Electronic properties of graphene: A multiphysics simulation approach

Graphene is a single atomic layer of hexagonally arranged carbon atoms. Since the experimental discovery of graphene in 2004, a wealth of research has been conducted on studying its electronic and optical properties, as well as on developing novel applications. To explaining the typically observed electronic properties of graphene and to evaluate its potential in novel applications it is vital to quantitatively examine the intrinsic limits and the influence of the dominant extrinsic factors on the electromagnetic response of this material. The two-dimensional nature of graphene makes it vulnerable to the influence of a host of extrinsic factors, such as the interface phonons from the supporting substrate and trapped charged impurities near the interface between graphene and the substrate.;In this dissertation, the electronic transport properties of graphene are examined in detail using multiphysics numerical simulations. Specifically, the following three aspects are studied: electron-phonon scattering rates and the intrinsic mobility, effect of clustered impurities on carrier transport, and substrate-dependent THz-frequency carrier transport. To calculate the electron-phonon scattering rates and predict the intrinsic mobility of graphene, the overlap between the electronic tight-binding Bloch wave functions (TB BWF), up to the third nearest neighbors, are used. Room-temperature carrier dynamics in suspended and supported graphene in the presence of different impurity distributions and densities is simulated using a numerical method that combines semiclassical carrier transport, using ensemble Monte-Carlo (EMC), with electrodynamics, using the finite-difference time-domain (FDTD) technique and molecular dynamics (MD).;The electron-phonon scattering rates calculated using TB BWFs provide a better estimate of the ``bare'' acoustic and optical deformation potential constants (Dac = 12eV, Dop = 5 x 109 eV cm-1), while the intrinsic mobility calculated exceeds experimentally observed values and agrees with theoretical predictions based on density functional theory. Clustered impurities (average cluster size between 40 nm--50 nm) are shown to have a significant effect on carrier transport in graphene and explain the experimentally observed average electron-hole puddle size of 20 nm. In addition, the residual conductivity and the linear-region slope of the conductvity versus carrier density dependence are found to be determined by the impurity distribution and density, while the high-carrier-density sublinearity in the conductivity is shown to stem from carrier-carrier interactions. There is excellent agreement between the THz-conductivity calculated with clustered impurities and the experimentally measured frequency-dependent conductivity. Moreover, the choice of the substrate (SiO2 or h-BN) is shown to be important below 4THz provided the ratio of impurity to carrier density (Ni/n) is less than 0.1, where carrier scattering with substrate phonons dominates transport. Electron-impurity interactions govern transport for 0.1 < 0.5. The Drude weight is shown to be reduced by both electron-electron and electron-impurity interactions, while the effecive scattering rate depends only on electron-impurity interactions.;These detailed numerical calculations provide a better understanding of the intrinsic limits of ideal suspended graphene and explain many of the observed electronic properties of realistic supported graphene samples.