Both blue and red shifts in the absorption spectrum of Co-doped ZnO have been reported at a similar concentration range of doped Co. Moreover, the sources of magnetism of Co-doped ZnO are controversial. To solve these problems, the geometry optimization and energy of different Co-doped ZnO systems were calculated at the states of electron spin polarization and nonspin polarization by adopting plane-wave ultra-soft pseudopotential technology based on density function theory. At the state of electron nonspin polarization, the total energies increased as the concentration of Co-doped increased. The doped systems also became unstable. The formation energies increased and doping became difficult. Furthermore, the band gaps widened and the absorption spectrum exhibited a blue shift. The band gaps were corrected by local-density approximation + [Formula: see text] at the state of electron spin polarization. The magnetic moments of the doped systems weakened as the concentration of doped Co increased. The magnetic moments were derived from the coupling effects of [Formula: see text]–[Formula: see text]. The band gaps narrowed and the absorption spectrum exhibited a red shift. The inconsistencies of the band gaps and absorption spectrum at the states of electron spin polarization and nonspin polarization were first discovered in this research, and the sources of Co-doped ZnO magnetism were also reinterpreted.
The N-Point Definite Integral Approximation Formula (N-POINT DIAF)
