Thermopower scaling in conducting polymers

Abstract

By directly converting heat into electricity, thermoelectric effects provide a unique physical process from heat waste to energy harvesting. Requiring the highest possible power factor defined as α 2 σ, with the thermopower α and the electrical conductivity σ, such a technology necessitates the best knowledge of transport phenomena in order to be able to control and optimize both α and σ. While conducting polymers have already demonstrated their great potentiality with enhanced thermoelectric performance, the full understanding of the transport mechanisms in these compounds is still lacking. Here we show that the thermoelectric properties of one of the most promising conducting polymer, the poly(3,4-ethylenedioxythiophene) doped with tosylate ions (PEDOT-Tos), follows actually a very generic behavior with a scaling relation as α ∝ σ −1/4. Whereas conventional transport theories have failed to explain such an exponent, we demonstrate that it is in fact a characteristic of massless pseudorelativistic quasiparticles, namely Dirac fermions, scattered by unscreened ionized impurities.

Fabrication of Oriented n‐Type Thermoelectric Polymers by Polarity Switching in a DPP‐Based Donor–Acceptor Copolymer Doped with FeCl3

“…As already demonstrated, [27] this regime is characterized by a power law scaling relationship such as α∝σ −1/s with the exponent s, which is the sum of the exponents of the energy dependence of the relaxation time, the charge carrier's velocity, and the density of states. [35] If the charge carriers are 3D Dirac fermions, the velocity is constant, the dos is parabolic, and the relaxation time due to unscreened ionized impurities scattering is also quadratic in energy leading thus to the scaling exponent s = 4 in agreement with the experimental behavior in Figure 7a over more than six decades. [35] Obviously, if it is chemically possible to further increase the doping, this regime is expected to breakdown due to the finite energy bandwidth.…”

“…[35] If the charge carriers are 3D Dirac fermions, the velocity is constant, the dos is parabolic, and the relaxation time due to unscreened ionized impurities scattering is also quadratic in energy leading thus to the scaling exponent s = 4 in agreement with the experimental behavior in Figure 7a over more than six decades. [35] Obviously, if it is chemically possible to further increase the doping, this regime is expected to breakdown due to the finite energy bandwidth. It means that a real dos necessarily displays a maximum separating the electron side from the hole one.…”

“…Furthermore, Figure 6b also displays the behavior expected according to the scaling relationship α∝σ −1/s with s = 4, which is followed by a wide variety of conducting polymers away from the maximum of the dos (|α| ≠ 0). [35] Interestingly, a good adequacy with the experimental data is clearly demonstrated in Figure 6b up to σ/σ W < 0.5. Since this scaling relationship is constrained by monotonic dos following a power law energy dependence, it cannot suitably reproduce the polarity switch regime.…”

“…Additionally, it has been shown recently that a parabolic dos could be one of the microscopic ingredients allowing to justify the unusual scaling relationship between the thermopower and the electrical conductivity such as α∝σ −1/s with s = 4. [7,27,35] Figure 6. a) Energy-dependence in reduced units of the Gaussian, the semicircular, and the modified parabolic density of states (dos).…”

“…This nondegenerate regime leads to a logarithmic correlation between the thermopower and the electrical conductivity as already discussed and observed experimentally. [27,30,35] By doping, the Fermi level can next decrease typically such as 0.5 < |E F /W ± | < 1 and then the system becomes degenerate. In such a regime, the dos can be considered monotonic and varies as a power law (quadratic in the present case).…”