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Poor electron-related cutting current in graphene-based field-effect transistors (FETs) can be solved by placing a graphene layer over a hexagonal boron nitride (BN) substrate, as established by Giovannetti et al. and other researchers. In order to produce high-quality results, this investigation uses 2 × 2 cells (~2.27% mismatch), given that larger cells lead to more favourable considerations regarding interactions on cell edges. In this case, the substrate-induced band gap is close to 138 meV. In addition, we propose a new material based on graphene on BN in order to take advantage of the wonderful physical properties of both graphene and BN. In this new material, graphene is rotated with respect to BN, and it exhibits a better mismatch, only ~1.34%, than the 1 × 1-graphene/1 × 1-BN; furthermore, it has a very small bandgap, which is almost zero. Therefore, in the bands, there are electronic states in cone form that are like the Dirac cones, which maintain the same characteristics as isolated graphene. In the first case (2 × 2-graphene/2 × 2-BN), for example, the resulting band gap of 138 meV is greater than Giovannetti’s value by a factor of ~2.6. The 2 × 2-graphene/2 × 2-BN cell is better than the 1 × 1-graphene/BN one because a greater bandgap is an improvement in the cutting current of graphene-based FETs, since the barrier created by the bandgap is larger. The calculations in this investigation are performed within the density functional theory (DFT) theory framework, by using 2 × 2-graphene/2 × 2-BN and 13 × 13-graphene/23 × 23-(0001) BN cells. Pseudopotentials and the generalized gradient approximation (GGA), combined with the Perdew–Burke–Ernzerhof parametrization, were used. Relaxation is allowed for all atoms, except for the last layer of the BN substrate, which serves as a reference for all movements and simulates the bulk BN.

Electronic Structure of Graphene on the Hexagonal Boron Nitride Surface: A Density Functional Theory Study