamical scaling forms of global correlation and response functions.
For global functions related to the surface width, we show that the scaling behavior of the response can depend on how the system is perturbed. Different dynamic regimes, characterized by a power-law or by an exponential relaxation, are identified, and a dynamic phase diagram is constructed. We discuss global fluctuation-dissipation ratios and how to use them for the characterization of non-equilibrium growth processes. We also numerically study the same two-time quantities for the non-linear Kardar-Parisi-Zhang equation.
For global functions related to the quantity which is conjugated to the diffusion constant of the linear Langevin equations, we show that the integrated response is proportional to the correlation in the linear response regime. In the aging regime, the autocorrelation and autoresponse exponents are identical and the aging exponent for the response is equal to the aging exponent for the correlation. We investigate the non-equilibrium fluctuation-dissipation theorem for non-equilibrium states based on this quantity. In the non-linear response regime a certain dissipation-fluctuation ratio approximates unity for small waiting times but approaches the ratio of perturbed and unperturbed diffusion constants for larger waiting times.Ph. D.
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Dragoni, Alberto. "Corrélations multi-corps dans les simulations ab initio du transport électronique quantique : une application aux dispositifs OxRAM de nouvelle génération." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAY039.
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Les mémoires résistives non volatiles basées sur les oxydes (OxRAM) acquièrent récemment un grand intérêt pour leurs performances, ce qui en fait des candidats prometteurs comme mémoire de stockage pour remplacer la technologie flash, et comme mémoires intégrées pour les applications réseau de neurones. Néanmoins, les dispositifs OxRAM émergents présentent encore certains inconvénients, comme la non-uniformité des paramètres de commutation et les défaillances de commutation. Surmonter ces inconvénients exige une compréhension plus profonde des principes de fonctionnement de l’OxRAM, jusqu’à présent pas complètement compris. Ceci peut être réalisé au moyen de simulations textit{ab initio}. Ce travail présente donc une étude approfondie de HfO₂, qui fait partie des matériaux les plus prometteurs pour la construction de dispositifs OxRAM, au moyen de calculs précis des états de quasi-particules (QP). Une étude des propriétés du transport électronique dans les dispositifs OxRAM est également de première importance. Toutefois, cela nécessite un cadre théorique solide et fiable afin de calculer la conductance des jonctions métal/isolant. L’approche standard, basée sur la théorie fonctionnelle de la densité, le formalisme de la fonction de Green et la formule de Landauer, a quelques limites et soucis de fiabilité. Ce travail propose une approche plus fiable basée sur les calculs QP, qui fournissent une structure électronique plus précise pour calculer la conductance, et teste en grande partie cette nouvelle méthode sur différentes jonctions imitant les dispositifs OxRAMResistive non-volatile memories based on oxides (OxRAM) are recently acquiring a wide interest for their performances, which make them promising candidates as storage memories to replace flash technology, and as embedded memories for neural network applications. Nevertheless, emerging OxRAM devices still present some drawbacks, like non-uniformity of switching parameters and switching failures. Overcoming these drawbacks requires a deeper comprehension of the OxRAM working principles, so far not completely understood. This can be achieved by means of textit{ab initio} simulations. Hence this work presents a careful characterization of HfO₂, which is within the most promising materials to build OxRAM devices, by means of accurate quasi-particle (QP) calculations. A study of the electronic transport properties in OxRAM devices is also of primary importance. However, this requires a robust and reliable theoretical framework to compute the conductance of bulk metal/insulator junctions. The standard approach, based on density functional theory, Green function formalism, and Landauer formula, has some limitations and reliability issues. This work proposes a more reliable approach based on QP calculations, which provide a more accurate electronic structure to compute the conductance, and largely tests this new method on different junctions mimicking OxRAM devices
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Berrada, Salim. "Etude théorique de nouveaux concepts de nano-transistors en graphène." Phd thesis, Université Paris Sud - Paris XI, 2014. http://tel.archives-ouvertes.fr/tel-01059811.
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Cette thèse porte sur l'étude théorique de nouveaux concepts de transistors en graphène par le formalisme des fonctions de Green dans l'hypothèse du transport balistique. Le graphène est un matériau bidimensionnel composé d'atomes de carbone organisés en nid d'abeille. Cette structure confère des propriétés uniques aux porteurs de charge dans le graphène, comme une masse effective nulle et un comportement ultra-relativiste (fermions de Dirac), ce qui conduit à des mobilités extraordinairement élevées. C'est pourquoi des efforts très importants ont été mis en œuvre dans la communauté scientifique pour la réalisation de transistors en graphène. Cependant, en vue de nombreuses applications, le graphène souffre de l'absence d'une bande d'énergie interdite. De plus, dans le cas des transistors conventionnels à base de graphène (GFET), cette absence de bande interdite, combinée avec l'apparition de l'effet tunnel de Klein, a pour effet de dégrader considérablement le rapport I_ON/I_OFF des GFET. L'absence de gap empêche également toute saturation du courant dans la branche N - là où se trouve le maximum de transconductance pour des sources et drain dopés N - et ne permet donc pas de tirer profit des très bonnes performances fréquentielles que le graphène est susceptible d'offrir grâce aux très hautes mobilités de ses porteurs. Cependant, de précédents travaux théorique et expérimentaux ont montré que la réalisation d'un super-réseau d'anti-dots dans la feuille de graphène - appelée Graphene NanoMesh (GNM) - permettait d'ouvrir une bande interdite dans le graphène. On s'est donc d'abord proposé d'étudier l'apport de l'introduction de ce type de structure pour former canal des transistors - appelés GNMFET - par rapport aux GFET " conventionnels ". La comparaison des résultats obtenus pour un GNM-FET avec un GFET de mêmes dimensions permettent d'affirmer que l'on peut améliorer le rapport I_ON/I_OFF de 3 ordres de grandeurs pour une taille et une périodicité adéquate des trous. Bien que l'introduction d'un réseau de trous réduise légèrement la fréquence de coupure intrinsèque f_T, il est remarquable de constater que la bonne saturation du courant dans la branche N, qui résulte de la présence de la bande interdite dans le GNM, conduit à une fréquence maximale d'oscillation f_max bien supérieure dans le GNM-FET. Le gain en tension dans ce dernier est aussi amélioré d'un ordre de grandeur de grandeur par rapport au GFET conventionnel. Bien que les résultats sur le GNM-FET soient très encourageants, l'introduction d'une bande interdite dans la feuille de graphène induit inévitablement une masse effective non nulle pour les porteurs, et donc une vitesse de groupe plus faible que dans le graphène intrinsèque. C'est pourquoi, en complément de ce travail, nous avons exploré la possibilité de moduler le courant dans un GFET sans ouvrir de bande interdite dans le graphène. La solution que nous avons proposée consiste à utiliser une grille triangulaire à la place d'une grille rectangulaire. Cette solution exploite les propriétés du type "optique géométrique" des fermions de Dirac dans le graphène, qui sont inhérentes à leur nature " Chirale ", pour moduler l'effet tunnel de Klein dans le transistor et bloquer plus efficacement le passage des porteurs dans la branche P quand le dopage des sources et drains sont de type N. C'est pourquoi nous avons choisi d'appeler ce transistor le " Klein Tunneling FET " (KTFET). Nous avons pu montrer que cette géométrie permettrait d'obtenir un courant I_off plus faible que ce qui est obtenu d'habitude, pour la même surface de grille, pour les GFET conventionnels. Cela offre la perspective d'une nouvelle approche de conception de dispositifs permettant d'exploiter pleinement le caractère de fermions de Dirac des porteurs de charges dans le graphène.
