Incorporating Large A Cations into Lead Iodide Perovskite Cages: Relaxed Goldschmidt Tolerance Factor and Impact on Exciton-Phonon Interaction.

The stability and formation of a perovskite structure is dictated by the Goldschmidt tolerance factor as a general geometric guideline. The tolerance factor has limited the choice of cations (A) in 3D lead iodide perovskites (APbI3), an intriguing class of semiconductors for high-performance photovoltaics and optoelectronics. Here, we show the tolerance factor requirement is relaxed in 2D Ruddlesden-Popper (RP) perovskites, enabling the incorporation of a variety of larger cations beyond the methylammonium (MA), formamidinium, and cesium ions in the lead iodide perovskite cages for the first time. This is unequivocally confirmed with the single-crystal X-ray structure of newly synthesized guanidinium (GA)-based (n-C6H13NH3)2(GA)Pb2I7, which exhibits significantly enlarged and distorted perovskite cage containing sterically constrained GA cation. Structural comparison with (n-C6H13NH3)2(MA)Pb2I7 reveals that the structural stabilization originates from the mitigation of strain accumulation and self-adjustable strain-balancing in 2D RP structures. Furthermore, spectroscopic studies show a large A cation significantly influences carrier dynamics and exciton-phonon interactions through modulating the inorganic sublattice. These results enrich the diverse families of perovskite materials, provide new insights into the mechanistic role of A-site cations on their physical properties, and have implications to solar device studies using engineered perovskite thin films incorporating such large organic cations.

Introduction

Three-dimensional (3D) lead iodide perovskites with a chemical formula of APbI3, where A is a small monovalent cation, are a new class of semiconductors for high-performance photovoltaics and optoelectronics.[1−3] The typical crystal structure consists of a 3D framework of corner-sharing PbI6 octahedra with the A cation occupying the 12 coordinate center site of each cuboid formed by eight PbI6 octahedra (see Figure a for crystal structure), referred to here as the “perovskite cage”. Despite the structural versatility,[4,5] the choice of A cations in perovskite cages is limited by the geometric considerations of the empirical Goldschmidt tolerance factor (t),in which rA, rPb, and rI are the effective radii of A, Pb2+, and I– ions, respectively.[6,7] Empirically, a t value between 0.8 and 1.0 is favorable for halide perovskite structures, but larger (>1) or smaller (<0.8) t values result in nonperovskite structures that adapt different types of connectivity of the PbI6 octahedra. Currently, only three cations [methylammonium (CH3NH3+, MA), formamidinium ([CH(NH2)2]+, FA), and cesium ion (Cs+)] have been demonstrated to support a 3D halide perovskite structure (Figure b). However, both Cs+ and FA cations barely support the A-site cavity in the case of iodides, resulting in metastable 3D perovskites of CsPbI3 and FAPbI3. The thermodynamically stable phases at room temperature are a “yellow” nonperovskite phase lacking a 3D perovskite framework. Organic cations such as ethylammonium (EA, CH3CH2NH3+) and guanidinium (GA, [C(NH2)3]+) with radii larger than that of FA are considered too large to enter the lead iodide perovskite cage,[6−8] as the increased elongation of the cage destabilizes the perovskite framework. In fact, all previous structural studies of GA-containing halide perovskites invariably showed that the GA cations do not occupy the A-sites in the perovskite cages.[8−11]

Figure 1

Crystal structures of APbI3 and 2D RP perovskites of (HA)2(A)Pb2I7. (a) The schematic crystal structure of 3D lead iodide perovskites APbI3, A = Cs, MA, or FA. (b) Goldschmidt tolerance factor of APbI3 perovskite with different A cations. The inset images depict the molecular structures of A cations. Large organic cations, such as dimethylammonium (DMA), ethylammonium (EA), guanidinium (GA), and acetamidinium (AA), do not support a 3D perovskite structure. (c) Photographs of yellow nonperovskite structures of APbI3 with various A cations. (d) Photographs of red 2D RP perovskites of (HA)2(A)Pb2I7 with various A cations. (e) The schematic crystal structure of 2D RP perovskites of (HA)2(A)Pb2I7, where HA is n-hexylammonium and A = MA, FA, DMA, EA, GA, and AA. (f) PXRD patterns of the (HA)2(A)Pb2I7 crystalline powder products prepared by antisolvent growth of APbI3 with excessive n-hexylammonium iodide, in comparison with the calculated PXRD pattern of (HA)2(MA)Pb2I7. (g) Absorption spectra of the suspension solutions of (HA)2(A)Pb2I7 with various cations.

