Electronic structure of narrow gap semiconductors: Understanding gap formation and thermoelectric properties

Electronic band structure calculations are invaluable theoretical tools to understand structural, transport, and optical properties of materials. We have used this tool in the search for new high performance thermoelectric materials, which are usually narrow-gap semiconductors. We have studied the electronic structures of these systems both to understand which properties of the band structure are most important for thermoelectric properties and the nature of the gap formation.; Narrow-gap semiconductors lie between metals and wide-gap semiconductors, so understanding the nature of the gap formation is very important. The small band gaps in the systems we have studied generally arise from hybridization between different bands. We have used the local density approximation (LDA) and the generalized gradient approximation (GGA) within density functional theory (DFT). These have been implemented using the full-potential linearized augmented planewave (FLAPW) method within the WIEN97 package. This state-of-the-art method is among the most accurate methods for calculating the electronic structure of solids.; We have studied four classes of compounds. These include the half-Heusler compounds, the ternary Zintl-phase compounds, the simple chalcogenides, and the complex chalcogenides.; The ternary half-Heusler compounds, considered having a stuffed NaCl structure, show promising thermoelectric properties. The band gap formation is understood by starting with the semi-metallic binary NaCl compounds from which they are formed. Adding the transition (or noble) metal atom causes a strong p-d hybridization near the Fermi energy which opens up the band gap. This hybridization also leads to highly anisotropic effective masses at the conduction band minimum which are found in the best thermoelectric materials. Similar band gap formation is found in the ternary Zintl-phase compounds which are considered a stuffed Th₃P₄ structure. The band gaps in these ternary compounds are larger than experiment, unlike what one usually finds in LDA/GGA calculations. We explain this discrepancy by the noting that the position of the d-levels are too high in energy in LDA/GGA calculations which increases the hybridization near the Fermi energy and gives a larger gap.; The best known thermoelectric materials belong to the class of simple chalcogenides, including Bi₂Te₃ for room temperature (300 K) and PbTe for high temperature (700 K) applications. In contrast to the previous materials, here the relativistic effects are important and the band gaps are found to agree very well with experiment. We also find that the band structure of these materials show large band degeneracy and highly anisotropic effective masses at the band extrema as well as a narrow band gap, ideal for good thermoelectrics. We have searched for these properties in complex chalcogenides BaBiTe₃, CsBi₄Te₆, and K₂Bi₈Se₁₃. We have found that the best thermoelectric of these three, CsBi₄Te₆, has the highest anisotropic effective mass ratio, similar to what we had found for Bi₂Te₃.