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Yoerger, Edward J. Jr. "Vertical Acoustic Propagation in the Non-Homogeneous Layered Atmosphere for a Time-Harmonic, Compact Source." ScholarWorks@UNO, 2019. https://scholarworks.uno.edu/td/2709.
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In this work we study vertical, acoustic propagation in a non-homogeneous media for a spatially-compact, time-harmonic source. An analytical, 2-layer model is developed representing the acoustic pressure disturbance propagating in the atmosphere. The validity of the model spans the distance from the Earth's surface to 30,000 meters. This includes the troposphere (adiabatic), ozone layer (isothermal), and part of the stratosphere (isothermal). The results of the model derivation in the adiabatic region yield pressure solutions as Bessel functions of the First (J) and Second (Y) Kind of order $-\frac{7}{2}$ with an argument of $2 \Omega \tau$ (where $\Omega$ represents a dimensionless frequency and $\tau$ is a dimensionless vertical height in z (vertical coordinate)). For an added second layer (isothermal region), the pressure solution is a decaying sinusoidal, exponential function above the first layer.
In particular, the vertical, acoustic propagation is examined for various configurations. These are divided into 2 basic classes. The first class consists of examining the pressure response function when the source is located on boundary interfaces, while the second class consists of situations where the source is arbitrarily located within a finite layer. In all instances, a time-harmonic, compact source is implicitly understood. However, each class requires a different method of solution. The first class conforms to a general boundary value problem, while the second requires the use of Green's functions method.
In investigating problems of the first class, 3 different scenarios are examined. In the first case, we apply our model to a semi-infinite medium with a time-harmonic source ($e^{-i \omega t}$) located on the ground. In the next 2 cases, a semi-infinite medium is overlain on the previous medium at a height of z=13,000 meters. Thus, there exist two boundaries: the ground and the layer interface between the 2 media. Sources placed at these interfaces represent the 2nd and 3rd scenarios, respectively. The solutions to all 3 cases are of the form $A \frac{J_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}} + B \frac{Y_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}}$, where \textit{A} and \textit{B} are constants determined by the boundary conditions.
For the 2nd class, we examine the application to a time-harmonic, compact source placed arbitrarily within the 1st layer. The method of Green's functions is used to obtain a particular solution for the model equations. This result is compared with a Fast Field Program (FFP) which was developed to test these solutions. The results show that the response given by the Green's function compares favorably with that of the FFP.
Keywords: Linear Acoustics, Inhomogeneous Medium, Layered Atmosphere, Boundary Value Problem, Green's Function Method
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Pons, Nicolas. "Modélisation tridimensionnelle multibandes du transport quantique dans les transistors à nanofil." Thesis, Aix-Marseille 1, 2011. http://www.theses.fr/2011AIX10039/document.
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L’amélioration des performances du transistor MOS passe par la réduction de ses dimensions. Dans quelques années, la longueur de grille des dispositifs va descendre en dessous de 10 nm. A cette échelle, les effets quantiques deviennent prépondérants et dégradent considérablement les performances électriques des transistors à simple grille. Le transistor à nanofil avec grille enrobante est une architecture alternative intéressante pour augmenter le contrôle électrostatique du canal de conduction. Malgré les améliorations apportées par cette architecture, le courant à l’état bloqué reste perturbé par l’effet tunnel dans la direction source-drain. Afin de réduire ce courant sans réduire celui à l’état passant, nous avons étudié l’impact d’un rétrécissement local de la section transverse du canal coté drain (architecture notch-MOSFET). Pour cela, nous avons développé un simulateur 3D basé sur le formalisme des fonctions de Green hors équilibre couplé de façon auto-cohérente avec l’équation de Poisson. Ces calculs sont effectués dans l’approximation de la masse effective. Nous avons ensuite étudié le transport des trous dans les transistors à nanofil de type p, ainsi que l’influence d’une impureté ionisée dans le canal de ces dispositifs. La complexité de la bande de valence a nécessité la mise en œuvre d’un modèle k∙p à 6 bandes inclus dans le simulateur 3D évoqué précédemmentPerformances improvement of MOS transistors involves reduction of its dimensions. In a few years, the gate length of devices will reach sub-10 nm regime. At this scale, quantum effects become preponderant and considerably degrade electric performances of simple-gate transistors. The Gate-all-around nanowire transistor is an interesting alternative architecture to improve electrostatic control of the conduction channel. Despite the improvements made thanks to this architecture, the OFF-current remains disturbed by tunneling effect in source-drain direction. In order to decrease this current without decreasing the ON-current, we have studied the impact of local narrowing of transverse cross-section in drain side of the channel (notch-MOSFET architecture). To this purpose, we have developed a 3D simulator based on Non-equilibrium Green function formalism coupled self-consistently with Poisson equation. These simulations are performed in the effective mass approximation. Then we have studied holes transport in p-type nanowire transistors and the influence of an ionized impurity in the channel of these devices. The valence band complexity required six-band k∙p model development include into previously mentioned 3D simulator
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Mohammadzadeh, Saeideh. "Electronic Transport Properties of Copper and Gold at Atomic Scale." Doctoral thesis, Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-63427.
