The Role of Connectivity on Electronic Properties of Lead Iodide Perovskite-Derived Compounds.

We use a layered solution crystal growth method to synthesize high-quality single crystals of two different benzylammonium lead iodide perovskite-like organic/inorganic hybrids. The well-known (C6H5CH2NH3)2PbI4 phase is obtained in the form of bright orange platelets, with a structure comprised of single ⟨100⟩-terminated sheets of corner-sharing PbI6 octahedra separated by bilayers of the organic cations. The presence of water during synthesis leads to formation of a novel minority phase that crystallizes in the form of nearly transparent, light yellow bar-shaped crystals. This phase adopts the monoclinic space group P21/n and incorporates water molecules, with structural formula (C6H5CH2NH3)4Pb5I14·2H2O. The crystal structure consists of ribbons of edge-sharing PbI6 octahedra separated by the organic cations. Density functional theory calculations including spin-orbit coupling show that these edge-sharing PbI6 octahedra cause the band gap to increase with respect to corner-sharing PbI6 octahedra in (C6H5CH2NH3)2PbI4. To gain systematic insight, we model the effect of the connectivity of PbI6 octahedra on the band gap in idealized lead iodide perovskite-derived compounds. We find that increasing the connectivity from corner-, via edge-, to face-sharing causes a significant increase in the band gap. This provides a new mechanism to tailor the optical properties in organic/inorganic hybrid compounds.

Introduction

Organic/inorganic hybrid perovskites have attracted growing attention for optoelectronic applications such as light-emitting diodes,[1,2] lasers,[3,4] photodetectors,[5] and efficient planar heterojunction solar cell devices.[6−10] Besides having unique optical[11,12] and excitonic[13,14] properties, they are easy to synthesize. While very high power-conversion efficiencies of up to 22.1% have been reported for lead iodide-based solar cells,[15] various challenges remain. One of these challenges is to improve resilience to ambient conditions, including moisture: it affects the morphology of the organic/inorganic hybrid perovskite layer, and low-quality perovskite films can have pinholes that create shunting pathways that drastically limit the device performance.

Recently, Conings et al. studied the influence of water contamination in organometal halide perovskite precursors on the resulting perovskite film and solar cells.[16] Their results suggest that water has no considerable influence on the photovoltaic performance of devices. Moreover, other studies have shown that moisture during film growth is of importance to enhance the formation and quality of the hybrid perovskite films, as well as their photoluminescence (PL) performance.[17,18] Furthermore, Eperon et al. used powder X-ray diffraction (XRD) to show that the expected CH3NH3PbI3 phase forms even at high levels of humidity.[18] However, we show here that water can also have undesired effects. The presence of water during the synthesis of the two-dimensional (2D) compound (C6H5CH2NH3)2PbI4 yields small quantities of a second benzylammonium lead iodide phase with a larger band gap. This new compound has the structural formula (C6H5CH2NH3)4Pb5I14·2H2O, with water incorporated into the crystal structure. The inorganic network consists of ribbons of edge-sharing PbI6 octahedra. Previously, we showed that face-sharing PbI6 octahedra exhibit an electronic confinement effect and force the band gap to increase.[19] Here, using density functional theory calculations with spin–orbit coupling (DFT+SOC), we study the electronic structure of (C6H5CH2NH3)4Pb5I14·2H2O and show how the charge distribution is affected when edge-sharing PbI6 octahedra are introduced. Thus, we provide a design rule for tuning the optical properties of organic/inorganic hybrid materials based on the connectivity of the metal-halide octahedra. Notably, the class of organic/inorganic hybrid perovskite(-derived) materials have several structural features that influence the optical properties. These structural features include the choice of metal and halide (ionic radii) and rotations/deformations of the inorganic backbone. These factors not only influence the band gap directly but also each other and hence the band gap indirectly. Several studies have investigated the effect of structural deformations on the optical properties in great detail.[19−24] In our study, we focus on the effect that connectivity of metal-halide octahedra has on the band gap in lead iodide systems. We demonstrate that the size of the band gap strongly depends on not only the dimensionality of the inorganic network but also on the number of iodides shared between two adjacent lead ions, resulting in corner-, edge-, or face-sharing PbI6 octahedra. We conclude that, counterintuitively, the band gap increases with the number of shared iodides.

