<div>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.</div><div><br></div><div>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.</div>

The spin filter capability of a (0,8) armchair graphene nanoribbon with Fe atoms at substitutional sites is investigated by density functional theory in combination with the non-equilibrium Green's function technique. For specific arrangements, a high degree of spin polarisation is achieved. These include a single substitution at an edge position or double substitution in the central sector of the transmission element. The possibility of switching between majority and minority spin polarisation by changing the double substitution geometry is predicted. Including the bias dependence of the transmission function proves to be essential for correct representation of the spin-resolved current-voltage profiles.

The spin-dependent transmission properties of (0,8) graphene nanoribbons (GNRs) with two substitutional Fe atom impurities (2Fe-aGNRs) have been studied by the non-equilibrium Green's function (NEGF) method in conjunction with density functional theory (DFT). Emphasis is placed on the spin-filtering activity of current transmission elements derived from these structures. In particular, it is shown that devices based on 2Fe-aGNR approach the limit of half-metallicity, where the magnitude and the sign of the current spin polarization is controlled by the bias across the device as well as the spin state of the 2Fe subsystem. This effect is rationalized by electronic structure and partial-density-of-states (PDOS) analysis of the transmission element. An occupied spin minority state, induced by the Fe-atom moiety and close to the Fermi energy of 2Fe-aGNR, accounts for the predominance of minority spin polarization. Comparison with nanosystems obtained from 2Fe-aGNR, involving vacancies rather than impurities, or both types of defects, reveals that substantial degrees of current spin polarization prevail across a wide variety of device types.

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.

