Low-energy electronic structure of perovskite and Ruddlesden-Popper semiconductors in the Ba-Zr-S system probed by bond-selective polarized x-ray absorption spectroscopy, infrared reflectivity, and Raman scattering

Chalcogenides in perovskite and the related layered Ruddlesden-Popper crystal structures (chalcogenide perovskites for brevity) are an exciting family of semiconductors but remain experimentally little studied. Chalcogenide perovskites share crystal structures and some physical properties with ionic compounds such as oxide and halide perovskites, but the metal-chalcogen bonds responsible for semiconducting behavior are substantially more covalent than in these more-studied perovskites. Here, we use complementary experimental and theoretical methods to study how the mixed ionic-covalent Zr-S bonds support the electronic structure and physical properties of perovskite ${\mathrm{BaZrS}}_3$ and Ruddlesden-Popper ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$. We apply theoretical methods to assign features of experimentally measured x-ray absorption spectroscopy (XAS) to particular orbital transitions, enabling a clear physical interpretation of angle-dependent, polarized XAS data measured on single-crystal samples, and an atomistic view of the covalent bonding network that facilitates charge transport. Polarized Raman measurements identify signatures of crystalline anisotropy in ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ and enable the first assignments of mode symmetry in this material. Infrared reflectivity reveals electronic transport properties that augur well for the use of chalcogenide perovskites in optoelectronic and energy-conversion technologies.

Figure 1

Crystal structures of (a) and (b) ${\mathrm{BaZrS}}_3$ and (c) and (d) ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ shown in orthographic projection; barium (blue), zirconium (red), and sulfur (yellow). Zr-S bonds are shown as connected red and yellow cylinders. In ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$, the Zr-S-Zr bond angles are closer to 180° than they are in ${\mathrm{BaZrS}}_3$, which explains differences in the low-energy electronic structure, including the bandgap. The labels in (c) indicate layers of distinct sulfur sites: interface (int.), equatorial (eq.), and bilayer (bi.).

Figure 2

Zr $L_{2,3}$-edge x-ray absorption near edge structure (XANES) data measured on powder samples of ${\mathrm{BaZrS}}_3$ and ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ and comparison with theory. (a) Experimental data for ${\mathrm{BaZrS}}_3$ and ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$. The $L_2$-edge spectra (b) as calculated by fdmnes and (c) measured experimentally. (d) Zr $4d$ density of states (DOS) resolved by orbitals in the octahedral crystal field basis. In fdmnes, the Fermi level ($E_{\mathrm{F}}$) is defined as the origin of the energy scale. In all panels, data for the two phases are colored as labeled in (a).

Figure 3

Sulfur $K$-edge x-ray absorption near edge structure (XANES) data measured on powder samples of ${\mathrm{BaZrS}}_3$ and ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ and comparison with theory. (a) S $K$ edge. The inset illustrates the role of metal-sulfur hybridization in generating the low-energy peak $\sim 2472\mathrm{eV}$. (b) Theoretical XANES spectrum for ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ (powder sample average) decomposed by atomic orbitals, allowing us to interpret the experimental data. The individual contributions are presented as a cumulative plot, so that the envelope approximates the XANES spectrum. Peak A derives from transitions to S $3p$-Zr $4d$ hybridized orbitals, as illustrated in the inset to panel (a). Peak B derives from transitions to higher-lying Ba $5d$ orbitals. The envelope of the projected orbital contributions lacks the steplike feature characteristic of the absorption spectra. This is because the projection operation requires partitioning, which results in some missing interstitial contributions that do appear in the total calculated spectrum, which we plot as a gray line.

Figure 4

Polarized S $K$-edge x-ray absorption near edge structure (XANES) measurements with varying $\theta$, the angle between x-ray electric field vector ($\underset{-}{E}$) and the sample surface, with crystallographic orientation as illustrated in the insets. Measurements on ${\mathrm{BaZrS}}_3$ and ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ are presented in (a) and (b), respectively; data with varying $\theta$ are offset vertically for clarity.