Figure 2

Crystal structure of (HA)2(GA)Pb2I7 in comparison with (HA)2(MA)Pb2I7. (a) Top-view of the crystal structures of (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7. (b) Side-view of the crystal structures of (HA)2(GA)Pb2I7 along a direction and (HA)2(MA)Pb2I7 along c direction. (c) Comparison of the perovskite cages of (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7. Also illustrated is the definition of the distance of the N atom in HA from the iodide plane. (d) PXRD and (e) optical images of single-crystal flakes of (HA)2(MA)Pb2I7 (top) and (HA)2(GA)Pb2I7 (bottom). The diffraction peaks of (HA)2(GA)Pb2I7 appear at higher angles than those of (HA)2(MA)Pb2I7, indicating even smaller interlayer distance in the former.

Halide perovskites generally exhibit intrinsic lattice softness and structural disorders, which lead to fundamentally different chemistry and physics from the rigid crystalline structures of conventional semiconductors and oxide perovskites.[12] Fundamental insights into structure–property relationships hold the key to understand the mechanistic origins of halide perovskite’s remarkable carrier properties, such as long carrier lifetimes and carrier diffusion lengths. These insights can also drive the design and discovery of new functional materials. There have been several theories on how the polar nature and dynamic behaviors of organic A cations can contribute to charge separation, long carrier lifetime, ferroelectricity, and the dynamic Rashba effect.[13−15] Recent studies have proposed that local structural fluctuation of the lead halide sublattice (which is coupled to cation motions) may play a dominant role in determining these properties.[16−18] Experimental study of these hypotheses has proven challenging, largely because of the limited options for A cations occupying the cages. Recent progress has shown that a fine-tuning of the Goldschmidt tolerance factor by using mixed cations can further boost solar conversion efficiency and stability of perovskite solar cells.[19−21] However, the impacts on the crystal lattice and optoelectronic properties of larger A cations inside the perovskite cage has not been examined.

In addition to 3D perovskites, when long-chain organo-ammonium ligands (LA) are introduced into the structure, 2D Ruddlesden–Popper (RP) perovskite can be formed. The RP structures with the chemical formula of (LA)2(A)PbI3 (n is an integer), can be described as 2D quantum well analogues of 3D APbI3 perovskites with a well thickness of n layers of lead iodide sheets.[22−24] RP perovskites with a n ≥ 2 accommodate A cations in the perovskite cage in a similar manner as 3D perovskites. Owing to increased chemical stability, RP lead iodide perovskites have been demonstrated as promising alternatives to the 3D perovskites in photovoltaics and light-emitting diodes,[25,26] but again the choices of A cations have been limited to MA, FA, and Cs cations so far[27] (in fact, most of the reported crystal structures have MA as the A-site cations).

Here, we show the Goldschmidt tolerance factor requirement is relaxed in 2D RP perovskites, enabling the incorporation of a series of large cations in the lead iodide perovskite cages. We have obtained the single-crystal structure of (HA)2(GA)Pb2I7 (HA = n-hexylammonium) to unequivocally confirm the occupancy of the large GA cation in the A-site of the lead iodide perovskite cage for the first time. By comparing the crystal structures of (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7, we found that this structural stabilization of an oversized A cation originates from the mitigation of strain accumulation and the capability of self-adjustable strain-balancing in 2D RP crystal structures. Low-frequency Raman spectroscopy studies revealed the large GA cation significantly influenced the exciton–phonon interactions, which is further correlated with the changes in the photoluminescence and carrier lifetime of (HA)2(GA)Pb2I7 relative to (HA)2(MA)Pb2I7. These more diverse and previously unavailable perovskite materials with large cations reveal the critical role of the A cations in modifying the lattice dynamics and carrier properties, which have important implications for understanding the exceptional carrier properties in halide perovskites.

