Fermi-level pinning of bilayer graphene with defects under an external electric field

The electronic structure of bilayer graphene, where one of the layers possesses monovacancies, is studied under an external electric field using density functional theory. Our calculations show that Fermi-level pinning occurs in the bilayer graphene with defects under hole doping. However, under electron doping, the Fermi level rapidly increases at the critical gate voltage with an increasing electron concentration. In addition to the carrier species, the relative arrangement of the gate electrode to the defective graphene layer affects the Fermi energy position with respect to the carrier concentration. Because the distribution of the accumulated carrier depends on the electrode position, the quantum capacitance of bilayer graphene with defects depends on the electrode position.