Electrical Properties of Graphene for Interconnect Applications

A semi-classical electrodynamical model is derived to describe the electrical transport along graphene, based on the modified Boltzmann transport equation. The model is derived in the typical operating conditions predicted for future integrated circuits nano-interconnects, i.e., a low bias condition and an operating frequency up to 1 THz. A generalized non-local dispersive Ohm's law is derived, which can be regarded as the constitutive equation for the material. The behavior of the electrical conductivity is studied with reference to a 2D case (the infinite graphene layer) and a 1D case (the graphene nanoribbons). The modulation effects of the nanoribbons' size and chirality are highlighted, as well as the spatial dispersion introduced in the 2D case by the dyadic nature of the conductivity

Computational modeling of thermal transport in low-dimensional materials

Over the past two decades, controlling thermal transport properties at the nanoscale has become more and more relevant. This is mostly motivated by the need of developing novel energy-harvesting techniques based on thermoelectricity and the necessity to control the heat dissipation in semiconductor devices. In this field, two major research lines can be identified: On one side 'phononics', which aims at developing devices such as thermal diodes, thermal transistors, and thermal logic gates, among others, and on the other side, phonon engineering aiming at controlling heat transport by producing or structurally modifying heterostructures made of novel nanomaterials (e.g., two-dimensional (2D) materials, nanotubes, organic systems). In order to gain insight into the factors controlling nanoscale heat flow and to be able to design highly-efficient thermal devices, the development of new computational approaches is crucial. The primary goal of the present thesis is the implementation of new methodologies addressing classical and quantum thermal transport at the nanoscale. We will focus on three major issues: (i) We will study thermal rectification effect in nanodevices made of novel 2D materials by means of nonequilibrium molecular dynamics simulations. The influence of structural asymmetry and substrate deposition on the thermal rectification will be investigated. (ii) To address quantum ballistic thermal transport in nanoscale systems, we will implement a nonequilibrium Green's functions (NEGF) treatment of transport combined with a density-functional based approach. Here, we will explore the dependence of the thermal transport properties of 2D materials and nanotubes on different intrinsic (structural anisotropy and grain boundaries) and external (molecular functionalization, strain engineering, and doping) factors. Finally, (iii) a time-dependent NEGF formalism will be developed and implemented to probe the transient and steady thermal transport in molecular junctions. In short, our results show that the mechanisms governing the thermal rectification effect in the 2D thermal rectifiers proposed in this work are shape asymmetries, interface material (planar stacking order), and changes in the degree of spatial localization of high-frequency modes (under nonequilibrium heat transport conditions). The rectification effect can be also controlled by substrate engineering. Moreover, we found that quantum ballistic thermal transport in 2D puckered materials displays an anisotropic behavior. The presence of structural disorder in the form of grain boundaries in graphene reduces overall its thermal transport efficiency. Dynamical disorder induced by coupling to a thermostat has however a weaker effect, suggesting that structural defects are playing a major role. External factors have a noticeable influence on the heat transport in new 2D materials and BNC heteronanotubes. On the other hand, we have also been able to characterize, from a quantum point of view, the phonon dynamics in carbon-based molecular junctions. We expect that the results obtained within this thesis will yield new insights into the thermal management of low-dimensional materials, and thus open new routes to the design of thermoelectric and phononic devices.In den letzten zwei Jahrzehnten hat die Kontrolle der thermischen Transporteigenschaften im Nanobereich immer mehr an Bedeutung gewonnen. Dies ist vor allem auf die Notwendigkeit zurückzuführen, neue Energiegewinnungstechniken zu entwickeln, die auf Thermoelektrizität basieren, sowie auf die Problematik, die Wärmeabfuhr in Halbleiterbauelementen kontrollieren zu müssen. In diesem Bereich lassen sich zwei große Forschungslinien identifizieren: Auf der einen Seite 'Phononik', die unter anderem auf die Entwicklung von Bauelementen wie thermischen Dioden, Transistoren und Logikgattern abzielt, und auf der anderen Seite die Phononentechnik, die den Wärmetransport durch Herstellung oder strukturelle Modifikation von Heterostrukturen aus neuartigen Nanomaterialien (z.B. zweidimensionalen (2D) Materialien, Nanoröhren, organischen Systemen) steuert. Um einen Einblick in die Faktoren zu erhalten, die den Wärmefluss im Nanobereich steuern, und um hocheffiziente thermische Bauteile entwickeln zu können, ist die Entwicklung neuer Berechnungsansätze entscheidend. Das Hauptziel der vorliegenden Arbeit ist die Implementierung neuer Methoden, die sich mit dem klassischen und dem quantenthermischen Transport auf der Nanoskala befassen. Wir werden uns auf drei Hauptthemen konzentrieren: (i) Wir werden den thermischen Rektifikationseffekt in Nanobauteilen aus neuartigen 2D-Materialien mit Hilfe von Nichtgleichgewichts-Molekulardynamiksimulationen studieren. Der Einfluss von Strukturasymmetrie und Substratablagerung auf die thermische Rektifikation wird untersucht. (ii) Um den quantenballistischen Wärmetransport in nanoskaligen Systemen anzugehen, werden wir eine NEGF-Behandlung (Nichtgleichgewichts-Greensche Funktionen) des Transports in Kombination mit einem dichtefunktionalen Ansatz implementieren. Hier wird die Abhängigkeit der thermischen Transporteigenschaften von 2D-Materialien und Nanoröhrchen von verschiedenen intrinsischen (strukturelle Anisotropie und Korngrenzen) und externen (molekulare Funktionalisierung, Stammtechnik und Dotierung) Faktoren untersucht. Schließlich wird (iii) ein zeitabhängiger NEGF-Formalismus entwickelt und implementiert, um den transienten und stetigen Wärmetransport in molekularen Verbindungen zu untersuchen. Unsere Ergebnisse zeigen, dass die wesentlichen Mechanismen für die thermische Gleichrichtung in 2D thermischen Gleichrichtern durch Asymmetrien der Bauteilform, das Interface-Material (planare Stapelung Reihenfolge), und änderungen im Grad der räumlichen Lokalisierung von Hochfrequenz-Modi (unter Nicht-Gleichgewicht Wärmetransport-Bedingungen) gegeben sind. Der Gleichrichteffekt kann auch durch die Wahl des Substrats gesteuert werden. Darüber hinaus haben wir festgestellt, dass der quantenballistische Wärmetransport in 2D-Puckered-Materialien ein anisotropes Verhalten zeigt. Das Vorhandensein von strukturellen Störungen in Form von Korngrenzen in Graphen reduziert insgesamt die Effizienz des Wärmetransports. Dynamische Störungen, die durch die Ankopplung an einen Thermostaten hervorgerufen werden, haben jedoch eine schwächere Wirkung, was darauf hindeutet, dass strukturelle Defekte eine große Rolle spielen. Externe Faktoren haben einen nachweislichen Einfluss auf den Wärmetransport in neuen 2D-Materialien und BNC-Heteronanotubes. Weiterhin konnten wir auch die Phononendynamik in kohlenstoffbasierten molekularen Verbindungen quantitativ charakterisieren. Wir erwarten, dass die Ergebnisse dieser Arbeit neue Erkenntnisse über das Wärmemanagement von niedrigdimensionalen Materialien liefern und damit neue Wege für das Design von thermoelektrischen und phononischen Bauelementen eröffnen

