Electronic properties of doped carbon-based nanostructures

Abstract

Carbon-based nanostructures have been at the forefront of scientific research for the last couple of decades due to their unique properties, giving rise to many potential applications especially for electronics. Their simple structure and the ease with which many of their electronic properties can be studied makes them particularly interesting from a theoretical perspective. These electronic properties can be modified by altering the atomic structure, for example through the introduction of dopants to the system. In this thesis a thorough investigation of several topics related to doping in bulk graphene, narrow strips of graphene (nanoribbons) and carbon nanotubes is be undertaken. A tight-binding Green function formalism is developed and then employed in the study of impurity modelling, Friedel oscillations, impurity scattering and sublattice segregation of impurities. The distinct advantage of using such a mathematically transparent approach is that it better reveals the underlying physical mechanisms than a purely numerical simulation. The first demonstration of this is to the case of impurity modelling. A self-consistent method is demonstrated for obtaining the tight-binding parameters that characterise the impurity, e.g. energy levels and overlap integrals. This requires only a handful of inputs from density functional theory and presents a computationally efficient alternative to the commonly used method of band structure matching. Tight-binding parameters for substitutional nitrogen, substitutional boron and adsorbed hydrogen are calculated for a host graphene system. The focus is then moved to the phenomenon of Friedel oscillations in graphene and carbon nanotubes, spatial modulations in the density of states and the carrier density, caused by symmetry breaking of the system due to the presence of an impurity. The differences between substitutional impurities, vacancies and several kinds of adsorbates will be studied. Closed-form analytic expressions describing the Friedel oscillations will be derived and compared to numerical calculations. The role of the bonding symmetry of adsorbed impurities on scattering and electronic transport properties in graphene is then studied. It is shown that scattering is heavily suppressed for particular bonding symmetries, making these impurity types quite poor for use with conventional graphene chemical sensors. This suppression is explained from the viewpoint of interference between the propagators describing electron propagation. By breaking the underlying system symmetry via uniaxial strain this scattering suppression can be mitigated, suggesting impurities exhibiting this quality would be ideal candidates for high-sensitivity strain sensors. The mathematical model is then used to investigate the recently observed experimental phenomenon of sublattice segregation, where under conditions large numbers of nitrogen dopants in graphene exhibit an overwhelming preference to occupy one of graphene’s two sublattices. It is proposed that inter-impurity interactions are driving this effect and that, moreover, this is not particular to nitrogen or graphene and is a consequence of symmetry breaking in the lattice. Alternative scenarios are then discussed where the same sublattice ordering behaviour should arise: in carbon nanotubes where their reduced dimensionality is predicted to enhance the effect; and Gaussian strain ‘bubbles’ in bulk graphene created in such a way that destroys the underlying sublattice symmetry and makes one more preferential for adsorption.