First-principle Study Of The Band Structure Of Strained Graphene

Graphene, a two-dimensional material, combines extreme mechanical strength, exceptionally high electronic and thermal conductivities, as well as many other supreme properties, all of which make it highly attractive for numerous applications. It has attracted an enormous amount of interest from both theoretical and experimental scientists since the discovery of it in 2004.However, for pristine graphene, a two-dimensional honeycomb carbon lattice is a zero gap semiconductor, which is one of the hurdle for graphene to be useful as an electronic material, for example, graphene-based FET. To solve this, scientists have explored many ways to modify the band structure of graphene, including lateral quantum confinement by constraining the graphene in nanoribbons and in graphene quantum dots, and by biasing bi-layer graphene. Moreover, Strain engineering is predicted to induce a gap in graphene, which has been observed experimentally. Nonetheless, bandgap engineering offers potential solutions to a significant obstacle in the path towards practical and scalable, high-performance graphene-based logic devices.In this thesis we mainly studied the band structure variation during the introduce of local strain in monolayer graphene and analyzed the band structure of rippled graphene by the first principle calculations method based on the density functional theory (DFT). Then we explained the result with tight binding calculations. The main content of the study is as followings:We adopted three methods to modify the band structure of graphene:(1) Moving a single atom in the lattice. Density functional theory calculations show that for the two different moving directions considered, an average of several tens of meV band gap was introduced in graphene at the Dirac point, and the size of the band gap increases with the degree of atomic deviation from the initial position. For the comparing of the selected two contrasting cases considering the direction of movement, the symmetry of the structure has a great relationship with the band gap opening. By the tight-binding calculation we find that the band gap is generated mainly by the change of π electron orbital interaction due to the structural changes after the introduce of strain.(2) Changing the geometry of a single hexatomic ring. The band structure at the Dirac point did not change after the changing of a single hexatomic ring, and by the tight-binding calculation, the result shows that it remains a very high symmetry though the geometry of the hexatomic ring has changed, the bandgap of graphene remains zero even after the fitting of hopping energy of π electron.(3) Constructing rippled graphene. We adopted two different directions in graphene to build rippled graphene, DFT calculations show that the band gap has no relation with the way the rippled graphene was build but only directly related to the degree and cycle of the ripple.