Edge effects on electronic band structure of graphene nanoribbons: a first principles study

Abstract

The aim of our research work presented in this thesis is on the studies of edge effects on electronic band structure of graphene nanoribbons (GNRs). Theoretical studies on GNRs predict that band gaps depend upon its width and crystallographic orientation (zigzag or armchair), in which armchair GNRs are found to be semiconducting in nature while zigzag to be semi-metallic. However, experiments carried out on GNRs fabricated, using the most commonly used technique of electron beam lithography followed by oxygen plasma etching, report non-zero band gap in both the crystallographic orientations. The electronic band gap ambiguity between theory and experiments on GNRs is a challenge for scientists around the globe since the first experiment on GNRs reported in 2007. Therefore, motive of our research work is to theoretically resolve the prolonged band gap ambiguities using first principles technique for a better understanding of the experimental results, which would greatly help in designing thought experiments for next generation electronic devices applications. On the basis of our theoretical calculations, we analyzed that the energy required to form zigzag GNRs is higher than that for armchair GNRs. Therefore, the energy difference can be incorporated as external parameter, such as temperature, in the formation of smooth edged GNRs (Chapter 3). To resolve the band gap ambiguities, we propose a fundamental approach for edge configurations of nearly smooth as well as rough edged GNRs, maintaining the inherent sp2 hybridization of the carbon atoms, and edge passivation with oxygen atoms. We report for the very first time a non-zero band gap in both the crystallographic orientations for nearly smooth as well as rough edged GNRs, consistent with the experimental results; which is a significant step in resolving the band gap ambiguities between the theory and the experiments (chapter 4 and 6). In addition, based on the modification in potential profiles in the periodic direction of two different edge configurations having the same number of atoms of each time in a supercell, we successfully explain the origin of multiple band gap values in the same width of GNRs, although both the configurations carry practically the same ground state energy (chapter 5). In the concluding remark, we predict that the edge configurations of the GNRs in both the crystallographic orientations and the nature of passivating atoms play a significant role in the band gap formation, in addition to its width and crystallographic orientations. In the future work, the effect of edges on electronic structure of nanoribbons can be explore by introducing defects and roughness at the edges, magnetism due to edge defects, and substrate-GNRs interactions to understand the electronic structure properties of fabricated GNRs. The research work presented in this thesis would be helpful in designing experiments on controlled edge formation and band gap tuning of graphene nanoribbons, which would greatly facilitate in advancement of sub-nanometer electronic device applications of GNRs and other two dimensional materials.