Technology scaling beyond Moore’s law demands cutting-edge solutions of the gate length scaling in sub-10 nm regime for low power high speed operations. Recently SOI technology has received considerable attention, however manufacturable solutions in sub-10 nm technologies are not yet known for future nanoelectronics. Therefore, to continue scalinginsub-10 nm region, new one(1D) and two dimensional(2D) “nano-materials” and engineering are expected to keep its pace. However, significant challenges must be overcome for nano-material properties in carrier transport to be useful in future silicon nanotechnology. Thus, it is very important to understand and modulate their electronic band structure and transport properties for low power nanoelectronics applications. This thesis tries to provide solutions for some problems in this area. In recent times, one dimensional Silicon nanowire has emerged as a building block for the next generation nano-electronic devices as it can accommodate multiple gate transistor architecture with excellent electrostatic integrity. However as the experimental study of various energy band parameters at the nanoscale regime is extremely challenging, usually one relies on the atomic level simulations, the results of which are at par with the experimental observations. Two such parameters are the band gap and effective mass, which are of pioneer importance for the understanding of the current transport mechanism. Although there exists a large number of empirical relations of the band gap in relaxed Silicon nanowire, however there is a growing demand for the development of a physics based analytical model to standardize different energy band parameters which particularly demands its application in TCAD software for predicting different electrical characteristics of novel devices and its strained counterpart to increase the device characteristics significantly without changing the device architecture. In the first part of this work reports the analytical modeling of energy band gap and electron transport effective mass of relaxed and strained Silicon nanowires in various crystallographic directions for future nanoelectronics. The technology scaling of gate length in beyond Moore’s law devices also demands the SOI body thickness, TSi0 which is essentially very challenging task in nano-device engineering. To overcome this circumstance, two dimensional crystals in atomically thin layered materials have found great attention for future nanolectronics device applications. Graphene, one layer of Graphite, is such 2D materials which have found potentiality in high speed nanoelectronics applications due to its several unique electronic properties. However, the zero band gap in pure Graphene makes it limited in switching device or transistor applications. Thus, opening and tailoring a band gap has become a highly pursued topic in recent graphene research. The second part of this work reports atomistic simulation based real and complex band structure properties Graphene-Boron nitride heterobilayer and Boron Nitride embedded Graphene nanoribbons which can improve the grapheme and its nanoribbon band structure properties without changing their originality. This part also reports the direct band-to-band tunneling phenomena through the complex band structures and their applications in tunnel field effect transistors(TFETs) which has emerged as a strong candidate for next generation low-stand by power(LSTP) applications due to its sub-60mV/dec Sub threshold slope(SS). As the direct band-to-band tunneling(BTBT) is improbable in Silicon(either its bulk or nanowire form), it is difficult to achieve superior TFET characteristics(i.e., very low SS and high ON cur-rent) from the Silicon TFETs. Whereas, it is explored that much high ON current and very low subthreshold slope in hybrid Graphene based TFET characteristics open a new prospect in future TFETs. The investigations on ultrathin body materials also call for a need to explore new 2D materials with finite band gap and their various nanostructures for future nanoelectronic applications in order to replace conventional Silicon. In the third part of this report, we have investigated the electronic and dielectric properties of semiconducting layered Transition metal dichalcogenide materials (MX2)(M=Mo, W;X =S, Se, Te) which has recently emerged as a promising alternative to Si as channel materials for CMOS devices. Five layered MX2 materials(exceptWTe2)in their 2D sheet and 1D nanoribbon forms are considered to study the real and imaginary band structure of thoseMX2 materials by atomistic simulations. Studying the complex dispersion properties, it is shown that all the five MX2 support direct BTBT in their monolayer sheet forms and offer an average ON current and subthresholdslopeof150 A/mand4 mV/dec, respectively. However, onlytheMoTe2 support direct BTBT in its nanoribbon form, whereas the direct BTBT possibility in MoS2 and MoSe2 depends on the number of layers or applied uniaxial strain. WX2 nanoribbons are shown to be non-suitable for efficient TFET operation. Reasonably high tunneling current in these MX2 shows that these can take advantage over conventional Silicon in future tunnel field effect transistor applications.