Diese Arbeit beschäftigt sich mit der „First-Principles“ atomskaligen Modellierung der HfO2-basierten high-k-Gate-Isolatorschichten der Metalloxid-Halbleiter-Feldeffekttransistoren. Die theoretischen Untersuchungen basieren auf Dichtefunktionaltheorie und Nichtgleichgewicht-Greensche-Funktion-Formalismen. Eine der wichtigsten Eigenschaften eines Gate-Isolators ist der Wert seiner Bandlücke. Die Bandlücke eines gemischten Festkörpers aus SiO2 und ZrO2 oder HfO2 wird auf der Grundlage der „Generalized Quasi-Chemical“ Approximation in Kombination mit dem „Cluster Expansion“ Ansatz berechnet. Zu diesem Zweck wurde Dichtefunktionaltheorie für die Berechnung der Eigenschaften verschiedener Konfigurationen möglicher Elementarzellen durchgeführt. Es wurde ein fast linearer Verlauf für die Bandlücke eines aus SiO2 und HfO2 gemischten Festkörpers berechnet. Im Vergleich zu dem üblichen SiO2 Gate-Isolator, haben die high-k-Gate-Isolatoren eine höhere Defektdichte, die hauptsächlich aus Sauerstoffleerstellen bestehen. Dies führt zu mehreren Problemen, wie zum Beispiel höherer Leckstrom, Schwellenspannungsverschiebung und Degradation des Gateoxids. Daher wurde eine umfassende Untersuchung der verschiedenen Eigenschaften von Sauerstofffehlstellen in HfO2 durchgeführt, indem wichtige Parameter wie zum Beispiel die Formationsenergien und die Lage der Defektniveaus in der Bandlücke berechnet wurden. Es wurde durch die theoretischen Berechnungen gezeigt, dass die schädlichen Auswirkungen von Sauerstofffehlstellen durch die Einführung von Lanthan-Atomen in dem HfO2 Kristallgitter teilweise zu verringern sind. Energetisch gesehen bevorzugen die Lanthan-Atome die Hf-Gitterplätze in der Nachbarschaft einer Sauerstofffehlstelle und führen dadurch zu der Passivierung durch Sauerstoffleerstelle induzierten Defektniveaus. Die high-k-Isolatorschicht in den heutigen Transistoren besteht aus drei Schichten: einem Metallgate, einer HfO2-Schicht als Haupt-Gate-Isolator und einer sehr dünnen SiO2 Übergangsschicht zwischen Gateoxid und Si. Die Einführung eines Metallgates führt zu einigen Problemen bei der Einstellung einer geeigneten Schwellenspannung in den Transistoren. Theoretische Berechnungen in einer komplexen Modellstruktur von der Si/SiO2/HfO2-Grenzfläche zeigen, dass die dotierten Lanthan-Atome energetisch die SiO2/HfO2-Grenzfläche bevorzugen, was wiederum ein Dipolmoment an der Grenzfläche erzeugt. Dieses Dipolmoment kann verwendet werden, um die richtige Schwellenspannung wieder einzustellen. Schließlich wird in den experimentellen Messungen festgestelltes progressives Degradationsverhalten von high-k-Gate-Isolatoren mit einem theoretischen Modell erklärt. Dieses Modell basiert auf ab-initio-Berechnungen und zeigt, wie die Erzeugung geladener Sauerstoffleerstellen und deren Migration unter der angelegten Gatespannung zu einer progressiven Erhöhung des Leckstroms und folglich zu einer Degradation der Isolatorschicht führt.:List of Figures 7 List of Tables 9 List of Symbols 10 List of Abbreviations 11 Chapter 1: Introduction 12 Chapter 2: Theory of Atomic-Scale First-Principles Calculations 15 2.1 Theoretical methods 15 2.2 Density functional theory 17 2.3 Non-equilibrium Green’s function formalism 23 Chapter 3: Calculations for Bulk High-k Materials 27 3.1 Bulk high-k materials 27 3.2 Crystalline insulators 27 3.3 Solid solutions 29 3.3.1 Cluster expansion approach 30 3.3.2 Band gap and bowing parameter 33 3.3.3 Calculation of internal stress 40 3.4 Leakage current 41 Chapter 4: Defects in Bulk High-k Materials 43 4.1 Defects in high-k gate dielectrics 43 4.2 Oxygen vacancies in monoclinic HfO2 44 4.2.1 Neutral oxygen vacancies 44 4.2.2 Charged oxygen vacancies 46 4.3 Hybrid functional 50 4.4 Double oxygen vacancies 56 4.5 Interaction of oxygen vacancies with La-doping 61 4.5.1 La doping in m-HfO2 61 4.5.2 Complex LaHfVO defects 64 Chapter 5: Interface Properties of High-k Gate Stack 72 5.1 high-k gate-stack 72 5.1.1 Atomic-scale model structure for a high-k gate-stack 72 5.1.2 Electronic structure 74 5.1.3 Leakage current 76 5.2 Band offset 80 5.3 Threshold voltage engineering with La doping 84 Chapter 6: Degradation of the High-k Gate Stack 90 6.1 Reliability issues in high-k gate-stack 90 6.2 Calculations and experimental methods 91 6.3 Leakage current 92 6.4 Defect generation 100 6.5 Explaining progressive SILC in high-k dielectrics 102 Chapter 7: Conclusions 104 Bibliography 106 Selbständigkeitserklärung 119 Danksagung 120 Lebenslauf 121 Veröffentlichungen 122 / This thesis deals with the first-principles atomic-scale modeling of the HfO2-based high-k gate-insulator layer of the metal-oxide-semiconductor field-effect transistors. The theoretical investigations are based on density functional theory and non-equilibrium Green's function formalisms. One of the important properties of the gate insulator is the value of its band gap. The band gap of amorphous solid mixtures of SiO2 and ZrO2 or HfO2 is calculated based on generalized quasi-chemical approximation combined with a cluster expansion approach, by performing density functional calculations on different configurations of possible unit cells. An almost linear variation of the band gap is obtained for solid mixtures of SiO2 and HfO2. One drawback of the high-k gate-insulator, comparing to the standard SiO2, is high density of defects, particularly oxygen vacancies, which leads to several problems such as enhancement of the leakage current, threshold voltage instability, and degradation of the gate-oxide. A comprehensive investigation of different properties of oxygen vacancies in HfO2 is conducted by the calculation of formation energies and induced trap levels. It is shown based on theoretical calculations that the harmful effects of oxygen vacancies can be partially healed by introducing lanthanum atoms into the defected HfO2 crystal. Lanthanum atoms energetically prefer to occupy Hf lattice sites close to the oxygen vacancies and passivate the induced defect levels. The state-of-the-art high-k gate-stacks consist of a metal-gate on a HfO2 layer, as the main part of the gate insulator, and a very thin SiO2 intermediate layer between high-k material and Si. The introduction of a metal-gate raises some problem in the adjustment of an appropriate threshold voltage. Theoretical calculations in a complex model structure of the Si/SiO2/HfO2 interface reveals that the lanthanum atoms energetically prefer to stay at the SiO2/HfO2 interface, which in turn results in a dipole moment. This dipole moment can be employed to adjust the threshold voltage in high-k/metal-gate stacks. Finally, a theoretical model, which can quiet well explain the experimental measurements, is introduced for the progressive degradation of the high-k gate-insulators. This model is based on ab-initio calculations and shows how the generation of charged vacancies and their migration under the applied gate voltage leads to the progressive enhancement of the leakage current and consequently to the degradation of the insulator layer.:List of Figures 7 List of Tables 9 List of Symbols 10 List of Abbreviations 11 Chapter 1: Introduction 12 Chapter 2: Theory of Atomic-Scale First-Principles Calculations 15 2.1 Theoretical methods 15 2.2 Density functional theory 17 2.3 Non-equilibrium Green’s function formalism 23 Chapter 3: Calculations for Bulk High-k Materials 27 3.1 Bulk high-k materials 27 3.2 Crystalline insulators 27 3.3 Solid solutions 29 3.3.1 Cluster expansion approach 30 3.3.2 Band gap and bowing parameter 33 3.3.3 Calculation of internal stress 40 3.4 Leakage current 41 Chapter 4: Defects in Bulk High-k Materials 43 4.1 Defects in high-k gate dielectrics 43 4.2 Oxygen vacancies in monoclinic HfO2 44 4.2.1 Neutral oxygen vacancies 44 4.2.2 Charged oxygen vacancies 46 4.3 Hybrid functional 50 4.4 Double oxygen vacancies 56 4.5 Interaction of oxygen vacancies with La-doping 61 4.5.1 La doping in m-HfO2 61 4.5.2 Complex LaHfVO defects 64 Chapter 5: Interface Properties of High-k Gate Stack 72 5.1 high-k gate-stack 72 5.1.1 Atomic-scale model structure for a high-k gate-stack 72 5.1.2 Electronic structure 74 5.1.3 Leakage current 76 5.2 Band offset 80 5.3 Threshold voltage engineering with La doping 84 Chapter 6: Degradation of the High-k Gate Stack 90 6.1 Reliability issues in high-k gate-stack 90 6.2 Calculations and experimental methods 91 6.3 Leakage current 92 6.4 Defect generation 100 6.5 Explaining progressive SILC in high-k dielectrics 102 Chapter 7: Conclusions 104 Bibliography 106 Selbständigkeitserklärung 119 Danksagung 120 Lebenslauf 121 Veröffentlichungen 122