Band gap evolution in Ruddlesden-Popper phases

TL;DR

This study explores how the band gap in Ruddlesden-Popper phases varies with structure and composition, revealing different behaviors in chalcogenides compared to oxides and halides, influenced by octahedral rotations and quantum confinement.

Contribution

It provides a detailed analysis of band gap evolution in RP phases, highlighting the roles of octahedral rotations and quantum confinement, aiding rational design of layered perovskites.

Findings

Chalcogenides show different band gap evolution compared to oxides and halides.

Octahedral rotations and quantum confinement influence band gap changes.

Insights enable targeted design of layered perovskite materials.

Abstract

We investigate the variation of the band gap across the Ruddlesden-Popper (RP) series (An+1BnX3n+1) in model chalcogenide, oxide, and halide materials to understand the factors influencing band gap evolution. In contrast to the oxides and halides, we find the band gap of the chalcogenides evolve differently with the thickness of the perovskite blocks in these natural superlattices. We show that octahedral rotations (i.e. deviation of the B-X-B bond angles from 180) and quantum confinement effects compete to decide the band gap evolution of RP phases. The insights gained here will allow us to rationally design layered perovskite phases for electronics and optoelectronics.

Full text

Perovskites host a variety of emergent phenomena such as colossal magnetoresistanceVisser et al. (1997); Raveau et al. (1998); Tokura (2006); Murakami et al. (2009), ferroelectricityCohen (1992); Fong et al. (2004); Fan et al. (2015), and superconductivityHe et al. (2001); Vaitheeswaran et al. (2007), and offer great structural and chemical flexibility to tune physical properties. The perovskite structure, with a chemical formula of ABX3, consists of an octahedrally coordinated cation (B-site) connected by the corners to form a three dimensional network. Further, perovskites can form two dimensional layered superlattices called as Ruddlesden-Popper (RP) phases, where a perovskite block of varying unit cell thickness $n$ is sandwiched between rock salt layers (AX) to form a natural superlattice. These RP phases possess a general formula of An+1BnX3n+1 with alternating perovskite blocks displaced by half a unit cell in the in-plane direction [see Fig. 1(a)]. The perovskite is the end member of the RP series with $n$=$\infty$.

Perovskite oxides containing early transition metals such as Ti, Zr, and main group elements such as Sn are wide band gap semiconductors, but the corresponding chalcogenides possess band gap in the visible-infrared energies. Our ability to control and modify the band gap of such semiconductors would vastly expand their range of applications, especially as heterostructures. Alloying is a common approach to tune the band gap of such semiconductors, yet the accompanying disorder has the undesirable effect of lowering carrier mobilityOgale and Madhukar (1984); Rode and Fedders (1983). RP phases offer an alternative approach to create long range ordered structures to tune the physical properties such as band gapBattle et al. (1998); Stoumpos et al. (2016); Tsai et al. (2016); Perera et al. (2016); Yu et al. (2017); Zhang et al. (2017); Chen et al. (2018); Li and Singh (2018). While the changes in the band gap through alloying can be understood in terms of orbital composition (by chemical substitutions) of the valence and/or conduction-band edge states, it is yet unclear how the quantum confinement through reduced dimensionality, and details of the crystal structure of the RP phases modify the band gap with respect to the ABX3 parent material. A fundamental understanding of the factors at play is crucial to design and tailor emerging perovskite based electronic and photonic materials.

To motivate our study, we summarize the band gap evolution of three representative materials: Oxide (Srn+1TinO3n+1), halide (BA2MAn-1PbnI3n+1), where MA is CH3NH3 and BA is CH${}_{3}($CH2)3NH3, and chalcogenide (Ban+1ZrnS3n+1) RP phases in Fig 1(b) and (c)Linz Jr. and Herrington (1958); Liu and Sohlberg (2014); Cherian et al. (2016); Lee et al. (2013); Stoumpos et al. (2016); Tsai et al. (2016). We use a combination of electronic structure calculations and photoluminescence spectroscopy measurements on single crystals of Ban+1ZrnS3n+1 RP series ($n$=$\infty$,1,2) to determine their band gap and compare them with trends in oxides and halides reported in the literature. We find that the band gap of Ban+1ZrnS3n+1 are much lower than that of the parent perovskite, BaZrS3, while the gaps of Srn+1TinO3n+1 and BA2MAn-1PbnI3n+1 are higher than that of SrTiO3 and MAPbI3. Our results clearly indicate that the factors controlling the band evolution in chalcogenides are different from oxides and halides. To understand the origin of these contrasting trends, we carried out in depth first principles calculations on the chalcogenide RP phases.

The first-principles calculations were performed using density functional theoryHohenberg and Kohn (1964); Kohn and Sham (1965) as implemented in the VASP codeKresse and Hafner (1993a, b). The interactions between the valence electrons and the ionic cores are described using projector augmented wave potentialsBlöchl (1994); Kresse and Joubert (1999). For structure optimization, we used the generalized gradient approximation PBEsolPerdew et al. (2008, 2009) for exchange and correlation, while band structures were computed using the HSE06 hybrid functionalHeyd et al. (2003, 2006). All the calculations were performed with a kinetic energy cutoff of 500 eV for the plane wave basis set. We used $\Gamma$-centered 6$\times$6$\times$6 grid for the 5-atom cubic ABX3 structures, and similar density $k$-meshes for the 20-atom orthorhombic structure, and the tetragonal RP A2BX4 and A3B2X7 structures. The calculated lattice parameters are listed in the Supplemental Material.

