Ab-initio calculations within the framework of density functional (DFT) have been performed to study the electronic and optical properties of Be and N co-doped graphene. The results have been compared with that of Be-doped, N-doped, and pristine graphene. The effect of doping and isomerization on the electronic and the optical properties of these systems have been studied by varying the impurity concentrations of Be-doped and N-doped graphene systems from 3.13% through 12.5%, whereas for Be and N co-doped graphene, the concentration has been varied from 6.25% through 25.0 % impurity concentration.
The formation energies of the systems with different impurity configurations were calculated to examine their relative stabilities. It was found that for Be-N co-doped graphene, the configuration of which N and Be coexisting as the nearest neighbors is energetically the most favorable configuration. Moreover, at the same impurities concentration, Be-N co-doped graphene was observed to be more stable than Be-doped graphene due to its lower formation energy. Thus these results reveal that it is much easier to synthesize Be-N co-doped graphene than to synthesize Be-doped graphene. Hence, the relatively high formation energy of Be-doped graphene could be the reason why the system is yet to be synthesis experimentally despite a recent theoretical report on it.

The results of the electronic structure calculations reveal that Be-N co-doped and Be-doped graphene are p-type semiconductors while N-doped graphene has been verified to be an n-type semiconductor. For all the doped systems considered in this study, it was observed that the size of the band gap increases with impurity concentration with respect to the aforementioned energetically most favorable isomer. At impurity concentration of 3.13%, a minimum band gap of 0.44 eV and 0.21eV was realized for Be-doped and N-doped graphene respectively while at 12.5 % corresponding maximum gap of 1.41 eV and 0.6 eV were observed. Besides, Be-N co-doped graphene was found to have a minimum band gap of 0.43 eV at 6.25% and a maximum gap of 1.54 eV at 25.0% impurities concentration.

The dielectric matrices of the doped systems were calculated using first-order time-dependent perturbation theory in the simple dipole approximation. It was found that all the systems investigated were transparent within the frequency interval of 7.0eV-10eV for parallel EM polarization. In general, we observed that the optical properties of the doped systems investigated respond to doping concentration differently across the EM spectrum with respect to the anisotropic signature of the host system.
The results of our study demonstrate that the band gap of graphene can be tailored to meet the requirements of specific applications in nanoelectronic and optoelectronic devices.