Full textAbstract:
The factors governing electronic transport properties of copper and gold atomic-size contacts are theoretically examined in the present work. A two-terminal conductor using crystalline electrodes is adopted. The non-equilibrium Green’s function combined with the density functional tight-binding method is employed via gDFTB simulation tool to calculate the transport at both equilibrium and non-equilibrium conditions. The crystalline orientation, length, and arrangement of electrodes have very weak influence on the electronic characteristics of the considered atomic wires. The wire width is found to be the most effective geometric aspect determining the number of conduction channels. The obtained conductance oscillation and linear current-voltage curves are interpreted. To analyze the conduction mechanism in detail, the transmission channels and their decomposition to the atomic orbitals are calculated in copper and gold single point contacts. The presented results offer a possible explanation for the relation between conduction and geometric structure. Furthermore, the results are in good agreement with available experimental and theoretical studiesIn der vorliegenden Arbeit werden die wesentlichen Faktoren, die die elektronischen Transporteigenschaften von Kontaktstrukturen atomarer Größe aus Kupfer bzw. Gold bestimmen, theoretisch untersucht. Untersuchungsgegenstand ist eine leitfähige Struktur zwischen zwei kristallinen Elektroden. Um Transportberechungen sowohl unter Gleichgewichts- als auch unter Nicht-Gleichgewichts-Bedingungen durchführen zu können, wird die Simulations-Software gDFTB, die auf dem Nicht-Gleichgewichts-Green-funktionenformalismus in Kombination mit der Dichtefunktional-Tight-Binding-Methode beruht, eingesetzt. Die elektronischen Eigenschaften der betrachteten atomaren Drähte werden nur sehr schwach von ihrer kristallinen Orientierung, ihrer Länge und der Elektrodenanordnung beeinflusst. Als effektivster geometrischer Faktor wurde der Leiterquerschnitt gefunden, weil dieser die Anzahl der Leitungskanäle bestimmt. Darüber hinaus werden die erhaltenen Leitfähigkeitsoszillationen und die linearen Strom-Spannungs-Kennlinien erklärt. Für eine detaillierte Analyse des Leitungsmechanismus werden bei den Ein-Atom-Kontakten aus Kupfer und Gold die Übertragungskanäle und ihre Aufspaltung in Atomorbitale betrachtet. Die präsentierten Ergebnisse bieten eine mögliche Erklärung für den Zusammenhang zwischen Leitfähigkeit und geometrischer Struktur. Die Resultate zeigen eine akzeptable Übereinstimmung mit den verfügbaren experimentellen und theoretischen Studien
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Zienert, Andreas. "Electronic Transport in Metallic Carbon Nanotubes with Metal Contacts." Doctoral thesis, Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-108205.
Full textAbstract:
The continuous migration to smaller feature sizes puts high demands on materials and technologies for future ultra-large-scale integrated circuits. Particularly, the copper-based interconnect system will reach fundamental limits soon. Their outstanding properties make metallic carbon nanotubes (CNTs) an ideal material to partially replace copper in future interconnect architectures. Here, a low contact resistance to existing metal lines is crucial. The present thesis contributes to the theory and numerical description of electronic transport in metallic CNTs with metal contacts. Different theoretical approaches are applied to various contact models and electrode materials (Al, Cu, Pd, Ag, Pt, Au) are compared. Ballistic transport calculations are based on the non-equilibrium Greens function formalism combined with tight-binding (TB), extended Hückel theory (EHT) and density functional theory (DFT). Simplified contact models allow a qualitative investigation of both the influence of geometry and CNT length, and the strength and extent of the contact on the transport properties. In addition, such simple contact models are used to compare the influence of different electronic structure methods on transport. It is found that the semiempirical TB and EHT are inadequate to quantitatively reproduce the DFT-based results. Based on this observation, an improved set of Hückel parameters is developed, which remedies this insufficiency. A systematic investigation of different contact materials is carried out using well defined atomistic metal-CNT-metal structures, optimized in a systematic way. Analytical models for the CNT-metal interaction are proposed. Based on that, electronic transport calculations are carried out, which can be extended to large systems by applying the computationally cheap improved EHT. The metal-CNT-metal systems can then be ranked by average conductance: Ag ≤ Au < Cu < Pt ≤ Pd < Al. This corresponds qualitatively with calculated contact distances, binding energies and work functions of CNTs and metals. To gain a deeper understanding of the transport properties, the electronic structure of the metal-CNT-metal systems and their respective parts is analyzed in detail. Here, the energy resolved local density of states is a valuable tool to investigate the CNT-metal interaction and its influences on the transportDie kontinuierliche Verkleinerung der Strukturgrößen stellt hohe Anforderungen an Materialen und Technologien zukünftiger hochintegrierter Schaltkreise. Insbesondere die Leistungsfähigkeit kupferbasierte Leitbahnsystem wird bald an fundamentale Grenzen stoßen. Aufgrund ihrer hervorragenden Eigenschaften könnten metallische Kohlenstoffnanoröhren (engl. Carbon Nanotubes, CNTs) Kupfer in zukünftigen Leitbahnsystemen teilweise ersetzen. Dabei ist ein geringer Kontaktwiderstand mit vorhandenen Leitbahnen von entscheidender Bedeutung. Die vorliegende Arbeit liefert grundlegende Beiträge zur Theorie und zur numerischen Beschreibung elektronischer Transporteigenschaften metallischer CNTs mit Metallkontakten. Dazu werden verschiedene theoretische Ansätze auf diverse Kontaktmodelle angewandt und eine Auswahl von Elektrodenmaterialen (Al, Cu, Pd, Ag, Pt, Au) verglichen. Die Beschreibung ballistischen Elektronentransports erfolgt mittels des Formalismus der Nichtgleichgewichts-Green-Funktionen in Kombination mit Tight-Binding (TB), erweiterter Hückel-Theorie (EHT) und Dichtefunktionaltheorie (DFT). Vereinfachte Kontaktmodelle dienen der qualitativen Untersuchung des Einflusses von Geometrie und Länge der Nanoröhren, sowie von Stärke und Ausdehnung des Kontaktes. Darüber hinaus erlauben solch einfache Modelle mit geringem numerischen Aufwand den Einfluss verschiedener Elektronenstrukturmethoden zu untersuchen. Es zeigt sich, dass die semiempirischen Methoden TB und EHT nicht in der Lage sind die Ergebnisse der DFT quantitativ zu reproduzieren. Ausgehend von diesen Ergebnissen wird ein verbesserter Satz von Hückel-Parametern generiert, der diesen Mangel behebt. Die Untersuchung verschiedener Kontaktmaterialien erfolgt an wohldefinierten atomistischen Metall-CNT-Metall-Strukturen, welche systematisch optimiert werden. Analytische Modelle zur Beschreibung der CNT-Metall-Wechselwirkung werden vorgeschlagen. Darauf aufbauende Berechnungen der elektronischen Transporteigenschaften, können mit Hilfe der verbesserten EHT auf große Systeme ausgedehnt werden. Die Ergebnisse ermöglichen eine Reihung der Metall-CNT-Metall-Systeme hinsichtlich ihrer Leitfähigkeit: Ag ≤ Au < Cu < Pt ≤ Pd < Al. Dies korrespondiert qualitativ mit berechneten Kontaktabständen, Bindungsenergien und Austrittarbeiten der CNTs und Metalle. Zum tieferen Verständnis der Transporteigenschaften erfolgt eine detaillierte Analyse der elektronischen Struktur der Metall-CNT-Metall-Systeme und ihrer Teilsysteme. Dabei erweist sich die energieaufgelöste lokale Zustandsdichte als nützliches Werkzeug zur Visulisierung und zur Charakterisierung der Wechselwirkung zwischen CNT und Metall sowie deren Einfluss auf den Transport
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Fuchs, Florian. "Feldeffekttransistoren auf Basis von Kohlenstoffnanoröhrchen: Vergleich zwischen atomistischer Simulation und Bauelementesimulation." Master's thesis, Universitätsbibliothek Chemnitz, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-157276.
