Measurements of the energy band gap and valence band structure of ${\text{AgSbTe}}_2$

The de Haas-van Alphen effect, galvanomagnetic and thermomagnetic properties of high-quality crystals of ${\text{AgSbTe}}_2$ are measured and analyzed. The transport properties reveal the material studied here to be a very narrow-gap semiconductor $\left(E_g\approx 7.6\pm 3\text{meV}\right)$ with $\sim 5\times {10}^{19}{\text{cm}}^{-3}$ holes in a valence band with a high density of states and thermally excited $\sim {10}^{17}{\text{cm}}^{-3}$ high-mobility $\left(2200{\text{cm}}^2/\text{Vs}\right)$ electrons at 300 K. The quantum oscillations are measured with the magnetic field oriented along the $⟨111⟩$ axis. Taken together with the Fermi energy derived from the transport properties, the oscillations confirm the calculated valence band structure composed of 12 half-pockets located at the $X$-points of the Brillouin zone, six with a density-of-states effective mass $m_{da}^{\ast }⪢0.21m_e$ and six with $m_{db}^{\ast }⪢0.55m_e$, giving a total density-of-states effective mass, including Fermi pocket degeneracy, of $m_d^{\ast }\approx 1.7\pm 0.2m_e$ ($m_e$ is the free electron mass). The lattice term dominates the thermal conductivity, and the electronic contribution in samples with both electrons and holes present is in turn dominated by the ambipolar term. The low thermal conductivity and very large hole mass of ${\text{AgSbTe}}_2$ make it a most promising $p$-type thermoelectric material.

Figure 1

(Color online) Powder x-ray diffraction spectrum of the ingot of ${\text{AgSbTe}}_2$ used in this work. The insert shows the AF-IIb structure (Ref. 15) with ordering of Ag and Sb in metallic sublattice.

Figure 2

(Color online) Experimental temperature dependence of the zero-field resistivity and Seebeck coefficients $(\times )$, and of the low-field Hall and Nernst $(○)$ coefficients of one sample of ${\text{AgSbTe}}_2$. The lines are guides to the eye.

Figure 3

Experimental magnetic field dependence of the relative magnetoresistance $\Delta \rho /\rho$, magnetoseebeck effect $\Delta S/S$, transverse Hall resistivity ${\rho }_{xy}$, and transverse Nernst thermopower $S_{xy}$. The data are only shown at the few selected temperatures indicated.

Figure 4

(Color online) Fitted electron (dashed lines) and hole (dotted lines) densities $\left(n,p\right)$, mobilities $\left({\mu }_e,{\mu }_h\right)$ and partial electrical conductivities $\left({\sigma }_e,{\sigma }_h\right)$ as a function of temperature. Also shown are the total calculated conductivity compared to experimental values $(\times )$.

Figure 5

(Color online) Fit of the zero-field Seebeck and of the low-field isothermal Nernst coefficients: the partial electron (dashed lines) and hole (dotted lines) thermopowers and Nernst coefficients are shown, alongside the calculated total (full lines), which can be compared to the data points $(\times )$. The fit assumes that only acoustic phonon scattering is present at all temperatures, and that the energy gap is temperature-independent; therefore the Nernst coefficient, which is very sensitive to the scattering mechanism, is reproduced with only moderate accuracy.

Figure 6

(Color online) Experimental temperature dependence of the thermal conductivity of an ${\text{AgSbTe}}_2$ from the same ingot as was used for Figs. 2, 3 $(●)$. The ambipolar thermal conductivity (dashed-dotted line) dominates the total electronic contribution (full line), which contains estimates of the electron (dashed line) and hole (dotted line) contributions. The crosses are the difference between the experimental data points and the electronic contributions, and represent the lattice thermal conductivity.

Figure 7

De Haas-van Alphen oscillations in the magnetic field dependence of the magnetic susceptibility, with the diamagnetic background subtracted, of a $4{\text{mm}}^3$ crystal of ${\text{AgSbTe}}_2$ oriented with the magnetic field along the $⟨111⟩$ axis at 5 K (bottom frame). The top frame shows the Fourier component amplitude of the oscillations plotted as a function of the inverse magnetic field frequency, identifying two frequencies at 25.9 and 62.0 Tesla.

Figure 8

(Color online) Calculated hole Fermi surfaces for ${\text{AgSbTe}}_2$ per Ref. 32 with Ag and Sb atoms ordered on the metal sublattice, case AF-IIb. The small pockets around ${\Delta }^{\prime }$ are not populated in the sample studied here; the masses for the other pockets are given in Table along the directions indicated.