Experimental Section

Crystal Growth

Single crystals of (C6H5CH2NH3)2PbI4 and (C6H5CH2NH3)4Pb5I14·2H2O were grown at room temperature using the same layered solution technique as used in our previous work.[19] PbI2 (74 mg, 0.16 mmol; Sigma-Aldrich; 99%) was dissolved in 3.0 mL of concentrated (57 wt %) aqueous hydriodic acid (Sigma-Aldrich; 99,95%). Absolute methanol (3.0 mL; Lab-Scan; anhydrous, 99.8%) was carefully placed on top of the PbI2/HI mixture, without mixing the solutions. A sharp interface was formed between the two layers due to the large difference in densities. Benzylamine (Sigma-Aldrich; 99%) was added in great excess by gently adding 15 droplets, using a glass pipet, on top of the methanol layer. The reaction mixtures were kept in a fume hood under ambient conditions. After 2 d, a small number of crystals started to form. The crystals were collected after two weeks by washing three times with diethyl ether (Avantor). A mixture of three types of crystals was obtained: bright orange platelets ((C6H5CH2NH3)2PbI4), colorless needles (an unidentified phase), and nearly transparent, light yellow bar-shaped crystals ((C6H5CH2NH3)4Pb5I14·2H2O). Figure S1 shows a photograph of all three types of crystals.

X-ray Diffraction

Single-crystal X-ray diffraction (XRD) measurements were performed using a Bruker D8 Venture diffractometer equipped with a Triumph monochromator and a Photon100 area detector, operating with Mo Kα radiation. A 0.3 mm nylon loop and cryo-oil were used to mount the crystals. The crystals were cooled with a nitrogen flow from an Oxford Cryosystems Cryostream Plus. Data processing was done using the Bruker Apex III software, the structure was solved using direct methods, and the SHELX97 software[25] was used for structure refinement.

Computational Methods

The calculations were performed within DFT[26] in the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA)[27] including relativistic SOC effects with the Vienna Ab initio Simulation Package (VASP)[28,29] using the projector augmented wave (PAW) method.[30,31] PAW data sets supplied with were used with a frozen 1s, 1s, [Kr]4d10, and [Xe] core for C, N, I, and Pb, respectively. The calculations were performed using the experimental lattice parameters and atomic positions, except for the hydrogen atoms, which were optimized. Furthermore, the water molecules were left out. Structural models were rendered using VESTA.[32]

Results and Discussion

High-quality single crystals of benzylammonium lead iodide organic/inorganic hybrids were obtained using the layered solution crystal growth method as described in the Experimental Section. We performed this synthesis under ambient conditions and used methanol and hydriodic acid (57 wt % in H2O) as solvents. As a result, water was present during crystal growth. We identified three different phases after synthesis, which could easily be distinguished as bright orange platelets, very thin colorless needles, and slightly thicker pale yellow bar-shaped crystals (see Figure S1). The first two phases were abundantly present, whereas the pale yellow bar-shaped crystals were present only in small quantities. We identified the orange platelets as the known (C6H5CH2NH3)2PbI4 compound (space group Pbca), consisting of ⟨100⟩-terminated sheets of corner-sharing PbI6 octahedra separated by bilayers of the organic cation.[19,33] The structure of the thin colorless needles could not be solved, because the crystal quality was very poor. However, the pale yellow bar-shaped crystals were of good crystal quality and represent a novel benzylammonium lead iodide phase, the focus of this work.

Here, we investigate the crystal and electronic structure of the light yellow bar-shaped crystals and compare them to (C6H5CH2NH3)2PbI4. Our single-crystal XRD measurements reveal that these crystals exhibit a completely different structure to the orange platelets and have the chemical formula (C6H5CH2NH3)4Pb5I14·2H2O. The crystallographic data are given in Table . Figure shows the crystal structures of (C6H5CH2NH3)2PbI4 and (C6H5CH2NH3)4Pb5I14·2H2O. The asymmetric unit of (C6H5CH2NH3)4Pb5I14·2H2O, showing thermal ellipsoids, is given in Figure S2.

Table 1

Crystallographic Data of (C6H5CH2NH3)4Pb5I14·2H2O

(C6H5CH2NH3)4Pb5I14·2H2O
temperature (K)	100(2)
formula	C28H44N4O2Pb5I14
formula weight (g/mol)	3281.34
crystal size (mm3)	0.26 × 0.12 × 0.08
crystal color	very light yellow
crystal system	monoclinic
space group	P21/n (No. 14)
symmetry	centrosymmetric
Z	2
D (calculated) (g/cm3)	3.572
F(000)	2432
a (Å)	17.4978(9)
b (Å)	7.9050(4)
c (Å)	22.6393(12)
α (deg)	90.0
β (deg)	103.0544(19)
γ (deg)	90.0
volume (Å3)	3050.5(3)
μ (mm–1)	20.102
min/max transmission	0.161/0.780
θ range (degrees)	3.17–36.30
index ranges	–21 < h < 21
	–9 < k < 9
	–28 < l < 28
data/restraints/parameters	6218/2/245
GOF on F2	1.082
No. total reflections	75 145
No. unique reflections	6218
No. obs Fo > 4σ(Fo)	5307
R1 [Fo > 4σ(Fo)]	0.0269
R1 [all data]	0.0354
wR2 [Fo > 4σ(Fo)]	0.0586
wR2 [all data]	0.0617
largest peak and hole (e Å–3)	1.25 and −1.40

