Roles of Carrier Doping, Band Gap, and Electron Relaxation Time in the Boltzmann Transport Calculations of a Semiconductor’s Thermoelectric Properties
Yukari Katsura, Hidenori Takagi, Kaoru Kimura
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 εg, electron relaxation time τel, and phonon thermal conductivity κph 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 Leff, indicating the importance of a wide enough εg (several multiples of kBT or higher) for high zT. Thus, the underestimation of εg, 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 κph/τel, where κph/τel 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 τel 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.