In this work, by means of density functional theory, we systematically investigate the geometric structure and electronic properties of the vertical heterostructure by stacking graphene on top of single-layered hexagonal boron nitride and molybdenum diselenide (Gr/h-BN/MoSe2). Our results show that the interlayer coupling in the heterostructure is mainly governed by the weak van der Waals interactions. We find that in the heterostructure, a tiny band gap of 82 meV is opened around the Dirac K point of graphene due to sublattice symmetry breaking, and a minigap of 39 meV is opened between the π band of graphene and the vertical orbitals of MoSe2 due to their hybridization. This band gap opening in graphene makes it suitable for application in novel high-performance nanoeclectronic devices. Furthermore, the Gr/h-BN/MoSe2 heterostructure with inserting insulated h-BN layer forms an n-type Schottky contact with a small Schottky barrier height of 0.1 eV. These findings could provide helpful information for designing novel nanoelectronic devices by stacking graphene on top of single-layered h-BN and MoSe2.
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