Photoemission study of the electronic structure of valence band convergent SnSe

IV-VI semiconductor SnSe has been known as the material with record high thermoelectric performance. The multiple close-to-degenerate (or “convergent”) valence bands in the electronic band structure has been one of the key factors contributing to the high power factor and thus figure of merit in the SnSe single crystal. To date, there have been primarily theoretical calculations of this particular electronic band structure. In this paper, however, using angle-resolved photoemission spectroscopy, we perform a systematic investigation of the electronic structure of SnSe. We directly observe three predicted hole bands with small energy differences between their band tops and relatively small in-plane effective masses, in good agreement with the ab initio calculations and critical for the enhancement of the Seebeck coefficient while keeping high electrical conductivity. Our results reveal the complete band structure of SnSe and help to provide a deeper understanding of the electronic origin of the excellent thermoelectric performances in SnSe.

Figure 1

Crystal structure and characterization of SnSe. (a) (i) Orthorhombic crystal structure of low-temperature SnSe, (ii) the corresponding BZ of SnSe; high-symmetry points are labeled. (b) (i) Photograph of the high-quality SnSe single crystal, (ii)–(iv) XRD pattern of the (001), (010), (100) surface of SnSe. (c) STM topography image of cleaved SnSe measured at $\sim 77\mathrm{K}$. (d) The x-ray photoelectron spectrum (XPS) of SnSe showing characteristic $4s$, $4d$ core level peaks of Sn and LMM, $3p$, $3d$ core level peaks of Se.

Figure 2

Basic electronic structure of SnSe. (a) Stacking plots of constant energy contours in broad energy range showing the band structure evolution with high-symmetry directions labeled. (b) (i)–(iv) Photoemission spectral intensity map showing constant energy contours at $E\text{−}{E}_{\mathrm{VBM}}=0,0.07,0.27$, and 0.47 eV, respectively. (v)–(viii) Corresponding calculated constant energy contours at the same energies as (i)–(iv), respectively. (c) (i) High-symmetry cut along the $\overline{Y}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{Y}$ with α, β band marked. (ii) Corresponding slab calculations along the $\overline{Y}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{Y}$ direction. (d) (i) High-symmetry cut along the $\overline{X}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ direction with γ band marked; black dotted line indicates the top of the γ band. (ii) Corresponding slab calculations along the $\overline{X}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ direction. All data measured by 21 eV photons with linear horizontal polarization.

Figure 3

$k_z$ evolution of the electronic band structure of SnSe. (a) (i)–(v) High-symmetry cuts along the $k_y$ direction ($k_x=0$) probed with different photon energies. Corresponding $k_z$ values of each dispersion are labeled. Perpendicular black dotted lines indicate the position ($k_x=k_y=0$) where the EDC is extracted and analyzed in (c)(i). (vi)–(x) Corresponding ab initio calculated dispersions as in (i)–(v). (b) (i)–(v) High-symmetry cuts along the $k_x$ direction ($k_y=0$) probed with different photon energies. Corresponding $k_z$ values of each dispersion are labeled. (vi)–(x) Corresponding ab initio calculated dispersion as in (i)–(v). (c) (i) Stacked line plots of the energy distribution curves (EDC) extracted at $k_x=k_y=0$ from different high-symmetry cuts in (a)(i)–(v). Red marks indicate the identified peak positions. (ii) The second-derivative image of the intensity plot of (i) shows the dispersion along the $Z$-Γ-$Z$ direction at $k_x=k_y=0$. (iii) Corresponding ab initio calculated dispersion as in (ii). All data measured by photons with linear horizontal polarization.

Figure 4

Extraction of the in-plane effective mass of valence bands in SnSe. The in-plane effective masses of band α, β, γ along $k_x$ directions are extracted and labeled in (a)(i), (b)(i), and (c)(i), respectively; those along the $k_y$ directions are extracted and labeled in (a)(ii), (b)(ii), and (c)(ii), respectively. Green curves indicate a high-order polynomial curve to fit the dispersion and red curves indicate the parabolic curves near the band top to extract the effective masses.

Figure 5

Ab-initio calculation of the Seebeck coefficient. (a),(c) Band structure of Pnma SnSe obtained from (a) HSE06 and (c) GGA calculations. The dashed lines from top to bottom correspond to the chemical potentials with the carrier concentrations of $5.0\times {10}^{17}\mathrm{c}{\mathrm{m}}^{-3}$, $1.4\times {10}^{19}\mathrm{c}{\mathrm{m}}^{-3}$, $2.5\times {10}^{19}\mathrm{c}{\mathrm{m}}^{-3}$, $1.6\times {10}^{20}\mathrm{c}{\mathrm{m}}^{-3}$, and $3.0\times {10}^{20}\mathrm{c}{\mathrm{m}}^{-3}$ at 300 K, respectively. (b),(d) The Seebeck coefficients from the HSE06 and GGA calculations as a function of temperature, with respect to the chemical potentials with the same color in (a) and (c), respectively.