Using the firs-principles method based on density functional theory, we study the stability and doping performance of double h-BN/Graphene structure, here the exchange correlation potential is expressed through the local density approximation and the interactions between ions and electrons are described by the projective-augmented wave method. Because double layer h-BN/Graphene represents a kind of epitaxial semiconductor system, which can be applied to tunnel pressure sensor, the research is very meaningful. In order to improve the application of this special double layer structures, we often carry out the dopings of some atoms. Unlike previous research work, in which the dopings of the metals Au, Co, Mn and other atoms were took into account, we now mainly consider the dopings of the active metal atoms, such as the dopings of Li, Na, and K atoms. The band structure, electronic density of states, as well as the charge density and stability are studied on the double h-BN/Graphene structure after alkali metal doping. At the same time, bonding and electronic properties of double h-BN/Graphene are discussed under the different biaxial strain conditions. The results show that for the dopings of Li and K atoms, the structure deformation is very large, and the band structure of double h-BN/Graphene can show a small band gap at the K point in the first Brillouin zone, taking on a linear dispersion relation the same as that of the perfect graphene. We can tune the band gap by applying external strain and dopings of atoms, and find a new level appearing near the Fermi level after doping, which is mainly due to the contribution of N atoms. In addition, there exists charge transfer between Na atom and N and C atoms, and the material is converted into metal. We find obvious charge overlapping in the vicinity of Na atoms, these charge overlaps appearing around the Na and C atoms indicate the existence of covalent bond and this covalent bond also appears around the Na atoms and N atoms. We prove the existence of the chemical bonds by adopting the Bader charge analysis, which suggests that the C atoms in the lower graphene layer obtain 0.11 e and dopant atoms around the three N atoms obtain 0.68 e. We infer that the increasing of Na atom doping can increase the charge transfer, so the method of changing the substrate to increase the graphene layer charge density is very conducive to the application of graphene in electronic devices. Because the double h-BN/Graphene has been successfully synthesized, our calculations provide a theoretical basis for the further development and application of technology. We can expect that Na atom doped double h-BN/Graphene can be well applied to the future electronic devices.
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