| Graphene, a single sheet of graphite, has many interesting electronic and mechanical properties, making it a viable candidate for tomorrow's electronics. It remains the most widely studied material in condensed matter physics as of 2011. Due to various disorder effects, many useful properties of pristine graphene predicted by theory may not show up in real world systems, and the exact effects of disorder on graphene nanoelectronics have not been investigated to any satisfaction. The research goal of this thesis is to provide first principles calculations to study disorder scattering in graphene nanostructures.;This theoretical framework is then applied to study quantum transport in graphene with atomistic disorder. We shall investigate effects of substitutional boron (B)and nitrogen (N) doping in a graphene device connected to intrinsic graphene electrodes. We have calculated quantum transport of two-probe graphene devices versus disorder concentration x, device length L, electron electron energy E, and our results suggest that doping greatly affects quantum transport properties by inducing significant diffusive scattering.;In particular, it is the first time in literature that conductance versus doping concentration x is obtained from atomic first principles. Importantly, the NVC theory allows us to directly determine the diffusive scattering contribution to the total conductance. Since B and N atoms are located on either side of carbon in the periodic table, a very interesting finding is that disorder scattering due to these impurities are mirrored almost perfectly on either side of the graphene Fermi level. Such a behavior can be understood from the point of view of charge doping.;We shall briefly review the basic concepts of electronic structure theory of condensed matter physics, followed by a more detailed discussion on density functional theory (DFT) which is the most widely applied atomistic theory of materials physics. We then present the LMTO implementation of DFT specialized in calculating solid crystals. LMTO is computationally very efficient and is able to handle more than a few thousand atoms, while remaining reasonably accurate. These qualities make LMTO very useful for analysing quantum transport. We shall then discuss applying DFT within the Keldysh non-equilibrium Green's function formalism (NEGF) to handle non-equilibrium situations such as current flow. Finally, within NEGF-DFT, we shall use the coherent potential approximation (CPA) and the non-equilibrium vertex correction (NVC) theory to carry out configurational disorder averaging. |
