Kinetic controlled synthesis for 2d perovskite materials

Abstract

Methods of making a two-dimensional perovskite, a two-dimensional perovskite composition are disclosed. The two-dimensional perovskite comprises: a layered material having the formula (I) (A')(A)n-1MnX3n+1, where A' is an organic cation selected from the group consisting of butyl ammonium, 3-(aminomethyl)piperidium (3-AMP), 4- (aminomethyl)piperidium, and combinations thereof; A is a perovskitizer-cation selected from the group consisting of formamidinium (FA), guanidinium, dimethylamine, cesium, and combinations thereof; M is a divalent metal selected from the group consisting of Pb, Ge, Sn, Cu, and combinations thereof; X is a halide selected from the group consisting of I, Br, Cl, F, and combinations thereof; and n is greater than or equal to 2. The layered material comprises alternating layers of a first type and a second type, where the first type comprises the organic cation (A') and the second type comprises a hybrid anion having the formula (II) (A)n-1MnX3n+1, and the layered material has a tetragonal crystal structure with space group symmetry P4 / mmm.

Description

PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT KINETIC CONTROLLED SYNTHESIS FOR 2D PEROVSKITE MATERIALS STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0001] This invention was made with government support under Grant Nos. DE- EE0008843 and DE-EE0010738 awarded by the Department of Energy. The government has certain rights in the invention. BACKGROUND

[0002] Symmetry is a foundationally important concept, which influences our understanding of the fundamental laws of the universe. For example, symmetries are directly linked to fundamental interactions, conservation laws and govern selection rules. Symmetry also plays an important role in chemistry and biology, being responsible, for example, for the reactivity of a specific molecular enantiomer. In materials science, symmetry breaking is key to understanding phase transitions, which are identified by lattice symmetry and are directly linked to the discovery and development of many physical behaviors, such as altermagnetism, high harmonic generation, and topological materials. The high crystal symmetry of semiconductors like Silicon (diamond cubic) and GaAs (zinc blende) drastically influences their electronic, optical, and thermal properties. In Silicon, symmetry leads to an indirect bandgap, reducing optical absorption but enabling high carrier mobility and thermal conductivity due to reduced phonon scattering. In GaAs, symmetry allows a direct bandgap, making it ideal for optoelectronics with efficient light emission and higher electron mobility. These properties have enabled Silicon for its use in microelectronics, and GaAs in photonic and high-speed applications.

[0003] In contrast, in materials with a soft lattice, such as metal halide perovskite materials (MHPs or perovskite materials), and in particular embodiments organic- inorganic (hybrid) halide perovskite materials, crystal symmetry is often lowered due to octahedra tilting, which results from the process of relieving lattice strain without bond breaking. For example, among the most studied three-dimensional (3D) perovskite materials, FAPbI3 (FA=formamidinium) and MAPbI3 (MA = methylammonium) exhibit a non-perovskite hexagonal phase and a tetragonalPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT perovskite phase at room temperature, respectively. Both transform to a higher symmetric perovskite phase only at elevated temperatures. In the non-perovskite phase of FAPbI₃, charge transport properties are poor due to the high density of edge-sharing octahedra (also known as delta phase or yellow phase). In contrast, the cubic perovskite phase of FAPbI₃, also referred to as cubic FAPbI3, 3D FAPbI3, or 3D α-FAPbI3, which features corner-sharing octahedra, exhibits electron or hole diffusion lengths ranging from 6.6 µm to 600 µm. For comparison, the lower-symmetry tetragonal phase of MAPbI₃ has electron or hole diffusion lengths between approximately 10 and 170 µm. While these are about an order of magnitude smaller than silicon, they are exceptional for many applications based on solution-processed thin films and have led to highly efficient optoelectronic devices. However, 3D perovskite materials suffer from stability issues, specifically under humidity, heat, and light, which can induce ion transport within the film.

[0004] Two-dimensional (2D) perovskite materials, on the other hand, offer a viable solution to the stability challenge due to the intercalation of hydrophobic organic cations, forming an organic-inorganic superlattice structure. Two-dimensional (2D) perovskite materials have been intensively studied in the past decade for their promise of high-stability photovoltaics compared to 3D perovskite materials and climbing efficiencies approaching 20%. The general chemical formula of two-dimensional perovskite materials is (A′)m(A)n−1MnX3n+1 (where A′ is a bulky organic cation, A is a small organic cation, M is a divalent metal, X is a halide, with m=2 in Ruddlesden- Popper (RP) phases and m=1 in Dion-Jacobson (DJ) phases, and n determines the thickness of the perovskite layer), which consists of alternate layers of organics (A’)m and hybrid (A)n−1MnX3n+1, providing a perfect platform to engineer hybrid composites with attractive optoelectronic properties. However, most of the studies on 2D perovskite materials have been performed on lower n-values (n=1, 2) largely due to difficulties in reproducibly growing higher n-value phase pure crystals and films (n>2), while higher n-value 2D perovskite materials are of tremendous interest. For instance, the exciton diffusion constant, diffusion length and mobility (both in-plane and out-of- plane) of 2D perovskite materials all increase as n increases, while the band gap of decreases as n increases, making higher-n 2D perovskite materials more suitable candidates for semiconductor applications such as solar cells, light emitters, transistors,PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT and ionizing radiation detectors. Also, the majority of 2D perovskite materials are methylammonium (MA) based, which hinders the path toward higher stability since MA is highly volatile and causes degradation in perovskite materials, films, and devices. The larger formamidinium cation (FA), on the other hand, is much more stable than MA. FA-based 3D perovskite materials also show improved carrier transmission (longer carrier lifetime) compared to MA-based 3D perovskite materials. Therefore, FA-based, multiple layered (n>2) 2D perovskite materials are of great interest for their potential in both efficiency and stability. It has been shown recently that it is difficult to synthesize FA-based 2D perovskite materials with high layer thickness (n>2) using the classic synthesis method (CS), where only the stoichiometry is tuned. Accordingly, there exists a need for a reproducible synthesis method to fabricate perovskite materials including high-n 2D perovskite materials, particularly high-n FA-based 2D perovskite materials. SUMMARY

[0005] This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter.

[0006] In one aspect, embodiments herein relate to a two-dimensional perovskite material composition. The two-dimensional perovskite material composition includes a layered material having the formula (I) (A′)(A)n-1MnX3n+1, where A′ is an organic cation selected from the group consisting of butyl ammonium, 3- (aminomethyl)piperidium (3-AMP), 4-(aminomethyl)piperidium, and combinations thereof, A is a perovskitizer-cation selected from the group consisting of formamidinium (FA), guanidinium (GA), dimethylammonium, cesium, and combinations thereof, M is a divalent metal selected from the group consisting of Pb, Ge, Sn, Cu, and combinations thereof, X is a halide selected from the group consisting of I, Br, Cl, F, and combinations thereof, and n is greater than or equal to 2. The layered material includes alternating layers of a first type and a second type, where the first type comprises the organic cation (A′) and the second type comprises a hybrid anion havingPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT the formula (II) (A)n-1MnX3n+1. The layered material has a tetragonal crystal structure with space group symmetry P4 / mmm.

[0007] The layered material having the formula (I) (A′)(A)n-1MnX3n+1, may have an n value ranging from 2 to 10. The layered material may have a lattice mismatch between the first type and second type of 1% or less. The layered material may be linear and may have an equatorial M-X-M angle ranging from 160 to 180 °C. The layered material may have a formula (III) (3-AMP)(FA)n-1PbnI3n+1 and n may be 2, 3, or 4. The layered material of formula (III) may have an interlayer distance ranging from 3.8 to 7 Å. The layered material may have a band gap of from 1.6 eV to 2.0 eV. The layered material may be a film. The film may be included in a device, such as an electronic or optoelectronic device. The device may be a solar cell, and the solar cell may be a tandem cell.

