Replacement of Ge in GeTe by [Ag$+$Sb] and rare earths: effect on thermoelectric properties

High-efficiency $p$-type Te-Sb-Ge-Ag (TAGS) thermoelectric materials are based on the GeTe narrow-band self-dopant semiconductor where Ge can be replaced by up to 16 at.{\%} [Ag$+$Sb]. To understand the effect of Ge replacement by 4 at.{\%} [Ag$+$Sb] as well as rare earths atoms, we have synthesized and studied XRD, thermopower, electrical resistivity, thermal conductivity, and $^{125}$Te NMR of GeTe and Ag$_2$Sb$_2$Ge$_{\mathrm{46-x}}$R$_{\mathrm{x}}$Te$_{50}$ with R$=$Gd, Dy and $x=$1, 2. At 700 K, GeTe exhibits a thermopower of $+$146 $\mu $VK$^{-1}$ and a large power factor, 42 $\mu $Wcm$^{-1}$K$^{-2}$. Replacement of Ge by [Ag$+$Sb] and rare earths enhances the thermopower, but slightly reduces the power factor due to an increase in electrical resistivity. The thermal conductivity at 300 K of all alloys studied is reduced by a factor of two compared to GeTe. $^{125}$Te NMR spin-lattice relaxation time and resonance frequency reflect changes in carrier concentration. However, decrease of thermal conductivity due to carriers and increase of electrical resistivity are mostly due to a reduction of carrier mobility and indicate strong scattering produced by [Ag$+$Sb] and rare earth atoms. At 700 K, the thermoelectric figure of merit of GeTe is 0.8, whereas that in Ag$_2$Sb$_2$Ge$_{45}$Dy$_1$Te$_{50}$ is much larger, 1.2, due to a reduction in thermal conductivity. Enhancement of thermopower is discussed within a model of energy filtering.