The technological interest in a material depends very much on its electrical, magnetic, optical and/or mechanical properties. In carbon nanotubes the atoms form a cylindrical structure with a diameter of the order 1 nm, but the nanotubes can be up to several hundred micrometers in length. This makes carbon nanotubes a remarkable model for one-dimensional systems. A lot of efforts have been dedicated to manufacturing carbon nanotubes, which is expected to be the material for the next generation of devices. Despite all the attention that carbon nanotubes have received from the scientific community, only rather limited progress has been made in the theoretical understanding of their physical properties. In this work, we attempt to provide an understanding of the electron-phonon and electron-defect interactions in semiconducting zigzag carbon nanotubes using a tight-binding approach. The electronic energy dispersion relations are calculated by applying the zone-folding technique to the dispersion relations of graphene. A fourth-nearest-neighbour force constant model has been applied to study the vibrational modes in the carbon nanotubes. Both the electron-phonon interaction and the electron-defect interaction are formulated within the tight-binding approximation, and analyzed in terms of their quantum mechanical scattering rates. Apart from the scattering rates, their components in terms of phonon absorption, phonon emission, backscattering and forward scattering have been determined and analyzed. The scattering rates for (5,0), (7,0), (10,0), (13,0) and (25,0) carbon nanotubes at room temperature and at 10K are presented and discussed. The phonon scattering rate is dependent on the lattice temperature in the interval 0-0.17 eV. We find that backscattering and phonon emission are dominant over forward scattering and phonon absorption in most of the energy interval. However, forward scattering and phonon absorption can be comparable to backscattering and phonon emission in limited energy intervals. The phonon modes associated with each peak in the electron-phonon scattering rates have been identified, and the similarities in the phonon scattering rates between different nanotubes are discussed. The dependence of the defect scattering rate on the tube diameter is similar to that of the phonon scattering rate. Both the phonon and the defect scattering rates show strong dependence on the tube diameter (i.e., the scattering rate decreases as a function of the index of the nanotube). It is observed that the backscattering and forward scattering for electrons interacting with defects occur with same frequency at all energies, in sharp contrast to the situation for phonon scattering. It is demonstrated that the differences in the scattering rate between different tubes are mainly due to the differences in their band structures.

Since the advent of nanoscale material based electronic devices, there has been a considerable interest in exploring carbon nanotubes from fundamental science and technological perspectives. In carbon nanotubes, the atoms form a cylindrical structure with a diameter of the order 1nm. The length of the nanotubes can extend up to several hundred micrometers. Carbon nanotubes exhibit a variety of intriguing electronic properties such as semiconducting and metallic behaviour, due to the quantum confinement of the electrons in the circumferential direction. Much of the study dedicated to describe the behaviour of carbon nanotube-based devices assumes for simplicity the nanotube to be a ballistic material. However, in reality the phonon scattering mechanism exists also in nanotubes, of course, and can generally not be neglected, except in very short nanotubes. In this work, we focus attention on exploring the steady-state electron transport properties of semiconducting single-walled carbon nanotubes, including both phonon scattering and defect (vacancy) scattering, using the semi-classical bulk single electron Monte Carlo method.   The electron energy dispersion relations are obtained by applying the zone folding technique to the dispersion relations of graphene, which are calculated using the tight-binding description. The vibrational modes in the carbon nanotubes are studied using a fourth nearest-neighbour force constant model. Both the electron-phonon and the electron-defect interactions are formulated within the tight-binding framework, and their corresponding scattering rates are computed and analyzed. In particular, the dependence of the phonon scattering rate and the defect scattering rate on the diameter of the nanotube, on temperature and on electron energy is studied. It is shown that the differences observed in the scattering rate between different nanotubes mainly stem from the differences in their band structure.   A bulk single electron Monte Carlo simulator was developed to study the electron transport in semiconducting zigzag carbon nanotubes. As a first step, we included only electron-phonon scattering, neglecting all other possible scattering mechanisms. With this scattering mechanism, the steady-state drift velocity and the mobility for the nanotubes (8,0), (10,0), (11,0), (13,0) and (25,0) were calculated as functions of the electric-field strength and lattice temperature, and the results are presented and analysed here. The dependence of the mobility on the lattice temperature can be clearly seen at low electric-field strengths. At such electric-field strengths, the scattering is almost entirely due to acoustic phonons, whereas at high electric-field strengths optical phonon emission processes dominate. It is shown that the saturation of the steady-state drift velocity at high electric-field strengths is due to the emission of high-energy optical phonons. The results indicate the presence of Negative differential resistance for some of the nanotubes considered in this work. The discrepancy found in the literature concerning the physical reason for the appearance of negative differential resistance is clarified, and a new explanation is proposed. It is also observed that the backward scattering is dominant over the forward scattering at high electric-field strengths.                                                                                   We then included also defect scattering, actually electron-vacancy scattering, for the nanotubes (10,0) and (13,0). The steady-state drift velocities for these nanotubes are calculated as functions of the density of vacancies, electric-field strength and the lattice temperature, using three different vacancy concentrations. The results indicate the presence of Negative differential resistance at very low concentration of defects, and how this feature may depend on the concentration of defects. The dependence of the steady-state drift velocity on the concentration of defect and the lattice temperature is discussed. The electron distribution functions for different temperatures and electric field strengths are also calculated and investigated for all the semiconducting nanotubes considered here. In particular, a steep barrier found in the electron distribution function is attributed to the emission of high energy optical phonons.

