Tight-binding model for the electronic structures of SiC and BN nanoribbons

The distinct variation trends of SiC and BN nanoribbons as a function of ribbon width have not been understood clearly. We present a simple tight-binding (TB) model to reveal the physics behind these phenomena. The edge effects are taken into account by modifying the on-site energies and hopping integrals of the atoms on the two edges. We show the charge redistribution at the edges is responsible for the band gap oscillation of SiC and BN nanoribbons. Our TB model reproduces not only the band gaps but also the band dispersion of the highest valence band and lowest conduction band very well. This model can be applied to other low-dimensional nanostructures whose electronic structures are dominated by π electrons.