Full textAbstract:
Kohlenstoffnanoröhrchen (CNTs) sind vielversprechende Kandidaten für neuartige nanoelektronische Bauelemente, wie zum Beispiel Transistoren für Hochfrequenzanwendungen. Simulationen CNT-basierter Bauelemente sind dabei unverzichtbar, um deren Anwendungspotential und das Verhalten in Schaltungen zu untersuchen. Die vorliegende Arbeit konzentriert sich auf einen Methodenvergleich zwischen einem atomistischen Ansatz basierend auf dem Nichtgleichgewichts-Green-Funktionen-Formalismus und einem Modell zur numerischen Bauelementesimulation, welches auf der Schrödinger-Gleichung in effektiver-Massen-Näherung basiert. Ein Transistor mit zylindrischem Gate und dotierten Kontakten wird untersucht, wobei eine effektive Dotierung genutzt wird.
Es wird gezeigt, dass die Beschränkungen des elektronischen Transports durch Quan-
teneffekte im Kanal nur mit dem atomistischen Ansatz beschrieben werden können. Diese Effekte verhindern das Auftreten von Band-zu-Band-Tunnelströmen, die bei der numerischen Bauelementesimulation zu größeren Aus-Strömen und einem leicht ambipolaren Verhalten führen. Das Schaltverhalten wird hingegen von beiden Modellen vergleichbar beschrieben. Durch Variation der Kanallänge wird das Potential des untersuchten Transistors für zukünftige Anwendungen demonstriert. Dieser zeigt bis hinab zu Kanallängen von circa 8 nm einen Subthreshold-Swing von unter 80 mV/dec und ein An/Aus-Verhältnis von über 10⁶.
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Gezahagne, Azamed Yehuala. "Qualitative Models of Neural Activity and the Carleman Embedding Technique." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1875.
Full textAbstract:
The two variable Fitzhugh Nagumo model behaves qualitatively like the four variable Hodgkin-Huxley space clamped system and is more mathematically tractable than the Hodgkin Huxley model, thus allowing the action potential and other properties of the Hodgkin Huxley system to be more readily be visualized. In this thesis, it is shown that the Carleman Embedding Technique can be applied to both the Fitzhugh Nagumo model and to Van der Pol's model of nonlinear oscillation, which are both finite nonlinear systems of differential equations. The Carleman technique can thus be used to obtain approximate solutions of the Fitzhugh Nagumo model and to study neural activity such as excitability.
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Tautenhahn, Martin, and Ivan Veselic'. "A note on correlated and non-monotone Anderson models." Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800063.
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Arhinful, Daniel Andoh. "Lorenzův systém: cesta od stability k chaosu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-417087.
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The theory of deterministic chaos has generated a lot of interest and continues to be one of the much-focused research areas in the field of dynamics today. This is due to its prevalence in essential parts of human lives such as electrical circuits, chemical reactions, the flow of blood through the human system, the weather, etc. This thesis presents a study of the Lorenz equations, a famous example of chaotic systems. In particular, it presents the analysis of the Lorenz equations from stability to chaos and various bifurcation scenarios with numerical and graphical interpretations. It studies concepts of non-linear dynamical systems such as equilibrium points, stability, linearization, bifurcation, Lyapunov function, etc. Finally, it discusses how the Lorenz equations serve as a model for the waterwheel (in detail), and the convection roll for fluid.
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Lee, Youseung. "Traitement quantique original des interactions inélastiques pour la modélisation atomistique du transport dans les nano-structures tri-dimensionnelles." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0345.
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Le formalisme des fonctions de Green hors-équilibre (NEGF pour « Non-equilibrium Green’s function) a suscité au cours des dernières décennies un engouement fort pour étudier les propriétés du transport quantique des nanostructures et des nano-dispositifs dans lesquels les interactions inélastiques, comme la diffusion des électrons-phonons, jouent un rôle significatif. L'incorporation d'interactions inélastiques dans le cadre du NEGF s’effectue généralement dans l'approximation auto-cohérente de Born (SCBA pour « Self-consistent Born approximation) qui représente une approche itérative plus exigeante en ressources numériques. Nous proposons dans ce travail de thèse une méthode efficace alternative dite LOA pour (« Lowest Order Approximation. Son principal avantage est de réduire considérablement le temps de calcul et de décrire physiquement la diffusion électron-phonon. Cette approche devrait considérablement étendre l'accessibilité de l'utilisation de codes atomistiques de transport quantique pour étudier des systèmes 3D réalistes sans faire à des ressources numériques importantesNon-equilibrium Green’s function (NEGF) formalism during recent decades has attracted numerous interests for studying quantum transport properties of nanostructures and nano-devices in which inelastic interactions like electron-phonon scattering have a significant impact. Incorporation of inelastic interactions in NEGF framework is usually performed within the self-consistent Born approximation (SCBA) which induces a numerically demanding iterative scheme. As an alternative technique, we propose an efficient method, the so-called Lowest Order Approximation (LOA) coupled with the Pade approximants. Its main advantage is to significantly reduce the computational time, and to describe the electron-phonon scattering physically. This approach should then considerably extend the accessibility of using atomistic quantum transport codes to study three-dimensional (3D) realistic systems without requiring numerous numerical resources
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Song, In Ho. "Essays on House Prices and Consumption." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306848116.
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BONENTI, FRANCESCA. "La matematica come occasione e stimolo per la formulazione di un giudizio critico." Doctoral thesis, Università degli studi di Bergamo, 2013. http://hdl.handle.net/10446/28639.
Full textAbstract:
The thesis develops an analysis of the scientific knowledge construction based on a psychological description of the mental procedures which in our mind help to construct the mathematical thought.
The analysis was carried on in the Part I of the thesis and was supported by a deep insight in the scientific research experience concerning mathematics. This research was the opportunity for the personal encounter with the mathematical discipline and gave also the possibility and ispiration to question the meaning of the mathematical thinking and the reliability of its cognitive procedures.
In Part II the results of psychological and cognitive experience of the scientific research, discussed in Part I, have been described in details.
The results of the scientific research, both in basic and applied fields of mathematics, has been described in different papers appeared in national and international journals and are collected in the thesis' appendix.
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Dednam, Wynand. "Atomistic simulations of competing influences on electron transport across metal nanocontacts." Thesis, Universidad de Alicante, 2019. http://hdl.handle.net/10500/26155.