[0008] In another aspect, embodiments herein relate to a method of making a two- dimensional perovskite material, the method includes: mixing a divalent metal source and a salt containing a perovskitizer-cation in a halogen acid solution, forming a first suspension; stirring the suspension at an elevated temperature of from about 100 °C to 400 °C; adding a solution comprising an organic cation and an acid to the suspension, forming a mixture; cooling the mixture to a temperature of from about 80 °C to 120 °C at a cooling rate of 0.01 to 200 °C / s, to form crystals; and filtering and drying the crystals to obtain a two-dimensional perovskite material. The first suspension may further include H3PO2.

[0009] The halogen acid may be selected from the group consisting of hydroiodic acid, hydrochloric acid, hydrobromic acid, hydrofluoric acid, and combinations thereof. The salt containing a perovskitizer-cation may be selected from the group consisting of FACl, FABr, FAI, GACl, GABr, GAI, CsBr, CsCl, CsI, and combinations thereof. The divalent metal source may be selected from the group consisting selected from the group consisting of PbI2, PbCl2, PbBr2, PbO, and combinations thereof. The acid may be selected from the group consisting of H3PO2, and combinations thereof The two- dimensional perovskite material may have the formula (III) (3-AMP)(FA)n-1PbnI3n+1 and n may be 2, 3, or 4. The two-dimensional perovskite material may be free of δ- phase formamidinium lead iodide (FAPbI3).PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT

[0010] Other aspects and advantages of the claimed subject matter will be apparent from the following description and the appended claims. BRIEF DESCRIPTION OF DRAWINGS

[0011] Specific embodiments of the disclosed technology will now be described in detail with reference to the accompanying figures.

[0012] FIG.1 shows a block flow diagram of a method in accordance with one or more embodiments of the invention.

[0013] FIG.2 shows a schematic of a method in accordance with General Example 1.

[0014] FIG.3 depicts the experimental and calculated powder X-ray diffraction pattern of FA-DJ n=2, in accordance with Example 3.

[0015] FIG.4 depicts the experimental and calculated powder X-ray diffraction pattern of FA-DJ n=3, in accordance with Example 4.

[0016] FIG.5 depicts the experimental and calculated powder X-ray diffraction pattern of FA-DJ n=4, in accordance with Example 5.

[0017] FIG. 6 depicts a schematic phase diagram in accordance with one or more embodiments of the invention.

[0018] FIG. 7 shows the crystal structures of FA-DJ n=1, 2, 3, and 4, in accordance with Examples 2-5.

[0019] FIG.8 shows the normalized 1D X-ray diffraction patterns of FA-DJ n=1, 2, 3, and 4, in accordance with Examples 2-5.

[0020] FIG. 9 depicts the interlayer distances of FA-DJ, MA-DJ, and MA-RP, in accordance with Examples 2-5.

[0021] FIG. 10 shows the top and side view of MA-BA, MA-DJ, and FA-DJ, in accordance with one or more embodiments of the invention.

[0022] FIG. 11 depicts the average equatorial Pb-I-Pb angle of FA-DJ, MA-DJ, and MA-BA, in accordance with one or more embodiments of the invention.PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT

[0023] FIG. 12 depicts the normalized absorption spectra of the FA-DJ series, in accordance with Examples 2-5.

[0024] FIG.13 shows the normalized photoluminescence spectra of the FA-DJ series, in accordance with Examples 2-5.

[0025] FIG. 14 shows the experimental and computed electronic band gap of the FA- DJ series and cubic FAPbI3, in accordance with Examples 2-5.

[0026] FIG. 15 depicts the room temperature Raman spectroscopy of FA-DJ n=1, 2, and 3, in accordance with Examples 2-4.

[0027] FIG. 16 compares the temperature-dependent PL FWHM of FA-DJ n=2, n=3, and 3D FAPbI3, in accordance with Examples 3 and 4.

[0028] FIG.17 shows the solid state 1DNMR spectra of FA-DJ n=1, 2, 3, and 3D α-FAPbI3, in accordance with Examples 2-4.

[0029] FIG.18a shows the pair distribution function of cubic FAPbI3 without the effect of lattice vibrations at 300 K, in accordance with one or more embodiments of the invention.

[0030] FIG. 18b shows the pair distribution function of polymorphous FA-DJ n=2 without the effect of lattice vibrations at 300 K, in accordance with one or more embodiments of the invention.

[0031] FIG. 18c shows the pair distribution function of polymorphous cubic FAPbI3 with the effect of lattice vibrations at 300 K, in accordance with one or more embodiments of the invention.

[0032] FIG.18d shows the pair distribution function of polymorphous FA-DJ n=2 with the effect of lattice vibrations at 300 K, in accordance with one or more embodiments of the invention.

[0033] FIG.19 compares the exciton diffusivity of PEA-RP n=1, 2, 3 with BA-RP n=1, 2, 3 and mF-PEA-RP n=1 and FA-DJ n=2,3, in accordance with one or more embodiments of the invention.

[0034] FIG. 20 compares the exciton diffusion lengths of PEA-RP n=1, BA-Rp n=3, and FA-DJ n=3, in accordance with one or more embodiments of the invention.PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT DETAILED DESCRIPTION

[0035] Specific embodiments of the invention will now be described in detail with reference to the accompanying figures. In the following detailed description of embodiments, numerous specific details are set forth in order to provide a more thorough understanding of the invention. As used herein, “include” means “include, but is not limited to”.

[0036] In general, embodiments of this disclosure relate to a method of synthesizing high n-value 2D perovskite materials with high symmetry for use in devices, such as semiconductors. Realizing semiconductor materials with high symmetry of their crystallographic structures is highly desirable but has been primarily limited to inorganic materials. In contrast, hybrid (organic and inorganic) crystals such as two- dimensional metal halide perovskite materials exhibit much lower crystal symmetry due to in-plane or out-of-plane octahedral distortions. However, by utilizing the synthesis methods described below, a series of distortion-free, layered two-dimensional perovskite materials that exhibit the highest theoretically predicted symmetry with a tetragonal P4 / mmm space group, resulting in minimal octahedral distortion in both in- plane and out-of-plane directions, are disclosed herein. These 2D perovskite materials have short interlayer distances (4 Å), which results in systematically lower bandgaps (1.7 to 1.8 eV), compared to other 2D perovskite materials, making them ideal for Si / perovskite or perovskite / perovskite multijunction solar cells. Additionally, the absence of octahedral distortions results in an exciton diffusion length of 2.5 µm and a diffusivity of 4.4 cm2s-1, both of which are an order of magnitude larger compared to previously reported 2D perovskite materials and on par with monolayer transition metal dichalcogenides.

[0037] A process methodology termed kinetic controlled synthesis (KCS) of two- dimensional (2D) perovskite materials is provided. By controlling the kinetics of the crystallization of perovskite crystals, the synthesis of these 2D perovskite materials, which were challenging or even impossible to obtain using the traditional method, can be achieved. Using KCS, a series of 2D perovskite materials was synthesized, which are formamidinium (FA)-based Dion-Jacobson (DJ) two-dimensional perovskite materials with high inorganic layer thickness (n=1, n=2, n=3, and n=4). This series ofPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT 2D perovskite materials has the smallest bandgap among all the currently reported 2D perovskite materials. The structure of this series is linear with minimal distortion. The space group of this series is p4 / mmm which is the maximum symmetry that can be theoretically achieved in 2D perovskite materials, and the series shows ultra-high material stability in accelerated stability tests. In one or more embodiments, the method may be utilized to form quasi-2D or 3D perovskite materials. A quasi-2D or 3D perovskite material is a perovskite material with a mixture of n-values from n=1 to n=10 or n>10 and approaching the 3D limit.

[0038] Compared to the classic synthesis (CS) method, where stoichiometry is the only variable, the kinetic controlled synthesis (KCS) method described herein has two extra tuning factors – temperature and time of the crystallization. With full control of the crystallization for all three parameters, it is possible to synthesize 2D perovskite crystals with much higher purity and reproducibility. More importantly, some 2D perovskite materials which are considered challenging to synthesize using the classic synthesis method can now be targeted and obtained. Traditionally, the importance of kinetic control has not been realized, and the present disclosure demonstrates its impact on the synthesis of the 2D perovskite material synthesis.

