Temperature, Doping, and Chemical Potential Tuning Intrinsic Defects Concentration in Bi₂MoO₆: GGA + U Method

Using the GGA + U method, the formation energy and concentration of intrinsic defects in Bi₂MoO₆ are explored under different chemical conditions, with/without doping, from 120 to 900 K. We find that the intrinsic defect and carrier concentration can be deduced from the small range of calculated Fermi levels in the diagram of formation energy vs Fermi level under different conditions. Once the doping conditions or/and temperature are determined, the corresponding E_F is only limited to a special region in the diagram of formation energy vs Fermi level, from which the magnitude relationship of defects concentration can be directly derived from their formation energy. The lower the defect formation energy is, the higher the defect concentration is. With E_F moving under different doping conditions, the intrinsic defect concentration changes accordingly. At the same time, the highest electron concentration at the relative O-poor (point H) with only intrinsic defects confirms its intrinsic n-type behavior. Moreover, upon A^-/D⁺ doping, E_F moves closer to VBM/CBM for the increasing concentration of holes/electrons. The electron concentration can also be further improved after D⁺ doping, indicating that D⁺ doping under O-poor chemical growth conditions is positive to improve its photogenerated carriers. This provides us with a method to adjust the intrinsic defect concentration and deepens our knowledge about comprehension and application of the diagram of formation energy vs Fermi level.