Investigating thermal transport in isotope substituted nanomaterials using molecular simulations

Recent research related to carbon nanotubes, graphene and graphene analogous low-dimensional materials (Silicene, MoS2, WS2) have sparked tremendous interests in nanoscale sciences due to their promising applications associated with thermoelectrics and electronics. Heat conduction in these nanomaterials occurs by lattice vibration where energy is transmitted by interaction with neighboring atoms in a spring-like oscillating motion. As a result, quantized lattice vibrational elastic waves called phonons are emitted, which are the main contributors to heat conduction in these non-metallic nanomaterials. In analogous two-dimensional (2D) nanomaterials like graphene and silicene, thermal transport is mainly governed by three acoustic phonon modes (lattice vibration): in-plane longitudinal modes, in-plane transverse modes and out-of-plane vibrational modes. However, in carbon nanotubes there are four phonon modes contributing to the heat transport: longitudinal acoustic modes corresponding to the motion of atoms along the axis of the tube, two transverse degenerate modes and a twist mode. Out of all these modes, generally the low frequency, long-range modes are the ones which exert a dominant contribution towards heat transfer whereas high frequency, short-range modes have a very limited contribution to the thermal transport process. Literature contains inconsistent results identifying the dominant vibrational modes for these nanomaterials. In our research we explore this for carbon nanotubes, graphene and silicene. A clear understanding of the transport mechanism can enable design of novel nanomaterials that can be successfully used for targeted applications in thermal management. We have considered nanomaterials with varying dimensions and shape (carbon nanotube and graphene) and also nanostructures with varying isotope substitution but similar geometries (graphene and silicene). Using classical molecular dynamics simulations, we identify the delocalized transverse modes in carbon nanotubes and out-of-plane flexural modes in graphene as the dominant modes which contribute mostly to the thermal transport in them. We extend our investigation to analogous 2D materials, graphene and silicene. Even though they are structurally similar, their heat conduction mechanisms are found to vary drastically. In contrast to the dominant out-of-plane flexural modes in graphene, the heat conduction in silicene occurs predominantly due to in-plane transverse acoustic modes. Due to the buckled silicene structure, coupling of the out-of-plane flexural modes and in-plane longitudinal modes causes a mode softening effect. The weaker Si-Si bond strength implies low group velocity of the out-of-plane phonons making them essentially non-existent for silicene. But despite the differences in the phonon modes, the variation in k with increasing isotope substitution in both graphene and silicene are found to be similar. The shift in vibrational spectra towards lower frequencies indicating the reduced energy carrying capacity of phonons due to mass disorder is found to be consistent in silicene too. Our results showing decrease in k in graphene and silicene compared well with an analytical model based on mean-field approximation. We hope that our study will initiate many more fascinating researches in this rapidly evolving area