Results

Synthesis of 2D RP Lead Iodide Perovskites with Large A Cations

We first describe how 2D RP lead iodide perovskites offer more structural flexibility for the incorporation of large A cations relative to their 3D perovskite counterparts. Among various organic cations, only the MA cation can support a stable 3D perovskite structure of APbI3 at room temperature (Figure b). Large organic cations, such as dimethylammonium (DMA, CH3NH2+CH3,), ethylammonium (EA, CH3CH2NH3+), guanidinium (GA, [C(NH2)3]+), and acetamidinium (AA, [CH3C(NH2)2]+), exclusively form nonperovskite compounds with lead iodide. Typical antisolvent growth of APbI3 with these large A cations yield yellow precipitates (Figure c). The corresponding PXRD patterns confirm the nonperovskite structures with either edge-shared double chain or face-shared one-dimensional chain of PbI3– (illustrated in Figure S1). FA cations are considered at the edge of the tolerable size, as demonstrated by FAPbI3 adopting a thermodynamically stable nonperovskite structure at room temperature in addition to a metastable 3D perovskite lattice.[28] Interestingly, nanostructuring and surface functionalization have been shown to stabilize the 3D perovskite polymorph of FAPbI3 (or CsPbI3) because of the effects of surface energy relative to bulk energy.[28−30]

Inspired by the surface-ligand-induced phase stabilization of metastable FAPbI3,[28] we discovered that the perovskite lattices of APbI3 with large A cations contained in the perovskite cage can be stabilized in a reduced dimensionality, that is, 2D RP perovskites of (LA)2(A)PbI3 (see Figure e for a schematic crystal structure for the case of n = 2). When n-hexylammonium iodide (HAI) is introduced into the precursor solutions of APbI3 (see details in Materials and Methods in the Supporting Information), antisolvent growth yields red-colored precipitates (Figure d), in striking contrast to their yellow nonperovskite counterparts (Figure c). The corresponding PXRD patterns (Figure f) show a set of diffraction peaks similar to the PXRD pattern observed for (HA)2(MA)Pb2I7, confirming the formation of 2D RP perovskites of (LA)2(A)Pb2I7. Additionally, the absorption spectra from suspended solutions show a dominant excitonic peak located at ∼560 nm (Figure g), as expected from quantum confined (LA)2(A)Pb2I7.[31] The excitonic absorbance peak slightly blue shifts as the size of the A-site cation increases. Furthermore, when n-hexylammonium iodide is replaced with n-butylammonium (BA) iodide, similar results were obtained (Figure S2), which shows the generality of the Goldschmidt tolerance factor relaxation in 2D RP structures with different long-chain alkylammonium cations. It appears that the n = 2 perovskites are the most easily accessible structures, but for the case of the EA cation, the PXRD pattern suggests that the formation of higher n perovskite structures is possible (Figure S2).

Single Crystal Structure of (HA)2(GA)Pb2I7

To unequivocally confirm the capture of the large A cation in the perovskite cage, we grew single crystals of (HA)2(GA)Pb2I7 and solved the crystal structures via single-crystal XRD analysis (Table , see details in Supporting Information). We chose GA as a representative large cation, because there have been significant research interests in and many attempts at incorporating GA into perovskite lattice for improving solar devices.[19,32] However, rigorous crystallographic evidence of the successful incorporation of GA in the perovskite cage has not been demonstrated thus far. Instead, several crystal structures, such as (GA)2PbI4,[8] (FA)(GA)PbI4,[11] (Cs,GA)(Cs)Pb2Br7,[9] and (GA)(MA)PbI3,[10] have repeatedly shown that the GA cations occupy the interlayer space between the 2D lead halide sublattice (i.e., GA serves as the “LA cation” in these 2D RP perovskites). Moreover, GA is particularly interesting because it is the only nonpolar organic cation among the organic cations listed above.[33] This may benefit future fundamental studies regarding the role of polarity of A cations in optoelectronic and ferroelectric properties.