Technology scaling beyond Moore’s law demands cutting-edge solutions of the gate length scaling in sub-10 nm regime for low power high speed operations. Recently SOI technology has received considerable attention, however manufacturable solutions in sub-10 nm technologies are not yet known for future nanoelectronics. Therefore, to continue scalinginsub-10 nm region, new one(1D) and two dimensional(2D) “nano-materials” and engineering are expected to keep its pace. However, significant challenges must be overcome for nano-material properties in carrier transport to be useful in future silicon nanotechnology. Thus, it is very important to understand and modulate their electronic band structure and transport properties for low power nanoelectronics applications. This thesis tries to provide solutions for some problems in this area. In recent times, one dimensional Silicon nanowire has emerged as a building block for the next generation nano-electronic devices as it can accommodate multiple gate transistor architecture with excellent electrostatic integrity. However as the experimental study of various energy band parameters at the nanoscale regime is extremely challenging, usually one relies on the atomic level simulations, the results of which are at par with the experimental observations. Two such parameters are the band gap and effective mass, which are of pioneer importance for the understanding of the current transport mechanism. Although there exists a large number of empirical relations of the band gap in relaxed Silicon nanowire, however there is a growing demand for the development of a physics based analytical model to standardize different energy band parameters which particularly demands its application in TCAD software for predicting different electrical characteristics of novel devices and its strained counterpart to increase the device characteristics significantly without changing the device architecture. In the first part of this work reports the analytical modeling of energy band gap and electron transport effective mass of relaxed and strained Silicon nanowires in various crystallographic directions for future nanoelectronics. The technology scaling of gate length in beyond Moore’s law devices also demands the SOI body thickness, TSi0 which is essentially very challenging task in nano-device engineering. To overcome this circumstance, two dimensional crystals in atomically thin layered materials have found great attention for future nanolectronics device applications. Graphene, one layer of Graphite, is such 2D materials which have found potentiality in high speed nanoelectronics applications due to its several unique electronic properties. However, the zero band gap in pure Graphene makes it limited in switching device or transistor applications. Thus, opening and tailoring a band gap has become a highly pursued topic in recent graphene research. The second part of this work reports atomistic simulation based real and complex band structure properties Graphene-Boron nitride heterobilayer and Boron Nitride embedded Graphene nanoribbons which can improve the grapheme and its nanoribbon band structure properties without changing their originality. This part also reports the direct band-to-band tunneling phenomena through the complex band structures and their applications in tunnel field effect transistors(TFETs) which has emerged as a strong candidate for next generation low-stand by power(LSTP) applications due to its sub-60mV/dec Sub threshold slope(SS). As the direct band-to-band tunneling(BTBT) is improbable in Silicon(either its bulk or nanowire form), it is difficult to achieve superior TFET characteristics(i.e., very low SS and high ON cur-rent) from the Silicon TFETs. Whereas, it is explored that much high ON current and very low subthreshold slope in hybrid Graphene based TFET characteristics open a new prospect in future TFETs. The investigations on ultrathin body materials also call for a need to explore new 2D materials with finite band gap and their various nanostructures for future nanoelectronic applications in order to replace conventional Silicon. In the third part of this report, we have investigated the electronic and dielectric properties of semiconducting layered Transition metal dichalcogenide materials (MX2)(M=Mo, W;X =S, Se, Te) which has recently emerged as a promising alternative to Si as channel materials for CMOS devices. Five layered MX2 materials(exceptWTe2)in their 2D sheet and 1D nanoribbon forms are considered to study the real and imaginary band structure of thoseMX2 materials by atomistic simulations. Studying the complex dispersion properties, it is shown that all the five MX2 support direct BTBT in their monolayer sheet forms and offer an average ON current and subthresholdslopeof150 A/mand4 mV/dec, respectively. However, onlytheMoTe2 support direct BTBT in its nanoribbon form, whereas the direct BTBT possibility in MoS2 and MoSe2 depends on the number of layers or applied uniaxial strain. WX2 nanoribbons are shown to be non-suitable for efficient TFET operation. Reasonably high tunneling current in these MX2 shows that these can take advantage over conventional Silicon in future tunnel field effect transistor applications.

