Complex Band Structures and Lattice Dynamics of Bi₂Te₃‐Based Compounds and Solid Solutions

Abstract

Bi 2 Te 3 -based compounds and derivatives are milestone materials in the fields of thermoelectrics (TEs) and topological insulators (TIs). They have highly complex band structures and interesting lattice dynamics, which are favorable for high TE performance as well as strong spin orbit and band inversion underlying topological physics. This review presents rational calculations of properties related to TEs and provides theoretical guidance for improving the TE performance of Bi 2 Te 3 -based materials. Although the band structures of these TE materials have been studied theoretically and experimentally for many years, there remain many controversies on band characteristics, especially the locations of band extrema and the exact values of bandgaps. Here, the key factors in the theoretical investigations of Bi 2 Te 3 , Bi 2 Se 3 , Sb 2 Te 3 , and their solid solutions are reviewed. The phonon spectra and lattice thermal conductivities of Bi 2 Te 3 -based materials are discussed. Electronic and phonon structures and TE transport calculations are discussed and reported in the context of better establishing computational parameters for these V 2 VI 3 -based materials. This review provides a useful guidance for analyzing and improving TE performance of Bi 2 Te 3 -based materials.nologies, including cooling and power generation. [1] They have been attracting increased attention in the last decade as a promising potential solution for harvesting waste heat to produce useful electrical power. The key challenge is to improve the efficiency of TE energy conversion, which is determined by the dimensionless figure of merit zT = S 2 σT/(κ e + κ L ), where S, σ, T, κ e , and κ L are the Seebeck coefficient, electrical conductivity, absolute temperature, and the electronic and lattice components of total thermal conductivity κ, respectively. [2] In order to improve zT, one can increase the numerator S 2 σ, which is also called power factor, and decrease the denominator κ. However, the tradeoff among the three properties makes it difficult to realize a high zT. [3] Since all three properties (S, σ, κ e ) are carrier concentration dependent, optimizations of the carrier concentration are needed for maximizing zT. [4] It is often convenient to evaluate TE materials through several empirical parameters, which can be combined into a term called the quality factor B ∼ N v /m I *κ L , [5] where N v is the band degeneracy and m I * is the inertial mass (m I * is equal to the band effective mass m b * for an isotropic single band). This suggests that high N v with low m b * and low κ L are beneficial for TE performance. However, materials such as Bi 2 Te 3 -based alloys, with the highest known roomtemperature TE performance, have complex band structures that are not well described in effective mass models. More sophisticated treatments involving the actual electronic structure are imperative.Since the discovery of the Seebeck effect, a rapid progress in TEs has been made in the 1950s and 1960s, when the classic TE materials Bi 2 Te 3 , ...

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