Full textAbstract:
In our pursuit of ever smaller transistors, with greater computational throughput, many
questions arise about how material properties change with size, and how these properties
may be modelled more accurately. Metallic nanocontacts, especially those for which
magnetic properties are important, are of great interest due to their potential spintronic
applications. Yet, serious challenges remain from the standpoint of theoretical and
computational modelling, particularly with respect to the coupling of the spin and lattice
degrees of freedom in ferromagnetic nanocontacts in emerging spintronic technologies. In
this thesis, an extended method is developed, and applied for the first time, to model the
interplay between magnetism and atomic structure in transition metal nanocontacts. The
dynamic evolution of the model contacts emulates the experimental approaches used in
scanning tunnelling microscopy and mechanically controllable break junctions, and is
realised in this work by classical molecular dynamics and, for the first time, spin-lattice
dynamics. The electronic structure of the model contacts is calculated via plane-wave and
local-atomic orbital density functional theory, at the scalar- and vector-relativistic level of
sophistication. The effects of scalar-relativistic and/or spin-orbit coupling on a number of
emergent properties exhibited by transition metal nanocontacts, in experimental
measurements of conductance, are elucidated by non-equilibrium Green’s Function
quantum transport calculations. The impact of relativistic effects during contact formation
in non-magnetic gold is quantified, and it is found that scalar-relativistic effects enhance the force of attraction between gold atoms much more than between between atoms which
do not have significant relativistic effects, such as silver atoms. The role of non-collinear
magnetism in the electronic transport of iron and nickel nanocontacts is clarified, and it is
found that the most-likely conductance values reported for these metals, at first- and lastcontact,
are determined by geometrical factors, such as the degree of covalent bonding in
iron, and the preference of a certain crystallographic orientation in nickel.Physics
Ph. D. (Physics)
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Miloswzewski, Jacek. "Simulations of semiconductor laser using non-equilibrium Green's functions method." Thesis, 2012. http://hdl.handle.net/10012/6611.
Full textAbstract:
A novel method of simulating edge-emitting semiconductor lasers in a non-equilibrium steady-state is developed. The simulation is based on a non-equilibrium Green's function (NEGF) method. The Dyson equation (central equation of this method) is derived and written in a basis suitable for numerical implementation. The electron-photon self-energy is derived form scratch for the case of the edge-emitting laser. Other interactions present in the simulation are phenomenological scattering and scattering due to longitudinal optical phonons. This microscopic approach significantly reduce the number of phenomenological parameters needed to simulate laser. As an example, the theory is applied to analyze quantum well laser with the effective mass Hamiltonian. The major laser characteristics such as modal gain, threshold gain, carrier and current densities are determined.
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Yu-FengHsieh and 謝宇峰. "Quantum Transport Modeling for Nanoscale FET with Non-Equilibrium Green’s Function Formalism." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/es8b59.
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碩士國立成功大學
奈米積體電路工程碩士學位學程
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As complementary metal–oxide–semiconductor (CMOS) technology progresses, device dimensions have been scaled into the nanometer regime. The electronic devices would show more pronounced wave characteristics of carriers when operating. The non-equilibrium Green’s function (NEGF) approach, which is a powerful conceptual tool and a practical analysis method to treat nanoscale electronic devices with quantum mechanical. At the start of this thesis, we calculated the band structure based on the tight-binding theory. The calculations of band structure used to extract band gap, longitudinal and transverse effective electron masses. Then, we explore the impact of the parameter of confinement modulated on double-gate (DG) MOSFET, by explicitly incorporating the quantum confinement effects in the band structure calculations using the tight-binding theory. Using the nanoMOS 4.0 simulator, we calculate the drain current in DG MOSFET using the quantum ballistic transport model. At last, we choice the tunneling barrier junction (TBJ) MOSFET structure in order to suppress the short channel effects (SCE). To further enhance the TBJ MOSFET performance, we try to use single barrier structure. The single barrier at source structure which still have ability of SCE suppression, and have higher drive current than TBJ MOSFET.
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Sheng-HanWang and 王聲翰. "Machine Learning Assisted Non-Equilibrium Green’s Function Simulations of Double-Gate nMOSFET." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/tbtjqq.
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Steuber, Sarah Jane. "A study of the effect of surface bandwidth and other many-body effects in atom-surface collisions using a non-equilibrium Green's function technique." Thesis, 1995. http://hdl.handle.net/1911/13998.
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We are studying the charge transfer in atom-surface scattering using a recently developed many-body theory. The final population of the atom is studied as a function of the surface workfunction, which has a strong effect on the final population. The effects caused by degeneracy, surface bandwidth and velocity are investigated. The formation of the Kondo peak, strongly controls both the initial population and the rate of charge transfer, and consequently the final population. The results show a strong degeneracy and velocity dependence for both the positive and negative ion. For the negative ion we also find a significant bandwidth dependence.
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(5929571), James A. Charles. "Modeling Nonlocality in Quantum Systems." Thesis, 2020.
Find full textAbstract:
The widely accepted Non-equilibrium Greens functions (NEGF) method and the Self-Consistent Born Approximation, to include scattering, is employed. Due to the large matrix sizes typically needed when solving Greens functions, an efficient recursive algorithm is typically utilized. However, the current state of the art of this so-called recursive Greens function algorithm only allows the inclusion of local scattering or non-locality within a limited range. Most scattering mechanisms are Coulombic and are therefore non-local. Recently, we have developed an addition to the recursive Greens function algorithm that can handle arbitrary non-locality. Validation and performance will be assessed for nanowires.
The second half of this work discusses the modeling of an active ingredient in a liquid environment. The state of the art is outlined with options for different modeling approaches - mainly the implicit and the explicit solvation model. Extensions of the explicit model to include an open, quantum environment is the main work of the second half. First results for an extension of the commonly used molecular dynamics with thermodynamic integration are also presented.
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Saidaoui, Hamed Ben Mohamed. "Impact of Disorder on Spin Dependent Transport Phenomena." Diss., 2016. http://hdl.handle.net/10754/619953.
Full textAbstract:
The impact of the spin degree of freedom on the transport properties of electrons traveling through magnetic materials has been known since the pioneer work of Mott [1]. Since then it has been demonstrated that the spin angular momentum plays a key role in the scattering process of electrons in magnetic multilayers. This role has been emphasized by the discovery of the Giant Magnetoresistance in 1988 by Fert and Grunberg [2, 3]. Among the numerous applications and effects that emerged in mesoscopic devices two mechanisms have attracted our attention during the course of this thesis: the spin transfer torque and the spin Hall effects. The former consists in the transfer of the spin angular momentum from itinerant carriers to local magnetic moments [4]. This mechanism results in the current-driven magnetization switching and excitations, which has potential application in terms of magnetic data storage and non-volatile memories. The latter, spin Hall effect, is considered as well to be one of the most fascinating mechanisms in condensed matter physics due to its ability of generating non-equilibrium spin currents without the need for any magnetic materials. In fact the spin Hall effect relies only on the presence of the spin-orbit interaction in order to create an imbalance between the majority and minority spins.