Figure 1

Polyhedral model of (a) (C6H5CH2NH3)2PbI4 and (b) (C6H5CH2NH3)4Pb5I14·2H2O at 100 K, projected along the [010] direction. The H2O molecules are rotationally disordered, and the orientation drawn should be considered illustrative only. Figure (a) is adapted from previous work.[19]

As can be seen in Figure b, the crystal structure of (C6H5CH2NH3)4Pb5I14·2H2O is rather different from its layered analogue. Despite consisting of the same building blocks, that is, benzylammonium and octahedrally coordinated lead iodide, (C6H5CH2NH3)4Pb5I14·2H2O adopts an unusual structure. Whereas (C6H5CH2NH3)2PbI4 forms a 2D structure comprised of layers of corner-sharing PbI6 octahedra, (C6H5CH2NH3)4Pb5I14·2H2O forms a one-dimensional (1D) structure consisting of [Pb5I14]4– building blocks that form ribbons along the [010] direction. This is shown in Figure . Surprisingly, the connectivity in the inorganic part consists solely of edge-sharing PbI6 octahedra. The starting compound, PbI2, also consists of layers of edge-sharing PbI6 octahedra. However, these layers are neutrally charged. In (C6H5CH2NH3)4Pb5I14·2H2O, these layers are cut into ribbons, giving rise to negatively charged [Pb5I14]4– building blocks. As a result, these ribbons are neutrally charged in their center and negatively charged at their edges, where the neutral PbI2 pattern is broken. Therefore, the benzylammonium cations form hydrogen bonds with the outermost iodides of the inorganic ribbons. As a result, the phenyl rings are positioned between the inorganic ribbons. Notably, water molecules are also incorporated into the (C6H5CH2NH3)4Pb5I14·2H2O crystal structure. After the inorganic backbone and the organic molecules were refined, using our single-crystal XRD data, a nonbonded center of electron density remained in a structural void. This intensity maximum closely matched the electron density of a water molecule, present during synthesis. Therefore, we conclude that water is incorporated in the crystal lattice. Thus, the presence of water during crystal growth induces the formation of an additional phase with completely different structural features and optical properties, as will be discussed below.

Figure 2

Polyhedral model of a single inorganic layer of (a) (C6H5CH2NH3)2PbI4 and (b) (C6H5CH2NH3)4Pb5I14·2H2O at 100 K. (a) Projection along the [001] direction, where the corner-sharing PbI6 octahedra form a slab that has translational symmetry along the a- and b-directions. Figure adapted from previous work.[19] (b) Projection perpendicular to the inorganic slabs, showing edge-sharing PbI6 octahedra forming a [Pb5I14]4– ribbon with translational symmetry along the b-direction only.

In our previous work, we studied the photoluminescence (PL) response and electronic structure of (C6H5CH2NH3)2PbI4 in more detail and found an experimental direct band gap of 2.12–2.19 eV in single crystals and a calculated direct band gap of 0.42 eV at the Γ point within DFT+SOC using the local density approximation (LDA).[19] We reason that this difference is likely due to the level of approximation employed and that incorporating quasiparticle corrections and excitonic effects would resolve the discrepancy. However, given the extended size of the unit cell, the inclusion of quasiparticle and electron–hole interaction effects is computationally prohibitive. For reference, in the case of CH3NH3PbI3 quasiparticle effects increase the DFT+SOC band gap by more than 1 eV.[34−36] In addition, low-dimensional structures are known to exhibit enhanced quasiparticle corrections and excitonic effects with respect to their bulk counterparts, due to the reduction of the dielectric screening.[37] Here we measured the PL response of (C6H5CH2NH3)4Pb5I14·2H2O and observed no significant signal with respect to the noise level. Therefore, we studied the electronic structure to investigate the nature of the band gap. Since the water molecules are disordered in the structure, we considered the full structure without the water molecules, that is, (C6H5CH2NH3)4Pb5I14, within GGA-DFT+SOC. Figure shows the resulting band structure, which is represented more elaborately in Figure S3.