The present thesis deals with a theoretical study of electronic structures in -conjugated molecular materials with focus on their application in organic elec-tronics. We also discuss a modified and efficient symmetrized DMRG algorithm for studying excited states in these systems. In recent times, organic conjugated systems have emerged as potential candidates in a wide range of fascinating fields by virtue of their tunable electronic properties, easy processability and low cost. Tunability in the electronic and optical properties primarily are centered on the or-dering and nature of the low-lying excited states. Probing these important excited states also demands development of efficient and adaptable techniques. Chapter 1 provides a basic overview of conjugated organic polymers which have been utilized over decades in diverse fields as in organic light emitting diodes (OLED), organic solar cells (OSC) and non-linear optical (NLO) devices. These systems also contribute significantly to theoretical understanding as they pro vide important insights of one and quasi-one dimensional systems. In this chapter, we have given basic description of the electronic processes in OLED and OSC along with a brief theoretical description of -conjugated organic systems. Chapter 2 gives an account of the numerical techniques which are necessary for the study of low-dimensional strongly correlated systems like -conjugated sys-tems. For this purpose, effective low-energy model Hamiltonians viz. Huckel,¨ Hubbard and Pariser-Parr-Pople Hamiltonians are discussed. Exact diagonalization technique within the diagrammatic valence bond (DVB) basis and density matrix renormalization group (DMRG) technique are discussed in details. We have also given brief accounts of the methods employed to study real-time dynamics. A short description of different computational techniques for the study of NLO properties in -conjugated systems is also provided. Engineering the position of the lowest triplet state (T1) relative to the first excited singlet state (S1) is of great importance in improving the efficiencies of organic light emitting diodes and organic photovoltaic cells. In chapter 3, we have carried out model exact calculations of substituted polyene chains to understand the fac-tors that affect the energy gap between S1 and T1. The factors studied are backbone dimerization, different donor-acceptor substitutions and twisted backbone geome-try. The largest system studied is an eighteen carbon polyene which spans a Hilbert space of about 991 million in the triplet subspace. We show that for reverse inter-system crossing (RISC) process, the best choice involves substituting all carbon sites on one half of the polyene with donors and the other half with acceptors. Singlet fission (SF) is a potential pathway for significant enhancement of efficiency in OSC. In chapter 4, we study singlet fission in a pair of polyene molecules in two different stacking arrangements employing exact many-body wave packet dy-namics. In the non-interacting model, SF is absent. The individual molecules are treated within Hubbard and Pariser-Parr-Pople (PPP) models and the interac-tion between them involves transfer terms, intersite electron repulsions and site-charge—bond-charge repulsion terms. Initial wave packet is construc ted from ex-cited singlet state of one molecule and ground state of the other. Time develop-ment of this wave packet under the influence of intermolecular interactions is fol-lowed within the Schrodinger¨ picture by an efficient predictor-corrector scheme. In unsubstituted Hubbard and PPP chains, 21A state leads to significant SF yield while the 11B state gives negligible fission yield. On substitution by donor-acceptor groups of moderate strength, the lowest excited state will have sufficient 2 1A char-acter and hence gives significant SF yield. Because of rapid internal c onversion, the nature of the lowest excited singlet will determine the SF contribution to OSC effi - ciency. Furthermore, we find the fission yield depends considerably on th e stacking arrangement of the polyene molecules. In chapter 5, we have given an account of a new modified algorithm for symmetry adaptation within symmetrized density matrix renormalization group (SDMRG) technique. SDMRG technique has been an efficient method for studying low-lying eigenstates in one and quasi-one dimensional electronic systems. However, SDMRG method until now, had bottlenecks involving construction of linearly in-dependent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. Our modified algorithm overcomes this bottleneck. T he new method incorporates end-to-end interchange symmetry (C2), electron-hole symmetry (J) and parity or spin-flip symmetry (P) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new ba-sis with maximum sparseness, just one non-zero matrix element per row. Using methods similar to those employed in exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the eighties, it is possible to construct or-thogonal SDMRG basis states while bypassing the slow step of Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited states of 1,12-benzoperylene. In chapter 6, we have studied the correlated excited states of coronene and ova-lene within Pariser-Parr-Pople (PPP) model employing symmetry adapted density matrix renormalization group technique. These polynuclear aromatic hydrocar-bons can be considered as graphene nanoflakes and study of their ele ctronic struc-tures will shed light on the electron correlation effects in these finite-size gr aphene analogues. The electron correlation effect usually diminishes on going from one-dimensional to higher-dimensional systems, yet, it is significant within these fin ite-size graphene derivatives where it depends on the molecular topology. We have characterized these low-lying energy states by calculating bond orders, spin den-sities in the lowest triplet state and two-photon absorption cross-sections for low-lying two-photon states. vi

