Charge carrier effective mass and concentration derived from combination of Seebeck coefficient andTe125NMR measurements in complex tellurides

Abstract

Thermoelectric materials utilize the Seebeck effect to convert heat to electrical energy. The Seebeck coefficient (thermopower), $S$, depends on the free (mobile) carrier concentration, $n$, and effective mass, ${m}^{*}$, as $S\ensuremath{\sim}{m}^{*}/{n}^{2/3}$. The carrier concentration in tellurides can be derived from $^{125}\mathrm{Te}$ nuclear magnetic resonance (NMR) spin-lattice relaxation measurements. The NMR spin-lattice relaxation rate, $1/{T}_{1}$, depends on both $n$ and ${m}^{*}$ as $1/{T}_{1}\ensuremath{\sim}{({m}^{*})}^{3/2}n$ (within classical Maxwell-Boltzmann statistics) or as $1/{T}_{1}\ensuremath{\sim}{({m}^{*})}^{2}{n}^{2/3}$ (within quantum Fermi-Dirac statistics), which challenges the correct determination of the carrier concentration in some materials by NMR. Here it is shown that the combination of the Seebeck coefficient and $^{125}\mathrm{Te}$ NMR spin-lattice relaxation measurements in complex tellurides provides a unique opportunity to derive the carrier effective mass and then to calculate the carrier concentration. This approach was used to study $\mathrm{A}{\mathrm{g}}_{x}\mathrm{S}{\mathrm{b}}_{x}\mathrm{G}{{\mathrm{e}}_{50\text{\ensuremath{-}}2}}_{x}\mathrm{T}{\mathrm{e}}_{50}$, well-known GeTe-based high-efficiency tellurium-antimony-germanium-silver thermoelectric materials, where the replacement of Ge by [Ag+Sb] results in significant enhancement of the Seebeck coefficient. Values of both ${m}^{*}$ and $n$ derived using this combination show that the enhancement of thermopower can be attributed primarily to an increase of the carrier effective mass and partially to a decrease of the carrier concentration when the [Ag+Sb] content increases.