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Lead telluride crystallizes in the NaCl structure with face-centered cubic unit
cells [232]. The resulting Brillouin zone with its first octant as
well as its irreducible wedge and high symmetry points are illustrated in
Fig. 5.7. The band structure of lead telluride and its alloys has been
investigated extensively both theoretically and by experiments. The principle
position and alignment of the valleys as well as the band gap have been
obtained by several measurement techniques, like investigations on the optical
absorption, recombination spectra, reflectivity, as well as magneto- and
piezoresistivity [233,234,235,236,237].
Parameters for models based on the
-theory have been
obtained for lead chalcogenides in [238,239,240].
Theoretical band structure calculations have been performed applying the
augmented plane-wave method [241]. The results of relativistic
orthogonalized plane-wave calculations are published in [242], while
Johnson generally pointed out the importance of relativistic effects within
band structure calculations on lead telluride [243]. Extensive
calculations based on the empirical pseudopotential method, extended by
non-local effects and spin-orbit coupling have been performed in
[244,245,246,247,248] and the temperature dependent
band-structure has been investigated in [249,250,251].
Lead telluride is a direct semiconductor where the conduction band minima and
valence band maxima are located at the L point of the Brillouin zone. The
valleys are both heavily anisotropic and non-parabolic. The major alignment is
in [111] direction with the band minima located exactly at the L point, thus
the valleys have a multiplicity of 4. Furthermore, a second valence band with
band minima at
exists with an alignment of the valleys in [100]
direction [252,253].
In PbSnTe, a band inversion occurs, meaning that the highest valence band and
the lowest conduction band change their roles throughout a variation of the
alloy composition between PbTe and SnTe [254]. This band inversion
model has been supported by several measurements [255,256].
However, there is still some uncertainty about the band parameters within the
band inversion zone [257].