Influence of band structure on the large thermoelectric performance of lanthanum telluride

We investigate the carrier density and temperature dependence of the Seebeck coefficient of ${\text{La}}_{3-x}{\text{Te}}_4$ via density-functional calculations and Boltzmann transport theory. The pertinent band structure has light bands at the band gap and heavy degenerate bands with band minima near energies corresponding to the experimentally determined optimum carrier density. Heavy bands increase the energy dependence of the density of states, which increases the magnitude of the Seebeck coefficient in an itinerant conduction regime, while the light bands provide a conduction channel that works against carrier localization promoted by La vacancies. The net result is thermoelectric performance greater than current $n$-type materials above 1000 K.

Figure 1

Electronic band structure for ${\text{La}}_3{\text{Te}}_4$ for (a) large energy scale and (b) energy of pertinent conduction bands with $E_F=0$. The band minima are found to be nearly parabolic, with band mass and degeneracy noted in the text.

Figure 2

(Color online) The density of states $N\left(E\right)$ demonstrates a sharp increase near $-0.16\text{eV}$ due to the presence of heavy bands. This behavior is similarly reflected in the inset, which shows the Hall carrier concentration at 300 K in units of ${10}^{21}{\text{cm}}^{-3}$. Solid lines indicate the location of the heavy band minima, which correspond to the optimum doping level.

Figure 3

Similar temperature dependence of the (a) experimental (Ref. 7) and (b) theoretical Seebeck coefficients is observed. Doping levels are indicated by (a) $n_H^{\ast }=n_H/4.49\times {10}^{21}{\text{cm}}^{-3}$ and (b) $e^{-}/\text{f.u.}$ Note that at 300 K, $e^{-}/\text{f.u.}=n_H^{\ast }:1=0.96$, $0.80=0.77$, $0.60=0.59$, $0.40=0.38$, $0.20=0.17$, $0.10=0.09$, $0.08=0.07$, $0.06=0.05$, $0.04=0.04$, and $0.02=0.02$.

Figure 4

(Color online) The experimental Seebeck coefficient at 400 K (open markers) is compared to several models, while the inset shows similar data for 1000 K. Single-band (SPB) models (gray curves with $m^{\ast }/m_e$ indicated) fail to describe the experimental data. The ab initio calculations (red curves) demonstrate a relative increase in $\left|\alpha \right|$ at moderately high $n$, as does the multiparabolic band model utilizing ab initio parameters as input (blue curve). A semiempirical multiparabolic model (black curve) is generated using $m_1^{\ast }/m_e=0.844$, with all other parameters identical to those used in the blue curve; at 1000 K the black curve utilizes $m_1^{\ast }/m_e=1.13$.