Investigation of the electronic structure and lattice dynamics of the thermoelectric material Na-doped SnSe

SnSe has drawn considerable attention on a global scale due to its intrinsic low thermal conductivity and large figure of merit along the $b$ axis. In Na-doped SnSe, further enhancement of the thermoelectric performance has been reported. Using angle-resolved photoemission spectroscopy and inelastic neutron scattering, we have studied how electronic structures and lattice dynamics evolve with temperature in Na-doped SnSe. Our data show that the effective mass of the Se $p_z$ orbital along the $\mathrm{\Gamma }\text{−}Z$ direction has a very weak temperature dependence, while the chemical potential shifts significantly along with the increase in the gap size evidenced by infrared absorption measurements. Inelastic neutron scattering reveals one acoustic TA and two low-lying optical (TO1 and TO2) phonon modes. Their temperature-dependent behaviors indicate that the TO1 and TA modes contribute more to the reduction of the lattice thermal conductivity with temperature increases. The estimated value of the lattice thermal conductivity based on the lattice dynamics is significantly larger than that determined by transport measurements, suggesting that extrinsic factors, such as the imperfection of the lattice, could drastically suppress the lattice thermal conductivity. Our data suggest that temperature-dependent properties of both electronic structures and phonon dynamics need to be taken into account for the investigation of the underlying physics of hole-doped SnSe.

Figure 1

(a) The crystal structure of Na-doped SnSe in the $Pnma$ phase; here, Sn(Na) and Se atoms are represented by the gray and green balls, respectively. (b) The Brillouin zone of Na-doped SnSe with high-symmetry points. (c) The core-level photoemission spectrum of Na-doped SnSe; the Na $2p$ and Sn $4d$ characteristic peaks are illustrated in the inset. (d) and (e) Rietveld refinement of neutron powder diffraction data collected at 15 and 410 K, respectively. The black dots represent the observed results. The red and blue lines correspond to the calculated and difference patterns, respectively. The green ticks are the Bragg positions. (f) Temperature dependence of the lattice constants $a$, $b$, and $c$, derived from the Rietveld refinements of the neutron power diffraction patterns. (g) The volume of Na-doped SnSe as a function of temperature. The solid line is the parabolic fitting of the volume.

Figure 2

(a) Fermi surface mapping of the $k_y\text{−}{k}_z$ plane using the incident photon energy of 30 eV at $T=20$ K. (b) The photon energy dependence plot of the photoemission intensity at the Fermi level along the $\mathrm{\Gamma }\text{−}Z$ direction taken at $T=20$ K. (c) and (d) The ARPES intensity plot along the $\mathrm{\Gamma }\text{−}Z$ and $\mathrm{\Gamma }\text{−}Y$ directions, respectively. (e) and (f) The ARPES intensity distribution along cuts 1 and 2, respectively, in (a). The red dashed lines in (c)–(f) indicate the dispersions around the tops of these bands, which can approximately evaluate the effective masses.

Figure 3

Temperature dependence of the ARPES intensity along the $\mathrm{\Gamma }\text{−}Z$ direction. (a) and (b) The electronic structures along the $\mathrm{\Gamma }\text{−}Z$ direction that were observed at an incident photon energy of 30 eV at $T=60$ and 240 K, respectively. (c) Temperature-dependent energy distribution curves integrated over a momentum window of 0.03 ${\AA }^{-1}$ centered around the top of the $\alpha$ band. (d) Infrared absorption data plotted as ${\left(\alpha h\nu \right)}^2$ versus photon energy to show the variation of the direct band gap with temperature.

Figure 4

Phonon dispersions of Na-doped SnSe using the incident neutron energy of 7.74 meV. (a) and (c) The phonon dispersions along the $[H,1,1]$ and $[0,K,1]$ directions, respectively. The data were taken at $T=100$ K. (b) and (d) The same as (a) and (c), but taken at $T=450$ K. The lower and upper transverse optical modes are labeled as TO1 and TO2, respectively.

Figure 5

Transverse acoustic and optical phonon modes along the $[H,1,1]$ direction. (a) The comparison of the low-lying TO modes between the pristine and Na-doped SnSe. The red symbols are derived from the Na-doped SnSe, and the black symbols are from the pristine SnSe [20]. (b) The dispersion relationship of the TA phonon at $T=100$, 300, and 450 K. The solid lines correspond to the parabolic curve fitting. (c) Lorentzian fittings of spectra for Na-doped SnSe for different wave vectors. (d)–(f) Temperature dependence of the experimental phonon linewidth of the low-lying TO branches at $Q=[0,1,1]$, [0.12,1,1], and [0.18,1,1], respectively. (g) Temperature dependence of the experimental phonon linewidth of the TA branch at $Q=[0.54,1,1]$ and [0.78,1,1].