Figure 3

Band structure of (C6H5CH2NH3)4Pb5I14 within DFT+SOC using the PBE functional,[27] with Γ = (0, 0, 0), X = (0.5, 0, 0), Y = (0, 0.5, 0), Z = (0, 0, 0.5), C = (0.5, 0, 0.5) or equivalent (0.5, 0, −0.5), and C1 = (0.5, 0.5, 0.5) or equivalent (0.5, 0.5, −0.5). The coordinates denote multiples of the reciprocal lattice basis vectors , and , respectively.

As can be seen in Figure , the band gap is direct at the C point and has the large value of 2.0 eV within DFT+SOC. We reason that this value is underestimated with respect to the real band gap due to the level of approximation used. The wide band gap can explain why no significant PL signal was observed for the (C6H5CH2NH3)4Pb5I14·2H2O crystals. While this can be consistent with the observation that the crystals are nearly transparent in color, it does not exclude the possibility that the material can be a weak emitter due to its specific crystal structure, which might enhance nonradiative decay pathways as well. Still, the PL response differs significantly from (C6H5CH2NH3)2PbI4. The fact that the crystal structure consists of layers of inorganic PbI6 octahedra greatly affects the size of the band gap due to the 2D confinement effect.[12,19,38] However, we find here that the connectivity between the inorganic PbI6 octahedra within a layer has a major, additional influence on the size of the band gap. As the inorganic layers are well-separated from each other, as far as the valence and conduction bands are concerned, the electronic structure can be approximated by that of the inorganic part only.[39] We did this by taking just one [Pb5I14]4– ribbon from the full crystal structure. In fact, we removed the organic groups and placed the ribbons at large distances from each other such that they do not interact. Figure b shows that consideration of a single [Pb5I14]4– ribbon results in a relatively similar band structure to the full crystal structure. Assembling the ribbons into the complete crystal structure gives rise to a widening of the band gap on Γ–Y. The gap shifts to C, and is slightly larger than for the ribbon only. Thus, the size of the band gap is mainly determined by the inorganic slabs. Therefore, we decided to investigate the influence of edge-sharing PbI6 octahedra in more detail. Figure c shows the band structure of a 2D PbI2 sheet. We constructed this model by taking the experimental positions of the [Pb5I14]4– ribbons and translating them to form a 2D sheet; that is, a sheet that is infinitely extended in two dimensions. For comparison, we also made a simplified model structure in which all the Pb–I distances in the 2D PbI2 sheet were fixed to 3.15 Å (which is a typical value for the Pb–I bond lengths in (C6H5CH2NH3)4Pb5I14·2H2O). We found that this influences the band structure but not the magnitude of the band gap. Figure c shows an indirect band gap of ∼1.78 eV for both models, and Figure S4 shows the band structure of the idealized 2D slab for more directions. The confinement effect involved in breaking the 2D PbI2 sheet into [Pb5I14]4– ribbons is small. Therefore, our result shows that the connectivity of the PbI6 octahedra within a layer is the key factor determining the size of the band gap, as evidenced by the significantly smaller band gap calculated for the orange counterpart (C6H5CH2NH3)2PbI4, which consists of sheets of corner-sharing octahedra rather than edge-sharing octahedra. To obtain a better understanding of the band structure, we also explored the effect that edge-sharing PbI6 octahedra have on the dispersion using a tight-binding (TB) approximation. This can be found in the Supporting Information, Figures S5, S6, and Table S1.

Figure 4

Comparison of the electronic band structures of (a) the full (C6H5CH2NH3)4Pb5I14 crystal, (b) a single [Pb5I14]4– ribbon of the full crystal, and (c) an infinite 2D PbI2 sheet created by translation of the experimental [Pb5I14]4– ribbon (black) and an idealized infinite 2D PbI2 sheet with fixed Pb–I distances of 3.15 Å (red), along the common direction Γ–Y, within DFT+SOC using the PBE functional.

In Figure we show the spatial distributions of the electronic wave functions for the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) at the C point in the crystal structure of (C6H5CH2NH3)4Pb5I14. Figure a clearly shows that the HOMO predominantly has states at the edges of the ribbons, where the terminal iodide ions are located, as can be seen in Figure b. Furthermore, it shows that the charges are to lesser extent distributed over the iodide ions that are part of the edge-sharing network and almost absent from the lead ions, whereas they are distributed over both parts in (C6H5CH2NH3)2PbI4.[19]Figure b shows that the charge is predominately distributed over the lead ions in the LUMO, similar to (C6H5CH2NH3)2PbI4.[19] Here, the distribution is largest in the middle of the inorganic ribbons.