[0039] The synthesis of these 2D perovskite materials, as well as synthesis of new members (higher n) of the existing series with high purity, are disclosed. The crystal structure of the 2D FA-based perovskite material series is determined by powder diffraction, single crystal diffraction, Grazing-Incidence Wide-Angle X-ray Scattering, absorption, and photoluminescence. The space group is also determined to be p4 / mmm. Phase transition behavior is also studied using DSC measurements.

[0040] According to one or more embodiments of the present invention, a two- dimensional perovskite material is disclosed. In one or more embodiments, the two- dimensional perovskite material comprises a layered material having the formula (I) (A′)(A)n-1MnX3n+1, where A′ is an organic cation selected from the group consisting of butyl ammonium, 3-(aminomethyl)piperidium (3-AMP), 4-(aminomethyl)piperidium, and combinations thereof, A is a perovskitizer-cation selected from the group consisting of formamidinium (FA), guanidinium, dimethylamine, cesium, and combinations thereof, M is a divalent metal selected from the group consisting of Pb, Ge, Sn, Cu, and combinations thereof, X is a halide selected from the group consisting of I, Br, Cl, F,PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT and combinations thereof, and n is greater than or equal to 2 is disclosed. In one or more embodiments, n ranges from 2 to 10, and may be 2, 3, 4, 5, 6, 7, 8, 9, or 10. In one or more embodiments, A’ is an organic cation selected from Table 1, below. For example, the two-dimensional perovskite material may be (3-AMP)(FA)n-1PbnI3n+1 where n = 1, 2, 3, or 4, (4-AMP)(FA)n-1PbnI3n+1where n = 1, 2, 3, or 4, BA2FAPb2I7, or BA2FAPb3I10. Throughout the disclosure, it should be understood that the variables describing the stoichiometry of various components, such as “n” in the crystal structure recited in the aforementioned formulae, do not necessarily correspond to an exact whole number value. As will be appreciated by those skilled in the art, crystal systems can include elemental substitutions, vacancies, and other defects. Therefore, it should be understood that a reference to a whole number for a value such as n can include variations on the order of 0.1 to 30%.PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT Table 1: List of Suitable A' organic cations. A’ Cation List Methylammonium Benzimidazolium 1,6-hexanediammoniumpropylammoniumСyclopropylammonium Cyclohexylammonium bromphenylethylammoni2-bromoethylammonium 4-amidinopyridinium Methylhydrazinium But-3-yn-1-ammonium 5-hydroxypentylammonium 2-ethyl-hexylammonium4- 1,7- 3-aminopropanol 3-(dimethylamino)-1- 1,8-Diamino-3,6- protonated propylammonium dioxaoctane 2-iodoethylammonium 2-(2-thienyl)ethanaminiumOctylammonium1,3-propanediamine 1,4-butyldiamine 4,4'-bipyridinePiperazinium 3- (aminomethyl)piperidinium N-Benzylpiperazinium 3-bromopropylammonium 5-bromoxypentylammonium 1,9-nonanediammonium CyclohexylmethylammoniuPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT 4-hydroxybutylammonium 4-methylbenzylammonium 1,10-decanediammoniumonium 3-iodopropylammonium o-fluorophenylethylammonium aminopropyl)imidazoleN1-methylpropane-1,3- p- Pyrene-O- diammonium fluorophenylethylammonium ethylammonium 1,4-butanediamine 5-iodopentylammonium 4,4′-Ethylenedipyridineonium 2,2′-bithiopheneoniumum minium onium1,2-ethanediammonium 3-(2- 2-methyl-1,5- ammonioethyl)anilinium diaminopentaneProtonated 4-amino-1-PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT p- Cycloheptylammonium 1-methylimidazolium methylphenylethylammo nium 2-(3″′,4′-dimethyl- p- Cyclooctylammonium [2,2′:5′,2″:5″,2″′- - bromphenylethylammonium trimethylammonioethylamm chlorophenylethylammon onium ium Phenylpropylammonium 2,2'-biimidazolium pyridiniumium 2-(2- 2- thienyl)methylaminium naphthyleneethylammonium imidazoliumPerylene-O- ylammonium (dimethylam 2-methyl-1,5- eth ino)propylamm onium pentanediammoniumpyrene- yl)-2,2′-bithiophene niumPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT 5,6 R-1-(4- trimethylsulfonium - dicarboxybenzimidazolium chlorophenyl)ethylammo nium butane-1,4- 2-(4-(3- S-1-(4- diylbis(dimethylsulfonium fluoro)stilbenyl)ethanammon chlorophenyl)ethylammo ) ium niumrac-1-(4- difluoroethylammonium cyclohexenyl)ethylammoniu chlorophenyl)ethylammo m nium

[0041] In one or more embodiments, the layered material comprises alternating layers of a first type and a second type. The first type may comprise the organic cation (A′) and the second type may comprise a hybrid anion having the formula (II) (A)n-1MnX3n+1. Without being bound by any particular theory, it is believed that layers with minimal lattice mismatch will produce higher quality 2D perovskite materials. Lattice mismatch may be calculated by comparing the effective lattice parameters as described below in Table 3. Thus, in one or more embodiments, the layered material has a lattice mismatch between the first type and second type of 10% or less, such as a lattice mismatch ranging from 1 to 10%, or a lattice mismatch of 1% or less.

[0042] In one or more embodiments, the two-dimensional perovskite material has a tetragonal crystal structure with space group symmetry P4 / mmm. The two-dimensional perovskite material may be linear with a space group of p4 / mmm under the tetragonal crystal system. The p4 / mmm space group is regarded as the highest symmetry in theory that a 2D perovskite material can achieve. Without being bound to any particular theory, it is believed that distortion in the perovskite structure will increase the effective mass of the carrier and therefore shorten the diffusion length, impeding the carrier transport performance. In one or more embodiments, the two-dimensional perovskite material has an equatorial M-X-M angle ranging from 160 to 180°, such as from a lower limit of 160°, 165°, 170°, or 175°, to any upper limit of any one of 165°, 170°, 175°, or 180°, where any lower limit may be paired with any suitable upper limit. The equatorialPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT M-X-M angle refers to the angle formed by the M-X-M atoms along the equatorial plane. In one or more embodiments, the two-dimensional perovskite material has an interlayer distance ranging from 3.8 to 7 Å, such as from a lower limit of 3.8 Å, 4 Å, 5 Å, or 6 Å, to any upper limit of any one of 4 Å, 5 Å, 6 Å, or 7 Å, where any lower limit may be paired with any suitable upper limit. The interlayer distance of less than 7 Å may enhance the interlayer transportation along the out-of-plane direction, which is in general a concern for 2D perovskite materials when compared to 3D perovskite materials. In one or more embodiments, the layered material has a band gap of from about 1.6 eV to 2.0 eV, such as from a lower limit of 1.6 eV, 1.7 eV, 1.8 eV, or 1.9 eV, to any upper limit of any one of 1.7 eV, 1.8 eV, 1.9 eV, or 2.0 eV, where any lower limit may be paired with any suitable upper limit.

[0043] In one or more embodiments, the layered material is in the form of a film. The film may be included in a device. In one or more embodiments, a device comprising the film may be an electronic device such as a capacitor or an optoelectronic device based on minority carriers such as (photo) or radiation detectors, photovoltaic devices including solar cells, wide band gap tandem solar cells, perovskite-perovskite, silicon- perovskite, and multijunction solar cells, as well as LEDs, micro lasers, lasing for optoelectronics, FETs, and thin-film transistors.