The objective of this thesis is to investigate the impact of disorder on spin dependent transport phenomena. To do so, we identified three classes of systems on which such disorder may have a dramatic influence: (i) antiferromagnetic materials, (ii) impurity-driven spin-orbit coupled systems and (iii) two dimensional semiconducting electron gases with Rashba spin-orbit coupling.
Antiferromagnetic materials - We showed that in antiferromagnetic spin-valves, spin transfer torque is highly sensitive to disorder, which prevents its experimental observation. To solve this issue, we proposed to use either a tunnel barrier as a spacer or a local spin torque using spin-orbit coupling. In both cases, we demonstrated that the torque is much more robust against impurities, which opens appealing venues for its experimental observation.
Extrinsic spin-orbit coupled systems - In disordered metals accommodating spin orbit coupled impurities, it is well-known that spin Hall effect emerges due to spin dependent Mott scattering. Following a recent prediction, we showed that another effect coexists: the spin swapping effect, that converts an incoming spin current into another spin current by "swapping" the momentum and spin directions. We showed that this effect can generate peculiar spin torque in ultrathin magnetic bilayers.
Semiconductors spintronics - This last field of research has attracted a massive amount of hope in the past fifteen years, due to the ability of coherently manipulating the spin degree of freedom through interfacial, so-called Rashba, spin-orbit coupling. However, numerical simulations failed reproducing experimental results due to coherent interferences between the very large number of modes present in the system. We showed that spin-independent disorder can actually wash out these interferences and promote the conservation of the spin signal. In the course of this PhD, we showed that while disorder-induced dephasing is usually detrimental to the transmission of spin information, in selected situation, it can actually promote spin transport mechanisms and participate to the enhancement of the desired spintronics phenomenon.
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Nadimi, Ebrahim. "Quantum Mechanical and Atomic Level ab initio Calculation of Electron Transport through Ultrathin Gate Dielectrics of Metal-Oxide-Semiconductor Field Effect Transistors." Doctoral thesis, 2007. https://monarch.qucosa.de/id/qucosa%3A18893.
Full textAbstract:
The low dimensions of the state-of-the-art nanoscale transistors exhibit increasing
quantum mechanical effects, which are no longer negligible. Gate tunneling current is
one of such effects, that is responsible for high power consumption and high working
temperature in microprocessors. This in turn put limits on further down scaling of
devices. Therefore modeling and calculation of tunneling current is of a great interest.
This work provides a review of existing models for the calculation of the gate
tunneling current in MOSFETs. The quantum mechanical effects are studied with a
model, based on a self-consistent solution of the Schrödinger and Poisson equations
within the effective mass approximation. The calculation of the tunneling current is
focused on models based on the calculation of carrier’s lifetime on quasi-bound states
(QBSs). A new method for the determination of carrier’s lifetime is suggested and then
the tunneling current is calculated for different samples and compared to measurements.
The model is also applied to the extraction of the “tunneling effective mass” of electrons
in ultrathin oxynitride gate dielectrics.
Ultrathin gate dielectrics (tox<2 nm) consist of only few atomic layers. Therefore,
atomic scale deformations at interfaces and within the dielectric could have great
influences on the performance of the dielectric layer and consequently on the tunneling
current. On the other hand the specific material parameters would be changed due to
atomic level deformations at interfaces. A combination of DFT and NEGF formalisms
has been applied to the tunneling problem in the second part of this work. Such atomic
level ab initio models take atomic level distortions automatically into account. An atomic
scale model interface for the Si/SiO2 interface has been constructed and the tunneling
currents through Si/SiO2/Si stack structures are calculated. The influence of single and
double oxygen vacancies on the tunneling current is investigated. Atomic level
distortions caused by a tensile or compression strains on SiO2 layer as well as their
influence on the tunneling current are also investigated.Die vorliegende Arbeit beschäftigt sich mit der Berechnung von Tunnelströmen in MOSFETs (Metal-Oxide-Semiconductor Field Effect Transistors). Zu diesem Zweck wurde ein quantenmechanisches Modell, das auf der selbstkonsistenten Lösung der Schrödinger- und Poisson-Gleichungen basiert, entwickelt. Die Gleichungen sind im Rahmen der EMA gelöst worden. Die Lösung der Schrödinger-Gleichung unter offenen Randbedingungen führt zur Berechnung von Ladungsverteilung und Lebensdauer der Ladungsträger in den QBSs. Der Tunnelstrom wurde dann aus diesen Informationen ermittelt. Der Tunnelstrom wurde in verschiedenen Proben mit unterschiedlichen Oxynitrid Gatedielektrika berechnet und mit gemessenen Daten verglichen. Der Vergleich zeigte, dass die effektive Masse sich sowohl mit der Schichtdicke als auch mit dem Stickstoffgehalt ändert. Im zweiten Teil der vorliegenden Arbeit wurde ein atomistisches Modell zur Berechnung des Tunnelstroms verwendet, welche auf der DFT und NEGF basiert. Zuerst wurde ein atomistisches Modell für ein Si/SiO2-Schichtsystem konstruiert. Dann wurde der Tunnelstrom für verschiedene Si/SiO2/Si-Schichtsysteme berechnet. Das Modell ermöglicht die Untersuchung atom-skaliger Verzerrungen und ihren Einfluss auf den Tunnelstrom. Außerdem wurde der Einfluss einer einzelnen und zwei unterschiedlich positionierter neutraler Sauerstoffleerstellen auf den Tunnelstrom berechnet. Zug- und Druckspannungen auf SiO2 führen zur Deformationen in den chemischen Bindungen und ändern den Tunnelstrom. Auch solche Einflüsse sind anhand des atomistischen Modells berechnet worden.
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Virk, Kuljit. "Decoherence in Optically Excited Semiconductors: a Perspective from Non-equilibrium Green Functions." Thesis, 2010. http://hdl.handle.net/1807/24385.
Full textAbstract:
Decoherence is central to our understanding of the transition from the quantum to the classical world. It is also a way of probing the dynamics of interacting many-body systems. Photoexcited semiconductors are such systems in which the transient dynamics can be studied in considerable detail experimentally. Recent advances in spectroscopy of semiconductors provide powerful tools to explore many-body physics in new regimes. An appropriate theoretical framework is necessary to describe new physical effects now accessible for observation. We present a possible approach in this thesis, and discuss results of its application to an experimentally relevant scenario.
The major portion of this thesis is devoted to a formalism for the multi-dimensional Fourier spectroscopy of semiconductors. A perturbative treatment of the electromagnetic field is used to derive a closed set of differential equations for the multi-particle correlation functions, which take into account the many-body effects up to third order in the field. A diagrammatic method is developed, in which we retain all features of the double-sided Feynman diagrams for bookkeeping the excitation scenario, and complement them by allowing for the description of interactions.
