Thermoelectric properties and investigations of low thermal conductivity in Ga-doped Cu${}_{2}$GeSe${}_{3}$

Thermoelectric properties and investigations of low thermal conductivity in Ga-doped Cu $_{2}$ GeSe $_{3}$

J. Y. Cho, X. Shi, J. R. Salvador, G. P. Meisner, J. Yang, H. Wang, A. A. Wereszczak, X. Zhou, and C. Uher

Phys. Rev. B 84, 085207 – Published 25 August 2011

Abstract

In this study, we synthesized a series of low thermal conductivity diamondlike materials with the general formula Cu $_{2}$ Ga $_{x}$ Ge $_{1 - x}$ Se $_{3}$ for 0 ≤ $x$ ≤ 0.1, and their transport properties were evaluated to establish their suitability for thermoelectric-based waste heat recovery applications. We report results for the Seebeck coefficient ( $S$ ), electrical resistivity (ρ), thermal conductivity (κ), Hall coefficient ( $R_{H}$ ), crystal structure, and elastic properties of Cu $_{2}$ Ga $_{x}$ Ge $_{1 - x}$ Se $_{3}$ for $x$ = 0.01, 0.03, 0.05, 0.07 and 0.1. Powder x-ray diffraction revealed that a small amount of a related cubic polymorph appeared, along with the orthorhombic parent phase, at high Ga concentrations. This cubic phase is related to the parent phase in that both contain three-dimensional tetrahedral diamondlike substructures. All samples showed positive values of $S$ and $R_{H}$ over the entire temperature range studied, indicative of $p$ -type charge carriers. The largest value of $S$ = 446 μV K $^{- 1}$ was observed at 745 K for undoped Cu $_{2}$ GeSe $_{3}$ . With increasing Ga content, both $S$ and ρ decreased. Low values of κ were observed for all samples, with the lowest value of κ = 0.67 W m $^{- 1}$ K $^{- 1}$ at 745 K for undoped Cu $_{2}$ GeSe $_{3}$ . This value approaches the theoretical minimum thermal conductivity for these materials at high temperatures. An unusually large Grüneisen parameter (γ), a measure of bonding anharmonicity, was observed for Cu $_{2}$ Ga $_{0.1}$ Ge $_{0.9}$ Se $_{3}$ even though this diamondlike material has highly symmetric, lower coordination number tetrahedral bonding. A value of γ = 1.7 was calculated from the measured values of the elastic properties, heat capacity, and volume thermal expansion. Given that all materials investigated have similar elastic property values and likely comparable coefficients of thermal expansion, we surmise that this large Grüneisen parameter is a general feature for this material system. We conclude that this high level of anharmonicity gives rise to enhanced phonon–phonon scattering, in addition to the scattering brought about by the disordered structure, resulting in very low values of thermal conductivity.