Discovery of grapheme has paved way for experimental realization of many physical phenomena such as massless Dirac fermions, quantum hall effect and zero-field conductivity. Search for other two dimensional (2D) materials led to the discovery of boron nitride, transition metal dichalcogenides(TMDs),transition metal oxides(MO2)and silicene. All of these materials exhibit different electronic and transport properties and are very promising for nanodevices such as nano-electromechanical-systems(NEMS), field effect transistors(FETs),sensors, hydrogen storage, nano photonics and many more. For practical utility of these materials in electronic and photonic applications, varying the band gap is very essential. Tuning of band gap has been achieved by doping, functionalization, lateral confinement, formation of hybrid structures and application of electric field. However, most of these techniques have limitations in practical applications. While, there is a lack of effective method of doping or functionalization in a controlled fashion, growth of specific sized nanostructures (e.g., nanoribbons and quantum dots),freestanding or embedded is yet to be achieved experimentally. The requirement of high electric field as well as the need for an extra electrode is another disadvantage in electric field induced tuning of band gap in low dimensional materials. Development of simpler yet effective methods is thus necessary to achieve this goal experimentally for potential application of these materials in various nano-devices. In this thesis, novel methods for tuning band gap of few 2D materials, based on strain and stacking, have been proposed theoretically using first principles based density functional theory(DFT) calculations. Electronic properties of few layered nanomaterials are studied subjected to mechanical and chemical strain of various kinds along with the effect of stacking pattern. These methods offer promising ways for controlled tuning of band gap in low dimensional materials. Detailed methodology of these proposed methods and their effect on electronic, structural or vibrational properties have also been studied. The thesis has been organized as follows: Chapter1 provides a general introduction to the low dimensional materials: their importance and potential application. An overview of the systems studied here is also given along with the traditional methods followed in the literature to tune their electronic properties. The motivation of the current research work has also been highlighted in this chapter. Chapter 2 describes the theoretical methodology adopted in this work. It gives brief understanding of first principles based Density Functional Theory(DFT) and various exchange and correlation energy functionals used here to obtain electronic, structural, vibrational and magnetic properties of the concerned materials. Chapter 3 deals with finding the origin of a novel experimental phenomenon, where electromechanical oscillations were observed on an array of buckled multiwalled carbon nanotubes (MWCNTs)subjected to axial compression. The effect of structural changes in CNTs in terms of buckling on electronic properties was studied. Contribution from intra-as well as inter-wall interactions was investigated separately by using single-and double-walled CNTs. Chapter 4 presents a method to manipulate electronic and transport properties of graphene bilayer by sliding one of the layers. Sliding caused breaking of symmetry in the graphene bilayer, which resulted in change in dispersion in the low energy bands. A transition from linear dispersion in AA stacking to parabolic dispersion in AB stacking is discussed in details. This shows a possibility to use these slid bilayers to tailor graphene based devices. Chapter 5 develops a method to tune band gap of bilayers of semiconducting transition metal dichalcogenides(TMDs) by the application of normal compressive strain. A reversible semiconductor to metal(S-M) transition was reported in this chapter for bilayers of TMDs. Chapter 6 shows the evolution of S-M transition from few layers to the bulk MoS2 under various in-plane and out of plane strains. S-M transition as a function of layer number has been studied for different strain types. A comparison between the in-plan and normal strain on modifying electronic properties is also presented. Chapter 7 discusses the electronic phase transition of bulk MoS2 under hydrostatic pressure. A hydrostatic pressure includes a combined effect of both in-plane and normal strain on the structure. The origin of metallic transition under pressure has been studied here in terms of electronic structure, density of states and charge analysis. Chapter 8 studies the chemical strain present in boron nitride nanoribbons and its effect on structural, electronic and magnetic properties of these ribbons. Properties of two achiral (armchair and zig-zag) edges have been analyzed in terms of edge energy and edge stress to predict stability of the edges. Chapter9 summarizes and concludes the work presented in this thesis.

