Abstract
The effective mass is a convenient descriptor of the electronic band structure used to characterize the density of states and electron transport based on a free electron model. While effective mass is an excellent first-order descriptor in real systems, the exact value can have several definitions, each of which describe a different aspect of electron transport. Here we use Boltzmann transport calculations applied to ab initio band structures to extract a density-of-states effective mass from the Seebeck Coefficient and an inertial mass from the electrical conductivity to characterize the band structure irrespective of the exact scattering mechanism. We identify a Fermi Surface Complexity Factor: {N}_{{rm{v}}}^{ast }{K}^{ast } from the ratio of these two masses, which in simple cases depends on the number of Fermi surface pockets ({N}_{{rm{v}}}^{ast }) and their anisotropy K*, both of which are beneficial to high thermoelectric performance as exemplified by the high values found in PbTe. The Fermi Surface Complexity factor can be used in high-throughput search of promising thermoelectric materials.
Highlights
The calculation of electronic band structures using density functional theory (DFT) is so routine that it is becoming faster to compute certain physical properties than make samples and measure them—inspiring the materials genome initiative efforts worldwide
Using a constant relaxation time approximation, very precise predictions of transport properties that depend on fine details of the band structure can be made, the electrical conductivity predicted for instance can be greatly misleading because the relaxation time is approximated, often to an arbitrary constant
Because m*c and m*S are less influenced by τ and scattering mechanism than σ and S, they are better descriptors of a band structure’s contribution to transport than a constant relaxation time approximation (CRTA) value of σ and S itself
Summary
The calculation of electronic band structures using density functional theory (DFT) is so routine that it is becoming faster to compute certain physical properties than make samples and measure them—inspiring the materials genome initiative efforts worldwide. Dielectric, optical and transport properties such as electrical conductivity, Hall effect, and thermoelectric power (Seebeck effect) require knowledge of the electronic structure readily available from ab initio calculations, but may require an assumption about the scattering. A recent study performed by the authors demonstrated that while Seebeck coefficient was reproduced fairly well across a variety of compounds (provided that the band gap was not severely underestimated), the experimental values on conductivities can be highly inaccurate using a constant relaxation time.[1] While some scattering mechanisms can be calculated using ab initio methods, they are far from routine and require special algorithms. The goal of this study is to extract transport information from band structure calculations that does not depend on any scattering assumption
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