The Role of Electronic Bandstructure Shape in Improving the Thermoelectric Power Factor of Complex Materials

The large variety of complex electronic structure materials and their alloys offer highly promising directions for improvements in thermoelectric (TE) power factors (PFs). Their electronic structure contains rich features, referred to as "surface complexity", such as highly anisotropic, warped energy surface shapes with elongated features and threads in some cases. In this work, we use Boltzmann transport simulations to quantify the influence that the shape of the electronic structure energy surfaces has on the PF. Using analytical ellipsoidal bands, as well as realistic bands from a group of half-Heuslers, we show that band shape complexity alone can offer an advantage to the PF by similar to 3x in realistic cases. However, the presence of anisotropic scattering mechanisms, such as ionized impurity or polar optical phonon scattering, can reduce these improvements by up to similar to 50%. We show that expressions based on the simple ratio of the density of states effective mass to the conductivity effective mass, m(DOS)/m(C), together with the number of valleys, can capture the anisotropy shape with a moderate to high degree of correlation. For this, we use a convenient way to extract these masses by mapping the complex bandstructures of materials to parabolic electronic structures, which can be done without the need for Boltzmann transport codes. Despite the fact that the PF depends on many parameters, information about the benefits of the band shape alone, may be very useful for identifying and understanding the performance of novel thermoelectric materials.