Einzelschichten von Graphen-Nanobänders (GNRs) wurden auf SiC(0001)-Substraten mit zwei unterschiedlichen Fehlschnitten bei Temperaturen von 1410 bis 1460 °C synthetisiert. Das GNR-Wachstum lässt sich bei niedriger Stufenkantenhöhe am besten durch eine exponentielle Wachstumsrate, welche mit der Energiebarriere für die Ausdiffusion von Si korreliert ist. Anderseits wird bei Substraten mit höheren Stufenkanten eine nicht-exponentielle Rate beobachtet, was mit der Bildung von mehrlagigen Graphen an den Stufenkanten in Verbindung gebracht wird. Die Sauerstoffinterkalation von epitaktischen GNRs mittels Ausglühen an Luft von Bändern wird als nächstes untersucht, welche auf unterschiedlichen SiC-Substraten gewachsen wurden. Neben der Umwandlung von monolagigem zu zweilagigem Graphen in der Nähe der Stufenkanten von SiC, führt die Sauerstoffinterkalation zusätzlich zu der Bildung einer Oxidschicht auf den Terrassen des Substrats, was die zweilagigen GNRs elektrisch isoliert voneinander zurücklässt. Die elektrische Charakterisierung der zweilagigen GNRs zeigten dass die Bänder durch die Behandlung mit Sauerstoff elektrisch voneinander entkoppelt sind. Eine robuste Lochkonzentration von etwa 1x10¹³ cm-² und Mobilitäten von bis zu 700 cm²/(Vs) wurden für die GNRs mit einer typischen Breite von 100 nm bei Raumtemperatur gemessen. Wohl definierte Mesastrukturen gebildet mittels Elektronenstrahllithographie auf SiC-Substraten, wurde zuletzt untersucht. Die Charakterisierung des Ladungsträgertransports von GNRs die auf den Seitenwänden der strukturierten Terrassen gewachsen wurden, zeigt eine Mobilität im Bereich von 1000 bis 2000 cm²/(Vs), welche für verschiedene Strukturen auf der gesamten Probe homogen ist, was die Reproduzierbarkeit dieses Herstellungsverfahrens hervorhebt, sowie dessen Potential für die Implementierung in zukünftigen Technologien, welche auf epitaktischgewachsenene GNRs basieren. / Monolayer graphene nanoribbons (GNRs) were synthesized on SiC(0001) substrates with two different miscut angles at temperatures ranging from 1410 to 1460 °C. The GNR growth in lower step heights is best described by an exponential growth rate, which is correlated with the energy barrier for Si out-diffusion. On the other hand, a non-exponential rate is observed for substrates with higher steps, which is associated with the formation of few-layer graphene on the step edges. Oxygen intercalation of epitaxial GNRs is investigated next by air annealing ribbons grown in different SiC(0001) substrates. Besides the conversion of monolayer into bilayer graphene near the step edges of SiC, the oxygen intercalation also leads to the formation of an oxide layer on the terraces of the substrate, leaving the bilayer GNRs electronically isolated from each other. Electrical characterization of bilayer GNRs reveals that the ribbons are electrically decoupled from the substrate by the oxygen treatment. A robust hole concentration of around 1x10¹³ cm-² and mobilities up to 700 cm²/(Vs) at room temperature are measured for GNRs whose typical width is 100 nm. Well defined mesa structures patterned by electron beam lithography on the surface of SiC substrates is lastly researched. Transport characterization of GNRs grown on the sidewalls of the patterned terraces shows a mobility in the range of 1000 – 2000 cm²/(Vs), which is homogeneous for various structures throughout the sample, indicating the reproducibility of this fabrication method and its potential for implementation in future technologies based on epitaxially grown GNRs.

