Modeling and Simulation of the Electronic Properties in Graphene Nanoribbons of Varying Widths and Lengths Using Tight-Binding Hamiltonian

This research emphasizes the modelling and simulation of electronic properties of Graphene Nanoribbon (GNR) of varying widths and lengths, by employing single-neighbour tight binding models based on Non-Equilibrium Green's Function (NEGF) formalism via numeric computation methods on MATLAB. Justifiable simplifying assumptions such as applying basis functions, discretization of Hamiltonian operator and plane wave approximation, based on many body theories and modified Hartree's simplification theory, are made to obtain final model. The overall concept on how to derive dispersion relation, Density-of-States (DOS) and subsequently transmission coefficient which leads to crucial electronic properties, is explained in a simple and concise manner in light that this research will be reproducible and even customizable for different materials without requiring strong background in nanophysics. Appropriate unit cell for GNR has been defined along with its interaction coupling matrix to collapse the model into a 1D problem. Hamiltonian matrix of both Armchair GNR (AGNR) and Zigzag GNR (ZGNR) are generated with open boundary conditions to mimic real structure. Results of all simulations based on NEGF tight binding model such as the sub-band structures, DOS plots and bandgap values agrees closely to benchmark obtained from various research work.