Table 1

Complete Crystal Data and Structure Refinement of (HA)2(MA)Pb2I7 and (HA)2(GA)Pb2I7 at 100 K

compound name	(HA)2(MA)Pb2I7	(HA)2(GA)Pb2I7
empirical formula	(C6H13NH3)2(CH3NH3)Pb2I7	(C6H13NH3)2[C(NH2)3]Pb2I7
formula weight	665.04	1567.16
crystal system	monoclinic	triclinic
space group	C2/c	P-1
a/Å; α/°	45.146(16); 90	8.8195(14); 79.965(13)
b/Å; β/°	8.814(3); 100.030(5)	9.0300(15); 87.341(9)
c/Å; γ/°	8.695(3); 90	21.699(4); 89.986(10)
volume/Å3	3407(2)	1699.8(5)
Z	4	2
ρcalc, g/cm3	3.000	3.062
reflections collected	61721	28779
independent reflections	3931 [Rint = 0.0456, Rsigma = 0.0170]	28779 [Rint = 0.0390, Rsigma = 0.0463]
goodness-of-fit on F2	1.061	1.047
final R indexes [I ≥ 2σ (I)]	R1 = 0.0211, wR2 = 0.0497	R1 = 0.0315, wR2 = 0.0886
final R indexes [all data]	R1 = 0.0241, wR2 = 0.0509	R1 = 0.0335, wR2 = 0.0928
largest diff. peak/hole/e Å–3	2.36/–1.32	2.40/–1.74

To gain mechanistic insights of the relaxed t requirement and to study the structure–property relationship, we also synthesized crystals of (HA)2(MA)Pb2I7 to compare with the structure of (HA)2(GA)Pb2I7 (see Figure e for representative optical images). All crystals were grown from concentrated hydroiodic acid using an off-stoichiometry protocol.[22] It is noted that we did not observe any (HA)2(GA)PbI3 structures with n > 2 by varying the precursor stoichiometries. Crystallographic data and important structural refinement information for the two compounds are listed in Table (full details listed in Table S3). The crystal structures (Figure a,b) consist of two layers of corner-sharing PbI6 octahedra (n = 2) with bilayer of HA cations separating the inorganic slabs, and the GA or MA cations filling in the perovskite cages.

One significant feature of (HA)2(GA)Pb2I7 is that the occupancy of GA in the perovskite cage significantly elongates the Pb–I bond distances, swelling the volume of the perovskite cage (see Figure c), which is defined by the volume of the cuboid made up by the three Pb–Pb distances in the a, b, and c directions. As shown in Table that compares the structural parameters of the two compounds, the volume of the perovskite cage increases by 14.776 Å3 (∼5.9% volume expansion) for (HA)2(GA)Pb2I7 compared with (HA)2(MA)Pb2I7. Moreover, we find that the volume of the cage for (HA)2(GA)Pb2I7 is larger than all previously reported 2D RP perovskites with n = 2 (Table S4). This exceptionally large cage volume indicates large tensile strain on the inorganic sublattice, which is further confirmed by the higher octahedral distortion parameters of bond angle variance (σ2) and quadratic elongation (⟨λ⟩) in (HA)2(GA)Pb2I7 relative to (HA)2(MA)Pb2I7 (Table , see Equation S1 and S2 for calculations).[34,35] Because the inorganic framework is templated by both the A-site cation and HA cation, different conformation of HA cations can also influence the Pb–I network distortion. One may expect that strain will accumulate as successive 2D slabs of GA cages are stacked, leading to the eventual destabilization of a 3D perovskite structure.

Table 2

Comparison of the Structural and Bonding Parameters between (HA)2(MA)Pb2I7 and (HA)2(GA)Pb2I7

structural parameters	(HA)2(MA)Pb2I7	(HA)2(GA)Pb2I7	difference (GA-MA)
volume of cage (Å3)	250.2589	264.446	14.187
a,b axis Pb-plane to Pb-plane distance (avg) (Å)	6.1905	6.3112	0.1207
c-axis Pb-plane to Pb-plane distance (cage) (Å)	6.5150	6.6412	0.1262
c-axis Pb-plane to Pb-plane distance (ligand bilayer) (Å)	15.713	14.702	–1.011
ammonium - iodide plane distance d (avg) (Å)	0.75	0.834	0.084
Pb–I–Pb angle (a, b) (deg)	155.73	162.02	6.29
Pb–I–Pb angle (c) (deg)	179.228	178.87	–0.358
bond angle variance (σ2, deg2)	10.5161	15.1104	4.5943
quadratic elongation (⟨λ⟩)	1.0031	1.0046	0.0015