Computational modeling of thermal interfaces in graphene based nanostructures

L'abstract è presente nell'allegato / the abstract is in the attachmen

Electronic, optical, mechanical and thermoelectric properties of graphene

Graphene, a two-dimensional allotrope of graphite with sp2 bonded carbon atoms, is arranged in honeycomb structure. Its quasi one-dimensional form is graphene nanoribbon (GNR). Graphene related materials have been found to display excellent electronic, chemical, mechanical properties along with uniquely high thermal conductivity, electrical conductivity and high optical transparency. With excellent electrical characteristics such as high carrier transport properties, quantum Hall effect at room temperature and unusual magnetic properties, graphene has applications in optoelectronic devices. Electronically, graphene is a zero bandgap semiconductor making it essential to tailor its structure for obtaining specific band structure. Narrow GNRs are known to open up bandgap and found to exhibit variations for different chiralities i.e., armchair and zigzag. Doping graphene, with p- or n- type elements, is shown to exhibit bandgap in contrast to pristine graphene. In this study, optical properties including dielectric functions, absorption coefficient, transmittance, and reflectance, as a function of wavelength and incident energy, are studied. Refractive index and extinction coefficient of pristine graphene are presented. A key optical property in the infrared region, emissivity, is studied as a function of wavelength for various multilayered configurations having graphene as one of the constituent layers. Application of such a structure is in the fabrication of a Hot Electron Bolometer (a sensor that operates on the basis of temperature-dependent electrical resistance). Graphene is found to have very high elastic modulus and intrinsic strength. Nanoindentation of graphene sheet is simulated to study the force versus displacement curves. Effects of variation of diameter of indenter, speed of indentation and number of layers of graphene on the mechanical properties are presented. Shrinking size of electronic devices has led to an acute need for thermal management. This prompted the study of thermoelectric (TE) effects in graphene based systems. TE devices are finding applications in power generation and solid state refrigeration. This study involves analyzing the electronic, thermal and electrical transport properties of these systems. Electronic thermal conductivity, of graphene based systems (κe), is found to be negligible as compared to its phonon-induced lattice thermal conduction (κp). Variations in κp of graphene and GN Rs are evaluated as a function of their width and length of their edges, chiralities, temperature, and number of layers. The interdependence of transport parameters, i.e., electrical conductivity (σ), thermoelectric power (TEP) or Seebeck coefficient (S), and κ of graphene are discussed. The thermoelectric performance of these materials is determined mainly by a parameter called Figure-of-Merit. Effective methods to optimize the value of Figure-of-Merit are explored. Reducing the thermal conductivity and increasing the power factor of these systems are found to improve the Figure-of-Merit significantly. This involves correlation of structure and transport properties. Effects of doping on σ, κ and Hall coefficient are discussed

Numerical Modelling of Graphene Nanoribbon-fets for Analog and Digital Applications