[0044] According to one or more embodiments of the present invention, a method of making a two-dimensional perovskite material is disclosed. The method is exemplified by FIG.1. FIG. 1 discloses a method 100 comprising forming 102 a first suspension by mixing a divalent metal source and a salt containing a perovskitizer-cation in a halogen acid solution, then stirring 104 the suspension at an elevated temperature of from about 100 °C to 400 °C, followed by adding 106 a solution comprising an organic cation and an acid to the suspension, forming a mixture, cooling 108 the mixture to a temperature of from about 80 °C to 120 °C at a cooling rate of 0.01 to 200 °C / s, to form crystals, and filtering 110 and drying the crystals to obtain a two-dimensional perovskite material. In one or more embodiments, the two-dimensional perovskite material is free of δ-phase formamidinium lead iodide (FAPbI3).

[0045] The disclosed method is suitable for synthesizing a 2D perovskite material having the formula (I) (A′)(A)n−1MnX3n+1, wherein A′ is an organic cation selected from the group consisting of butyl ammonium, 3-(aminomethyl)piperidium (3-AMP), 4-PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT (aminomethyl)piperidium, and combinations thereof, A is a perovskitizer-cation selected from the group consisting of formamidinium (FA), guanidinium, dimethylamine, cesium, and combinations thereof, M is a divalent metal selected from the group consisting of Pb, Ge, Sn, Cu, and combinations thereof, X is a halide selected from the group consisting of I, Br, Cl, F, and combinations thereof, and n is greater than or equal to 2. In one or more embodiments, the two-dimensional perovskite material has the formula (III) (3-AMP)(FA)n-1PbnI3n+1 and n is 2, 3, or 4 and the two-dimensional perovskite material is free of δ-phase formamidinium lead iodide (FAPbI3). The perovskite material is described in detail above.

[0046] As noted above, the method includes, at block 102, forming a first suspension by mixing a divalent metal source and a salt containing a perovskitizer-cation in a halogen acid solution. In one or more embodiments, the first suspension comprises an amount ranging from 0.5 M to 1.5 M of the divalent metal source and an amount ranging from 0.5 M to 1.5 M of the salt containing a perovskitizer-cation, in the halogen acid solution. The halogen acid solution contains an amount ranging from 40 to 75% wt.% of the halogen acid in H2O. In one or more embodiments, the halogen acid is selected from the group consisting of hydroiodic acid, hydrochloric acid, hydrobromic acid, hydrofluoric acid, and combinations thereof.

[0047] In one or more embodiments, the salt containing a perovskitizer-cation is selected from the group consisting of FACl, FABr, FAI, GACl, GABr, GAI, CsBr, CsCl, CsI and combinations thereof in any suitable ratio. Because there is a large excess amount of halide from hydrohalic acid in the solution, the content of halogen in the final perovskite materials product is only determined by the halide in the hydrohalic acid (e.g. HI acid solution will lead to iodine based perovskite materials, HBr acid solution will lead to bromine based perovskite materials, and HI / HBr mixed solution will lead to I / Br perovskite materials).

[0048] In one or more embodiments, the divalent metal source is selected from the group consisting selected from the group consisting of PbI2, PbCl2, PbBr2, PbO, divalent Ge salts, divalent Ge oxides, divalent Sn salts, divalent Sn oxides, and combinations thereof. In one or more embodiments, the first suspension further comprises H3PO2. The H3PO2is present in an amount of 1% to 50%.PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT

[0049] After forming the first suspension, the method 100 includes stirring 104 the suspension at an elevated temperature of from about 100 °C to 400 °C, such as from a lower limit of 100 °C, 110 °C, 120 °C, 130 °C, 140 °C, 150 °C, 160 °C, 170 °C, 180 °C, 190 °C, 200 °C, 210 °C, 220 °C, 230 °C, 240 °C, 250 °C, 300 °C, 350 °C, 380 °C, or 390 °C, to any upper limit of any one of 110 °C, 150 °C, 180 °C, 200 °C, 210 °C, 220 °C, 230 °C, 240 °C, 250 °C, 300 °C, 350 °C, 380 °C, or 390 °C, where any lower limit may be paired with any suitable upper limit. The stirring 104 may be performed over an amount of time ranging from 0.1 to 1000 minutes.

[0050] Then, the method includes adding 106 a solution comprising an organic cation and an acid to the suspension, forming a mixture. The organic cation may be present in amounts ranging from 100 µL to 5000 µL, the acid may be present in amounts ranging from 1 mL to 1000 mL, and the total solution volume may range from 1 mL to 1000 mL.

[0051] In one or more embodiments, the solution comprising an organic cation and an acid, comprises an acid selected from the group consisting of H3PO2, HI, HCl, HBr, HF and combinations thereof. The acid may be any suitable acid that can neutralize the organic cation. The solution comprising an organic cation and an acid is then added to the first suspension.

[0052] The method 100 further includes cooling 108 the mixture to a temperature of from about 80 °C to 120 °C, such as from a lower limit of 80 °C, 90 °C, 100 °C, or 110 °C, to any upper limit of any one of 90 °C, 100 °C, 110 °C, or 120 °C, where any lower limit may be paired with any suitable upper limit, at a cooling rate of from about 0.01 to 200 °C / s, such as from a lower limit of 0.01 °C / s, 0.1 °C / s, 0.5 °C / s, 1 °C / s, 5 °C / s, 10 °C / s, 20 °C / s, 40 °C / s, 60 °C / s, 80 °C / s, 100 °C / s, 150 °C / s, or 180 °C / s, to any upper limit of any one of 0.1 °C / s, 0.5 °C / s, 1 °C / s, 5 °C / s, 10 °C / s, 20 °C / s, 40 °C / s, 60 °C / s, 80 °C / s, 100 °C / s, 120 °C / s, 140 °C / s, 160 °C / s, 180 °C / s, or 200 °C / s, where any lower limit may be paired with any suitable upper limit, to form crystals. The crystals may then be filtered 110 and dried to obtain a two-dimensional perovskite material. The filtering and drying may be conducted by methods known in the art.

[0053] The cooling 108 temperature may be lowered to 100 °C, to increase the yield of the two-dimensional perovskite material. However, the cooling 108 temperature willPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT depend on the desired two-dimensional perovskite material. For example, when the two-dimensional perovskite material has the formula (3-AMP)(FA)n-1PbnI3n+1,more FAPbI3 δ-phase may be in the product as impurity if the cooling 108 temperature is too low. If the temperature is lowered below 100 ˚C, for example room temperature (25 ˚C), the yellow FAPbI3δ-phase will dominate the crystallization. Without being bound by any particular theory, kinetically FA Dion-Jacobson (FA-DJ) 2D is much slower in terms of crystallization compared to the yellow FAPbI3 δ-phase, which is why high temperatures and longer times are utilized to have phase-pure (3-AMP)(FA)n-1PbnI3n+1(FA-DJ 2D hereafter, 3-AMP=3-(aminomethyl)piperidine).

[0054] The previously described 2D FA-based perovskite materials synthesized by this method may be used as a platform to study the interfaces, fundamental physics and carrier transport because of its super linear structure. For example, the super linear structure of the (3-AMP)(FA)n-1PbnI3n+1 series makes it an excellent templating material which other materials may grow on, just like ZrTiO3 as an analogue. ZrTiO3 is one of the most commonly used substrate materials for superconductor thin films (epitaxial growth), but it is rigid and much more expensive than hybrid 2D perovskite materials. The (3-AMP)(FA)n-1PbnI3n+1 series has excellent properties for being a next-generation substrate material with its symmetric structure, and the flexibility as a soft material plus the low cost as a result of the synthesis procedure (scalable, low temperature, solution based, facile, fast).