Carbon-based conductors like carbon nanotubes (CNTs) and graphene nanoribbons (GNRs) have many properties, which make them relevant for potential electronic applications. Among them are high conductances and tunable band gap sizes. These properties make CNTs and GNRs useful in many circumstances, e.g. as channel material in transistors or transparent electrodes in solar cells. Plenty of literature can be found on the topic of single linear CNTs/GNRs. Some applications however require a large network of these conductors. In addition, a single conductor has only a small impact on the network conductance, which reduces the need to control the properties of each individual nanotube/-ribbon. This leads to networks being easier to apply. In this work, the conductance of large networks of GNRs is calculated using the quantum-transport formalism (QT). This has not been done before in literature. In order to apply QT to such a large amount of atoms, the recursive Green's function formalism is used. For this the networks are devided into subcells, which are represented by tight-binding matrices. Similar networks are also examined using two different nodal analysis (NA) approaches, where the nanoribbons are treated as ohmic conductors. For NA with one-dimensional conductors, major discrepancies are found in regards to the QT model. However, networks consisting of two-dimensional conductors (NA-2D) have many properties similar to the QT networks. A recipe to approximate the QT results with NA-2D is presented.:1. Introduction 2. Theoretical Principles 2.1 Carbon-based Conductors 2.1.1 Structure and Properties 2.1.2 Networks 2.2 Tight-Binding Model 2.3 Quantum Transport 2.3.1 Introduction 2.3.2 Level Broadening 2.3.3 Current Flow 2.3.4 Transmission 2.4 Nodal Analysis 3. Implementation 3.1 Quantum Tranport 3.1.1 Network Generation 3.1.2 Density-Functional based Tight-Binding Method 3.1.3 Recursive Green's Function Algorithm 3.1.4 Conductance 3.2 Nodal Analysis 3.2.1 One-dimensional Conductors 3.2.2 Two-dimensional Conductors 4. Results 4.1 Quantum Transport 4.1.1 Band Structures and Fermi Energies 4.1.2 Ideal Transmission and Consistency Tests 4.1.3 Percolation 4.1.4 Transmission 4.1.5 Conductance 4.1.6 Power Law Scaling 4.1.7 Size Dependence and Confinement Effects 4.1.8 Calculation Time 4.2 Nodal Analysis 4.2.1 One-dimensional Conductors 4.2.2 Two-dimensional Conductors 4.2.3 Calculation Time 4.3 Approximating QT with NA 4.3.1 Optimal Parameters 4.3.2 Percolation 4.3.3 Conductance 4.3.4 Power Law Scaling 5. Conclusions / Graphenbasierte Leiter wie Kohlenstoff-Nanoröhrchen (engl. 'carbon nanotubes', CNTs) oder Graphen-Nanobänder (engl. 'graphene nanoribbons', GNRs) haben viele Eigenschaften, die sie für potenzielle elektronische Anwendungen interessant machen. Darunter sind hohe Leitfähigkeiten und einstellbare Bandlückengrößen. Dadurch sind CNTs und GNRs in vielen Bereichen nützlich, z.B. als Kanalmaterial in Transistoren oder als transparente Elektroden in Solarzellen. Es gibt viel Literatur über einzelne, lineare CNTs/GNRs. Einige Anwendungen benötigen jedoch ein großes Netzwerk dieser Leiter. Zusätzlich hat ein einzelner Leiter wenig Einfluss auf die Leitfähigkeit des Netzwerks, wodurch die Eigenschaften der einzelnen Nanoröhrchen/-streifen weniger streng kontrolliert werden müssen. Dies führt dazu, dass es einfacher ist Netzwerke zu nutzen. In dieser Arbeit wird die Leitfähigkeit von großen GNR-Netzwerken mittels Quantentransport (QT) berechnet. Dies wurde in der Literatur noch nicht getan. Um QT auf eine so große Menge an Atomen anzuwenden wird der rekursive Greenfunktions-Formalismus benutzt. Dazu werden die Netzwerke in Unterzellen unterteilt, die durch Tight-Binding-Matrizen dargestellt werden. Ähnliche Netzwerke werden auch mit zwei Versionen der Knotenanalyse (engl. 