Quantenkaskadenlaser (QCLs) wurden vor gerade zwanzig Jahren erfunden und haben seitdem stetig im weltweiten Markt der optoelektronischen Bauelemente für den Infrarot an Bedeutung gewonnen. Anwendungsbeispiele für aktuelle und potenzielle Einsatzgebiete von QCLs sind photoakustische Spektroskopie, Umweltüberwachung, Simulation von heißen Körpern, und optische Freiraumdatenübertragung. Rekord optische Leistungen von 14 W und Leistungseffizienzen zwischen 15-35 % wurden bei mittelinfraroten QCLs für Betriebstemperaturen zwischen 80-300 K erreicht. Die weitere Verbesserung dieser Eigenschaften hängt nicht nur von Aspekten wie Wärmemanagement und Chip-Packaging ab, sondern auch von Verbesserungen im Laserdesign zwecks der Reduzierung des Ladungsträgerleckstroms. Dennoch sind die verschiedenen Mechanismen und Komponenten des Leckstroms in Quantenkaskadenlasern leider noch nicht gründlich untersucht worden. Die vorliegende Arbeit liefert a realistische Beschreibung der Ladungsträgertransports in QCLs. Wir beschreiben u.a. Leckströme vom Quantentopf- in höhere Zustände und diskutieren elastische und inelastische Streumechanismen von Ladungsträgern bei mittelinfraroten Quantenkaskadenlasern. Wir illustrieren außerdem die Notwendigkeit zur Berücksichtigung der Elektronentemperatur für eine vollständigere Analyse der Ladungsträgertransporteigenschaften von Quantenkaskadenlasern. Methoden zur experimentellen Ermittlung des temperaturabhängigen Leckstroms in Quantenkaskadenlasern werden präsentiert. Unser Ansatz liefert eine Methode zur effektiven Analyse von der QCL-Leistung und Vereinfacht die Optimierung von QCL aktive Regionen. / Two decades after their invention in 1994, quantum-cascade lasers (QCLs) become increasingly important in the global infrared optoelectronics market. Photoacoustic spectroscopy, environment monitoring, hot object simulation, and free-space communication systems are selected examples of the current and potential applications of QCLs. Record optical powers as large as 14 W and power-conversion efficiencies ranging between 15-35 % have been reported for MIR QCLs for temperatures 80-300 K. Further improvement of these characteristics depends not only of aspects as heat management and chip-packaging, but also on improving the active-region design to reduce several leakage channels of charge carriers. However, mechanisms through which leakage of charge carriers affects QCLs performance have not been thoroughly researched. A better understanding of the several (non-radiative) scattering mechanisms involved in carrier transport in QCLs is needed to design new structures and optimize their performance. This work provides a realistic description of charge carriers transport in QCLs. We discuss in particular carrier leakage from QCL quantum-well confined states into higher and lower states. The two main mechanisms for non-radiative intersubband scattering in MIR QCLs are electron-longitudinal-optical-phonon scattering and interface roughness-induced scattering. We present methods for the experimental determination of the leakage current in QCLs at and above laser threshold, which allowed us to estimate the sheet distributions of conduction band states and better understand the impact of temperature activated leakage on QCLs characteristics. We found that even at temperatures low enough to neglect ELO scattering, carriers leakage due to IFR becomes significant for devices operating at high electron temperatures. Altogether, this approach offers a straightforward method to analyze and troubleshoot new QCL active region designs and optimize their performance.