Polycrystalline and single crystal samples of the three Ba-Zr-S RP series compounds were synthesized by solid-state reaction and salt flux growth, respectively, using methods similar to those reported earlier Niu et al. (2017, 2018). We performed structural characterization using x-ray diffraction (XRD) and optical characterization using photoluminescence (PL) spectroscopy. We performed single crystal diffraction studies at 100 K. Powder XRD studies were performed on the ground crystallites with Cu Kα radiation in Bragg-Brentano geometry at room temperature. There will be a separate report on the details of crystal growth and X-ray diffraction analysis of the single crystals. Obtained structural parameters are included in the Supplemental Material. PL measurements of the three materials were performed on the single crystals at room temperature with a microscope in back-reflecting geometry.. Emission spectra in 1.5-2.2 eV range were collected in a setup with 532 nm excitation laser while the lower energy range (1.2-1.5 eV) were collected in another setup with 785 nm excitation laser.

As noted earlier, the RP phases of the Sr-Ti-O and (BA,MA)-Pb-I systems follow the trend of increasing band gap with decreasing number of ABX3 perovskite layers that are separated by an AX layer. In contrast, we find that for the Ba-Zr-S system, the band gap of BaZrS3 is significantly larger than the gaps of Ba3Zr2S7 and Ba2ZrS4, as shown in Fig. 1(b)-(c). Our calculated band gaps of BaZrS3, Ba3Zr2S7 and Ba2ZrS4 are 1.79 eV ($n$=$\infty$), 1.21 eV ($n$=2) and 1.33 eV ($n$=1), which are in agreement with past calculationsLi and Singh (2018); Bennett et al. (2009). To verify this predicted anomalous band gap evolution, we performed PL spectroscopy measurements on single crystals of BaZrS3, Ba3Zr2S7 and Ba2ZrS4. First, we structurally characterized these materials using XRD. The XRD patterns for the ground powders of the single crystals are shown in Fig. 2(a). The distinct low angle reflections in XRD are clear fingerprints for the RP phases and agree well with the larger unit cells with alternating perovskite and rock-salt layers. The PL spectra and the scanning electron microscopy (SEM) images are shown in Fig.2(b). BaZrS3 ($n$=$\infty$) showed a relatively broad PL peak at around 1.82 eV while the two RP phases showed narrower PL peaks at 1.28 eV ($n$=2) and 1.33 eV ($n$=1) respectively. Thus, our experimental studies confirm the theoretically predicted anomalous band gap evolution in chalcogenide RP phases of Ba-Zr-S.

Now, to address the origin of the anomalous band gap evolution in chalcogenide RP phases compared to the oxides and halides, we need to understand the factors influencing the position and orbital character of the conduction and valence bands in perovskite and RP phases. The valence-band maximum (VBM) and conduction-band minimum (CBM) of the early transition metal (Ti, Zr, Hf) perovskites and related phases have significant contributions from the orbitals of the species that constitute the octahedra (Zr and S in the case of BaZrS3), and almost none from the orbitals of the A-site species. Specifically, the lowest energy conduction bands are largely composed of transition metal d orbitals, while highest energy valence bands are composed of chalcogen p orbitals. Therefore, one could expect that the band gap would be significantly influenced by the arrangement of the network of BX6 corner-sharing octahedra, i.e. octahedral tilting, rotation, and distortion. We then discuss how these structural modifications to the highly symmetric corner shared octahedral connectivity affect the band gap of the Ban+1ZrnS3n+1 RP series for decreasing thickness of the perovskite blocks, i.e. from $n$=$\infty$ to $n$=2 and $n$=1.

First, we compare the calculated orbital-projected density of states of BaZrS3 in the orthorhombic $Pnma$ structure (stable at room temperature) with the hypothetical cubic structure where we removed the octahedral tilt and rotation yet keeping the same equilibrium volume per formula unit. Orthorhombic BaZrS3 displays an in-plane Zr-S-Zr bond angle of 156.6∘ and out-of-plane Zr-S-Zr bond angle of 160.0∘, with in-plane Zr-S bond lengths of 2.527 Å  and 2.538 Å, and out-of-plane Zr-S bond lengths of 2.521 Å, thus featuring a small distortion of the octahedra. By removing the octahedral tilting and rotation the band gap is significantly reduced, by as much as 0.65 eV, as shown in Fig. 3(a). The octahedral distortion has a negligible contribution to the band gap, changing it by only 0.06 eV. From the orthorhombic to the cubic structure, we find that most of the change in the gap is due to a broadening of the valence band, pushing up the VBM by 0.63 eV, while the CBM is pushed down by only 0.02 eV, as shown in Fig. 3.