Relaxing the Goldschmidt Tolerance Factor

We believe the issue of strain accumulation due to large A cations in 3D perovskites is circumvented in 2D RP perovskites with reduced dimensionality. Strain relaxation readily occurs at the top and bottom of PbI6 octahedra due to less geometric constraint. This is aided by the structural flexibility of the HA cation bilayers outside the cage that can accommodate the PbI6 octahedral distortions. Strain dissipation into the interlayer space thus leads to different molecular conformations of the HA cations in (HA)2(MA)Pb2I7 and (HA)2(GA)Pb2I7 (Figure b). As a result, (HA)2(GA)Pb2I7 exhibits an even smaller interlayer distance despite having a larger perovskite cage than (HA)2(MA)Pb2I7 (Table and Figure b). On the other hand, the interlayer HA cations act as strain compensation layers by applying opposite strain from the GA cages to balance the global strain of the overall structure. Specifically, the tensile strain in the GA cage is balanced by compressive strain applied from the bilayers of HA cations. Compressive molecular packings of the interlayer HA in the (HA)2(GA)Pb2I7 is supported by the surprisingly smaller interlayer spacing and unit cell volume of the (HA)2(GA)Pb2I7 (see Figure d for PXRD peak shifts and Table ) relative to the (HA)2(MA)Pb2I7 (considered as a strain-free structure), despite the fact that (HA)2(GA)Pb2I7 has a larger perovskite cage.

Moreover, to compensate for the strained GA cage, the HA ammonium head inserts deeper into the octahedral pocket, as characterized by the increased distance between the N atom and the iodide plane (d) in the (HA)2(GA)Pb2I7 relative to the (HA)2(MA)Pb2I7 (illustrated in Figure c and values shown in Table ). The interaction between the N and I atoms is through hydrogen bond N–H–I. These structural features show that the increased structural flexibility of 2D RP perovskites relative to their 3D counterparts reduces cumulative strain and balances the strain in a self-adjustable manner, thus facilitating the incorporation of large A cations and relaxing the tolerance factor requirement. In addition to these 2D lead iodide perovskites with DMA, EA, GA, and AA cations reported herein, there are examples of 2D RP lead chloride or bromide perovskites[36,37] (EA)2(EA2)Pb3X10 (X = Br or Cl) and 2D RP tin iodide perovskite[38] (IPA)2(IPA)Sn2I7 (IPA = isopropylammonium) that exhibit a relaxed tolerance factor. This indicates the relaxed tolerance factor is likely a universal property of the 2D RP perovskite structure, which is understandable based on the lattice strain mitigation in 2D RP perovskite structures that is not possible in 3D perovskite structures.

The GA cation has a symmetric planar structure forcing the perovskite cage to elongate diagonally to accommodate this cation. Therefore, one may expect the molecular motions of GA to be sterically hindered in the cage. Indeed, the configuration of the GA cation in the perovskite cage is fixed while the MA cations can adopt several disordered configurations (Figure c) in the (HA)2(MA)Pb2I7. The MA cation is disordered over two positions about a crystallographic 2-fold axis with relative occupancies of 30.2% and 19.8% (determined from the crystal structure refinements at 100 K) and thus generating four partially occupied positions (Figure a,c). We note that carbon and nitrogen atoms in the MA cation could not be definitively identified. We consider this dynamic disorder of MA cation as a reflection of the structural flexibility of the inorganic cage in (HA)2(MA)Pb2I7. We further compared the Raman vibration modes of the GA cation occupying the cage of (HA)2(GA)Pb2I7, with those of the GA cation occupying the interlayer gallery of (GA)2PbI4 (Figure S3). Raman peaks at ∼505 and 1010 cm–1 are respectively assigned to the angle deformations and stretching vibrations of the CN3 group.[8] The stretching mode of cage-GA is blue-shifted by 4 cm–1 than that of GA in the gallery. Moreover, the bending vibration of cage-GA is significantly suppressed, which is demonstrated by the much lower relative intensity (Ibending/Istretching, 0.65 versus 2.08). These results confirm a large degree of steric hindrance experienced by the GA cation in the cage.

