Estimation of effective electron relaxation times in real thermoelectric materials

Good samples of thermoelectric materials should be Phonon-Glass-Electron-Crystal (PGEC) [1], which scatters phonons without scattering electrons. However, the actual values of electron relaxation time $\tau_{\mathrm{el}}$ are not well investigated, and $\tau _{\mathrm{el}}$ is simply set as 10$^{\mathrm{-14}}$ s in many first-principles calculations of thermoelectric properties. In this study, we attempted to estimate the effective values of $\tau _{\mathrm{el}}$ of various thermoelectric materials, by fitting the calculation results by WIEN2k [2] and BoltzTraP [3] with experimental Seebeck coefficient and electrical conductivity. When we fitted experimental thermoelectric properties of Si$_{\mathrm{0.8}}$Ge$_{\mathrm{0.2}}$ samples [4][5], $\tau_{\mathrm{el}}$'s at 300 K were 9x10$^{\mathrm{-15}}$ s in a highly crystalline sample [4], and 5-6x10$^{\mathrm{-15}}$ s in ball-milled polycrystalline samples [5]. Temperature dependences of $\tau _{\mathrm{el}}^{\mathrm{-1}}$ were also different between samples, implying the difference in dominant electron scattering mechanisms. Various samples of thermoelectric materials with fairly high figures of merit exhibited $\tau_{\mathrm{el}}$ of several 10$^{\mathrm{-15\thinspace }}$s at 300 K. [1] G. A. Slack, \textit{CRC Handbook of Thermoelectrics}, 407 (1995). [2] P. Blaha, \textit{et al}., \textit{WIEN2k Users' Guide}, Vienna Univ. of Technology, Austria (2001). [3] G.K.H. Madsen et al., \textit{Comp. Phys. Comm.} 175, 67 (2006). [4] J.P. Dismukes et al., \textit{J. Appl. Phys.} 10 2899 (1976). [5] C.B. Vining et al., \textit{J. Appl. Phys.} 69 4333 (1991).