Graphene, that is a monolayer of carbon atoms arranged in a honeycomb lattice, has been isolated only recently from graphite. This material shows very attractive physical properties, like superior carrier mobility, current carrying capability and thermal conductivity. In consideration of that, graphene has been the object of large investigation as a promising candidate to be used in nanometer-scale devices for electronic applications. In this work, graphene nanoribbons (GNRs), that are narrow strips of graphene, for which a band-gap is induced by the quantum confinement of carriers in the transverse direction, have been studied. As experimental GNR-FETs are still far from being ideal, mainly due to the large width and edge roughness, an accurate description of the physical phenomena occurring in these devices is required to have valuable predictions about the performance of these novel structures. A code has been developed to this purpose and used to investigate the performance of 1 to 15-nm wide GNR-FETs. 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 a tight-binding (TB) Hamiltonian model and transport has been solved within the formalism of the non-equilibrium Green's functions (NEGF). Both ballistic and dissipative transport are considered. The inclusion of the electron-phonon interaction has been taken into account in the self-consistent Born approximation. In consideration of their different energy band-gap, narrow GNRs are expected to be suitable for logic applications, while wider ones could be promising candidates as channel material for radio-frequency applications

Modeling Of Two Dimensional Graphene And Non-graphene Material Based Tunnel Field Effect Transistors For Integrated Circuit Design

The Moore’s law of scaling of metal oxide semiconductor field effect transistor (MOSFET) had been a driving force toward the unprecedented advancement in development of integrated circuit over the last five decades. As the technology scales down to 7 nm node and below following the Moore’s law, conventional MOSFETs are becoming more vulnerable to extremely high off-state leakage current exhibiting a tremendous amount of standby power dissipation. Moreover, the fundamental physical limit of MOSFET of 60 mV/decade subthreshold slope exacerbates the situation further requiring current transport mechanism other than drift and diffusion for the operation of transistors. One way to limit such unrestrained amount of power dissipation is to explore novel materials with superior thermal and electrical properties compared to traditional bulk materials. On the other hand, energy efficient steep subthreshold slope devices are the other possible alternatives to conventional MOSFET based on emerging novel materials. This dissertation addresses the potential of both advanced materials and devices for development of next generation energy efficient integrated circuits. Among the different steep subthreshold slope devices, tunnel field effect transistor (TFET) has been considered as a promising candidate after MOSFET. A superior gate control on source-channel band-to-band tunneling providing subthreshold slopes well below than 60 mV/decade. With the emergence of atomically thin two-dimensional (2D) materials, interest in the design of TFET based on such novel 2D materials has also grown significantly. Graphene being the first and the most studied among 2D materials with exotic electronic and thermal properties. This dissertation primarily considers current transport modeling of graphene based tunnel devices from transport phenomena to energy efficient integrated circuit design. Three current transport models: semi-classical, semi-quantum and numerical simulations are described for the modeling of graphene nanoribbon tunnel field effect transistor (GNR TFET) where the semi-classical model is in close agreement with the quantum transport simulation. Moreover, the models produced are also extended for integrated circuit design using Verilog-A hardware description language for logic design. In order to overcome the challenges associated with the band gap engineering for making graphene transistor for logic operation, the promise of graphene based interlayer tunneling transistors are discussed along with their existing fundamental physical limitation of subthreshold slope. It has been found that such interlayer tunnel transistor has very poor electrostatic gate control on drain current. It gives subthreshold slope greater than the thermionic limit of 60 mV/decade at room temperature. In order to resolve such limitation of interlayer tunneling transistors, a new type of transistor named “junctionless tunnel effect transistor (JTET)” has been invented and modeled for the first time considering graphene-boron nitride (BN)-graphene and molybdenum disulfide (MoS2)-boron nitride (BN) heterostructures, where the interlayer tunneling mechanism controls the source-drain ballistic transport instead of depleting carriers in the channel. Steep subthreshold slope, low power and high frequency THz operation are few of the promising features studied for such graphene and MoS2 JTETs. From current transport modeling to energy efficient integrated circuit design using Verilog-A has been carried out for these new devices as well. Thus, findings in this dissertation would suggest the exciting opportunity of a new class of next generation energy efficient material based transistors as switches

Novel effects of strains in graphene and other two dimensional materials

The analysis of the electronic properties of strained or lattice deformed graphene combines ideas from classical condensed matter physics, soft matter, and geometrical aspects of quantum field theory (QFT) in curved spaces. Recent theoretical and experimental work shows the influence of strains in many properties of graphene not considered before, such as electronic transport, spin-orbit coupling, the formation of Moir\'e patterns, optics, ... There is also significant evidence of anharmonic effects, which can modify the structural properties of graphene. These phenomena are not restricted to graphene, and they are being intensively studied in other two dimensional materials, such as the metallic dichalcogenides. We review here recent developments related to the role of strains in the structural and electronic properties of graphene and other two dimensional compounds.Comment: 75 pages, 15 figures, review articl