Figure 5

Spatial distributions of the electronic wave function for (a) the HOMO and (b) the LUMO at the C point, within DFT+SOC using the PBE functional. Shown are the pseudo charge densities augmented with soft charges near the atomic cores. Figure rendered with VESTA.[32]

To isolate the role of the connectivity (i.e., corner-, edge-, and face-sharing PbI6 octahedra) on the electronic structure, we modeled several crystal structures and calculated their electronic structures. These idealized theoretical model structures exhibit fixed Pb–I distances of 3.15 Å (which is a typical value of the Pb–I bond lengths in (C6H5CH2NH3)4Pb5I14·2H2O) and fixed Pb–I–Pb angles of 180° (corner-sharing), 90° (edge-sharing), and 70.5° (face-sharing). To generalize our approach, we included three-dimensional (3D), 2D, and 1D structures. Note that corner-sharing can exist in 1D, 2D, and 3D. Edge-sharing can only occur in 1D and 2D structures, without creating corner-sharing pathways as well (see Figure S5 for further details on the 2D structure). Face-sharing can only exist in a 1D linear chain: higher-dimensional structures will also include edge- and corner-sharing, which we avoid in our models to isolate the influence of face-sharing. For all the theoretical structures, we calculated the approximate band gap within DFT, with and without SOC. The results are listed in Table . All of the relevant electronic band structures can be found in the Supporting Information (Figures S7–S12), together with a description of the procedure used to obtain the band gap for the charged systems.

Table 2

Approximate Band Gaps (eV) of Theoreticala Model Structures with Different Connectivity and Dimensionality

	3D	2D	1D
	with spin–orbit coupling
corner-sharing	0.10	0.94	1.82
edge-sharing		1.89	2.21
face-sharing			2.45
	without spin–orbit coupling
corner-sharing	1.26	1.76	2.27
edge-sharing		2.48	2.61
face-sharing			2.78

Calculated within DFT with and without SOC.

Our results show that the band gap increases with decreasing dimensionality, which is commonly understood as a quantum confinement effect. This trend holds not only for corner-sharing PbI6 octahedra but also for edge-sharing PbI6 octahedra. Moreover, our results reveal another clear trend: as the connectivity varies from corner- to edge- to face-sharing (i.e., an increase in the number of I ions shared with neighboring octahedra), the band gap also increases. Thus, although the number of hopping pathways for carriers between neighboring Pb ions increases, the paths become less favorable. These trends hold for calculations that both include and exclude SOC. Furthermore, it is apparent that if the dimensionality increases, the effect of SOC is enhanced.

Notably, the size of the band gap of organic/organic hybrid materials is influenced by the interplay between the choice of metal and halide (ionic radii), structural deformations,[19−24] and the connectivity. In our study, we focused only on the aspect of connectivity, using model systems with idealized atom distances and angles, and ignored the choice of the organic cation. As a result, we directly studied the effect that connectivity has on the band gap in lead iodide systems.

Conclusions

In conclusion, we have used a layered-solution crystal-growth technique to synthesize two different benzylammonium lead iodide hybrid compounds with different ratios of constituents. Beside the known (C6H5CH2NH3)2PbI4 phase, we have characterized a new (C6H5CH2NH3)4Pb5I14·2H2O phase consisting of ribbons of edge-sharing PbI6 octahedra that are separated by the organic groups. Water is also incorporated into this structure. No significant photoluminescence could be measured for the latter crystal. Thus, the presence of water during synthesis can give rise to secondary phases with different structural features and undesirable optical properties. We have calculated the electronic structure of (C6H5CH2NH3)4Pb5I14·2H2O within DFT+SOC and found a very large band gap, in agreement with our PL measurements. Moreover, by comparing the band structures of the full crystal, a single [Pb5I14]4– ribbon, and an extended 2D PbI2 sheet, we found that edge-sharing of the PbI6 octahedra is responsible for increasing the band gap relative to (C6H5CH2NH3)2PbI4, which is comprised of corner-shared octahedra. Furthermore, we modeled idealized crystal structures with different dimensionalities and octahedral connectivity and calculated their electronic structures. Our results show that the band gap increases not only with decreased dimensionality but also with increased connectivity; that is, as the connectivity of the octahedral increases from corner- to edge- to face-sharing, the band gap increases.

Our current study adds to the understanding of how the band structure is controlled by the connectivity of the inorganic lattice. Our results show that the band gap is determined by the number of iodides shared between two adjacent lead ions and is increased by higher connectivity. This understanding will facilitate direct tuning of the band gap of such materials for desired applications.