Seit ihrer Erfindung in 1994 haben sich Quantenkaskadenlaser (QCL) zu der Standard-Halbleiterlaserquelle im mittleren und weiten Infrarotspektrum entwickelt. Diese unipolaren Laser basieren auf der Populations-Inversion zwischen quantisierten sub-Bändern in Halbleiterheterostrukturen. Ein gutes theoretisches Modell ist essenziell für die Optimierung und weitere Entwicklung von neuen QCL Laserquellen. Eine einfache Methode, Elektronentransport in QCL zu beschreiben, stützt sich auf ein phänomenologisches Modell für die Streuraten zwischen elektronischen sub-Bändern. Das Hauptziel dieser Arbeit ist die Entwicklung eines kompakten Ansatzes für Streuraten für die effiziente Vorhersage der temperaturabhängigen Charakteristika von QCLs im mittleren Infrarotspektrum. Die Arbeit beginnt mit einem kurzen Überblick über Halbleiterheterostrukturen und die wichtigsten Streumechanismen für Übergänge zwischen sub-Bändern in QCLs. Dabei sind elastische Übergänge sowie Phononenstreuung für die Übergangsraten zwischen verschiedenen sub-Bändern relevant. Außerdem werden die notwendigen Modellierungstechniken für Simulationsprozesse in QCLs mit einem selbst-konsistenten Streuraten-Modell vorgestellt. In dieser Arbeit wurde ein vereinfachtes Modell für vertikalen Elektronentransport zwischen sub-Bändern bei der Temperatur von Flüssigstickstoff entwickelt. Die Übergangsrate ist in diesem Ansatz das Produkt des Überlappintegrals der quadrierten Moduli der einhüllenden Funktion und einem phänomenologischen Faktor, der von der Übergangsenergie abhängt. Der Übergangsfaktor wird für verschiedene Übergangsmechanismen einzeln hergeleitet, und eine Erweiterung des Modells auf einen breiten Temperaturbereich wird vorgestellt. Schließlich analysieren wir die sogenannte T0-Charakteristik für einige Designs der aktiven Region, die aus Rechnungen mit vorhandenen temperaturabhängigen Modellen und experimentellen Daten gewonnen wurden. / Since their invention in 1994, quantum cascade lasers (QCLs) have become the standard semiconductor laser source for the mid- and far-infrared spectral range. These unipolar devices are based on the population inversion between quantized subbands in biased semiconductor heterostructures. A useful theoretical model is essential for the optimization and further development of new QCL sources. A simple method for describing the electron transport in QCL is based on scattering rates between electron subbands. These can be described easiest using a phenomenological model with experimental or empirical parameters. The main goal of this work is development of compact description of scattering processes in the frame of scattering-rate approach for the reliable prediction of temperature dependent characteristics of mid-infrared quantum cascade lasers. We start this work with a brief overview of semiconductor heterostructures and main intersubband scattering mechanisms for quantum cascade lasers. The resulting transition rates from initial states to another subbands are described by phonons and elastic scattering. Additionally, necessary modeling techniques are considered for simulation processes in QCLs using self-consistent scattering-rate model. Based on original work we introduce a simplified model for vertical electron transport between separated subbands at liquid nitrogen temperatures. In this approach the transition rate is written as the product of the overlap integral for the squared moduli of the envelope functions and a phenomenological factor that depends on the transition energy. The approach is reviewed and extended for a broad temperature range. There, the transition factor is derived and written for different scattering mechanisms separately. Then we analyze “so-called” T0 characteristic for a number of active region designs received from the calculations by present temperature dependent model and the experimental data.

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 importantes. / Non-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.

Die vorliegende Doktorarbeit beschäftigt sich mit der experimentellen Studie zweier miteinander verbundener Phänomene: Dem intrinsischen Timing-Jitter in einem supraleitendenden Nanodraht-Einzelphotonen-Detektor (SNSPD) und der Relaxation der Elektronenenergie in supraleitenden Filmen. Supraleitende Nanodrähte auf einem dielektrischen Substrat als mikroskopische Grundbausteine jeglicher SNSPDs stellen sowohl für theoretische als auch für experimentelle Studien komplexe Objekte dar. Die Komplexität ergibt sich aus der Tatsache, dass SNSPDs in der Praxis stark ungeordnete und ultradünne supraleitende Filme verwenden, die eine akustische Fehlanpassung zu dem zugrundeliegenden Substrat aufweisen und einen Nichtgleichgewichts-Zustand implizieren. Die Arbeit untersucht die Komplexität des am weitesten in der SNSPD Technologie verbreiteten Materials, Niobnitrid (NbN), indem verschiedene experimentelle Methoden angewandt werden. Als eine mögliche Anwendung der SNSPD-Technologie wird ein Prototyp eines dispersiven Raman-Spektrometers mit Einzelphotonen-Sensitivität demonstriert. / This Ph.D. thesis is based on the experimental study of two mutually interconnected phenomena: intrinsic timing jitter in superconducting nanowire single-photon detectors (SNSPDs) and relaxation of the electron energy in superconducting films. Microscopically, a building element of any SNSPD device, a superconducting nanowire on top of a dielectric substrate, represents a complex object for both experimental and theoretical studies. The complexity arises because, in practice, the SNSPD utilizes strongly disordered and ultrathin superconducting films, which acoustically mismatch with the underlying substrate, and implies a non-equilibrium state. This thesis addresses the complexity of the most conventional superconducting material used in SNSPD technology, niobium nitride (NbN), by applying several distinct experimental techniques. As an emerging application of the SNSPD technology, we demonstrate a prototype of the dispersive Raman spectrometer with single-photon sensitivity.