168
6 Band Structure
6.10.3 Valence-Band Fine Structure
In Fig. 6.44, the schematic structure of the band edges for zincblende structure semiconductors is
shown. The s-o holes in the zincblende structure are split-off due to the spin-orbit interaction so , the
8 band is degenerate (heavy and light holes). Degeneracies for the holes are removed in the wurtzite
and chalcopyrite structures by the additional crystal field splitting cf due to the anisotropy between
the a- and c-axes. Typically, e.g. for CdS, the topmost valence band in the wurtzite structure has 9
symmetry (allowed optical transitions only for E ⊥ c); an exception is ZnO for which the two upper
bands are believed to be reversed. In the chalcopyrite structure optical transitions involving the 6 band
are only allowed for E ⊥ c. The three hole bands are usually labeled A, B, and C from the top of the
valence band.
The energy positions of the three bands (with respect to the position of the 15 band) in the presence
of spin-orbit interaction and crystal field splitting are given within the quasi-cubic approximation
[525] by
E 1 =
so + cf
2
(6.54a)
E 2,3 = ±
so + cf
2
2
−
2
3
so cf .
(6.54b)
In chalcopyrites the crystal field splitting is typically negative (Fig. 6.45). It is approximately linearly
related to 1 − η (for η = c/2a see Sect. 3.4.6).
Fig. 6.44 Schematic band structure of zincblende and the valence-band splitting due to spin-orbit interaction so and
crystal field splitting cf for chalcopyrites (typically cf < 0, see Fig. 6.45) and wurtzites. For the wurtzites the situation
is schematically shown for CdS ( so = 67 meV, cf = 27meV) (or GaN) and ZnO ( so = −8.7 meV, cf = 41 meV)
6 Band Structure
6.10.3 Valence-Band Fine Structure
In Fig. 6.44, the schematic structure of the band edges for zincblende structure semiconductors is
shown. The s-o holes in the zincblende structure are split-off due to the spin-orbit interaction so , the
8 band is degenerate (heavy and light holes). Degeneracies for the holes are removed in the wurtzite
and chalcopyrite structures by the additional crystal field splitting cf due to the anisotropy between
the a- and c-axes. Typically, e.g. for CdS, the topmost valence band in the wurtzite structure has 9
symmetry (allowed optical transitions only for E ⊥ c); an exception is ZnO for which the two upper
bands are believed to be reversed. In the chalcopyrite structure optical transitions involving the 6 band
are only allowed for E ⊥ c. The three hole bands are usually labeled A, B, and C from the top of the
valence band.
The energy positions of the three bands (with respect to the position of the 15 band) in the presence
of spin-orbit interaction and crystal field splitting are given within the quasi-cubic approximation
[525] by
E 1 =
so + cf
2
(6.54a)
E 2,3 = ±
so + cf
2
2
−
2
3
so cf .
(6.54b)
In chalcopyrites the crystal field splitting is typically negative (Fig. 6.45). It is approximately linearly
related to 1 − η (for η = c/2a see Sect. 3.4.6).
Fig. 6.44 Schematic band structure of zincblende and the valence-band splitting due to spin-orbit interaction so and
crystal field splitting cf for chalcopyrites (typically cf < 0, see Fig. 6.45) and wurtzites. For the wurtzites the situation
is schematically shown for CdS ( so = 67 meV, cf = 27meV) (or GaN) and ZnO ( so = −8.7 meV, cf = 41 meV)