[0055] Without being bound by any particular theory, higher symmetry in perovskite structures facilitates higher conductivity, because of the increased orbital overlap between metal and the halide. This, plus the outstanding stability and the short interlayer distance, which is good for interlayer transportation, make it a suitable material for photovoltaic solar cells. In addition, it is an ideal material for the wide band gap (WBG) layer in tandem solar cells for its small bandgap (~1.7 eV) compared to other 2D perovskite materials. EXAMPLES

[0056] For the following Examples, the reagents used are as follows, PbO (99.9%), hydroiodic acid (HI, 57 wt % in H2O, distilled, stabilized, 99.95%), hypophosphorous acid solution (H3PO2, 50 wt % in H2O) were purchased from Sigma-Aldrich. 3-PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT (aminomethyl)piperidine (3-AMP, 98%) was purchased from TCI, and formamidinium chloride (FACl) was purchased from Great cell solar. All chemicals were used as received. Since FACl is highly hygroscopic, it was stored and weighed in the glovebox under inert conditions. General Example 1

[0057] FIG.2 shows the general kinetic synthesis (KCS) procedure of the 2D FA-based DJ perovskite material of n=2 to n=4, the (3-AMP)(FA)n-1PbnI3n+1 series. Firstly, lead oxide (PbO) and Formamidinium chloride (FACl) are mixed in a hydroiodic acid (HI) acid solution with stirring at room temperature (25 ˚C), rapidly forming a fresh yellow suspension, which is δ-phase formamidinium lead iodide (FAPbI3). Then the solution is heated to 230̊ C with continuous stirring and the color of the suspension slowly turnsto black, indicating the formation of the α-phase FAPbI3. Next, a solution with 3- (aminomethyl)piperidine (3-AMP) neutralized by acid is added into the hot FAPbI3 suspension, leading to the complete dissolution of black α-phase FAPbI3, and a clear yellow solution is obtained. From this point, the solution is slowly cooled down to 120 ˚C with a cooling speed of 1 ˚C / 4s. After the temperature of the solution reaches 120 ˚C, black plate-like crystals, which is the 2D FA-based DJ perovskite material, will slowly precipitate out in 1 hour. The crystals are then filtered out rapidly without further cooling and dried in vacuum oven at 120 °C overnight. The kinetic control in this case is critical to prevent the formation of the yellow δ-phase formamidinium lead iodide (FAPbI3). In terms of thermodynamics, the yellow δ-phase FAPbI3is highly preferred to form over the 2D FA-based perovskite material at low temperatures (e.g. room temperature). Therefore, if the crystallization process is too rapid by cooling down to room temperature, the major product will be yellow δ-phase FAPbI3 instead of (3-AMP)(FA)n-1PbnI3n+1. For the FA-DJ 2D crystals, the color changes from fresh-red to dark-red and finally black with increasing n.

[0058] By applying kinetic control over the crystallization process, the synthesis of high-n (n>2) 2D FA-based perovskite materials is possible. Overall, the series of exemplary FA-based DJ 2D perovskite materials, is highly compact along out-of-plane direction, with an interlayer distance of 3.96 Å between two perovskite octahedra layers, which is one of the shortest among all 2D perovskite materials. More significantly, the structure of n=2, 3, 4 are all nearly perfectly liner, showing bondPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT angles of 180 degree along both out-of-plane and in-plane direction, which is almost like a 3D perovskite material. As a result, since the linearity has impacts on the bandgap, and more linear the structure is the smaller the bandgap will be, the band gap of this series is super small, ranging from 1.97 eV for n=2 to 1.74 eV for n=4. The (3- AMP)(FA)n-1PbnI3n+1series also showed incredible stability, remaining intact for several months in the ambient air with humidity of Houston (75% daily).

[0059] Generally, for the (3-AMP)(FA)n-1PbnI3n+1 series, synthesis of n=1 to n=3 powders are highly reproducible, but when changing between precursor chemicals (for example, from different batches, or from different vendors), or between seasons (there is large variation of humidity in Houston, where synthesis has been performed), occasionally the method needs to be slightly adjusted to get phase-pure crystals. The adjustment is simply changing the FACl to 3-(aminomethyl)piperidine (3-AMP) (cage cation to spacer cation) ratio. Increasing FACl will lead to higher n materials and lowering the amount of FACl will lead to lower n materials. For example, if a n=2 and n=3 mixture is obtained when targeting n=3, adding more FACl and less 3-AMP will lead to pure n=3. This rule is generally applicable to all the 2D halide perovskite materials synthesis and very useful practically.

[0060] For the synthesis of the powder form n=4, this rule holds true; however, there are thermodynamic factors that must be considered. Specifically, when increasing the ratio of FACl to 3-AMP, the formation of n=4 comes at the expense of the formation of side products, namely, yellow FAPbI3δ-phase, and the amount of FAPbI3δ-phase increases as the FACl:3-AMP ratio is increased. Without being bound by any particular theory, the enthalpy of formation (an indicator of whether a 2D perovskite material is favorable or not) of FAPbI3 δ-phase will be between FA-DJ n=3 and n=4. Therefore, n=4 will be less favorable compared to FAPbI3δ-phase. However, it is possible to synthesize small but pure n=4 single crystals using the modified procedure described below, as it enabled the growth of the unfavorable phase over long time via transformation from lower n to higher n. Example 2: Synthesis of (3-AMP)(FA)n-1PbnI3n+1, n=1 Crystalline Powder

[0061] For n=1, PbO powder (223.2 mg, 1mmol) was dissolved in a mixture of 57% w / w aqueous HI solution (5.0 mL, 39.2 mmol) at room temperature (25 °C) underPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT constant magnetic stirring for 10 mins, which formed a bright yellow solution (PbI2). In a separate beaker, 3-AMP (101.6 μL, 0.85 mmol) was neutralized with H3PO250 wt % in aqueous solution (1.0 mL, 9.1 mmol) in an ice bath resulting in a clear colorless solution. Then the 3-AMP solution was added into the PbI2 solution under heating at 230 °C (hotplate temperature) with constant stirring. The addition initially produced red precipitates, which were slowly dissolved under heating over 5 to 60 minutes. Then the solution was cooled down to room temperature and red needle-like crystals precipitated. The product n=1 sometimes contains both monoclinic phase and tetragonal phase crystals. If the crystal is heated up to 190 °C, it will be locked at tetragonal phase even after being cooled down to room temperature. Example 3: Synthesis of (3-AMP)(FA)n-1PbnI3n+1, n=2 Crystalline Powder

[0062] For n=2, firstly, FACl (483mg, 6 mmol) was added in to a 50 ml glass conical flask sealed with a glass stopper prior to removal from the glovebox. The subsequent steps were conducted on a hot plate with vigorous stirring inside a fume hood: The glass stopper was removed and 57% wt % aqueous HI solution (20.0 mL, 152 mmol) and aqueous H3PO250 wt % (2.0 mL, 18.2 mmol) were quickly added to dissolve the FACl until a clear yellow solution was obtained. PbO powder (2678.4 mg, 12 mmol) was added into the FACl solution to form a yellow suspension at room temperature, then the hotplate was set to 230 °C (500 RPM stirring), until the color of suspension turned black. In a second beaker, 3-AMP (427.4 μL, 3.6 mmol) was neutralized with 50 wt % aqueous H3PO2(3.0 mL, 27.3 mmol) in an ice bath resulting in a clear colorless solution. Then the 3-AMP / H3PO2solution was added into the black suspension in the first flask with vigorous stirring, within 1~2 minutes a clear yellow solution was obtained and it was further stirred for 5 mins. From this point, the temperature of hotplate was turned down to 120 ˚C, with a cooling rate of the hotplate around 1 ˚C / 4s. After the temperature reached 120 ˚C, the solution was left at this temperature for 1 hour, and dark-red plate-like crystals slowly precipitated out. The crystals were then isolated rapidly without further cooling by suction filtration, followed by drying on the filtration funnel for a further 5 min. Finally, the crystals were put in a clean vial and dried in vacuum at 60 °C overnight and characterized with powder X-ray diffraction, shown in FIG.3. Example 4: Synthesis of (3-AMP)(FA)n-1PbnI3n+1, n=3 Crystalline PowderPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT

