Electric and thermoelectric properties of graphene bilayers with extrinsic impurities under applied electric field

Abstract In contrast to monolayer graphene, in bilayer graphene (BLG) one can induce a tunable bandgap by applying an external electric field, which makes it suitable for field effect applications. Extrinsic doping of BLGs enriches the electronic properties of the graphene-based family, as their behavior can be switched from an intrinsic small-gap semiconductor to a degenerate semiconductor. In the framework of density functional theory (DFT) calculations, we investigate the electronic and thermoelectric properties of BLGs doped with extrinsic impurities from groups III (B, Al, Ga), IV (Si, Ge) and V (N, P, As), in the context of applied external electric fields. Doping one monolayer of the BLG with p- or n-type dopants results in a degenerate semiconductor, where the Fermi energy depends on the type of the impurity, but also on the magnitude and orientation of the electric field, which modifies the effective doping concentration. Doping one layer with isoelectronic species like Si and Ge opens a gap, which may be closed upon applying an electric field, in contrast to the pristine BLG. Furthermore, dual doping by III-V elements, in a way that the BLG system is formed by one n-type and one p-type graphene monolayer, leads to intrinsic semiconductor properties with relatively large energy gaps. Si-Si and Ge-Ge substitutions render a metallic like behavior at zero field similar to the standard BLG, however with an asymmetric density of states in the vicinity of the Fermi energy. We analyze the suitability of the highly doped BLG materials for thermoelectric applications, exploiting the large asymmetries of the density of states. In addition, a sign change in the Seebeck coefficient is observed by tuning the electric field as a signature of narrow bands near the Fermi level.