$GW$ quasiparticle band structures of stibnite, antimonselite, bismuthinite, and guanajuatite

We present first-principles calculations of the quasiparticle band structures of four isostructural semiconducting metal chalcogenides $A_2{B}_3$ (with $A$ = Sb, Bi and $B$ = S, Se) of the stibnite family within the $G_0{W}_0$ approach. We perform extensive convergence tests and identify a sensitivity of the quasiparticle corrections to the structural parameters and to the semicore $d$ electrons. Our calculations indicate that all four chalcogenides exhibit direct band gaps, if we exclude some indirect transitions marginally below the direct gap. Relativistic spin-orbit effects are evaluated for the Kohn-Sham band structures, and included as scissor corrections in the quasiparticle band gaps. Our calculated band gaps are 1.5 eV (Sb${}_2$S${}_3$), 1.3 eV (Sb${}_2$Se${}_3$), 1.4 eV (Bi${}_2$S${}_3$), and 0.9 eV (Bi${}_2$Se${}_3$). By comparing our calculated gaps with the ideal Shockley-Queisser value we find that all four chalcogenides are promising as light sensitizers for nanostructured photovoltaics.

Figure 1

Ball-and-stick model of $A_2{B}_3$ semiconducting metal chalcogenides of the stibnite family, with $A$ standing for Sb or Bi (brown), and $B$ for S or Se (yellow). The two inequivalent ${\left(A_4{B}_6\right)}_n$ ribbons in the unit cell are highlighted in red, and the perspective view is along the direction of the ribbons.

Figure 2

Convergence tests for the quasiparticle band gap of antimonselite. (a) Calculated $G_0{W}_0$ band gap as a function of the polarizability cutoff, for calculations without (red circles) or with (blue disks) semicore states. The solid lines correspond to the fits obtained from Eq. (3). We find $a_0=1.33$ eV and 1.16 eV for calculations without and with semicore electrons, respectively. (b) Same as in (a), with the band gap reported as a function of the largest energy denominator used for calculating the polarizability. In this case we find $a_0=1.32/1.14$ eV for calculations without/with semicore electrons. All calculations were performed using optimized lattice parameters.

Figure 3

Band structures of (a) stibnite, (b) antimonselite, (c) bismuthinite, and (d) guanajuatite calculated using DFT/LDA, experimental lattice parameters, and without semicore electrons (black solid lines), as well as corresponding density of states (DOS, black dashed lines). The contributions to the DOS from the $p$ states of S and Se (Sb and Bi) are indicated by the green (blue) shaded areas in each case. The $\mathit{GW}$ quasiparticle energies of the band extrema at high-symmetry points are also shown, with blue squares and red circles indicating calculations with or without semicore electrons, respectively. The connecting lines are guides to the eye. The coordinates of the high-symmetry points in reciprocal lattice units are as follows: $Z$: $(0,0,0.5)$, $X$: $(0.5,0,0)$, $Y$: $(0,0.5,0)$.

Figure 4

Quasiparticle corrections as a function of the corresponding DFT/LDA eigenvalues for (a) stibnite, (b) antimonselite, (c) bismuthinite, and (d) guanajuatite. Only eigenvalues at the high-symmetry points $\Gamma$, $X$, and $Z$ are considered. Blue disks and red circles indicate calculations with and without semicore electrons, respectively. All calculations were performed using experimental lattice parameters.

Figure 5

Exchange (black disks and circles) and correlation (red filled and empty squares) contributions to the quasiparticle corrections vs DFT/LDA eigenvalues for (a) stibnite, (b) antimonselite, (c) bismuthinite, and (d) guanajuatite. Only eigenvalues at the high-symmetry points $\Gamma$, $X$, and $Z$ are considered. Filled and empty symbols indicate calculations with and without semicore states, respectively. All calculations were performed using experimental lattice parameters.

Figure 6

Schematic summary of the band gaps of stibnite, antimonselite, bismuthinite, and guanajuatite calculated in this work: Kohn-Sham gaps (empty rectangles) and $\mathit{GW}$ gaps (filled rectangles) including relativistic corrections. The band gaps were obtained by including semicore electrons and using the experimental lattice parameters. The pink rectangles indicate the range of experimental optical gaps reported in Table .

Figure 7

Ideal efficiency of nanostructured solar cells based on semiconductors of the stibnite family. The theoretical efficiency as a function of the band gap energy (black solid curve) is calculated using the prescription of Ref. 74 with a loss in potential of 0.3 eV and a fill factor of 73$\%$.