[0063] For n=3, firstly, FACl (655mg, 8.1 mmol) was added to a 50 ml glass conical flask sealed with a glass stopper prior to removal from the glovebox. The subsequent steps were conducted on a hot plate with vigorous stirring inside a fume hood. The glass stopper was removed, H3PO250 wt % aqueous (2.0 mL, 18.2 mmol) and 57% wt % aqueous HI solution (18.0 mL, 136.8 mmol) were quickly added to dissolve the FACl until a clear yellow solution was obtained. PbO powder (2566.8 mg, 11.5 mmol) was added into the FACl solution to form a yellow suspension at room temperature, then the hotplate was set to 230 °C (500 RPM stirring), until the color of suspension turned black. In a second beaker, 3-AMP (150 μL, 1.3 mmol) was neutralized with 50 wt % aqueous H3PO2 (4.0 mL, 36.4 mmol) in an ice bath resulting in a clear colorless solution. Then the 3-AMP / H3PO2 solution was added into the black suspension in the first flask with vigorous stirring, within 1~2 minutes a clear yellow solution was obtained and then further stirred for 5 mins. From this point, the temperature of hotplate was turned down to 120 ˚C, with a cooling rate of the hotplate around 1 ˚C / 4s. After the temperature reached 120 ˚C, the solution was left at this temperature for 1 hour, and black plate-like crystal slowly precipitated out. The crystals were then isolated rapidly without further cooling by suction filtration, followed by drying on the filtration funnel for a further 5 min. Finally, the crystals were put in a clean vial and dried in vacuum at 60 °C overnight and characterized with powder X-ray diffraction, shown in FIG.4.

[0064] To avoid the corrosion of the vacuum oven, which is mostly made of steel, the crystals can be washed using heptane to get rid of the residual HI before drying in the oven. Example 5: Synthesis of (3-AMP)(FA)n-1PbnI3n+1, n=4 Single Crystal

[0065] Synthesis of the n=1, n=2 and n=3 powders are highly reproducible and scalable. For powder synthesis of n=4, it is difficult to obtain pure product as the yellow, δ-phase FAPbI3 always forms together as the impurity. Pure n=4 was obtained using a modified KCS method, described below.

[0066] First, a solution of n=3 was prepared using the stoichiometry introduced above. After the addition of the 3-AMP / H3PO2 solution to the black suspension in the first flask, a yellow solution was obtained. From this point, instead of cooling the solution down, 1 ml of boiling yellow solution was taken out and added in to a 500 μL HIPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT solution (57% wt % aqueous) in a separate vial to be added to a substrate. Yellow needle-like crystals, NH4PbI3·2H2O, could be observed occasionally as impurity if the reaction period is too long, for example more than 244 hours, due to the partial decomposition of formamidine to ammonia in acidic media.

[0067] Glass was used as the substrate for the 2D perovskite material growth. Glass substrates were cut into 1-inch* 1-inch squares, cleaned in soap water, acetone, isopropanol by ultrasonication for 20 min each; then dried by argon. The substrates were transferred into a UV-Ozone cleaner and cleaned for 10 mins. The substrates were put on a hot plate, 12.5 μL of the parent solution was dropped onto the glass surface, another glass slide was put on top to fully cover the bottom glass and annealed at 80 °C for 7 hours. Then the top glass is removed, the crystal with the bottom glass is placed on spin coater, heptane as the washing solvent was dropped (80 μl) instantly on the crystal while spin coated at 3000 r.p.m for 30 seconds to remove all the residue parent acid solution. The crystal was characterized with powder X-ray diffraction, shown in FIG.5 Example 6: Synthesis of (3-AMP)(FA)n-1PbnI3n+1, n=1-3 Single Crystal

[0068] This method for synthesis of large thin crystals is applicable to n=1 to n=3. Each n value uses the solution with the corresponding stoichiometry described above. Specifically, for a n=1 large thin crystal, a solution of n=1 was prepared using the stoichiometry introduced above, and then annealed at 70 °C for 5 hours; for a n=2 crystal, a solution of n=2 was prepared using the stoichiometry introduced above, and then annealed at 70 °C for 4 hours; and for a n=3 crystal, a solution of n=3 was prepared using the stoichiometry introduced above, and then annealed at 70 °C for 4 hours. Construction of a Schematic Phase Diagram for General Example 1

[0069] As discussed above, the method of synthesizing FA-DJ crystals is unusual compared to previous approaches of growing 2D perovskites crystals. Specifically, the FA-DJ 2D crystals must be extracted from solution at elevated temperatures, greater than 80 °C, since at lower temperatures the δ-phase FAPbI3will precipitate alongside FA-DJ. This phenomenon can be understood by means of a schematic (non- quantitative) binary phase diagram, as shown in FIG. 6. The two sides of the phase diagram, (3-AMP)PbI4and FAPbI3, represent the two extreme stoichiometries of thePATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT FA-DJ series when in an HI solution. Intermediate stoichiometries can be written as [(3-AMP)PbI4]1-x[FAPbI3]xwith 0<x<1, or equivalently as [(3-AMP)PbI4][FAPbI3]n-1with n being the n-value. FIG. 6 shows the schematic phase diagram generated by tracking which phases intersect with the convex hull of the Gibbs free energy landscape as the temperature rises and the free energy of the solution phase decreases. The method to construct the phase diagram are expanded upon below. For example, for FA-DJ n=3, moving along the dashed line from the high-temperature liquid phase to the FA-DJ n=3 phase, the temperature must be reduced. However, if the temperature decreases too much, the solution moves into a two-phase region of both FA-DJ n=3 and δ-FAPbI3. FIG. 3 also captures why growing phase-pure FA-DJ n=4 from solution is difficult, since the n=4 region is quite narrow and emerges at higher temperatures in comparison to n=3.

[0070] The schematic phase diagram shown in FIG. 6 was created from a simple model of the Gibbs free energy of the various phases present in the perovskite material solution (DJ n=1-4, δ-FAPbI3, α-FAPbI3, and a solvated phase). Free energies were plotted together on a HI-DJ n1-FAPbI3 ternary plot, and the corresponding ternary phase diagram was obtained from the convex hull of this free energy landscape. Crystalline phases were given Kronecker delta – like free energy functions positioned at their crystal stoichiometry, with the height of the delta tuned to reproduce the observed order of crystal growth from solution (|G(DJ n2)| > |G(n3)| > |G(n4)| > |G(n1)| > |G(α-FAPbI3)|). The free energy of these phases was taken to be temperature- invariant, while |G(δ -FAPbI3)| was made to decrease from |G(DJ n2)| to 0 with temperature. The free energy of the solution phase was taken to be a convex function with a maximum near the center of the ternary plot and zeros at the corners and along the DJ – FAPbI3edge. The magnitude of the solution-phase free energy was increased with temperature.

[0071] The ternary phase diagram constructed from the free energy of these phases was made to evolve with temperature, not shown. A specific concentration of crystals in solution was chosen and the intersection of each region of the phase diagram was tracked as temperature was increased, not shown. In this way the binary phase diagram representing FA-DJ at a specific concentration in HI solution was constructed. Structural Analysis of Examples 2-5PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT Crystal Structures of Examples 2-5