Impacts of A Cations on Physical Properties

Having established the structural information from single-crystal XRD analysis, we turn to studying the impacts of varying the A cation on the physical properties, such as optical bandgaps, and carrier and phonon properties. UV–vis diffuse reflectance spectroscopy was collected for (HA)2(GA)Pb2I7 in comparison with (HA)2(MA)Pb2I7. The corresponding absorption spectra (Figure a) converted by the Kubelka–Munk function show an excitonic absorption feature of (HA)2(GA)Pb2I7 located at 582 nm (2.13 eV), which is blue-shifted from that of (HA)2(MA)Pb2I7 at 596 nm (2.08 eV). This blue shift can be attributed to the expansion of the GA cage with increased Pb–I bond lengths. Room-temperature PL emission peaks (Figure b) are at 577 and 582 nm (2.15 and 2.13 eV) for (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7, respectively. Under continuous laser illumination (λ = 532 nm), (HA)2(GA)Pb2I7 showed less decrease in PL intensity, indicating the 2D perovskite incorporating the larger GA cation may have enhanced photostability relative to that incorporating MA cation (Figure S9). Strikingly, the PL emission intensity of (HA)2(MA)Pb2I7 is about 1 order of magnitude higher than that of (HA)2(GA)Pb2I7, suggesting more pronounced nonradiative recombination in the (HA)2(GA)Pb2I7. These results suggest that the A cations can influence the optical properties by modulating the distortion of the Pb–I inorganic sublattices, which dictates the electronic band structures.

Figure 3

Comparison of the optical properties of (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7. (a) Absorption spectra, (b) steady-state PL, and (c) time-resolved PL of (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7 single-crystals.

To further probe the carrier dynamics, we performed time-resolved PL (TRPL) measurements on the single crystals of both compounds under the same excitation power density. Representative pseudocolor plots of the TRPL spectra (Figure S4) reveal a fast band-edge emission at early time (<100 ps) and a slower band-edge emission at longer time (>100 ps). Long-lived PL emission up to 2 ns is observed in (HA)2(MA)Pb2I7, but PL emission diminish after ∼500 ps in (HA)2(GA)Pb2I7. The corresponding PL decay curves (Figure c) are quantitatively fitted using a biexponential function [] to yield a fast decay lifetime of τ1 = 31 and 46 ps, and a slow decay lifetime of τ2 = 440 and 927 ps for (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7, respectively. Statistical analysis of the TRPL spectra from multiple samples shows the average lifetime (A1τ1 + A2τ2) of (HA)2(MA)Pb2I7 is 2 times longer than that of (HA)2(GA)Pb2I7 (Table S5), which corroborates the stronger PL emission observed.

Phonons that interact with charge carriers and excitons govern many important physical properties, such as carrier mobility, and PL line width broadening with temperature, and phonon mediated nonradiative recombination. Studies on 3D lead halide perovskites suggested that charge carriers in perovskite materials are coupled to low-frequency optical phonons (<100 cm–1) that mainly involve vibrational modes of the inorganic framework.[16,39−42] A recent report correlated the nonradiative recombination rate in 2D n = 1 RP perovskites with the exciton–phonon coupling strength and molecular rigidity of the long chain organic cations (LA).[43]

To probe the low-frequency phonons, we collected Raman spectra of the (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7 single crystals in a broad range of the temperatures from 77 to 300 K (Figure S5). Representative spectra at three temperatures are highlighted in Figure a,b. Broad Raman peaks at ∼50 cm–1 regions can be assigned to the collective framework modes and local Pb–I vibrations, while the modes of organic cations reside at >200 cm–1 regions (such as those for the GA cation shown in Figure S3). In a previous study on MAPbBr3, the low-frequency Raman spectra show dramatic changes as the temperature is increased from 77 to 295 K.[39] In the more crystalline and ordered low temperature orthorhombic phase of MAPbBr3, phonon modes attributed to the inorganic framework were well-resolved. As the crystal enters the tetragonal phase at intermediate temperatures and the cubic phase at room temperature, the Raman spectra are characterized by a broad and featureless central peak characteristic of extensive dynamic disorder.[39] In contrast, low-frequency Raman spectra of both (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7 show little change with temperature in the 77–295 K window, suggesting that there are no transitions of crystalline phases. Comparing these two 2D perovskite materials, both the phonon peaks and the diffuse background are broader in (HA)2(MA)Pb2I7 than those in (HA)2(GA)Pb2I7 at each temperature. This can be attributed to the small size of the MA cation, which allows significant free space for a wider range of inorganic cage motion and thus more phonon disorder. The inorganic cage motions of (HA)2(GA)Pb2I7 might be constrained because of the synergistic steric hindrance of the large GA cation in the perovskite cage and more compressed interlayer HA cations.

