Thermoelectric transport properties of electron doped pyrite FeS2

TL;DR

The study addresses the variability of the Seebeck coefficient in FeS$_2$ by evaluating the thermoelectric response of electron-doped FeS$_2$ using three doping approaches: explicit Co substitution, jellium doping, and rigid-band approximation (RBA). Density functional theory with LDA–PAW and Boltzmann transport under CRTA are employed to compute $S(T)$ and compare how each scheme captures the electronic structure changes accompanying doping. The results show negative $S$ values that stay below $50\,\mu$V/K across doping levels, with RBA consistently overestimating $S$ due to the Fermi level residing in a steeper region of the DOS, while explicit Co substitution and jellium doping place EF in broader DOS regions, reducing $S$. These findings imply limited thermoelectric potential for electron-doped FeS$_2$ and underscore the caution required when using RBA for doped semiconductors. For example, at room temperature with 25% Co, $S$ is $-46.71\,\mu$V/K (RBA), $-14.68\,\mu$V/K (jellium), and $-19.67\,\mu$V/K (Co substitution). Overall, the work clarifies the intrinsic thermopower behavior in this material and highlights the importance of accounting for doping-induced structural and screening effects in transport predictions.

Abstract

Pyrite FeS$_2$ has been investigated for a wide range of applications, including thermoelectrics due to previous observation of large thermopower at room-temperature. However, the values of thermopower reported in the literature is extremely sensitive to the nature of sample -- whether they are natural or lab grown, bulk crystals or thin films -- and an ambiguity in the magnitude and sign of thermopower of pure FeS$_2$ exists. Variation in the magnitude of room-temperature thermopower has also been observed in Co-doped samples. Therefore, it is of interest to clarify the intrinsic thermopower of this system that could be measured in more pure samples. In this paper, we investigate the thermoelectric properties of Co-doped FeS$_2$ using first principles calculations. We apply three different doping schemes to understand the effect of electron doping in FeS$_2$, namely explicit Co-substitution, jellium doping and electron addition within rigid band approximation (RBA) picture. The calculated thermopower is less than $-50$ $μ$V/K for all values of Co doping that we studied, suggesting that this system may not be useful in thermoelectric applications. Interestingly, we find that RBA substantially overestimates the magnitude of calculated thermopower compared to the explicit Co-substitution and jellium doping schemes. The overestimation occurs because the changes in the electronic structure due to doping-induced structural modification and charge screening is not taken into account by the rigid shift of the Fermi level within RBA. RBA is frequently used in first principles investigations of the thermopower of doped semiconductors, and Co-substituted FeS$_2$ illustrates a case where it fails.

Figures (6)

• Figure 1: The unit cell of pyrite FeS$_2$ belonging to the space group $Pa\overline{3}$. The yellow-brown nearest-neighbour Fe-S bonds illustrates the octahedral coordination of the Fe atoms and the S-S dimer bonds are shown by solid yellow lines. The Fe atoms are marked by numbers. Sequential substitution of Fe1 and Fe2 by Co atoms leads to Fe$_{0.75}$Co$_{0.25}$S$_2$ and Fe$_{0.5}$Co$_{0.5}$S$_2$ corresponding to $x = 0.75$ and $0.5$, respectively.
• Figure 2: Seebeck coefficient of the composition equivalent to Fe$_{0.75}$Co$_{0.25}$S$_2$ ($x = 0.75$) using RBA, jellium doping and explicit Co substitution within LDA. The left and the right columns show the results for the nonmagnetic and ferromagnetic phases, respectively.
• Figure 3: Nonmagnetic total density of states (left) and band structures (right) of Fe$_{0.75}$Co$_{0.25}$S$_2$ using RBA, jellium doping and explicit Co substitution within LDA. For the electronic structure in the RBA scheme, the Fermi energy is set to an electronic carrier concentration of $6.32 \times 10^{21}$ cm$^{-3}$ corresponding to one additional electron/unit cell.
• Figure 4: Seebeck coefficient of the composition equivalent to Fe$_{0.5}$Co$_{0.5}$S$_2$ using RBA, jellium doping and explicit Co substitution within LDA. The left and the right columns show the results for the nonmagnetic and ferromagnetic phases, respectively.
• Figure 5: