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Thomas Johann Seebeck discovered the thermoelectric (TE) conversion from heat to electrical energy just 200 years ago. Recently, high-performance TE materials have attracted research interest as energy-harvesting technologies. Most of the experimentally discovered TE materials are impurity-doped semiconductors i.e., disordered systems. High-TE effects are expected near the band edge in the impurity-doped semiconductors, where the electronic states are under the influence of strong impurity scattering not properly treated by the conventional Boltzmann transport theory (BTT). Therefore, it is necessary to develop a sophisticated theory beyond BTT. Recently, the authors (T.Y. and H.F.) have alleviated this drawback using the linear response theory (Kubo–Luttinger formula) in conjunction with the thermal Green's function technique [1–3].

The TE linear response theory was successfully applied to nitrogen-doped semiconducting carbon nanotubes (N-CNTs) in the present study. The N-CNTs functioned as lightweight, flexible, and high-performance TE materials. The power factor, PF (=L₁₁S²), was dependent on the nitrogen concentration, c (up to 10^-2), per unit cell of a CNT at various temperatures. The electrical conductivity and Seebeck coefficient were designated as L₁₁ and S, respectively. The PF increased with a decrease in c at 300 K. When cdecreased to less than the optimal impurity concentration, c_opt (= 3.1×10^-5), the PF started to decrease. This behavior was explained based on L₁₁ and S, considering the c-dependence of the chemical potential, μ. The μ at c = 10^-3located below the donor level formed via nitrogen doping, and the electrons were thermally excited from the donor level to conduction band. The μ level shifted downward with a decrease in c owing to a decrease in the net carrier density of the N-CNTs. Here, |S| increased with a decrease in c. A decrease in c, corresponding to a decrease in the rate of scattering by the impurities, was accompanied by an increase in L₁₁owing to the electrons in the conduction band. Consequently, the PFincreased with a decrease in c. A further lowering of c promoted the asymptotic approach of μ toward the center of the band gap owing to the thermally excited holes. The holes contributed to an increase in L₁₁; however, |S| decreased rapidly because the hole contribution to S cancels out the electron contribution to S. Therefore, the PF started to decrease below c_opt. These results facilitated successful estimation of the optimal nitrogen concentration to maximize the PF at various temperatures. A PF of 0.30 W/K²m was obtained for c_opt at 300 K, which is significantly higher than the PF of commercial Bi₂Te₃alloys. These theoretical predictions will facilitate the development of new materials with optimal TE performances.

(written by M. Matsubara on behalf of all authors)

References

[1] T. Yamamoto and H. Fukuyama, J. Phys. Soc. Jpn. 87, 024707 (2018).
[2] T. Yamamoto and H. Fukuyama, J. Phys. Soc. Jpn. 87, 114710 (2018).
[3] M. Ogata and H. Fukuyama, J. Phys. Soc. Jpn. 88, 074703 (2019).