Chapter 2: Theoretical Foundations and Modelling of Inorganic Thermoelectric Materials

This chapter aims to illustrate the simple models used to guide the search for new thermoelectric materials and to provide introductory information on strategies to harvest the power of quantum mechanical calculations based on density functional theory. The study of the properties of inorganic thermoelectric materials is rooted in the quantum mechanical treatment of the many-body system formed with interacting nuclei and electrons and also in the principles of diffusive transport phenomena. Starting from these foundations, the chapter develops two models to rationalise the electronic and thermal transport: the Drude–Sommerfeld model and the anharmonic phonon gas model, respectively. Difficulties and design rules to optimise the thermoelectric efficiency are also discussed, focusing on two main property descriptors: effective masses and mode-resolved Grüneisen parameters. Examples of first-principles band structure calculations and phonon dispersions are presented and linked to electronic and thermal transport using qualitative considerations. A comparison between the theoretical and experimental perspectives concludes the chapter, underlining the strengths and the limits of theory in a few significant cases.