Restructured single parabolic band model for quick analysis in thermoelectricity

Xuemei Zhang,Jiehe Sui,Wei Cai,Jinsuo Hu,Jianbo Zhu,Muchun Guo,Songting Cai,Jingyu Li,Yongsheng Zhang

doi:10.1038/s41524-021-00587-5

Abstract

The single parabolic band (SPB) model has been widely used to preliminarily elucidate inherent transport behaviors of thermoelectric (TE) materials, such as their band structure and electronic thermal conductivity, etc. However, in the SPB calculation, it is necessary to determine some intermediate variables, such as Fermi level or the complex Fermi-Dirac integrals. In this work, we establish a direct carrier-concentration-dependent restructured SPB model, which eliminates Fermi-Dirac integrals and Fermi level calculation and emerges stronger visibility and usability in experiments. We have verified the reliability of such restructured model with 490 groups of experimental data from state-of-the-art TE materials and the relative error is less than 2%. Moreover, carrier effective mass, intrinsic carrier mobility and optimal carrier concentration of these materials are systematically investigated. We believe that our work can provide more convenience and accuracy for thermoelectric data analysis as well as instructive understanding on future optimization design.

Highlights

Thermoelectric (TE) materials can enable reversible conversion between electrical and thermal energy via strong electrical-thermal coupling effect, have enormous potential in waste heat power generation and refrigeration[1,2]
In the single parabolic band (SPB) model, all transport properties can be established by four isolated key factors[25]: (i) Fermi level EF, which reflects the doping level, (ii) the effective mass m*, which estimates the band dispersion, (iii) the scattering factor λ, which represents the mechanism of carrier scattering, and (iv) the relaxation time τ, which reflects the scattering intensity
We introduced a restructured SPB model, in which all thermoelectric parameters are directly associated with carrier concentration by simple analytic expressions with less than 2%

Summary

INTRODUCTION

Thermoelectric (TE) materials can enable reversible conversion between electrical and thermal energy via strong electrical-thermal coupling effect, have enormous potential in waste heat power generation and refrigeration[1,2]. In the SPB model, all transport properties can be established by four isolated key factors[25]: (i) Fermi level EF (or reduced Fermi level η = EF/kBT), which reflects the doping level, (ii) the effective mass m*, which estimates the band dispersion, (iii) the scattering factor λ, which represents the mechanism of carrier scattering, and (iv) the relaxation time τ, which reflects the scattering intensity. One can obtain these important parameters from fitting the experimental transport measurements or from the density-functional theory (DFT) calculations. We have collected 490 groups of experimental data of state-of-the-art TE materials

RESULTS AND DISCUSSION

METHODS

Design restructured model

CODE AVAILABILITY