Roles of Carrier Doping, Band Gap, and Electron Relaxation Time in the Boltzmann Transport Calculations of a Semiconductor’s Thermoelectric Properties

Abstract

Although there is a growing demand for first-principles predictions of the thermoelectric properties of materials, the contribution of various errors in Boltzmann transport calculations is not negligible. We conducted a typical first-principles calculation and a Boltzmann transport analysis on a typical semiconductor (Si) at various temperatures T while varying the band gap ε_g, electron relaxation time τ_el, and phonon thermal conductivity κ_ph to demonstrate how the calculated thermoelectric properties, which are functions of the carrier doping level, are affected by these parameters. Bipolar conduction drastically decreased zT via a degradation of the Seebeck coefficient S and an increase in the effective Lorenz factor L_eff, indicating the importance of a wide enough ε_g (several multiples of k_BT or higher) for high zT. Thus, the underestimation of ε_g, which frequently happens in first-principles calculations, could induce large errors in calculations for narrow-gap semiconductors. The calculation of the electron thermal conductivity without Peltier thermal conductivity was found to limit the zT of typical semiconductors to below 1. A small value of κ_ph/τ_el, where κ_ph/τ_el is the degree to which a material is a phonon-glass electron-crystal, was necessary to achieve a high zT. Fitting the calculations with experimental thermoelectric properties showed that τ_el can vary by an order of magnitude from 10⁻¹⁵ to 10⁻¹⁴ s, depending on both T and the samples. This indicates that the use of a fixed relaxation time is inappropriate for thermoelectric materials.