Electronic and thermoelectric properties of graphene/boron nitride in-plane heterostructures van Truong Tran To cite this version: van Truong Tran. Electronic and thermoelectric properties of graphene/boron nitride in-plane het- erostructures. Materials Science [cond-mat.mtrl-sci]. Université Paris Saclay (COmUE), 2015. En- glish. NNT : 2015SACLS133. tel-01374739 HAL Id: tel-01374739 https://tel.archives-ouvertes.fr/tel-01374739 Submitted on 1 Oct 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. NNT : 2015SACLS133 THESE DE DOCTORAT DE L’UNIVERSITE PARIS-SACLAY, préparée à l’Université Paris-Sud ÉCOLE DOCTORALE N° 575 Electrical, Optical, Bio – physics and Engineering (EOBE) IEF - Institut d'Electronique Fondamentale Spécialité de doctorat : Electronique et Optoélectronique, Nano et Microtechnologies Par Van-Truong Tran Propriétés électroniques et thermoélectriques des hétérostructures planaires de graphène et de nitrure de bore Thèse présentée et soutenue à Orsay, le 26 Novembre 2015 : Composition du Jury : M. VOLZ Sebastian EM2C, CNRS Président M. GOUPIL Christophe LIED, Université Paris Diderot Rapporteur M. PALA Marco IMEP-LAHC, CNRS Rapporteur M. SAINT-MARTIN Jérôme IEF, Université Paris-Sud Examinateur M. DOLLFUS Philippe IEF, CNRS Directeur de thèse Contents Contents .................................................................................................................................................... i List of figures .......................................................................................................................................... v Acknowledgements ............................................................................................................................... xv Abstract ................................................................................................................................................... 1 Résumé .................................................................................................................................................... 2 Introduction ........................................................................................................................................... 12 1 Chapter 1: ...................................................................................................................................... 17 1.1 The semi-empirical methods ................................................................................................. 17 1.1.1 Tight Binding model for electron study ........................................................................ 18 1.1.2 Force Constant model for phonon study ....................................................................... 21 1.1.3 Matrix representation for Tight Binding and Force Constant calculations ................... 23 1.1.4 Operator form of Tight Binding Hamiltonian ............................................................... 26 1.1.5 Eigen value problem for infinite periodic structures ..................................................... 28 1.2 Physical quantities that can be obtained from band structure ............................................... 30 1.2.1 Bandgap ......................................................................................................................... 30 1.2.2 Density of states and local density of states .................................................................. 31 1.2.3 Electron and hole distributions ...................................................................................... 31 1.2.4 Group velocity ............................................................................................................... 32 1.2.5 Effective mass ............................................................................................................... 32 1.3 Coupled Schrödinger -Poisson’s equations ........................................................................... 33 i 1.4 Green's function method ........................................................................................................ 34 1.4.1 General definition of a Green's function ....................................................................... 34 1.4.2 Green's function in Physics. Atomistic Green's function .............................................. 35 1.4.3 Green's functions for an open system ............................................................................ 36 1.4.4 Calculation of DOS by Green function ......................................................................... 37 1.5 Physical quantities obtained from transport study ................................................................. 38 1.5.1 Calculation of the Transmission from Green's function ................................................ 38 1.5.2 Local density of states ................................................................................................... 39 1.5.3 Electron current ............................................................................................................. 40 1.5.4 Conductance .................................................................................................................. 41 1.5.5 Thermoelectric effects ................................................................................................... 42 1.6 Computational Techniques .................................................................................................... 44 1.7 Examples: electrons and phonons in linear chain, graphene and Boron Nitride (BN). ......... 45 1.7.1 Linear chain ................................................................................................................... 45 1.7.2 Graphene ....................................................................................................................... 57 1.7.3 Boron Nitride ................................................................................................................. 64 1.8 Conclusions ........................................................................................................................... 67 2 Chapter 2: ...................................................................................................................................... 68 2.1 Introduction ........................................................................................................................... 68 2.2 The modeling and methodologies ......................................................................................... 73 2.3 Results and discussion ........................................................................................................... 76 ii 2.3.1 Bandgap opening in armchair Graphene/BN ribbons .................................................... 76 2.3.2 Bandgap opening in zigzag Graphene ribbons .............................................................. 87 2.4 Conclusions ........................................................................................................................... 93 3 Chapter 3: ...................................................................................................................................... 94 3.1 Introduction ........................................................................................................................... 94 3.2 Modelling and methodology ................................................................................................. 95 3.3 Results and discussions ......................................................................................................... 97 3.3.1 Modulation of bandgap under effect of by a transverse electric field: First approach .. 97 3.3.2 Modulation of bandgap under effect of by a transverse electric field: Self-consistent study 102 3.3.3 Tuning of current using transverse electric fields ....................................................... 108 3.4 Conclusions ......................................................................................................................... 112 4 Chapter 4: .................................................................................................................................... 113 4.1 Introduction ......................................................................................................................... 113 4.2 Methodology ....................................................................................................................... 117 4.3 Results and discussion ......................................................................................................... 119 4.3.1 Hybrid states in a “one-interface” structure ................................................................ 119 4.3.2 Hybrid states in a “two-interface” structure ................................................................ 122 4.3.3 Dispersion of hybrid states: specific properties ........................................................... 126 4.3.4 From the effective model to hybrid states: the role of