  We study the effects of an attractive interaction between the boron (B) and
the nitrogen (N) atoms doped in a bilayer graphene (BLG), BC$_{14}$N, on the
electronic, the thermal and the optical properties for two different types of a
doping process: First, both the B and the N atoms are doped in the same layer
while the other layer is undoped. Second, the B and N atoms are doped in both
layers. An attractive interaction between the B and N atoms does not influence
the interlayer interaction in the first case, while it does in the second case.
We find that the strong B-N attractive interaction in one layer induces
metallic behavior due to the crossing of the valence band and the Fermi energy,
while the strong attractive interaction between both layers induces a
semiconductor property arising from the emergence a bandgap. We therefore
confirm that the metallic-like BLG is not a good material for thermal devices
because it has a low figure of merit, while we notice that the
semiconductor-like BLG has a high Seebeck coefficient and figure of merit as
well as a low thermal conductivity. The strong attractive interaction of the
B-N atoms between the layers gives rise to a prominent peak to appear in
dielectric function, the excitation and the absorption spectra in the low
energy, visible range, while a very weak peak is seen in the case of a strong
attractive interaction between the B and N doped in one layer. Controlling the
B and N atomic configurations in the BLG may help to improve the material for
use in both thermoelectric and optoelectronic devices.
