Material Dependence of the Thermoelectric Figure of Merit

Abstract

First-principles calculations were used to perform a cross-material investigation on the electronic structures of 13 parent compounds for thermoelectric materials. Boltzmann transport equations were used to calculate carrier doping level dependence of the Seebeck coefficient, electrical conductivity with respect to relaxation time, effective Lorenz numbers and the maximum possible thermoelectric figure of merit (Z_eT) in the limit of zero phonon thermal conductivity. High Z_eT was obtained only in semiconductors with finite band gaps. High Z_eT for high doping level was achieved in compounds that had a steep density of states at the band edge. Calculations were combined with experimental transport properties to evaluate electron relaxation time of the samples. These analyses can be used to understand the nature of electron scattering mechanisms in specific thermoelectric materials and reduce the number of experiments required to develop new thermoelectric materials.

Fig. 1 (a) DOS of the 12 thermoelectric material parent compounds, normalized by unit cell volume. TB–mBJ was employed as the exchange-correlation potential. One grid along the vertical axes corresponds to normalized DOS of 10³⁰ eVm⁻³. The letters in parentheses indicate the selected carrier types used for the transport calculations. (b) n-dependence of the absolute Seebeck coefficients at 300 K. (c) n-dependence of electrical conductivity (σ) divided by τ_el. (d) n-dependence of effective Lorenz number. The black line indicates the theoretical value L₀ obtained from the free electron model. (e), (f) n-dependence of Z_eT at (e) 300 K and (f) 900 K, assuming rigid crystal structures. (g) n-dependence of ZT at 900 K, assuming that κ_ph/τ_el decreased to 10¹⁴ Wm⁻¹K⁻¹s⁻² in all materials.