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Influence of single vacancy defect at varying length on electronic
 properties of zigzag graphene nanoribbons

Graphene, identified in 2004, is now an established two-dimensional (2D) material due to its outstanding physical and electronic characteristics namely its superior electrical conductivity. Graphene is a zero-gap material that has linear dispersion with electron-hole symmetry. As pristine sheet, it cannot be utilized in digital logic application without the induction of a band gap inside the band structure. In our work, the modeling and simulation of graphene nanoribbons (GNRs) are carried out to determine its electronics properties that are benchmarked with other published simulation data. A 4-Zigzag GNRs (4-ZGNRs) under different length are utilized. A single vacancy defects is introduced at various positions inside the atomic structure. The theoretical model is implemented based on single-neighbour tight binding technique coupled with a non-equilibrium Green’s function formalism. The single vacancy defects are represented by the elimination of tight binding energies in the Hamiltonian matrix. Subsequently, these matrix elements are utilized to compute dispersion relation and density of states (DOS) through Green’s function. It is found that single vacancy defects at different positions in 4-ZGNRs’ atomic structure under varying length has no significant impacts on the sub-band structure but these vacancies impact the DOS that are computed throught Green’s function approach.