5.3 Band Structure

Figure 5.7: Brillouin zone, its first octant, and irreducible wedge with high symmetry points and lines for a face centered cubic lattice.

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 $\ensuremath{\mathrm{k}}\cdot\ensuremath{\mathrm{p}}$ -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 $\Sigma$ 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].

Subsections

• 5.3.1 Band Gap
• 5.3.2 Effective Masses, Density of States, Intrinsic Carrier Density

M. Wagner: Simulation of Thermoelectric Devices