'nodal analysis', NA) untersucht, welche die Nanobänder wie ohmische Leiter behandelt. Die Ergebnisse der NA mit eindimensionalen Leitern weisen deutliche Unterschiede zu den mit QT erzielten Ergebnissen auf. Wenn jedoch zweidimensionale Leiter in NA verwendet werden (NA-2D) gibt es viele parallelen zu den QT Ergebnissen. Zuletzt wird ein Vorgehen präsentiert, mit dem QT Resultate durch NA-2D Rechnungen genähert werden können.:1. Introduction 2. Theoretical Principles 2.1 Carbon-based Conductors 2.1.1 Structure and Properties 2.1.2 Networks 2.2 Tight-Binding Model 2.3 Quantum Transport 2.3.1 Introduction 2.3.2 Level Broadening 2.3.3 Current Flow 2.3.4 Transmission 2.4 Nodal Analysis 3. Implementation 3.1 Quantum Tranport 3.1.1 Network Generation 3.1.2 Density-Functional based Tight-Binding Method 3.1.3 Recursive Green's Function Algorithm 3.1.4 Conductance 3.2 Nodal Analysis 3.2.1 One-dimensional Conductors 3.2.2 Two-dimensional Conductors 4. Results 4.1 Quantum Transport 4.1.1 Band Structures and Fermi Energies 4.1.2 Ideal Transmission and Consistency Tests 4.1.3 Percolation 4.1.4 Transmission 4.1.5 Conductance 4.1.6 Power Law Scaling 4.1.7 Size Dependence and Confinement Effects 4.1.8 Calculation Time 4.2 Nodal Analysis 4.2.1 One-dimensional Conductors 4.2.2 Two-dimensional Conductors 4.2.3 Calculation Time 4.3 Approximating QT with NA 4.3.1 Optimal Parameters 4.3.2 Percolation 4.3.3 Conductance 4.3.4 Power Law Scaling 5. Conclusions

La synthèse du graphène par traitement thermique d’un substrat de carbure de silicium (SiC) est une technique prometteuse pour l’intégration de ce nouveau matériau dans l’industrie, notamment dans les dispositifs électroniques. L’avantage de cette méthode réside dans la croissance de films minces de graphène de taille macroscopique directement sur substrat isolant. Toutefois, avant d’intégrer ce matériau, il convient d’en contrôler la synthèse et d’en moduler les propriétés. Dans ce travail de thèse, nous étudions les propriétés structurales et électroniques du graphène obtenu par la graphitisation des polytypes 3C-, 4H- et 6H-SiC. A partir de diverses méthodes de caractérisation, telles que la diffraction des électrons lents (LEED) ou la microscopie et spectroscopie à effet tunnel (STM/STS), nous avons vérifié, dans un premier temps, que le caractère discontinu du graphène sur les bords de marches peut introduire un confinement latéral supplémentaire des électrons dans le graphène. Dans un second temps, l’observation des singularités de Van Hove nous a permis de démontrer l’effet de confinement unidimensionnel dans les régions d’accumulations de marches du SiC. Enfin, l’introduction de désordre dans nos couches de graphène induit une réduction de la densité de porteurs de charges dans les couches. De même, ce désordre conduit à une transition de phase quantique entre le régime localisé et le régime d’effet Hall quantique. / The synthesis of graphene by thermal decomposition of silicon carbide (SiC) is a promising technique for the integration of this new material in the industry, especially in electronic devices. The advantage of this method lies in the growth of macroscopic graphene films directly on an insulator substrate. However, before using this material in electronic devices, it is advisable to control its synthesis and modulate its properties. In this thesis, we present the structural and electronic properties of graphene obtained by graphitization of 3C- , 4H - and 6H- SiC polytypes. Various characterization methods were used, including low energy electron diffraction (LEED) and microscopy and scanning tunneling spectroscopy (STM / STS). Based on STM / STS measurements, we show that the discontinuity of epitaxial graphene at the step edges may introduce an additional lateral confinement of electrons in graphene. The observation of Van Hove singularities in the STS spectra confirmed the one dimensional confinement of graphene in step bunching regions of SiC.Finally, we show that when disorder is introduced on our graphene samples, the charge carrier density is reduced. This disorder lead to the observation of a quantum phase transition from a localized regime to a quantum Hall effect regime.

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