Discovery of highly polarizable semiconductors $\mathrm{BaZr}{\mathrm{S}}_3$ and ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$

There are few known semiconductors exhibiting both strong optical response and large dielectric polarizability. Inorganic materials with large dielectric polarizability tend to be wide-band gap complex oxides. Semiconductors with a strong photoresponse to visible and infrared light tend to be weakly polarizable. Interesting exceptions to these trends are halide perovskites and phase-change chalcogenides. Here we introduce complex chalcogenides in the Ba-Zr-S system in perovskite and Ruddlesden-Popper structures as a family of highly polarizable semiconductors. We report the results of impedance spectroscopy on single crystals that establish $\mathrm{BaZr}{\mathrm{S}}_3$ and ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ as semiconductors with a low-frequency relative dielectric constant ${\varepsilon }_0$ in the range 50–100 and band gap in the range 1.3–1.8 eV. Our electronic structure calculations indicate that the enhanced dielectric response in perovskite $\mathrm{BaZr}{\mathrm{S}}_3$ versus Ruddlesden-Popper ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ is primarily due to enhanced IR mode-effective charges and variations in phonon frequencies along 〈001〉; differences in the Born effective charges and the lattice stiffness are of secondary importance. This combination of covalent bonding in crystal structures more common to complex oxides, but comprising sulfur, results in a sizable Fröhlich coupling constant, which suggests that charge carriers are large polarons.

Figure 1

Crystal structures of (a) $\mathrm{BaZr}{\mathrm{S}}_3$ and (b) ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$. The blue, gray, and yellow spheres represent Ba, Zr, and S, respectively. $\mathrm{Zr}{\mathrm{S}}_6$ octahedra are shaded in green. The blue arrows indicate the antipolar pattern of $\mathrm{B}{\mathrm{a}}^{2+}$ cation displacements in $\mathrm{BaZr}{\mathrm{S}}_3$.

Figure 2

Illustration of techniques used to enable accurate impedance measurements on microscopic crystals. (a) and (b) μCT cross-section images used to determine the sample dimensions. Images show crystals and Ag epoxy contacts. Pt wires used for electrical leads appear as small bright spots. (a) A $\mathrm{BaZr}{\mathrm{S}}_3$ crystal with the thickness determined to be 0.11 mm. (b) A $\mathrm{BaZr}{\mathrm{S}}_3$ crystal for which μCT revealed a macroscopic void beneath the crystal surface; this sample was subsequently not used for impedance measurements. (c) Drawing and photograph of the custom test fixture used to enable measurements of subpicofarad sample capacitance. The surface mounts are ultraminiature coaxial connectors. The photograph shows a sample mounted in epoxy and wired to the fixture (upper left and lower right contact pads).

Figure 3

Impedance measurement results for one representative sample each of (a)–(c) $\mathrm{BaZr}{\mathrm{S}}_3$ and (d)–(f) ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$. (a) and (d) ${\varepsilon }_{r,0}$ measured for frequency between 1 kHz and 1 MHz and temperature between 2 and 300 K. (b) and (e) Dependence of ${\varepsilon }_{r,0}$ on an applied electric field. (c) and (f) Nyquist plot of complex impedance ($Z^{\prime }-i{Z}^{\prime \prime }$) measured between 0.1 Hz and 1 MHz ambient conditions; points are the data and the line is the fit.

Figure 4

Phonon mode contributions to the ionic part of the low-frequency dielectric tensor for $\mathrm{BaZr}{\mathrm{S}}_3$ (pink) and ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ (black). The abscissa indicates the phonon frequencies; modes that contribute less than 5% of the total dielectric response are omitted for clarity. The insets show atomic motions for the dominant mode in each direction for each material: for ${\varepsilon }_{11}, 63.8\mathrm{c}{\mathrm{m}}^{-1}$ for PS and $102.2\mathrm{c}{\mathrm{m}}^{-1}$ for RP; for ${\varepsilon }_{22}, 74.8\mathrm{c}{\mathrm{m}}^{-1}$ for PS and $102.2\mathrm{c}{\mathrm{m}}^{-1}$ for RP; for ${\varepsilon }_{33}, 45.6\mathrm{c}{\mathrm{m}}^{-1}$ for PS and $161.3\mathrm{c}{\mathrm{m}}^{-1}$ for RP. Atomic displacements are indicated with arrows; PS and RP denote perovskite and Ruddlesden-Popper, respectively.

Figure 5

Ashby plot of the low-frequency relative dielectric constant ${\varepsilon }_{r,0}$ vs band gap, showing our results for $\mathrm{BaZr}{\mathrm{S}}_3$ and ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ together with results for a number of well-known semiconductor materials, grouped by crystal structure type as indicated by the symbols. The results for $\mathrm{BaZr}{\mathrm{S}}_3$ and ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$ are presented as orange box-and-whisker symbols and black points, which include measurements on multiple samples and using multiple techniques: seven unique samples and eleven independent measurements for $\mathrm{BaZr}{\mathrm{S}}_3$ and five unique samples and nine independent measurements for ${\mathrm{Ba}}_3{\mathrm{Zr}}_2{\mathrm{S}}_7$. Data for all but the lead salts are as presented in Ref. [1]; data for lead salts are as reported in Ref. [17].