The Study Of Electronic Properties For Graphene Nanoribbons

Carbon-related materials have been the subject of intensive research during the past several decades, and people got lots of important research results. Recent years, people's attention has focused on the new nano-material—graphene. When the graphene is used in circuit, people want to get the graphene properties when its geometrical features are be restricted, such as the graphene nanoribbons(GNRs).In the thesis, we introduce the graphene physics properties, geometry structure and the basic study methods of graphene nanoribbons. Based on the tight-binding model, two typical graphene nanoribbons are studied deeply. We improve the tight-binding model of AGNRs and combinate the model and the plane-wave method. Then, the non-nearest-neighbor hopping terms of electrons are taken into account and the energy spectra of the armchair graphene nanoribbons (AGNRs) are given analytically. The changes of the energy band and the gap with the non-nearest-neighbor terms are discussed. The results show that the next-nearest-neighbor term can increase the gap and the third-nearest-neighbor term can narrow the gap. The competition relationship between the edge relaxation and the non-neighbor term is compared. When the width n is odd, the Von-Hove singularity from graphene sheets leads to the dispersion-less band. When the width of AGNRs goes to infinity, the spectrum of AGNRs tends to that of graphene sheets.We discuss the electronic structures of the deformed graphene nanoribbons, because we need the different energy gap when we put the graphene nanoribbons into the application. Based on the model of deformed graphene nanoribbons and Harrison's formula, we get the analytical relations between the electron hopping integral and the C-C bond-length.And then, we get the analytical solution of the deformed GNRs. In the case of the nearest-neighbor hopping, We emphatically discuss the influence which different deformation level have effects on the electronic energy structures and the gaps. We find that deformation has no effects on the ZGNRs, but it has effects on the AGNRs. The deformation can change the gaps of the AGNRs and it will bring difficult influences to AGNRs of three bandwidths. When the deformation parameter is constant and the width of AGNRs goes to infinity, the spectrum of all AGNRs tends to the same value.In the thesis, we find that geometry structure and the different electron hopping integral have important influence on the electronic structures and energy gaps of graphene nanoribbons. According to the study of the GNRs, we can get different gaps needed.