  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.
