Abstract
Thermoelectric (TE) materials, which can convert heat to electricity and vice versa, have great potential for energy harvesting from waste heat and have seen renewed interest in recent years. These materials are also used in many niche applications, such as electrical generators in remote locations, sensors, and cooling for medical and scientific equipment. With the advent of computational methods like density functional theory (DFT), modeling is becoming an increasingly more important tool in the TE field. Providing, among other things, electronic band structures and electronic transport properties, DFT combined with Boltzmann transport theory provides both predictive and explanatory power. A limiting factor, however, has long been the modeling of electron scattering, resulting in the use of coarse approximations like the constant relaxation time approximation or textbook results based on heavily simplified models. More accurate modeling and understanding of electronic scattering in complex materials and band structures could lift the field of TE and result in new and improved TE materials. To find suitable candidate materials for more detailed analysis, a highthroughput (HT) screening of the Materials Project database was performed.
Based on criteria such as crystal structure complexity, elements, energy above convex hull, magnetic properties, and valence electron count, 6965 materials were selected. For more accurate band gap estimations, the MBJ functional was employed. This revealed band gaps in 189 materials predicted to be metallic with PBE, and an average band gap increase of 0.43 eV in 331 materials with narrow PBE band gaps. The electronic transport properties and thermoelectric figure of merit (zT) were calculated with a constant relaxation time (τ ) of 10 fs and with a lattice thermal conductivity (κℓ) of 5 W/mK for each material. Using the same, constant τ and κℓ for every material results in both false positives and negatives, but still yields a rough ranking on how applicable the electronic structure is for TE purposes.
Based on the high-throughput results, two promising full-Heusler materials were selected for further investigation. CsK2Sb, a known photocatode material, has a complex band structure with features akin to those of two-dimensional (2D) quantum wells. The other material, Na2TlSb, also has a quasi-low-dimensional band structure, but one-dimensional (1D), resulting in a Fermi surface consisting of sheets. Both band structures have a rapidly increasing density of states (DOS) with high-mobility carriers close to the band gap, a favorable trait for thermoelectric materials. Despite high DOS generally being associated with excessive electron scattering, this was not found to be the case in these materials, counterintuitive to conventional wisdom. Both materials were also found to have very low κℓ, resulting in a predicted zT of 2.6 and 4.4 for CsK2Sb and Na2TlSb, respectively. Compressive strain was found to improve the electronic transport properties of CsK2Sb by enhancing the 2D features and reducing electron scattering, but also increased κℓ, resulting in only a marginally increased zT of 2.7 at 1% strain.
The changes to materials properties and the resulting electronic scattering rates in strained CsK2Sb prompted further investigation. The materials properties of ZrNiSn were systematically adjusted, and the following changes to scattering rates were observed. While most materials properties changed scattering rates as expected, some gave less intuitive results. Other parameters relevant to scattering, such as carrier concentration (Nc) and temperature (T), were also investigated. In addition to directly affecting different scattering
mechanisms, both Nc and T change the location of the Fermi level and the magnitude of free-carrier screening, creating highly interconnected results. The low scattering rates could also, in part, be explained by the exotic geometries of the Fermi surfaces. For momentum-dependent scattering mechanisms, the large separation in k-space prevented scattering between large parts of the surface. Further, the combination of wavefunction overlaps and the geometrical momentum relaxation time factor strongly reduced elastic scattering to large portions of the total scattering space. The results for both materials indicate that Fermi surfaces delocalized in k-space tend to reduce electronic scattering. These insights, combined with knowledge of how materials properties affect scattering, can help build understanding and intuition that can aid the discovery and design of new TE materials.