Quantum-mechanical effects play a major role in the performance of modern electronic devices. In order to predict the behavior of novel devices, quantum effects are often included using Non-Equilibrium Green's Function (NEGF) methods in atomistic device representations. These quantum effects may include realistic inelastic scattering caused by device impurities and phonons. With the inclusion of realistic physical phenomena, the computational load of predictive simulations increases greatly, and a manageable basis through low-rank approximations is desired.<br><br>In this work, low-rank approximations are used to reduce the computational load of atomistic simulations. The benefits of basis reductions on simulation time and peak memory are assessed.<br>The low-rank approximation method is then extended to include more realistic physical effects than those modeled today, including exact calculations of scattering phenomena. The inclusion of these exact calculations are then contrasted to current methods and approximations.

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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 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.

The work discusses the development of molecular electronics based on the possibility of the usage of anorganic quantum dots and organic molecules as basis material. Of special interest are the properties of semiconductor quantum dots and their modification due to the coupling of quantum dots from different materials. Eventually these are proper candidates to avoid the fast recombination of excitons which is a problem in many organic photovoltaic materials, by local separation of charge carriers. Another materials class investigated are the so called charge transfer dimers. On the way to usable molecular building blocks switching and rectification behavior are important properties, therefore they were of special interest in the investigation. Especially the usage of charge transfer materials in rectification was already suggested in the 70’s, but could be realized till now only with a quiet limited success. Already around the millennium it was shown that a too strong coupling between the components leads to a resymmetrization of the I-V-characteristics. For all systems the electronic structure was investigated by means of density functional theory. Additional the charge transport in between gold leads was computed based on non equilibrium Greens functions. For the system of coupled quantum dots it is shown how the combination of several gates can be used to adjust the transport properties. This work shows that the rectification effect within weakly coupled charge transfer systems stays also small because also in this case a resymmetrization of the I-V-characteristics takes place.:1 Introduction 2 Molecular Electronics 3 Theoretical background 4 Computational details and software packages 5 Modeling 6 Results and Discussion 6.1 Quantum dots 6.2 Transport through coupled quantum dots 6.3 Charge transfer dimers 6.4 Transport through charge transfer dimers 7 Conclusion 8 Outlook Acknowledgement List of Figures List of Tables Bibliography List of own Publications / Die Arbeit befasst sich mit der Entwicklung der molekularen Elektronik und insbesondere mit der Prüfung der Verwendbarkeit von anorganischen Quantenpunkten und organischen Molekülen für diesen Bereich. Quantenpunkte aus Halbleitermaterialien besitzen eine grosse Bandbreite von Eigenschaften. Es wird untersucht, wie die Eigenschaften durch die Kopplung von Quantenpunkten unterschiedlicher Materialien modifiziert werden können. Eine Idee besteht in der lokalen Trennung von Ladungsträgern um die schnelle Rekombination von Exzitonen zu vermeiden, welche in organischen Solarzellen häufig ein Problem darstellt. Als weitere Materialklasse werden molekulare Ladungstransferdimere untersucht. Auf dem Weg zu nutzbaren Bauelementen sind das Schalt- und Gleichrichtverhalten wichtige Eigenschaften, daher sind sie von besonderem Interesse. Insbesondere die Frage des Ladungstransfers in Bezug auf das Gleichrichten wurde schon in den 1970ern vorgeschlagen, konnte aber bisher immer nur mit begrenztem Erfolg realisiert werden. Schon um die Jahrtausendwende wurde gezeigt, dass Systeme mit einer zu starken Kopplung zu einer Symmetrisierung der Strom-Spannungs-Kennlinie führen. Bei beiden Systemen wird jeweils die elektronische Struktur im Sinne der Dichtefunktionaltheorie berechnet. Zusätzlich wird jeweils der Ladungstransport zwischen Goldkontakten mittels Nichtgleichgewichts-Greenschen Funktionen berechnet. Für die Systeme gekoppelter Quantenpunkte wird gezeigt, wie die Transporteigenschaften mittels Gatespannungen eingestellt werden können. In der vorliegenden Arbeit wird gezeigt, dass es auch im Fall schwach gekoppelter Ladungstransferdimere zu weitgehend symmetrischen Strom-Spannungs-Kennlinien kommt und es auch für diese Systeme nur zu einem schwachen Gleichrichtverhalten kommt.:1 Introduction 2 Molecular Electronics 3 Theoretical background 4 Computational details and software packages 5 Modeling 6 Results and Discussion 6.1 Quantum dots 6.2 Transport through coupled quantum dots 6.3 Charge transfer dimers 6.4 Transport through charge transfer dimers 7 Conclusion 8 Outlook Acknowledgement List of Figures List of Tables Bibliography List of own Publications

This dissertation undertakes theoretical and computational research to characterize and understand in detail atomic configurations and electronic structural properties of surfaces and interfaces at the nano-scale, with particular emphasis on identifying the factors that control atomic-scale diffusion and transport properties. The overarching goal is to outline, with examples, a predictive modeling procedure of stable structures of novel materials that, on the one hand, facilitates a better understanding of experimental results, and on the other hand, provide guidelines for future experimental work. The results of this dissertation are useful in future miniaturization of electronic devices, predicting and engineering functional novel nanostructures. A variety of theoretical and computational tools with different degrees of accuracy is used to study problems in different time and length scales. Interactions between the atoms are derived using both ab-initio methods based on Density Functional Theory (DFT), as well as semiempirical approaches such as those embodied in the Embedded Atom Method (EAM), depending on the scale of the problem at hand. The energetics for a variety of surface phenomena (adsorption, desorption, diffusion, and reactions) are calculated using either DFT or EAM, as feasible. For simulating dynamic processes such as diffusion of adatoms on surfaces with dislocations the Molecular Dynamics (MD) method is applied. To calculate vibrational mode frequencies, the infinitesimal displacement method is employed. The combination of non-equilibrium Green’s function (NEGF) and DFT is used to calculate electronic transport properties of molecular devices as well as interfaces and junctions.

