Table 2.
Formation energies (ΔEf) and thermodynamic transition levels measured from the CBM (ε ′ (q/q′ )=Eg− ε(q/q′ )) of the O vacancy and the Zn interstitial at the octahedral site. Formation energies are obtained at the O-poor limit when the Fermi level is located at the CBM, i.e. a strong n-type condition. Values for the ε ′ (2+/0) level are listed for the O vacancy because it shows a negative U behavior, i.e. instability of the + charge state. CB denotes a transition level within the conduction band. All values are in eV.
| Method | O vacancy | Zn interstitial | Reference | ||||
|---|---|---|---|---|---|---|---|
| ΔEf | ε ′ (2+/0) | ΔEf | ε ′ (2+/+) | ε ′ (+/0) | |||
| Extrapolation using LDA and LDA+U | 3.72 | 1.3 | 6.95 | CB | CB | [92] | |
| GGA with VBM correction using GGA+U | 0.8 | 2.2 | 5.2 | 0.6 | 0.2 | [39] | |
| LSDA+Ud+Us | 2.0 | 2.5 | – | – | – | [93] | |
| Hybrid (HSE06) | 0.96a | 0.67a | – | – | – | [48] | |
| Hybrid (HSE, a=0.375) | 1.0 | 1.2 | 3.9 | 0.1 | 0.1 | [44] | |
| Hybrid (PBE0) | 0.9 | 1.2 | – | – | – | [44] | |
| Hybrid (B3LYP) | 1.13 | – | 0.09 | 0.16 | [85] | ||
| Hybrid (B97-1), QM/MM | 1.6b | – | – | – | – | [105] | |
| sX | 0.85 | 1.21 | 3.7 | 0.1 | <0.1 | [46] | |
| GW-HSE | – | 1.68a | – | – | – | [48] | |
aValues calculated for the zinc-blende structure.
bEstimated by the present authors, using the reported value for the formation energy with reference to the O2 molecule.