Carrier statistics of highly doped armchair graphene nanoribbons with edge disorder

Abstract Graphene has been observed to have a superior electronic property that can potentially revolutionise microelectronic circuits. In this study, highly doped armchair graphene nanoribbons (AGNRs) with randomly generated edge disorders are explored in terms of the band structure, density of state (DOS), Fermi energy, and carrier concentration. An AGNR model was generated based on the nearest-neighbour tight-binding (TB) approach, and computations of the electronic properties in a GNR were conducted using a recursive non-equilibrium Green's function (NEGF) formalism. This study focuses on 10-AGNRs of three varying ribbon lengths of 5, 15, and 30 unit cells. In addition, we also investigate two other varying ribbon widths, namely, 11-AGNRs and 12-AGNRs, with a length of 5-unit cells. The size of the Hamiltonian operator matrix is dependent on the varying dimensions. Nitrogen and boron dopants are used for n- and p-type doping, respectively. The electronic properties and carrier statistics are then compared and discussed for non-pristine AGNRs. In addition, the carrier concentration is also presented and computed based on the Fermi-Dirac probability function. It was found that a varying width causes non-pristine AGNRs to alternate between two semiconducting states, followed by a metallic state. The carrier concentration increases with width owing to a higher intrinsic carrier density. Van-Hove singularities of the DOS of non-pristine AGNRs increase with the dimensions of the crystalline solid. The Fermi level moves inside the conduction and valence bands for highly concentrated n- and p-type doping.