Electronic properties of graphene on a piezoelectric substrate

• Autores: David González González
• Directores de la Tesis: Francisco Guinea López (dir. tes.), Fernando Sols Lucia (dir. tes.)
• Lectura: En la Universidad Complutense de Madrid ( España ) en 2018
• Idioma: inglés
• Número de páginas: 155
• Títulos paralelos:
  • Propiedades electrónicas del grafeno sobre un sustrato piezoeléctrico
• Tribunal Calificador de la Tesis: María Varela del Arco (presid.), Óscar Rodríguez de la Fuente (secret.), Pedro L. de Andrés Rodríguez (voc.), Jorge Pedrós Ayala (voc.), Pablo San José Martín (voc.)
• Programa de doctorado: Programa de Doctorado en Física por la Universidad Complutense de Madrid
• Materias:
  • Física
    • Física del estado sólido
      • Propiedades de transporte de electrones
• Enlaces
  • Tesis en acceso abierto en: Docta Complutense
• Resumen
  • español

    En el presente trabajo investigamos teoricamente las propiedades electrónicas de una capa de grafeno sobre un sustrato piezoelectrico. Concretamente, estudiamos el efecto de los modos de vibracion acusticos de superficie sobre los electrones del grafeno. Este trabajo esta dividido en seis captulos y varios apendices, siendo el objetivo de estos ultimos el que el material sea lo mas autocontenido posible. El primer capítulo introduce una vision general de los actores principales en este trabajo. El grafeno es un material de dos dimensiones que ha atraído una atencion creciente internacionalmente desde su aislamiento por Novoselov y Geim en 2004. Esta formado por una red de átomos de carbono en forma de panal. El grafi to, la forma mas común de carbono puro, puede ser visto como si estuviera hecho por laminas de grafeno debilmente acopladas. El grosor atomico del grafeno, combinado con sus propiedades electrónicas únicas originadas por el comportamiento de sus electrones como si no tuvieran masa, convierte a este material en un objeto excepcional de elevado interés fundamental y aplicado...

  • English

    In the present work, we investigate theoretically the electronic properties of a graphene layer on a piezoelectric substrate. Specifically, we study the effect of the surface acoustic vibration modes on the graphene electrons.

    The first chapter introduces a basic survey of the main actors in this work. Graphene is a two-dimensional material that has received increasing worldwide attention since its isolation by Novoselov and Geim in 2004. It is formed by a honeycomb lattice of carbon atoms. The single-atom thickness of graphene, combined with its unique electronic properties stemming from the effectively massless behavior of electrons, converts this material into a special object of high fundamental and applied interest.

    The extremely high carrier mobility in suspended graphene is enabled by the high frequencies of the optical phonons in the stiff honeycomb lattice. Thus, the effects of electron-phonon scattering on transport are small in comparison with conventional metals. However, in most device architectures, graphene is deposited on a substrate, and all lattice modes of the substrate material that induce an electric field will influence the carriers in the graphene sheet, making the choice of substrate material crucial for the resulting transport characteristics of the device.

    On the other hand, surface acoustic waves (SAWs) created in piezoelectric materials reside at the surface of a solid or at the interface between two solids. They have for long been used to control the properties of semiconductor materials and structures. SAWs may be used to convert mechanical into electric signals and vice versa. A first basic description of piezoelectricity and these waves in the first chapter, is followed by a quantitative study of their propagation and main characteristics in the second chapter.

    Apart from the mechanical deformation, the vibration of the ionic lattice in a piezoelectric material produces an electric field travelling along with the SAW. The need to quantify its effects accurately both for macroscopic SAWs and their vibration quanta, the acoustic phonons, leads to the third chapter. There, the interaction between the electrons of a two-dimensional metal and the acoustic phonons of an underlying piezoelectric substrate is investigated. Fundamental inequalities can be obtained from general energy arguments.

    As a result, phonon-mediated attraction can be proven to never overcome electron Coulomb repulsion, at least for long phonon wavelengths. Therefore, in the fourth chapter, we study the influence of these phonons on the electron-electron interactions and the possible pairing instabilities of a two-dimensional electron gas such as graphene.

    In the fifth chapter, we investigate the many-body properties of graphene on top of a piezoelectric substrate, focusing on the interaction between the graphene electrons and the piezoelectric acoustic phonons. We calculate the electron and phonon self-energies as well as the electron mobility limited by the substrate phonons. We emphasize the importance of the proper screening of the electron-phonon vertex and discuss the various limiting behaviors as a function of electron energy, temperature, and doping level. The effect on graphene electrons of the piezoelectric acoustic phonons is compared with that of the intrinsic deformation acoustic phonons of graphene.

    The global conclusions of this work are contained in the last chapter. The numerical results for mean free paths and electron mobilities shown are seen to be applicable to a variety of piezoelectrical materials with different lattice structures and piezoelectric strengths. Our study can be thus relevant for graphene devices operating in the ballistic transport regime and for scenarios where quantum interference induces localization phenomena.