First-principles studies of the electronic properties of native and substitutional anionic defects in bulk iron pyrite

Systematic spin-polarized density functional theory calculations were performed to investigate the formation energies of native and substitutional anionic point defects in iron pyrite (FeS${}_2$) and their impact on bulk electronic structure. A detailed analysis indicates that neutral sulfur and iron vacancies do not act as efficient donors or acceptors. We find that substitutional oxygen does not induce gap states in pyrite and can actually passivate gap states created by sulfur vacancies. Most Group V and VII impurities create mid-gap states and produce spin polarization. In particular, Cl and Br are shallow donors that introduce delocalized spin-polarized electrons for potential use in photovoltaic and spintronics applications.

Figure 1

(a) The bulk unit cell of pyrite FeS${}_2$. Violet (dark) and yellow (light) gray spheres represent Fe and S atoms, respectively. The parameters $a$ and $u$ denote the lattice constant and the distance between the S atom and the walls of the cubic box as indicated by the red arrows. (b) Band structure and (c) density of states (in states/eV·cell) of perfect pyrite. The valence band maximum (VBM) has been set as reference energy. The red/dark gray curves in (b) indicate the topmost valence band and lowest conduction band, and the horizontal green dashed lines indicate the VBM and conduction band minimum (CBM).

Figure 2

Formation energies of native defects, including $V_{\mathrm{S}}$, $V_{\mathrm{S}–\mathrm{S}}$, $V_{\mathrm{Fe}}$, and $V_{\mathrm{Fe}–\mathrm{S}}$ as a function of sulfur chemical potential ($\Delta \mu$${}_{\mathrm{S}}$ $=$ ${\mu }_{\mathrm{S}}$ $-$ ${\mu }_{\mathrm{S}}^0$, where ${\mu }_{\mathrm{S}}^0$ is the sulfur chemical potential of its elemental phase, S${}_8$). The left and right boundaries of sulfur chemical potential correspond to the so-called Fe-rich (Fe bulk as the reservoir) and S-rich (S${}_8$ as the reservoir) conditions, respectively.

Figure 3

Band structures of a 3$\times$3$\times$3 pyrite supercell with (a) $V_{\mathrm{S}}$, (b) $V_{\mathrm{Fe}}$, or (c) $V_{\mathrm{Fe}–\mathrm{S}}$. The black solid and red dashed lines in (b) and (c) represent majority- and minority-spin bands, respectively. The VBM is set as the reference energy for each case. The horizontal green dotted lines indicate the corresponding Fermi level of each case. The insets provide the isosurfaces of single state charge densities (at 0.03 e/$\AA$${}^3$) of the defect states, indicated by arrows. Violet (dark) and yellow (light) spheres represent Fe and S atoms, respectively. The cross signs in dotted circles denote the positions of the missing S or Fe atoms.

Figure 4

Kohn-Sham defect levels for a 3$\times$3$\times$3 supercell containing one vacancy or impurity with respect to the valence and conduction bands (shaded regions) of the perfect bulk pyrite. Black and red (dark gray) lines denote defect levels in the majority and minority spin channels, respectively. Thick lines for $V_{\mathrm{Fe}}$ denote double degeneracy of defect states, and the rectangle for Br${}_{\mathrm{S}}$ indicates a Br-induced resonant band. Dots represent the electron occupancy of the neutral defects.

Figure 5

Results for oxygen-doped pyrite (FeS${}_{1.97}$O${}_{0.03}$). (a) Total and projected DOS. The notation in parentheses indicates the bonds to which the atoms belong. The VBM is set as the energy reference. (b) Band structure. The reference energy is the same as in (a). The red (dark gray) lines denote the topmost valence band and lowest conduction band. The inset is a magnified view of valence bands near the VBM around the $\Gamma$-point and the $y$-axis unit is eV. (c) Charge density difference [$\Delta$ρ $=$ ρ(O${}_{\mathrm{S}}$) $-$ ρ($V_{\mathrm{S}–\mathrm{S}}$) $-$ ρ(O) $-$ ρ(S)] viewed in the (110) plane. Note that the atomic positions in reference systems were fixed as those in O-doped pyrite. The isosurfaces are at the values of $\pm$0.03 $e$/$\AA$${}^3$, with blue (dark) and red (light) regions for charge gain and loss, respectively. Violet (dark) and yellow (light) spheres represent Fe and S atoms, respectively.

Figure 6

Total DOS of a 2$\times$2$\times$2 pyrite supercell with a single (a) N${}_{\mathrm{S}}$, (b) P${}_{\mathrm{S}}$, and (c) As${}_{\mathrm{S}}$ dopant, corresponding to a defect concentration of 7.8 $\times$ 10${}^{20}$ cm${}^{-3}$. The vertical dashed line indicates the Femi energy. The positive and negative DOS indicate majority and minority spin channels, respectively. The inset in (a) shows the isosurfaces (at 0.01 $e$/$\AA$${}^3$) of the single-state charge density of the defect state induced by N${}_{\mathrm{S}}$ in the minority spin channel at 0.7 eV above the VBM. Similar features were found for gap states of P${}_{\mathrm{S}}$ and As${}_{\mathrm{S}}$.

Figure 7

Total and projected DOS of a 2$\times$2$\times$2 pyrite supercell with a single $F_{\mathrm{S}}$ (a)–(c) or Cl${}_{\mathrm{S}}$ (d)–(f) defect. The respective VBM is set as the energy reference for both cases. The vertical dashed lines indicate the Femi energy. The positive and negative values of the DOS denote majority and minority spin channels, respectively.

Figure 8

(a) Band structures of pyrite with a single Cl${}_{\mathrm{S}}$ impurity in a 2$\times$2$\times$2 supercell (left) and 3$\times$3$\times$3 supercell (right). The solid black and dotted red (dark gray) lines denote the majority- and minority-spin states, respectively. The horizontal dashed lines give the Fermi energy for each case. The inset shows the spin density of FeS${}_{1.97}$Cl${}_{0.03}$, with the violet (dark) and yellow (light) spheres representing Fe, S, and Cl atoms, respectively. (b) Left and middle panels: sketches of the hybridization between the conduction band of pyrite (solid black line) and the atomic level of Cl (solid red/dark gray line) in 2$\times$2$\times$2 and 3$\times$3$\times$3 supercells, respectively. Right panel: the separation between Cl${}_{\mathrm{S}}$ impurity level and CBM in the majority-spin channel as a function of Cl concentration.