6.3 Band Structures of Selected Semiconductors
149
8
6
4
2
0
-2
-4
-6
-8
ZnCo O
2
4
ZnIr O
2
4
X
W
L
X
W
L
Fig. 6.16 Calculated band structures of ZnCo 2 O 4 and ZnIr 2 O 4 . Adapted from [470]
6.3.9 Spinels
The band structure of spinels (in particular CdIn 2 S 4 ) has been discussed in [473], the band structure
of ZnM 2 O 4 has been calculated in [470] for (M = Co, Rh, Ir) (Fig. 6.16) and in [474] for (M = Al,
Ga, In).
6.3.10 Delafossites
In Fig. 6.17, the theoretical band structures of the delafossites CuAlO 2 , CuGaO 2 , and CuInO 2 are
shown. The maximum of the valence band is not at but near the F point. The direct band gap at
decreases for the sequence Al → Ga → In, similar to the trend for AlAs, GaAs and InAs. The direct
band gap at F and L, causing the optical absorption edge, increases, however (experimental values are
3.5, 3.6, and 3.9 eV).
6.3.11 Perovskites
The calculated band structure of BaTiO 3 in the tetragonal phase is shown in Fig. 6.18. The minimum
of the conduction band is at the -point. The maximum of the valence band is not at the -point but at
the M point. The band gap of the LDA
3 calculation is too small (2.2 eV) compared to the experimental
value ∼ 3.2 eV.
The band structure of the halide perovskites has been calculated for hybrid organic-inorganic compounds like MAPbI 3 and FAPbI 3 [476] and fully inorganic compounds APbI 3 (A = Li, Na, K, Rb,
and Cs) [477]. Density of states and energy positions of (MA,FA,Cs)(Pb,Sn)(Cl,Br,I) 3 compounds are
3 local density approximation.