We apply the formalism to study decoherence between the states of optically excited excitons embedded in an electron gas, and compare it with the decoherence between these states and the ground state. We derive a dynamical equation for the two-time correlation functions of excitons, and compare it with the corresponding equation for the interband polarization. It is argued, and verified by numerical calculation, that the decay of Raman coherence depends sensitively on how differently the superimposed exciton states interact with the electron gas, and that it can be much slower than the decay of interband polarization.
We also present a new numerical approach based on the length gauge for modeling the time-dependent laser-semiconductor interaction. The interaction in the length gauge involves the position operator for electrons, as opposed to the momentum operator in the velocity gauge. The approach is free of the unphysical divergences that arise in the velocity gauge. It is invariant under local gauge symmetry of the Bloch functions, and can handle arbitrary electronic structure and temporal dependence of the fields.
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Kim, Moochan. "Problems on Non-Equilibrium Statistical Physics." Thesis, 2010. http://hdl.handle.net/1969.1/ETD-TAMU-2010-05-8007.
Full textAbstract:
Four problems in non-equilibrium statistical physics are investigated: 1. The
thermodynamics of single-photon gas; 2. Energy of the ground state in Multi-electron
atoms; 3. Energy state of the H2 molecule; and 4. The Condensation behavior in N
weakly interacting Boson gas.
In the single-photon heat engine, we have derived the equation of state similar
to that in classical ideal gas and applied it to construct the Carnot cycle with a single
photon, and showed the Carnot efficiency in this single-photon heat engine.
The energies of the ground state of multi-electron atoms are calculated using the
modi ed Bohr model with a shell structure of the bound electrons. The di erential
Schrodinger equation is simpli ed into the minimization problem of a simple energy
functional, similar to the problem in dimensional scaling in the H-atom. For the
C-atom, we got the ground state energy -37:82 eV with a relative error less than 6
%.
The simplest molecular ion, H+
2 , has been investigated by the quasi-classical
method and two-center molecular orbit. Using the two-center molecular orbit derived
from the exact treatment of the H+
2 molecular ion problem, we can reduce the number
of terms in wavefunction to get the binding energy of the H2 molecule, without using
the conventional wavefunction with over-thousand terms. We get the binding energy
for the H2 with Hylleraas correlation factor 1 + kr12 as 4:7eV, which is comparable
to the experimental value of 4:74 eV.
Condensation in the ground state of a weakly interacting Bose gas in equilibrium
is investigated using a partial partition function in canonical ensemble. The recursive
relation for the partition function developed for an ideal gas has been modi ed to
be applicable in the interacting case, and the statistics of the occupation number in
condensate states was examined. The well-known behavior of the Bose-Einstein Condensate
for a weakly interacting Bose Gas are shown: Depletion of the condensate
state, even at zero temperature, and a maximum
uctuation near transition temperature.
Furthermore, the use of the partition function in canonical ensemble leads to
the smooth cross-over between low temperatures and higher temperatures, which has
enlarged the applicable range of the Bogoliubov transformation. During the calculation,
we also developed the formula to calculate the correlations among the excited
states.
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Alharbi, Abdulrahman. "On the Lp-Integrability of Green’s function for Elliptic Operators." Thesis, 2019. http://hdl.handle.net/10754/655516.
Full textAbstract:
In this thesis, we discuss some of the results that were proven by Fabes and Stroock in 1984. Our main purpose is to give a self-contained presentation of the proof of this results. The first result is on the existence of a “reverse H ̈older inequality” for the Green’s function. We utilize the work of Muckenhoupt on the reverse Ho ̈lder inequality and its connection to the A∞ class to establish a comparability property for the Green’s functions. Additionally, we discuss some of the underlying preliminaries. In that, we prove the Alexandrov-Bakelman-Pucci estimate, give a treatment to the Ap and A∞ classes of Muckenhoupt, and establish two intrinsic lemmas on the behavior of Green’s function.
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Paeckel, Sebastian. "Topological and non-equilibrium superconductivity in low-dimensional strongly correlated quantum systems." Doctoral thesis, 2020. http://hdl.handle.net/21.11130/00-1735-0000-0005-1395-D.
Full text
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Melesse, Dessalegn Yizengaw. "Mathematical Analysis of an SEIRS Model with Multiple Latent and Infectious Stages in Periodic and Non-periodic Environments." 2010. http://hdl.handle.net/1993/4086.
Full textAbstract:
The thesis focuses on the qualitative analysis of a general class of SEIRS models in periodic and non-periodic environments. The classical SEIRS model, with standard incidence function, is, first of all, extended to incorporate multiple infectious stages. Using Lyapunov function theory and LaSalle's Invariance Principle, the disease-free equilibrium (DFE) of the resulting SEInRS model is shown to be globally-asymptotically stable whenever the associated reproduction number is less than unity. Furthermore, this model has a unique endemic equilibrium point (EEP), which is shown (using a non-linear Lyapunov function of Goh-Volterra type) to be globally-asymptotically stable for a special case. The SEInRS model is further extended to incorporate arbitrary number of latent stages. A notable feature of the resulting SEmInRS model is that it uses gamma distribution assumptions for the average waiting times in the latent (m) and infectious (n) stages. Like in the case of the SEInRS model, the SEmInRS model also has a globally-asymptotically stable DFE when its associated reproduction threshold is less than unity, and it has a unique EEP (which is globally-stable for a special case) when the threshold exceeds unity. The SEmInRS model is further extended to incorporate the effect of periodicity on the disease transmission dynamics. The resulting non-autonomous SEmInRS model is shown to have a globally-stable disease-free solution when the associated reproduction ratio is less than unity. Furthermore, the non-autonomous model has at least one positive (non-trivial) periodic solution when the reproduction ratio exceeds unity. It is shown (using persistence theory) that, for the non-autonomous model, the disease will always persist in the population whenever the reproduction ratio is greater than unity. One of the main mathematical contributions of this thesis is that it shows that adding multiple latent and infectious stages, gamma distribution assumptions (for the average waiting times in these stages) and periodicity to the classical SEIRS model (with standard incidence) does not alter the main qualitative dynamics (pertaining to the persistence or elimination of the disease from the population) of the SEIRS model.
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Zienert, Andreas. "Electronic Transport in Metallic Carbon Nanotubes with Metal Contacts." Doctoral thesis, 2012. https://monarch.qucosa.de/id/qucosa%3A19863.