Figure 4

Comparison of phonon properties of (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7. (a,b) Low-frequency Raman spectra of (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7 single crystals at three temperatures. (c) 2D pseudocolor plots of temperature-dependent PL spectra of (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7 single crystals. (d) The corresponding PL emission line widths as a function of temperature together with their fits.

To further compare the exciton–phonon interactions of these two compounds, we performed temperature-dependent PL studies (Figure c). The lack of drastic change of PL peak position for both compounds further confirms the absence of phase transition in this temperature range, consistent with the Raman results discussed above. The PL line width at low temperature (i.e., 10 K) is primarily due to inhomogeneous broadening. However, as temperature increases, phonon scattering leads to significantly observable broadening. Figure d shows the extracted emission line widths as a function of temperature for the two compounds, which are fitted according to following equation:[44]The first term, Γ0, is the inhomogeneous broadening term and the line width at 0 K. The second term describes the homogeneous broadening due to the longitudinal optical (LO) phonon scattering via Fröhlich interaction, where γLO is coupling strength and ELO represents a dominant phonon or an average phonon energy. Note, we ignore the negligible homogeneous broadening that results from acoustic phonon scattering with exciton.[44,45] The fits yield Γ0 = 34 meV, γLO = 58 meV, and ELO = 15.7 meV for (HA)2(GA)Pb2I7; Γ0 = 16.4 meV, γLO = 40 meV, and ELO = 10.6 meV for (HA)2(MA)Pb2I7. The inhomogeneous line width is larger in (HA)2(GA)Pb2I7 than in (HA)2(MA)Pb2I7, which can be attributed to the larger structural distortion of the inorganic sublattice as has been described above (Table ). The coupling strengths and phonon energies are similar to those values previously reported for MAPbI3 (40 meV, 11.5 meV),[44] (HA)2PbI4 (17 meV, 56 meV), and (BA)2PbI4 (10.9 meV, 34 meV).[46] (HA)2(GA)Pb2I7 exhibits a different coupling phonon energy (ELO) from (HA)2(MA)Pb2I7, as expected from the change of inorganic sublattice. The larger inhomogeneous broadening in (HA)2(GA)Pb2I7 than that in (HA)2(MA)Pb2I7 points to more structural disorder and/or defect density in the former. The structural defects may serve as centers for exciton trapping and nonradiative recombination, thus leading to lower PLQY and shorter PL lifetime in (HA)2(GA)Pb2I7 in comparison to (HA)2(MA)Pb2I7. All of these demonstrate that the A site cation can have dramatic effects on the exciton–phonon interactions and carrier properties of halide perovskites, which was not previously elucidated because of the limited choices of the three common cations (Cs+, MA, FA).

Discussion

Although potential technological applications of these new 2D perovskites remain to be explored, our results not only have enabled new insights into the structure–bandgap relationship in perovskite materials but also will spur spectroscopic studies to understand mechanistic origins of their varying optoelectronic properties. One of the most significant structural features due to the incorporation of large A-site cations is the perovskite cage expansion (see Table above), which induces a significantly blue-shifted bandgap and modifies the phonon properties of inorganic sublattice. In general, the electronic structures of valence band maxima and conduction band minima are dominated by the orbital overlap between lead and halide atoms. Therefore, the bandgap is correlated with the orbital overlap associated with the deformation of inorganic framework.[47] In the three available 3D perovskites APbI3 (A = Cs+, MA, FA), the redshift of bandgap from Cs+ to MA and then to FA can be attributed to the decreasing octahedral tilt angle with increasing cation size (while maintaining Pb–I bond length), which increases the orbital overlap.[48,49] However, the bandgap blueshift from MA to GA in our 2D perovskites comes from a different structural origin, i.e. the significantly increased Pb–I bond length due to the incorporation of the large GA cation in the cage, which decreases the orbital overlap of lead and iodine atoms. In addition, (HA)2(GA)Pb2I7 exhibits a smaller octahedral tilt angle than (HA)2(MA)Pb2I7 (Table ), further highlighting the dominant role that the increased bond length plays in the bandgap blueshift.