[0072] FIG.7 shows the crystal structure of the (3-AMP)(FA)n-1PbnI3n+1series (FA-DJ with n=1 to n=4), their detailed crystal data and structure refinement are listed below in Table 2. This homologous series is synthesized as described above and structurally built from inserting 3-AMP (3-(aminomethyl)piperidine) between layers of perovskites octahedra as the spacer, where the perovskite layer consists of formamidinium (FA) occupying the cage. All the analogs in this FA-DJ series have a highly ordered perovskite layer, specifically n=2 to n=4, which take P4 / mmm as the space group. This is the highest symmetry a 2D perovskite material system can theoretically have. The symmetry analysis was conducted using a known method from the literature. on a perfectly ordered 2D free-standing octahedra slab (considering only one horizontal plane and neglecting plane stacking along vertical direction) described by the P4 / mmm layer group. In literature, the all-inorganic Cs2PbI2Cl2, n=1 is the experimental 2D lead- halide perovskite structure exhibiting the highest symmetry. It belongs to the I4 / mmm tetragonal centered space group, corresponds to a Ruddlesden-Popper ordering, with a (1 / 2,1 / 2) in-plane shift between successive layers along the stacking axis. The FA-DJ series disclosed herein is the first multiple-layer 2D perovskite material series that takes the highest P4 / mmm symmetry. For n=1 crystals, two different polymorphs were found, a monoclinic phase exhibiting well defined motifs for the organic cations in the interlayer, and another tetragonal phase, which shows similar space group symmetry and cation disorder as the n=2 to n=4 structures. When a crystal initially in the monoclinic n=1 phase is heated up to 190 °C, it transforms into the tetragonal phase through a first order phase transition and stabilized in this high symmetry, even when cooled down later. Table 2: Crystal Data and Structure Refinement for (3-AMP)(FA)n-1PbnI3n+1, n=1, 2, 3, & 4. Compound (3-AMP)PbI4(3- (3- (3- AMP)(FA)Pb2I7AMP)(FA)2Pb3I10AMP)(FA)3Pb4I13Empirical C6 H16 I4 N2 C7 H16 I7 N4 formula Pb Pb2 C8 H16 I10 N6 Pb3 C9 H16 I13 N8 Pb4 Formula weight 831.00 1458.92 2086.84 2714.76PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT Temperature 285(14) K 293 K 293 K 293 K Wavelength 0.71073 Å 0.56083 Å 0.56083 Å 0.56083 Å Crystal system Tetragonal Tetragonal Tetragonal Tetragonal Space group P4 / mbm P4 / mmm P4 / mmm P4 / mmm a = 8.8950(2) a = 6.3465(9) Å, a = 6.3477(9) Å, α = a = 6.3505(9) Å, α = Å, α = 90° α = 90° 90° 90° Unit cell b = 8.8950(2) b = 6.3465(9) Å, b = 6.3477(9) Å, β = b = 6.3505(9) Å, β = dimensions Å, β = 90° β = 90° 90° 90° c = 10.4829(4) c = 16.722(3) Å, c = 23.054(5) Å, γ = c = 29.454(6) Å, γ = Å, γ = 90° γ = 90° 90° 90° Volume 829.42(5) Å3673.5(2) Å3928.9(3) Å31187.9(4) Å3Z 2 1 1 1 Density 3.327 g / cm33.597 g / cm33.730 g / cm333(calculated) .795 g / cm Absorption 17.588 mm-1 -1 -1 -1coefficient 10.946 mm 11.686 mm 12.070 mm F(000) 720 621 882 1143 θ range for data 3.239 to 2 1.922 to 24.992° 2.091 to 24.987° 2.182 to 19.981° collection 9.988° -12<=h<=12, - -9<=h<=9, - -9<=h<=9, - -7<=h<=7, - Index ranges 12<=k<=10, - 9<=k<=9, - 9<=k<=9, - 7<=k<=7, - 14<=l<=14 25<=l<=24 34<=l<=34 35<=l<=35 Reflections collected 14588 15960 29086 9528 Independent 694 [Rint = 796 [Rint = reflections 0.0232] 0.0677] 1086 [Rint = 0.0406] 773 [Rint = 0.1328] Completeness to θ = 99.8% 99.8% 98.6% 99.3% 25.242° Refinement Full-matrix least-squares Full-matrix least- Full-matrix least- Full-matrix least- method on squares on F2sq2 2F2uares on F squares on F Data / restraints / 694 / 65 / 82 796 / 65 / 91 1086 / 71 / 100 773 / 26 / 63 parameters Goodness-of- fit 1.056 0.829 1.068 0.984 Final R indices Robs = 0.0276, Robs = 0.0290, Robs = 0.0285, Robs = 0.0637, [I > 2σ(I)] wRobs = 0.0709 wRobs = 0.0641 wRobs = 0.0799 wRobs = 0.1496 R indices Rall= 0.0348, Rall= 0.0672, Rall= 0.0434, Rall= 0.1395, [all data] wRall = 0.0758 wRall = 0.0684 wRall = 0.0837 wRall = 0.1964PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT Largest diff. 1.587 and - 0.903 and - 1.238 and -1.954 6.944 and -2.056 peak and hole 1.861 e·Å-31.627 e·Å-3e·Å-3e·Å-3

[0073] The in-plane lattice parameter of the FA-DJ series and the one of α-FAPbI3 were plotted for comparison, not shown. After the introduction of FA into the structure, a dramatic increase of the in-plane lattice parameter from n=1 to n=2 is observed, 6.29 Å to 6.35 Å respectively, and then progressively approaching the parameter of 3D α- FAPbI3, 6.36 Å, when n further increases. Here, to compare the lattice parameters between structures exhibiting different symmetries, an “effective in-plane lattice parameter” is considered, see Table 3 below, which is essentially the width of a PbI6octahedron. On the other hand, the in-plane lattice parameter of the monoclinic n=1 structure, 6.32 Å, is larger than for the tetragonal n=1, 6.29 Å, because the conformation of the interlayer cation breaks the local symmetry. The 1D X-ray diffraction patterns on crystals of the FA-DJ series are shown in FIG. 8, where the low angle peaks are apparent and well-defined for n=1 to n=4. For n=4, the intensity of low angle peaks is weak and could be better observed with log-scaled intensity, not shown. Table 3. Effective lattice parameter, where a is the real lattice parameter and L corresponds to the effective parameter, which is essentially the distance between two in-plane neighboring Pb atoms. 3D α-phase FAPbI3, cubic Pm-3m a=L FA-DJ n=2 to n=4, tetragonal, P4 / mmm a=L a DJ n=1, tetragonal, P4 / mbm= L√2DJ n=1, monoclinic, P21 / c √^^ / 2 = ^

[0074] The interlayer distance of the FA-DJ 2D series is one of the shortest compared to reported 2D perovskite materials. FIG.9 shows the interlayer distances of the FA- DJ 2D series compared to a MA-DJ series and a MA-RP series, where MA is methylammonium. For MA-based 2D perovskite materials, the DJ type (e.g. MA 3- AMP 2D) is generally much shorter than the Ruddlesden Popper (RP) type (e.g. MAPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT butylammonium (BA) 2D) because there is one layer of divalent spacer cation in DJ versus two layers of monovalent spacer in RP. For RP 2D, the interlayer distance is the distance between two planes across apical iodides. For DJ 2D, the interlayer distance is essentially the distance between two apical iodides since the perovskite layers stack exactly on top of each other. While the interlayer distance of MA-DJ is already one of the shortest (~4.0 Å for n=4), for FA-DJ it is even shorter (3.96 Å for n=4).

[0075] To get a better understanding about the microscopic origin of observed dynamical disorder in the crystal structures of the FA-DJ 2D series, the anisotropic thermal displacement parameters extracted from the X-ray diffraction analysis of the FA-DJ structures was analyzed. X-ray diffraction is very sensitive to contributions from the Pb and I atoms, and I atoms are the most affected by octahedra rotations. For FA-DJ n=1, the apical iodine has an in-plane displacement parameter different from the ones in other FA-DJ compounds and α-FAPbI3. Internal iodines behave similarly in n>1 FA-DJ compounds and α -FAPbI3. The main difference comes from apical iodine atoms which exhibit a very large thermal disorder. These atoms are in direct contact with 3-AMP interlayer cations, which are disordered in these structures.

