Electronic structure of graphene nano-ribbons

Graphite is a known material to human kind for centuries as the lead of a pencil. Graphene as a two dimensional material, is the single layer of graphite. Many theoretical works have been done about it so far, however, it newer took attention as it takes nowadays. In 2004, Novoselov et al. was able to produce graphene in 2D. Now that, making experiments on graphene is possible scientists have to renew their theoretical knowledge about systems in two dimension because graphene, due to its electronic structure, is able to prove the ideas in quantum relativistic phenomena. Indeed, recent theoretical studies were able to show that, electrons and holes behave as if they are massless fermions moving at a speed about 106m/s (c/300, c being speed of light) due to the linear electronic band dispersion near K points in the brillouin zone which was observed experimentally as well. Having zero band gap, graphene cannot be used directly in applications as a semiconductor. Graphene Nano-Ribbons (GNRs) are finite sized graphenes. They can have band gaps differing from graphene, so they are one of the new candidates for band gap engineering applications such as field effect transistors. This work presents theoretical calculation of the band structures of Graphene NanoRibbons in both one (infinite in one dimension) and zero dimensions (finite in both dimensions) with the help of tight binding method. The calculations were made for Zigzag, Armchair and Chiral Graphene Nano-Ribbons (ZGNR,AGNR,CGNR) in both 1D and 0D. Graphene nano-ribbons with zero band gap (ZGNR and AGNR) are observed in the calculations as well as the ribbons with finite band gaps (AGNR and CGNR) which increase with the decrease in the size of the ribbon making them much more suitable and strong candidate to replace silicon as a semiconductor.