Electronic transport in graphene-based structures: An effective cross-section approach

Abstract

We show that transport in low-dimensional carbon structures with finite concentrations of scatterers can be modeled by utilising scaling theory and effective cross sections. Our reults are based on large scale numerical simulations of carbon nanotubes and graphene nanoribbons, using a tightbinding model with parameters obtained from first principles electronic structure calculations. As shown by a comprehensive statistical analysis, the scattering cross sections can be used to estimate the conductance of a quasi-1D system both in the Ohmic and localized regimes. They can be computed with good accuracy from the transmission functions of single defects, greatly reducing the computational cost and paving the way towards using first principles methods to evaluate the conductance of mesoscopic systems, consisting of millions of atoms.

Silicon and silicon-nitrogen impurities in graphene: Structure, energetics, and effects on electronic transport

“…To quantify the transport properties with any small value of defect concentration 48 , we calculated the scattering cross section. After l e (E) is obtained for a given concentration n, the effective scattering cross section with dimension of [length] in two dimensions is evaluated as…”

Self-consistent tight-binding model of B and N doping in graphene

“…Donor or acceptor levels may subsequently be identified as resonances in the local density of states. Several publications have investigated this problem at ab initio [11][12][13] and tight-binding [13][14][15][16][17][18][19][20][21] levels. The tight-binding approach is obviously highly suited for analysis of localized impurity states.…”

Ab initiotransport fingerprints for resonant scattering in graphene

“…(4) the localized regime can also be treated within the scattering cross section approach as shown in our previous work. 9 The vacancy TB model does not directly correspond to a real monovacancy or a hydrogen adsorbate. For comparison we have used also the impurity model of Eq.…”

“…Therefore, based on prior work on electron transmission in silicon nanowires, 7,8 we have recently applied the concept of energy-dependent scattering cross section to scale the transport properties of single defects to those of macroscopic samples with homogeneous defect concentrations. 9 The TB calculations can be parametrized based on the density functional theory (DFT) results or empirically based on experimental data. However, the modeling of defects beyond simple alterations in the topology, that is, the modeling of impurities, chemical adsorbates, or even carbon adatoms that create different bond configurations, becomes challenging since the parametrization should catch all the features of the chemical bonds relevant for the transport properties.…”

“…The cross section can, however, also be defined within the localized regime, as was done in our previous work. 9 This is seldom needed for cross sections based on single defect calculations and we concentrate on the Ohmic regime here.…”