1st Edition

Graphene Fundamentals, Devices, and Applications

By Serhii Shafraniuk Copyright 2015
    634 Pages 22 Color & 142 B/W Illustrations
    by Jenny Stanford Publishing

    Graphene is the first example of two-dimensional materials and is the most important growth area of contemporary research. It forms the basis for new nanoelectronic applications. Graphene, which comprises field-effect structures, has remarkable physical properties.

    This book focuses on practical applications determined by the unique properties of graphene. Basic concepts are elucidated by end-of-chapter problems, the answers to which are provided in the accompanying solutions manual. The mechanisms of electric and thermal transport in the gated graphene, interface phenomena, quantum dots, non-equilibrium states, scattering and dissipation, as well as coherent transport in graphene junctions are considered in detail in the book. Detailed analyses and comparison between theory and experiments is complemented with a variety of practical examples.

    The book has evolved from the author’s own research experience and from his interaction with other scientists at tertiary institutions and is targeted at a wide audience ranging from graduate students and postdoctoral fellows to mature researchers and industrial engineers.


    Chiral fermions in graphene

    Low-energy electron excitations in graphene

    Dirac equation for chiral fermions

    Berry phase and topological singularity in graphene

    Klein paradox and chiral tunneling

    Landau levels in graphene

    Modeling the graphene devices


    The field-biased graphene junctions

    Electron and hole excitations in graphene

    Quantum capacitance of graphene

    Einstein relation in graphene

    Electrostatics of gated graphene devices: charge traps near the graphene/oxide interface

    Steady-state electrostatics of graphene field-effect transistors

    Characteristic scales of gated graphene

    Solving the electrostatic equation

    Capacitance of the channel and of the gate

    Diffusion-drift current ratio of the diffusion and drift currents

    Continuity of electric current

    Inhomogeneous behavior of chemical and electrostatic potential along the channel

    Microscopic model of electron transport through the field-effect transistor

    Conventional tunneling via a rectangular barrier

    Chiral tunneling through a rectangular barrier

    Role of edges: armchair edges

    Role of edges: zigzag edges

    Deviation of an electron inside a wide chiral barrier

    Electric current density across the chiral barrier

    Gate voltage–controlled quantization

    A hybrid graphene–CNT junction

    Electric current characteristics

    The saturation regime (pinch-off)

    Linear behavior in low fields

    Transit time through the channel

    The diffusion-drift approximation

    Effects in the high field

    Generalized boundary conditions

    Pseudo-diffusive dynamics

    Confinement and Zitterbewegung


    Tight-binding model of bilayer graphene

    A bilayer graphene junction

    Heavy chiral fermion state in graphene stripe

    3.4. Quantum-confined Stark effect

    PT-invariance the Dirac Hamiltonian

    Heavy chiral fermions at zigzag edges of graphene stripe


    Phonon modes in the two-dimensional graphene

    Phonon spectra in graphene, and graphene nanoribbons

    The phonon transport in two-dimensional crystals

    Momentum diagram of phonon transport in graphene

    Thermal conductivity due to phonons in graphene nanoribbons

    Raman scattering

    Role the degrees of freedom

    Molecular vibrations and infrared radiation

    Various processes of light scattering

    Stokes and anti-Stokes scattering

    Raman scattering versus fluorescence

    Selection rules for Raman scattering

    Raman amplification and Stimulated Raman scattering

    A requirement of the coherence

    Practical applications

    Higher-order Raman spectra

    Raman spectroscopy of graphene

    Kohn anomalies, double resonance, and D and G peaks

    Deriving the electron–phonon coupling from Raman line width

    Raman spectroscopy of graphene and graphene layers

    Failure the adiabatic Born–Oppenheimer approximation and the Raman spectrum of doped graphene

    Influence of the atomic and structural disorders

    Graphene ribbons and edges


    Pseudospin conservation during the scattering of chiral fermions

    Phonon drag effect

    Screening by interacting electrons

    Plasma oscillations

    Plasma excitations in graphene

    Coupling between electrons and phonons

    Susceptibility of graphene


    Dielectric function in graphene and CNT

    Electron-impurity scattering time in graphene

    Scattering of phonons in a few-layer graphene


    Electron-electron Coulomb interaction

    Electron self-energy

    Quasi-particle excitation energy

    Computational results


    Wannier–Mott excitons

    Excitonic states

    Experimental observation of excitons in graphene

    Electron scattering on indirect excitons

    Tomonaga–Luttinger liquid

    Probing of intrinsic state of one-dimensional quantum well with a photon-assisted tunneling

