Concentration dependence of the band gaps of phosphorus and sulfur doped graphene

First principle calculations were applied to study the electronic properties of S and P-doped graphene. In particular, the PBE and HSE06 density functionals were utilized. The comparison of the band gaps obtained with both functionals indicated that the band gaps at the PBE level are only slightly smaller than those obtained with HSE06. Specifically, the deviation variation was much smaller than that observed for carbon nanotubes or graphane. Phosphorus doping is somewhat more effective in opening larger optical gaps. The latter decreases very fast, upon lowering of dopant concentration. In the case of S-doping, for a doping concentration smaller than 0.5 at.%, the gaps are close to 0.1–0.2 eV, making the material not too attractive to develop graphene based electronics. However, for phosphorus doping, a dopant concentration of 0.5% is still useful as band gaps close to 0.3–0.4 eV are expected. Further work must be devoted to obtain larger band gaps by doping graphene with heteroatoms, which are necessary to develop graphene based electronics.