Ab initio study of electron transport in lead telluride

Abstract

Last few years have witnessed significant enhancement of thermoelectric figure of merit of lead telluride (PbTe) via nanostructures. Despite the experimental progress, current understanding of the electron transport in PbTe is based on either band structure simulated using first-principles in combination with constant relaxation time approximation or empirical models, both requiring adjustable parameters obtained by fitting experimental data. This thesis aims to compute thermoelectric properties of PbTe all from first-principles. We start by discussing the formalism based on Boltzmann transport equation to calculate the electron transport properties in PbTe using first principles and identify the importance to calculate electron-phonon interaction accurately. We then discuss the challenges in studying electron-phonon interaction in semiconductors using first-principles and introduce electron-phonon Wannier interpolation which allows us to calculate the strength of electron-phonon coupling on a very fine mesh. In polar materials like PbTe, the Fröhlich interaction due to long-range dipole field of longitudinal optical phonons contributes to the electron-phonon coupling as well. As the long-range nature of the dipole field makes the standard Wannier interpolation fail, we have discussed the detailed procedures for correction. Next, we study the screening effect of free carriers on electron transport by modulating the polar scattering. These considerations enabled us to report parameter-free first-principles calculation of electron and phonon transport in PbTe, including mode-by-mode electron-phonon scattering, leading to detailed information on electron mean free paths and the cumulative contributions by electrons and phonons with different mean free paths to thermoelectric transport properties in PbTe. Such information will help to rationalize the use and optimization of nanostructures to achieve high thermoelectric figure of merit.