Figure 5

Polarization-dependent S $K$-edge x-ray absorption near edge structure (XANES) experimental data and theoretical interpretation for ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$. (a) Close-up of the $\theta$ dependence of the low-energy peak [full data range presented in Fig. 4]. (b)–(e) $\theta$ dependence of the theoretically-calculated XANES data, decomposed by discrete sulfur sites; here, we present (b) total, (c) equatorial, (d) bilayer, and (e) interface sulfur sites. In each of (b)–(e), the color intensity matches the $\theta$ series as in (a). Theoretically-calculated total XANES spectrum decomposed by sulfur sites for (f) $\theta ={30}^{\circ }$ and (g) $\theta ={85}^{\circ }$ with site contributions as shown in (b)–(e).

Figure 6

Normalized change in polarized infrared (IR) reflectivity after an optical pump for oriented ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ crystals. In both (a) and (b), the crystal structure is visualized as an orthographic projection along the probe beam incidence direction, and the probe beam polarization relative to the crystal axes is visualized on a compass rose. (a) Crystal oriented with the probe beam incident along $\left[1\overline{1}0\right]$. The crystal is rotated so that the IR electric field polarization ($\underset{-}{E}$) aligns with [110] (green), [111] (red), and [001] (blue). (b) Crystal oriented with the probe beam incident along [001]. The crystal is rotated so that $\underset{-}{E}$ aligns with [100] (green), [110] (red), and [010] (blue).

Figure 7

Polarization-resolved Raman spectra of a ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ crystal at 300 K; the crystal is prepared as in Fig. 5, with the [001] and [110] directions in the exposed surface. (a) Copolarized Raman spectra along [001] (red curve) and [110] (blue curve). The cross-polarized spectrum (black) was acquired with the laser polarized along [001] and the analyzer along [110]. The low-frequency region (dashed box) is magnified in (b)–(d) for the copolarized [001], [110], and cross-polarized spectra, respectively, with a polynomial background subtracted. The olive lines represent individual components of multi-Lorentzian fits to each spectrum, and the mode symmetries are indicated within each panel. (e)–(g) Atomic displacements for the dominant low wave number modes in panels (b)–(d), respectively. (h) and (i) Atomic displacements for the nearly degenerate $A_{1g}$ and $E_g$ modes at $346\mathrm{c}{\mathrm{m}}^{-1}$, respectively. Crystallographic orientation for atomic displacements is indicated in the figure. For these higher-frequency modes, we omit the Ba atoms for clarity, to emphasize the ${\mathrm{ZrS}}_6$ octahedra distortions, and because the Ba atoms hardly move.

Figure 8

Low-energy electronic structure of the conduction band and projected electron density distributions of the semiconductor ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ in the layered, Ruddlesden-Popper structure. Bands are colored according to their dominant orbital character, showing sulfur orbitals in (a) and zirconium orbitals in (b). The dotted lines illustrate the overall band structure, with colored markers representing the relative contribution of each orbital at a given point in the Brillouin zone. (a) Sulfur $3p$ orbital contributions from equatorial and bilayer sulfur sites. (b) Zr $4d$ orbital contributions. (c) and (d) Projected electron density distributions for an energy band at the conduction band minimum, highlighting the ${\pi }^{*}$ bonding between Zr $4d$ and S $3p$ orbitals, shown as slices of the (001) and (010) planes in (c) and (d), respectively.

Figure 9

Evaluating model for analysis of visible-pump, infrared (IR) probe experiments. (a) Instantaneous carrier injection as a function of position through the sample with experimental parameters, with the front face at $x=0$. (b) Comparing the Drude response (magnitude of complex dielectric constant) to $10{\epsilon }_0$; for all reasonable combinations of carrier concentration $n$ and mobility $\mu$, the Drude response is small compared with $10{\epsilon }_0$. (c) Comparing the Drude model scattering rate to the frequency of the IR probe. For all reasonable combinations of $\mu$ and carrier effective mass $m^{*}/m_0$ (where $m_0$ is the free electron mass), the IR probe is in the low-frequency limit. (d) IR probe beam attenuation for experimental parameters and a reasonable choice for $\mu =10\mathrm{c}{\mathrm{m}}^2/\mathrm{V}/\mathrm{s}$. The IR beam is only weakly attenuated. The layer of thickness $d$ responsible for IR attenuation is much smaller than the IR skin depth ($d\ll {\delta }_{\mathrm{IR}}$) and much smaller than the IR wavelength ($d\ll {\lambda }_{\mathrm{IR}}$).