6.11 Band Inversion
169
Fig. 6.45 Crystal field
splitting cf for various
chalcopyrite compounds
versus the tetragonal
distortion
2 − c/a = 2 (1 − η).
Dash-dotted line represents
cf = 1.5 b (2 − c/a) for
b = 1 eV. Data from [526]
-0.3
-0.2
-0.1
0
0.0
0.1
0.2
cf (eV)
2 c/a
0.0
CuInS 2
CuInSe 2
CuGaSe 2
AgInS 2 (w)
CuGaS 2
CuAlS 2
AgInSe 2
AgAlTe 2
AgGaTe 2
AgInS 2
AgGaSe 2
AgGaS 2
Fig. 6.46 Schematic band
structure of zincblende
with vanishing energy gap
for the ternary compounds
Mn x Hg 1−x Te. Note the
linear dispersion for the
zero-gap case at x ≈ 0.07
6.11 Band Inversion
In certain compounds, typically mixing a semiconductor with a semimetal [527, 528], the band gap
can shrink to zero (zero-gap semiconductor) and even become negative in the sense that the s-type 6
symmetry (conduction) band is inverted below the 8 (p-type) valence-band edge. HgTe is a classical
example for such material as shown in Fig. 6.46, but similar effects are also present in other semiconductors, for example various chalcopyrites [529]. Remember that such band structures are topologically
non-trivial (cf. Sect. 6.2.6).
For the zero-gap case, the dispersion of the two crossing bands is linear (like for graphene, cf.
Sect. 13.1.2). The dielectric function of zero-gap semiconductors is discussed in [530].
For the Cd x Hg 1−x Te system, around the zero-gap concentration of x ≈ 0.16, the change from normal
to inverted band structure will occur also as a function of temperature [531] as shown in Fig. 6.47. Such
effect had been described already 50 years ago for (Pb,Sn)Te at the L-point (cf. Sect. 6.3.6) in [532].
169
Fig. 6.45 Crystal field
splitting cf for various
chalcopyrite compounds
versus the tetragonal
distortion
2 − c/a = 2 (1 − η).
Dash-dotted line represents
cf = 1.5 b (2 − c/a) for
b = 1 eV. Data from [526]
-0.3
-0.2
-0.1
0
0.0
0.1
0.2
cf (eV)
2 c/a
0.0
CuInS 2
CuInSe 2
CuGaSe 2
AgInS 2 (w)
CuGaS 2
CuAlS 2
AgInSe 2
AgAlTe 2
AgGaTe 2
AgInS 2
AgGaSe 2
AgGaS 2
Fig. 6.46 Schematic band
structure of zincblende
with vanishing energy gap
for the ternary compounds
Mn x Hg 1−x Te. Note the
linear dispersion for the
zero-gap case at x ≈ 0.07
6.11 Band Inversion
In certain compounds, typically mixing a semiconductor with a semimetal [527, 528], the band gap
can shrink to zero (zero-gap semiconductor) and even become negative in the sense that the s-type 6
symmetry (conduction) band is inverted below the 8 (p-type) valence-band edge. HgTe is a classical
example for such material as shown in Fig. 6.46, but similar effects are also present in other semiconductors, for example various chalcopyrites [529]. Remember that such band structures are topologically
non-trivial (cf. Sect. 6.2.6).
For the zero-gap case, the dispersion of the two crossing bands is linear (like for graphene, cf.
Sect. 13.1.2). The dielectric function of zero-gap semiconductors is discussed in [530].
For the Cd x Hg 1−x Te system, around the zero-gap concentration of x ≈ 0.16, the change from normal
to inverted band structure will occur also as a function of temperature [531] as shown in Fig. 6.47. Such
effect had been described already 50 years ago for (Pb,Sn)Te at the L-point (cf. Sect. 6.3.6) in [532].