On the thermoelectric efficiency of warped electronic band structures: A comparison of the predictions of common scattering approximations
Within the linear response regime, calculation of a material’s thermoelectric transport parameters requires detailed knowledge of both the electronic band structure and the electronic scattering rates. While it is possible to calculate both from first-principles using density-functional theory, rigorous scattering rate calculations can be orders of magnitude more intensive than band structure calculations, and so in practice it is common to make use of a simplified scattering model instead. The two most common such scattering models are the constant-mean-free-path model, the constant-relaxation- time model. However, recent studies in which the electronic scattering rates have been rigorously calculated have motivated the use of a third scattering approximation known as the DOS-scattering model, wherein the electronic scattering rates are assumed to have the same energy dependence as the density-of-states. While the latter approximation is believed to be the most physical of the three, it is also the least commonly used, despite being no more difficult to implement. The overall goal of this thesis is to understand the extent to which the predictions of the more commonly used scattering approximations differ from those of the more physical DOS-scattering model when applied to different classes of electronic band structure. This work begins by comparing the predictions of these scattering models when applied to common analytic models of electronic dispersion. It is found that these models can differ significantly in their predictions, and can even disagree about whether a particular electronic dispersion feature should improve or degrade performance. In particular, we find that in the case of the so-called quartic-band model (a simple analytic model commonly used to describe warped bands), DOS scattering predicts the existence of a second local maximum in the thermoelectric power factor, a feature completely missed by both the constant-mean-free-path and constant-relaxation-time approximations. Motivated by these findings, we use first-principles calculations of electronic structure to investigate the thermoelectric properties of 2D quintuple-layered systems of Bi2Te3, Bi2Se3 and Sb2Te3 using the DOS scattering approximation. These materials display warped band structures qualitatively similar to those described by the quartic-band model, but have to date only been studied using the MFP and TAU approximations. To assist with the interpretation of our results, we introduce a new analytic model of electronic dispersion that qualitatively captures the main features of the band structures of these materials. It is found that while the presence of ring-like critical surfaces in the electronic dispersion can lead to excellent thermoelectric performance, such benefits are highly sensitive to the anisotropy and energetic alignment of these features. Our findings suggest that these quintuple-layer systems may be even better thermoelectrics than was previously believed, and suggests the possibility of a new approach for designing band structures that lead to highly efficient thermoelectric conversion.