Ba3Zr2S7 ($n$=2) crystallizes in two structures: the low temperature (LT) Ba3Zr2S7 phase Hung et al. (1997), featuring octahedral rotations, with equilibrium Zr-S-Zr in-plane bond angle of 167.0∘ and out-of-plane angle of 161.3∘, and the room-temperature (RT) phase featuring in-plane and out-of-plane angles of 180∘ yet a small Ba/S displacement Chen et al. (1994). The calculated band gap for the LT phase is 1.56 eV, and for the RT phase is 1.21 eV. This difference is attributed largely to the lack of octahedral rotations in the RT phase. For example, the removal of all the octahedral rotations and Ba/S displacements(0.45Å) in the LT phase to make the octahedral arrangements ideal reduces the band gap to 1.25 eV, very close to the result for the RT phase.

On the other hand, Ba2ZrS4 ($n$=1) compound crystallizes in one stable structure with all the Zr-S-Zr angles at 180*∘, i.e. there are no octahedral rotations, only octahedral distortion (four in-plane Zr-S bonds of 2.56 Å  and two out-of-plane bonds of 2.47 Å) and a Ba/S (antiferroelectric) displacement(0.35Å). This high symmetry phase is stable up to the room temperature. The calculated band gap of the relaxed Ba2ZrS4* is 1.33 eV, compared to 1.19 for a hypothetical structure where the Ba/S displacement is removed, and 1.30 eV for another hypothetical structure, where the Ba/S displacement is removed and the octahedron is made perfect, i.e., all Zr-S bond lengths are equal and Zr-S-Zr angles are 180*∘. The relatively small differences in the band gap for these three Ba2ZrS4* structures indicate that the Ba/S displacement or octahedral distortion have negligible effects on the band gap compared to the octahedral rotations, similar to BaZrS3 ($n$=$\infty$) and Ba3Zr2S7 ($n=2$).

We quantify the effects of octahedral tilting and rotations and quantum confinement on the band gap for the Ba-Zr-S system in Fig. 4(a). The lower dashed line represents only the effects of quantum confinement. From ideal cubic BaZrS3 ($n=\infty$, space group $Pm\bar{3}m$ to Ba3Zr2S7 ($n=2$, space group $I4/mmm$) the gap increases by 0.103 eV, and from Ba3Zr2S7 to Ba2ZrS4 ($n=1$, space group $I4/mmm$), the gap increases by only 0.049 eV. These changes represent purely the effects of quantum confinement, i.e. decreasing the thickness of the perovskite blocks from $n=\infty$ to $n=2$ to $n=1$ layer. This variation in the gap is much smaller than the changes brought about by the octahedral tilting and rotations. The upper dashed line in Fig. 4, connecting relaxed BaZrS3 (space group $Pnma$) to LT Ba3Zr2S7 (space group $P4_{2}/mnm$), and Ba2ZrS4 (space group $I4/mmm$) contains the effects of octahedral tilting and rotations and the quantum confinement. Since the later is relatively small, as revealed by the lower line, we conclude that the effect of octahedral tilting and rotation on the band gap evolution of the Ba-Zr-S system is dominant. The effects of Ba/S antiferroelectric displacements on the gap of Ba3Zr2S7 and Ba2ZrS4 are also small, as seen in the differences between the RT Ba3Zr2S7 and ideal Ba3Zr2S7 as well as between the two Ba2ZrS4 structures, where the upper value corresponds to the experimentally observed phase.

We found that other chalcogenide systems show band gap evolution similar to Ba-Zr-S. As shown in Fig. 4(b), the calculated band gap of the Ba-Hf-S, Sr-Zr-S, and Sr-Hf-S RP series also decrease with decreasing $n$. Our calculations confirm the dominant role of octahedral tilting and rotations in determining band gap, irrespective of the differences in the chemistry. We list all the structural parameters of these materials in Table I and II in the Supplemental Materials. Consistent with our observations for Ba-Zr-S system, the perovskite ABX3 ($n=\infty$) showed greater deviation of the Metal-S-Metal angles from 180*∘* compared to the A3B2X7 ($n=2$) and A2BX4 ($n=1$) in all the cases. The deviation quantitatively reflects the degree of octahedral tilting, and proportionately greater band gap values.

In conclusion, our study demonstrates the competition between quantum confinement and octahedral rotations to determine band gap evolution in the layered phases with octahedral coordination such as Ruddlesden Popper (RP) Perovskite phases. We demonstrate that the influence of octahedral rotations is dominant in chalcogenides, unlike oxides and halides, where quantum confinement dictates band gap evolution. We expect that this understanding will be useful to design next generation semiconductors based on such layered phases for electronic and photonic applications.

W.L. and A.J. acknowledge support from the National Science Foundation Faculty Early Career Development Program DMR-1652994. S.N. and J.R. acknowledge the Air Force Office of Scientific Research under award number FA9550-16-1-0335 and Army Research Office under award number W911NF-19-1-0137. S.N. acknowledges Link Foundation Energy Fellowship. This research was also supported by the the Extreme Science and Engineering Discovery Environment (XSEDE) facility, National Science Foundation grant number ACI-1053575, and the Information Technologies (IT) resources at the University of Delaware, specifically the high performance computing resources.