First-principle study of energy band structure of armchair graphene nanoribbons

First-principle calculation is carried out to study the energy band structure of armchair graphene nanoribbons (AGNRs). Hydrogen passivation is found to be crucial to convert the indirect band gaps into direct ones as a result of enhanced interactions between electrons and nuclei at the edge boundaries, as evidenced from the shortened bond length as well as the increased differential charge density. Ribbon width usually leads to the oscillatory variation of band gaps due to quantum confinement no matter hydrogen passivated or not. Mechanical strain may change the crystal symmetry, reduce the overlapping integral of C-C atoms, and hence modify the band gap further, which depends on the specific ribbon width sensitively. In practical applications, those effects will be hybridized to determine the energy band structure and subsequently the electronic properties of graphene. The results can provide insights into the design of carbon-based devices.