Effect of surface stoichiometry on the band gap of the pyrite FeS${}_2$(100) surface

Systematic spin-polarized density functional calculations were performed for a series of pyrite FeS${}_2$(100) surfaces to clarify the effect of surface stoichiometry on stability, electronic structure, and band gap. While the bulk FeS${}_2$ is nonmagnetic, the topmost layer of the stoichiometric and S-deficient FeS${}_2$(100) surfaces are spin polarized, with magnetic moments of 2 ${\mu }_{\mathrm{B}}$ or 4 ${\mu }_{\mathrm{B}}$ per Fe. These surfaces also have sizeable band gaps, 0.56–0.72 eV; they hence can be useful for spintronic and photovoltaic applications. On the contrary, S-rich surfaces have small-gaps, <0.3 eV, which might be responsible to the low open-circuit voltage of pyrite solar cells.

Figure 1

Relaxed structures of the nine FeS${}_2$(100) surfaces explored in this study. The yellow (light gray) and blue (medium gray) spheres represent S and Fe atoms, respectively. The large orange (dark gray) spheres represent the additional sulfur atoms added to the stoichiometric surface, Surf(0).

Figure 2

Calculated surface energies of different FeS${}_2$(100) surfaces versus the sulfur chemical potential, ${\mu }_{\mathrm{S}}$. The inset shows results in growth and annealing environments employing H${}_2$S, S${}_8$, or S${}_2$ as the sulfur reservoir.

Figure 3

(a) The band structure of Surf(0). (b) The projected density of states (PDOS) for Fe atoms in different surface layers, labeled Fe${}_1$ to Fe${}_6$. In both (a) and (b), bold black and thin red (gray) lines denote states in the majority and minority spin channels, respectively; arrows highlight the two surface states (denoted SS1 and SS2) that determine the surface band gap (0.72 eV); zero energy gives the position of the Fermi level. Insets in (a) show the wave function features of SS1 and SS2; shaded region under the DOS curve of Fe${}_6$ in (b) shows DOS of Fe in the bulk pyrite. (c) Isosurfaces of spin density and Bader charges of Surf(0). Positive and negative values of Bader charges represent electron depletion and accumulation on individual atoms. The atomic layers of Fe are labeled Fe${}_1$ to Fe${}_6$. S${}_{1\mathrm{a}}$ and S${}_{1\mathrm{b}}$ denote the sulfur atom layers above and below the first Fe layer. In (c) and insets of (a), yellow (light gray) and blue spheres represent sulfur and iron atoms, respectively.

Figure 4

Band structure of (a) Surf(−1) and (b) Surf(+1), with bold black and thin red (gray) lines for states in the majority and minority spin channels, respectively. (c) The band gap as a function of the surface composition parameter $n$. The solid triangle at $n$ $=$ 1.0 represents the band gap for Surf(+1) when sulfur dimerization is disallowed in the calculations. The inset in (c) shows the top view of the two atomic structures of Surf(+1) with orange (dark gray) and gray spheres indicating the positions of surface sulfur atoms with and without dimerization, respectively. The calculated (experimental) bulk band gap is 1.02 eV (0.95 eV). (d) The projected density of states (PDOS) for surface Fe atoms on Surf(−0.125). The positive and negative values indicate states in the majority and minority spin channels, respectively. The insets in (d) are the top and side views of charge density difference, ${\rho }_{\mathrm{Surf}\left(0\right)}-{\rho }_{\mathrm{Surf}(-0.125)}-{\rho }_{\mathrm{S}}$, with blue (dark gray) and purple (light gray) isosurfaces denoting electron accumulation and depletion, respectively. The position of the surface sulfur vacancy on Surf(−0.125) is indicated by the red (gray) arrow. Dashed A and B ellipses mark defected and defect-free regions on Surf(−0.125), respectively.