The discovery of these new 2D perovskites with unique A-site cations may further spur fundamental studies to understand the relationship between the structure and optoelectronic properties. Mechanistic studies have proposed that the favorable optoelectronic properties of perovskite materials are associated with structural fluctuations of the organic and inorganic sublattices,[50−52] such as the large dynamic disorder of the inorganic framework and fast reorientation of the polar organic cations in the cage. Comparative studies on the three available 3D perovskites APbI3 (A = Cs+, MA, FA) have examined the role of A-site cations on the photophysical properties.[16,53−55] However, providing a clear picture of the relationship remains challenging because of the limited three data points as well as the complex interplay between motions of the inorganic and organic sublattices.[14,15] In this regard, the series of new 2D perovskites incorporating various organic cations with different size and polarity reported herein provide a new platform for understanding the lattice disorder of inorganic sublattice,[40,56−58] cation dynamics,[59−62] and their mutual interactions; thus, they could reveal a more quantitative and comprehensive structure–property relationship. This is the first crystallographic report demonstrating the occupation of the 2D perovskite A-sites with large GA cations, and thus, the structural features and basic optical properties of this compound are discussed. Further in-depth investigations of the impact of such expanded perovskite cages on other physical properties, such as charge-carrier transport, ion migration,[63] spin–orbital coupling,[64−67] and defects[68,69] will guide the tuning of the properties and functionalities of perovskite materials.

Lastly, even though the large GA cation cannot support 3D perovskite structures alone, the above results are highly relevant to the many thin film composition engineering and solar device studies using such large A cations.[19,32,70−72] Specifically, studies that attempted to introduce the large GA cation into thin films of 3D perovskites for solar cell devices have demonstrated longer carrier lifetime, improved material stability, and increased energy conversion efficiency.[19,32,70−72] However, the mechanistic origin of the enhanced performance has been debated. Multiple reports claim the superior photophysical performance of thin-films with GA incorporation is attributed to grain boundary passivation.[32,73] In contrast, others have suggested incorporation of GA cation in the perovskite cage lead to enhanced solar cell performance.[70] The new crystal structure of the 2D perovskite incorporating GA as the A cation reported herein, (HA)2(GA)Pb2I7, suggests that it is possible for large A cations, such as DMA, EA, GA, and AA, to occupy the perovskite cages, provided there are means to dissipate the strain. Cation alloying with a small percentage of large A cations could occur in those thin films. However, the incorporation of the large GA cation in the perovskite cages could deteriorate the photophysical properties, as shown in this work by comparing (HA)2(GA)Pb2I7 and (HA)2(MA)Pb2I7. These results hence suggest that the observed enhanced photophysical properties in thin films is likely due to large A cations potentially passivating grain boundaries. Using this 2D perovskite structure (HA)2(A)Pb2I7, the role each of the individual large A cations play in the perovskite photophysical properties could be studied in-depth in the future.

Conclusions

In summary, we show that the decreased structural rigidity of 2D RP lead iodide perovskites can facilitate an expanded volume of the perovskite A-site cavity. This enables the incorporation of larger organic cations into the perovskite cages that are not able to form stable 3D perovskite structures. This phenomenon can be considered a relaxation of the Goldschmidt tolerance factor which enables a significantly expanded library of 2D RP lead iodide perovskites with exotic larger A cations that may exhibit unique properties and new applications. The successful incorporation of GA cation in the perovskite cage is unambiguously confirmed through the crystal structure determination of (HA)2(GA)Pb2I7. Comparison of the structural parameters of (HA)2(GA)Pb2I7 with (HA)2(MA)PbI7 reveals the flexible long-chain ammonium cations (i.e., HA) facilitates the perovskite cage expansion while maintaining the structural integrity, and the structural stabilization originates from strain balance in alternate tensile (inorganic sublattice with GA in the cage) and compressively strained layers (interlayer HA cations). Moreover, such large A cation significantly increases the distortion of inorganic perovskite sublattice and, subsequently, optoelectronic properties, carrier dynamics, and exciton–phonon interactions. These results not only enrich the diverse structural chemistry of halide perovskite materials that may lead to new applications but also highlight the critical role A-site cations plays in the remarkable physical properties of perovskite materials and have important implications to solar device studies using engineered perovskite thin films incorporating such large organic cations.