Sn $5s^2$ lone pairs and the electronic structure of tin sulphides: A photoreflectance, high-energy photoemission, and theoretical investigation

The effects of Sn $5s$ lone pairs in the different phases of Sn sulphides are investigated with photoreflectance, hard x-ray photoemission spectroscopy (HAXPES), and density functional theory. Due to the photon energy-dependence of the photoionization cross sections, at high photon energy, the Sn $5s$ orbital photoemission has increased intensity relative to that from other orbitals. This enables the Sn $5s$ state contribution at the top of the valence band in the different Sn-sulphides, SnS, ${\mathrm{Sn}}_2{\mathrm{S}}_3$, and ${\mathrm{SnS}}_2$, to be clearly identified. SnS and ${\mathrm{Sn}}_2{\mathrm{S}}_3$ contain Sn(II) cations and the corresponding Sn $5s$ lone pairs are at the valence band maximum (VBM), leading to $\sim 1.0$–1.3 eV band gaps and relatively high VBM on an absolute energy scale. In contrast, ${\mathrm{SnS}}_2$ only contains Sn(IV) cations, no filled lone pairs, and therefore has a $\sim 2.3$ eV room-temperature band gap and much lower VBM compared with SnS and ${\mathrm{Sn}}_2{\mathrm{S}}_3$. The direct band gaps of these materials at 20 K are found using photoreflectance to be 1.36, 1.08, and 2.47 eV for SnS, ${\mathrm{Sn}}_2{\mathrm{S}}_3$, and ${\mathrm{SnS}}_2$, respectively, which further highlights the effect of having the lone-pair states at the VBM. As well as elucidating the role of the Sn $5s$ lone pairs in determining the band gaps and band alignments of the family of Sn-sulphide compounds, this also highlights how HAXPES is an ideal method for probing the lone-pair contribution to the density of states of the emerging class of materials with $\mathrm{n}{s}^2$ configuration.

Figure 1

Ground-state structures of the tin sulphides used for this study. SnS (left), ${\mathrm{Sn}}_2{\mathrm{S}}_3$ (middle), and ${\mathrm{SnS}}_2$ (right). The tin atoms are green and the sulfur atoms are purple.

Figure 2

Photoionization cross sections for Sn $4d$, $5s$, and $5p$, demonstrating the advantage of using higher photon energies to probe the $\mathrm{n}{s}^2$ lone-pair configuration in Sn sulphides.

Figure 3

Raman spectra for all three Sn sulphide phases showing the phase purity of the materials.

Figure 4

Photoreflectance data for SnS (top), ${\mathrm{Sn}}_2{\mathrm{S}}_3$ (middle), and ${\mathrm{SnS}}_2$ (bottom). The pink dashed line represents the Aspnes fit applied to the data depicted by the black solid line. The transition energies determined from the fits are shown by the vertical dashed blue lines. The inset (bottom left) shows a Varshni fit (solid green line) to the temperature-dependent direct band gap values of ${\mathrm{SnS}}_2$ from PR to extract the direct band gap at 20 K.

Figure 5

HAXPES spectra of the Sn $3d_{5/2}$ along with the Voigt function fitting of the components for all three Sn sulphide phases.

Figure 6

HAXPES spectra of the S $2p$ region along with the Voigt function fitting of the components for all three Sn-sulphide phases.

Figure 7

(a) Calculated density of states for all three Sn sulphides, where the VBM is set at zero, (b) measured HAXPES valence band spectra from the different tin sulphide phases compared with the cross-section corrected and broadened calculated density of states, and (c) top of the valence band zoomed in to emphasize the region where the Sn $5s$ lone pair states contribute.