Full textAbstract:
The continuous migration to smaller feature sizes puts high demands on materials and technologies for future ultra-large-scale integrated circuits. Particularly, the copper-based interconnect system will reach fundamental limits soon. Their outstanding properties make metallic carbon nanotubes (CNTs) an ideal material to partially replace copper in future interconnect architectures. Here, a low contact resistance to existing metal lines is crucial. The present thesis contributes to the theory and numerical description of electronic transport in metallic CNTs with metal contacts. Different theoretical approaches are applied to various contact models and electrode materials (Al, Cu, Pd, Ag, Pt, Au) are compared. Ballistic transport calculations are based on the non-equilibrium Greens function formalism combined with tight-binding (TB), extended Hückel theory (EHT) and density functional theory (DFT). Simplified contact models allow a qualitative investigation of both the influence of geometry and CNT length, and the strength and extent of the contact on the transport properties. In addition, such simple contact models are used to compare the influence of different electronic structure methods on transport. It is found that the semiempirical TB and EHT are inadequate to quantitatively reproduce the DFT-based results. Based on this observation, an improved set of Hückel parameters is developed, which remedies this insufficiency. A systematic investigation of different contact materials is carried out using well defined atomistic metal-CNT-metal structures, optimized in a systematic way. Analytical models for the CNT-metal interaction are proposed. Based on that, electronic transport calculations are carried out, which can be extended to large systems by applying the computationally cheap improved EHT. The metal-CNT-metal systems can then be ranked by average conductance: Ag ≤ Au < Cu < Pt ≤ Pd < Al. This corresponds qualitatively with calculated contact distances, binding energies and work functions of CNTs and metals. To gain a deeper understanding of the transport properties, the electronic structure of the metal-CNT-metal systems and their respective parts is analyzed in detail. Here, the energy resolved local density of states is a valuable tool to investigate the CNT-metal interaction and its influences on the transport.Die kontinuierliche Verkleinerung der Strukturgrößen stellt hohe Anforderungen an Materialen und Technologien zukünftiger hochintegrierter Schaltkreise. Insbesondere die Leistungsfähigkeit kupferbasierte Leitbahnsystem wird bald an fundamentale Grenzen stoßen. Aufgrund ihrer hervorragenden Eigenschaften könnten metallische Kohlenstoffnanoröhren (engl. Carbon Nanotubes, CNTs) Kupfer in zukünftigen Leitbahnsystemen teilweise ersetzen. Dabei ist ein geringer Kontaktwiderstand mit vorhandenen Leitbahnen von entscheidender Bedeutung. Die vorliegende Arbeit liefert grundlegende Beiträge zur Theorie und zur numerischen Beschreibung elektronischer Transporteigenschaften metallischer CNTs mit Metallkontakten. Dazu werden verschiedene theoretische Ansätze auf diverse Kontaktmodelle angewandt und eine Auswahl von Elektrodenmaterialen (Al, Cu, Pd, Ag, Pt, Au) verglichen. Die Beschreibung ballistischen Elektronentransports erfolgt mittels des Formalismus der Nichtgleichgewichts-Green-Funktionen in Kombination mit Tight-Binding (TB), erweiterter Hückel-Theorie (EHT) und Dichtefunktionaltheorie (DFT). Vereinfachte Kontaktmodelle dienen der qualitativen Untersuchung des Einflusses von Geometrie und Länge der Nanoröhren, sowie von Stärke und Ausdehnung des Kontaktes. Darüber hinaus erlauben solch einfache Modelle mit geringem numerischen Aufwand den Einfluss verschiedener Elektronenstrukturmethoden zu untersuchen. Es zeigt sich, dass die semiempirischen Methoden TB und EHT nicht in der Lage sind die Ergebnisse der DFT quantitativ zu reproduzieren. Ausgehend von diesen Ergebnissen wird ein verbesserter Satz von Hückel-Parametern generiert, der diesen Mangel behebt. Die Untersuchung verschiedener Kontaktmaterialien erfolgt an wohldefinierten atomistischen Metall-CNT-Metall-Strukturen, welche systematisch optimiert werden. Analytische Modelle zur Beschreibung der CNT-Metall-Wechselwirkung werden vorgeschlagen. Darauf aufbauende Berechnungen der elektronischen Transporteigenschaften, können mit Hilfe der verbesserten EHT auf große Systeme ausgedehnt werden. Die Ergebnisse ermöglichen eine Reihung der Metall-CNT-Metall-Systeme hinsichtlich ihrer Leitfähigkeit: Ag ≤ Au < Cu < Pt ≤ Pd < Al. Dies korrespondiert qualitativ mit berechneten Kontaktabständen, Bindungsenergien und Austrittarbeiten der CNTs und Metalle. Zum tieferen Verständnis der Transporteigenschaften erfolgt eine detaillierte Analyse der elektronischen Struktur der Metall-CNT-Metall-Systeme und ihrer Teilsysteme. Dabei erweist sich die energieaufgelöste lokale Zustandsdichte als nützliches Werkzeug zur Visulisierung und zur Charakterisierung der Wechselwirkung zwischen CNT und Metall sowie deren Einfluss auf den Transport.
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Petersen, Charlotte Frances. "An Investigation Into the Significance of Dissipation in Statistical Mechanics." Phd thesis, 2016. http://hdl.handle.net/1885/110514.
Full textAbstract:
The dissipation function is a key quantity in nonequilibrium
statistical mechanics. It was originally derived for use in the
Evans-Searles Fluctuation Theorem, which quantitatively describes
thermal fluctuations in nonequilibrium systems. It is now the
subject of a number of other exact results, including the
Dissipation Theorem, describing the evolution of a system in
time, and the Relaxation Theorem, proving the ubiquitous
phenomena of relaxation to equilibrium. The aim of this work is
to study the significance of the dissipation function, and
examine a number of exact results for which it is the argument.
First, we investigate a simple system relaxing towards
equilibrium, and use this as a medium to investigate the role of
the dissipation function in relaxation. The initial system has a
non-uniform density distribution. We demonstrate some of the
existing significant exact results in nonequilibrium statistical
mechanics. By modifying the initial conditions of our system we
are able to observe both monotonic and non-monotonic relaxation
towards equilibrium.
A direct result of the Evans-Searles Fluctuation Theorem is the
Nonequilibrium Partition Identity (NPI), an ensemble average
involving the dissipation function. While the derivation is
straightforward, calculation of this quantity is anything but.
The statistics of the average are difficult to work with because
its value is extremely dependent on rare events. It is often
observed to converge with high accuracy to a value less than
expected. We investigate the mechanism for this asymmetric bias
and provide alternatives to calculating the full ensemble average
that display better statistics. While the NPI is derived exactly
for transient systems it is expected that it will hold in steady
state systems as well. We show that this is not true, regardless
of the statistics of the calculation.
A new exact result involving the dissipation function, the
Instantaneous Fluctuation Theorem, is derived and demonstrated
computationally. This new theorem has the same form as previous
fluctuation theorems, but provides information about the
instantaneous value of phase functions, rather than path
integrals. We extend this work by deriving an approximate form of
the theorem for steady state systems, and examine the validity of
the assumptions used.