    The TLL tunneling density of states of a long quantum well

    Identifying the charge and the spin boson energy levels

    Useful relationships


    Graphene/superconductor interface

    Conversion between Electrons and holes at the N/S interface

    BTK model of Andreev reflection

    Experimental study of the Andreev reflection in graphene

    Interpretation of Andreev reflection in graphene-based junctions

    Amplitude of composite Andreev reflection

    Amplitude of composite Andreev reflection

    Van Hove singularities and superconductivity in carbon nanotubes and graphene stripes

    Theoretical model


    Relevance of non-equilibrium effects in graphene junction

    Tunneling rates for a graphene junction

    Non-equilibrium electric current

    The Green Keldysh function of non-equilibrium electrons

    "Homogeneous" approximation inside the chiral barrier

    Expressions for the advanced Green functions

    The -function approximation

    Photon-assisted tunneling current through the chiral barrier

    Electron self-energy and many-body effects

    Quantum kinetic equation for

    Symmetric junction

    Non-equilibrium contribution

    The photon-assisted electric current

    Equilibrium current

    The gate current

    Excessive regular current

    Absorbed power

    Jarzynski equality for quantum systems

    Quantum Jarzynski equality for spin ½


    Thermoelectric effects on the nanoscale

    Performance of the thermoelectric device

    Quantum theory of electronic thermal transport

    Electron transport and elastic collisions

    Reversible Peltier effect in carbon nano-junctions

    Thermoelectric figure of merit and Fourier law

    Phonon transport and thermal conductivity

    Recent experiments for measuring the thermal conductivity of graphene

    Microscopic model of the thermoelectric effect

    Converting the heat into electricity by a graphene stripe with heavy chiral fermions

    Blocking the phonon flow by multilayered electrodes

    Molecular dynamics simulations

    Non-equilibrium thermal injection

    Perspectives of thermoelectric research for graphene


    Sensors of electromagnetic field

    THz sensor based on carbon nanotube quantum dot

    Microscopic model of the carbon nanotube quantum dot sensor

    Electromagnetic field influence

    Key assumptions

    Electron quantization in the steady state

    The THz field influence to quantum dot

    Characteristics of the electric transport

    Responsivity and quantum efficiency of the THz detector

    Intrinsic noise and the noise equivalent power

    Frequency range and operation temperature


    Atomic monolayers

    Monolayer and a few-layered materials

    Electric transport in nanodevices

    Electronic transport versus scattering mechanisms

    TMDC transistors

    Perspectives of the TMDC electronics

    Vibrational and optical properties of TMDCs

    The future applications of 2D materials


    Serhii Shafraniuk

    "Graphene: Fundamentals, Devices, and Applications provides a comprehensive textbook, primarily focused on graphene but also containing up-to-date coverage of carbon nanotubes, and even an introduction to few-layered transition metal dichalcogenides. Each of the 11 chapters ends with a problem set and an extensive list of references. Many examples of device applications are given in each chapter, thereby making the book attractive to practicing engineers and engineering students."

    —Prof. Mildred Dresselhaus, Massachusetts Institute of Technology, USA

    "This book is the most advanced introduction to a fascinating world of two-dimensional materials. Detailed and self-contained description of electric, thermal, and thermoelectric properties of graphene and graphene nanostructures is a valuable resource for researchers in physics, materials science, nanotechnologies, and sensing. Accessible presentation of the most complicated phenomena and interesting original problems will be appreciated by graduate students."

    —Prof. Vladimir Mitin, The State University of New York, USA

    "This is a long-awaited monograph that provides a direct link from the unique energy spectra, including the chiral properties, thermal and electric transport, as well as vibrational, interface, scattering, and dissipation phenomena in both ideal and dirty graphene, to their remarkable possible applications. Graphene nanocoolers and cogenerators of electricity are splendid examples of such novel applications in thermoelectricity. The miraculous potentialities of graphene-quantum-dot-based structures as THz detectors are supported by a big number of both theoretical analyses and experimental observations. I strongly recommend this book to all who are interested in the most recent advances in the fascinating field of monolayered nanostructures."

    —Prof. Vladimir M. Fomin, Leibniz Institute for Solid State and Materials Research (IFW), Germany