Dynamical thermoelectric coefficients of bulk semiconductor crystals: Towards high thermoelectric efficiency at high frequencies

Abstract

We investigate in this work the fundamental behavior of the dynamical thermoelectric coefficients of a bulk cubic semiconductor (SC) crystal. The treatment is based on solving Boltzmann electron transport equation in the frequency domain after simultaneous excitations by dynamical temperature and electric potential gradients, within the framework of the single relaxation time approximation. The SC crystal is assumed to be a linear, elastic homogenous, and isotropic medium having a parabolic energy band structure. We further assume to deal with one type of carriers (electrons or holes) that reside in a single energy band, and we neglect any phonon drag effect. Our approach allows us to obtain very compact expressions for the different dynamical thermoelectric coefficients that nicely capture the essential features of the dynamics of electron transport. We emphasize our study about the dynamical behavior of the thermoelectric figure of merit ZT(Ω) of the SC crystal by considering the coupled electron-phonon transport. Our study revealed a very interesting and compelling result in which ZT increases in the high frequency regime with respect to its steady-state value. The fundamental reason of this enhancement is due to the intrinsic uncoupling in the dynamics of electrons and phonons in the high frequency regime.