Spectroscopy and quantum transport constitute powerful ways to study the physics of matter and to access the electronic and atomic structure. Excitations, in turn determined by the electronic and atomic structure, lie at the origin of spectroscopy and quantum transport. Ab initio calculation of excited states requires to go beyond ground-state density-functional theory (DFT). In this work we review three theoretical frameworks beyond DFT: the first is time-dependent density-functional theory to describe neutral excitations and to address energy-loss and optical spectroscopies. We introduce the theory and the fundamental approximations, i.e. the RPA and the adiabatic LDA, together with the results one can get with them at the example of bulk silicon and graphite. We then describe the developments we contributed to the theory beyond TDLDA to better describe optical spectroscopy, in particular the long-range contribution-only and the Nanoquanta exchange-correlation kernel approximations. The second framework is many-body quantum field theory (or Green's function theory) in the GW approximation and beyond, well suited to describe photoemission spectroscopy. After a review of the theory and its main success on the prediction of the band gap, we present two applications on unconventional systems: 2D graphene and strongly correlated vanadium dioxide. We discuss the next frontiers of GW, closing with perspectives beyond GW and MBQFT. The last part presents non-equilibrium Green's function theory suited to address quantum transport. We show how it reduces to the state-of-the-art Landauer principal layers framework when neglecting correlations. We present a calculation of the conductance on a very simple system, a gold monoatomic chain, showing the effect of electron-electron scattering effects. Finally we present theoretical developments toward a new workbench beyond the principal layers, which led us to the introduction of new generalized Meir and Wingreen and Fisher-Lee formulas. This work compares the theoretical and practical aspects of both Green's function and density based approaches, each one benefiting insights from the other, and presents an overview of accomplishments and perspectives.

<div> Challenges in the semiconductor industry have resulted in the discovery of a plethora of promising materials and devices such as the III-Vs (InGaAs, GaSb, GaN/InGaN) and 2D materials (Transition-metal dichalcogenides [TMDs]) with wide-ranging applications from logic devices, optoelectronics to biomedical devices. Performance of these devices suffer significantly from scattering processes such as polar-optical phonons (POP), charged impurities and remote phonon scattering. These scattering mechanisms are long-ranged, and a quantitative description of such devices require non-local scattering calculations that are computationally expensive. Though there have been extensive studies on coherent transport in these materials, simulations are scarce with scattering and virtually non-existent with non-local scattering. </div><div> </div><div>In this work, these scattering mechanisms with full non-locality are treated rigorously within the Non-Equilibrium Green's function (NEGF) formalism. Impact of non-locality on charge transport is assessed for GaSb/InAs nanowire TFETs highlighting the underestimation of scattering with local approximations. Phonon, impurity scattering, and structural disorders lead to exponentially decaying density of states known as Urbach tails/band tails. Impact of such scattering mechanisms on the band tail is studied in detail for several bulk and confined III-V devices (GaAs, InAs, GaSb and GaN) showing good agreement with existing experimental data. A systematic study of the dependence of Urbach tails with dielectric environment (oxides, charged impurities) is performed for single and multilayered 2D TMDs (MoS2, WS2 and WSe2) providing guideline values for researchers. </div><div><br></div><div>Often, empirical local approximations (ELA) are used in the literature to capture these non-local scattering processes. A comparison against ELA highlight the need for non-local scattering. A physics-based local approximation model is developed that captures the essential physics and is computationally feasible.</div>

<div>The work involves two new method implementation and application in the Quantum transport community for nano-scale electronic devices. </div><div><br></div><div>First method: Ab-initio Tight-Binding(TB)</div><div> </div><div>As the surfacing of novel 2D materials, layers can be stacked freely on top of each other bound by Van der Waals force with atomic precision. New devices created with unique characteristics will need the theoretical guidance. The empirical tight-binding method is known to have difficulty accurately representing Hamiltonian of the 2D materials. Maximally localized Wannier function(MLWF) constructed directly from ab-initio calculation is an efficient and accurate method for basis construction. Together with NEGF, device calculation can be conducted. The implementation of MLWF in NEMO5 and the application on 2D MOS structure to demystify interlayer coupling are addressed. </div><div> </div><div>Second method: Büttiker-probe Recombination/Generation(RG) method:</div><div><br></div><div>The non-equilibrium Green function (NEGF) method is capable of nanodevice performance predictions including coherent and incoherent effects. To treat incoherent scattering, carrier generation and recombination is computationally very expensive. In this work, the numerically efficient Büttiker-probe model is expanded to cover recombination and generation effects in addition to various incoherent scattering processes. The capability of the new method to predict nanodevices is exemplified with quantum well III-N light-emitting diodes and photo-detector. Comparison is made with the state of art drift-diffusion method. Agreements are found to justify the method and disagreements are identified attributing to quantum effects. </div><div><br></div><div>The two menthod are individually developed and utilized together to study BP/MoS2 interface. In this vertical 2D device, anti-ambipolar(AAP) IV curve has been identified experimentally with different explanation in the current literature. An atomistic simulation is performed with basis generated from density functional theory. Recombination process is included and is able to explain the experiment findings and to provide insights into 2D interface devices.</div><div><br></div><div> </div>

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.