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 ¾ g , electron relaxation time¸e l , and phonon thermal conductivity ¬ 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 ¾ g (several multiples of k B T or higher) for high zT. Thus, the underestimation of ¾ 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 ¬ ph /¸e l , where ¬ ph /¸e l 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¸e l can vary by an order of magnitude from 10 ¹15 to 10 ¹14 s, depending on both T and the samples. This indicates that the use of a fixed relaxation time is inappropriate for thermoelectric materials.

Data-driven analysis of electron relaxation times in PbTe-type thermoelectric materials

“…Core/valence cut-off energy was set at −6.0 Ry, and the calculation was performed on a 50 × 50 × 50 k-mesh. Thermoelectric properties were calculated from the Boltzmann transport equations, using the BoltzTraP code [31], which was modified [9] to include secondorder terms for κ el . The chemical potential (μ) dependences of additional charges per unit cell N, S, σ/τ el , and κ el /τ el , at T = 300, 400, 500, 600, 700, and 800 K were obtained from output files generated by BoltzTraP.…”

“…Although first-principles calculation is a powerful tool to select many candidate thermoelectric materials [7,8], various kinds of uncertainties arise in predicting actual thermoelectric properties [9]. Calculations usually examine idealistically clean crystals, whereas experimental high-ZT samples are much dirtier.…”

“…As τ el is the time between electron scattering, long τ el is expected in PGEC materials. Although many studies assume constant τ el (often at 10 −14 s), a large sample dependence of τ el is reported in a few studies [9,10].…”