[0076] From X-ray diffraction procession images, not shown, systematic superlattice reflections are observed at 100K along the (h k 0) plane as compared to the room temperature P4 / mmm structure, which necessitates an expansion of the unit cell by a factor of √2 in both the a and b directions. This new unit cell meets all the systematic absence conditions for the P4 / mbm space group. Upon cooling down to 100K, the Pb- I-Pb bond angle is bent from 180˚ to 166º in the P4 / mbm structure, with all the distortion occurring in the plane of the PbI4 layers. Analogous transitions were observed for n = 3 and 4 compounds where the equatorial Pb-I-Pb angles transition from 180º to 164.21(5)º and 162.58(7)º, respectively, see Table 2 above. Differential Scanning Calorimetry

[0077] Antiferrodistorsive phase transitions from the high temperature maximally symmetrized cubic phase are commonly observed in 3D halide perovskite materials. Similar phase transitions for the 2D FA-DJ perovskite materials were evidenced by using Differential scanning calorimetry (DSC), not shown. Both n=2 and n=3 exhibit a symmetry reduction from α-tetragonal P4 / mmm to β-tetragonal P4 / mbm at 0 °C (273PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT K), corresponding to a second order phase transition. Similar phase transitions at low temperature was also observed in 3D FAPbI3(and CsPbI3), which exhibited a second order, cubic-to-tetragonal (α-to-β) phase transition at 280 K. It should be noted indeed that a classical symmetry analysis combined with Landau theory of phase transition predicted a continuous transition (second-order or weakly first order phase transition) for both Pm-3m to P4 / mbm (FAPbI3) and P4 / mmm to P4 / mbm (FA-DJ series). Optical Properties of Examples 2-5

[0078] Correlations between the maximal symmetry observed for the 2D tetragonal FA-DJ structures and their optical properties were investigated. As shown in FIG.10, the comparative 2D perovskite material structures, (BA)2(MA)2Pb3I10 and (3- AMP)(MA)2Pb3I10, exhibit either in-plane distortion or out-of-plane distortion, or both. However, the FA-DJ series shows a perfect linear structure with no distortion along both in-plane and out-of-plane directions. FIG.11 shows the average equatorial Pb-I- Pb angle of the 3 types of 2D perovskite materials in FIG.10 and α-phase FAPbI3. The average equatorial Pb-I-Pb angles of both MA-BA and MA-DJ series are smaller than the average Pb-I-Pb angle in 3D FAPbI3 (180°). After an initial steep variation from n=1 to n=2, they slowly change as a function of n toward values observed for the 3D reference MAPbI3, as the effect of organic cation on the inorganic slabs progressively weaken. However, the FA-DJ series shows for all the compounds with n>1 (n=2,3,4), equatorial Pb-I-Pb angles of 180˚, equivalent to the average Pb-I-Pb angle in the α- phase FAPbI3. This indicates that the Pb-I-Pb bond is fully stretched thanks to the introduction of FA into the cage, and the stress induced by the 3-AMP organic spacer cation is negligible by comparison to the negative pressure on the perovskite backbone imposed by FA. Optical Band Gaps

[0079] The almost perfect ordering of the perovskite backbone plays a crucial role in determining the electronic properties. It is known for layered perovskite materials that, as Pb−I−Pb bond angles increased to 180˚, overlapping between Pb s and I p orbitals increases, pushing up the valence band maximum and finally reducing the electronic bandgap. FIG.12 shows that, when compared to MA-RP and MA-DJ, the FA-DJ series shows indeed a systematic narrower band gap for a given n value, bringing the excitonPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT peak of FA-DJ n=4 close to the exciton of n=5 of the MA analogs. From the steady- state photoluminescence maximum shown in FIG.13, the optical band gaps of FA-DJ compounds may be extracted, as shown in FIG.14. The optical bandgap of 1.76 eV for n=4 is the smallest reported so far among all known pure 2D perovskite materials. The absorption spectra of the series, FIG.12, show the identical trend as the PL (2.22 eV for n=1, 2.02 eV for n=2, 1.87 eV for n=3, 1.78 eV for n=4). In FIG.14, the calculated electronic band gaps for the FA-DJ series are also shown. The calculations from first principles, clearly confirm the effect of quantum confinement for this family of layered materials. The DSH hybrid functional was used, described below, as it is known to give excellent agreement with experimental band-gaps of halide perovskite materials. Furthermore, the calculations capture the changes of both the bandgap and the dielectric constant when going from n=1 to n=4, see Table 4 below. As shown in FIG. 14, the calculations underestimate the band-gaps, partly due to not including self-energy corrections related to the anharmonic lattice dynamics. The order of magnitude of the effect on FAPbI3is estimated by calculating a band gap increase of 240 meV. Table 4. Optical dielectric constant (ε∞) calculated within DFPT, and electronic band gaps (Eg) using the DSH hybrid functional, for the FA-DJ series and for FAPbI3, with (1.31) and without (1.07) the correction due to polymorphism. ε∞ (PBE) Eg (DSH) n=1 5.18 1.93 n=2 5.76 1.69 n=3 6.04 1.50 n=4 6.20 1.42 FAPbI36.97 1.07 poly-FAPbI3 6.87 1.31 Lattice DynamicsPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT

[0080] Raman scattering experiments provide a first indication about the nature of lattice dynamics of the new FA-DJ series, as shown in FIG.15. The room temperature lattice dynamics of the FA-DJ compounds for n>2 exhibit mainly relaxation-like quasi- elastic signatures in the 0-100 cm-1range, which is commonly observed in 3D perovskite materials, including 3D α-FAPbI3. By comparison, the Raman scattering signature of the n=1 DJ compound, which does not contain any FA cations, exhibits several low-frequency peaks in the 0-60 cm-1range. The only clear Raman scattering resonance still observed for the n>1 compound is located at about 120cm-1(~15 meV), which is consistent with the same observation in 3D α-FAPbI3and with the effective optical phonon frequency determined from the PL broadening variation as a function of temperature, not shown. Photoluminescence

[0081] The exciton photoluminescence (PL) of FA-DJ 2D n=2 and n=3, not shown, exhibit a gradual energy evolution from 6K to 300K, consistent with a continuous phase transition from a low-temperature β-tetragonal to high temperature α-tetragonal phase in the FA-DJ series. At very low temperatures (6 - 100K), the PL demonstrates a further subtle blue shift in both n=2 and n=3 perovskite materials, which also agrees with experimental results for known FAPbI3films in the same temperature range where the orthorhombic γ phase is expected to be stable. No sub-bandgap spectroscopic signatures are detected in the PL or reflectance spectra, not shown, indicating ultralow densities of deep traps and excitonic transitions in FA-DJ perovskite materials. The exciton PL at 10K demonstrates an asymmetric line shape contributed by two emission peaks, which are assigned to free exciton and bound exciton states that shall be associated with shallow defects, respectively. The temperature-dependent energy splitting between the two peaks further confirms the assignment of bound exciton states instead of phonon replica. In FIG.16, the extracted PL linewidths of n=2, n=3, and 3D FAPbI3 as a function of temperature, are compared, see Table 5 below. Both FA-DJs show ~3 times increase of FWHM from 6K to 300K (30meV to ~80 meV), with similar trends of thermal broadening as 3D FAPbI3 thin films. Quantitative analysis of temperature-dependent linewidth was performed assuming an effective electron- phonon coupling mechanism for optical phonons. The detailed methods and fitting parameters are discussed below. The extracted effective longitudinal optical (LO)PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT phonon energy is ~10meV for n=2 and ~20meV for n=3, consistent with electron- phonon coupling mechanisms in the multi-layered 2D DJ perovskite materials similar to the ones in 3D FAPbI3. Table 5. The extracted values for inhomogeneous exciton linewidth (Γ0), strength of LO phonon coupling (ΓLO), and LO phonon energy (ELO) are listed for FA-DJ n=2 and n=3 perovskite materials, along with those reported for 3D FAPbI3 films and nanocrystals. Sample Γ0 (meV) ΓLO (meV) ELO (meV) n=2 29.6 ± 0.5 20 ± 4 8.5 ± 1.2 n=3 24.5 ± 1.6 56 ± 22 18.2 ± 4.9 FAPbI3 19 ± 1 40 ± 5 11.5 ± 1.2 FAPbI3(NC) 1.5 27 10.7

[0082] Steady state PL diffusion measurements allow extracting exciton diffusion length and diffusivity in 2D materials, by combining PL profiles around the excitation spot and time resolved PL (TRPL) measurements on the same samples. In steady state conditions, the solution of the diffusion equation for the radial distribution of the exciton concentration ^(^) corresponds to the convolution between the laser’s Gaussian profile and the modified Bessel function of the second kindwhere ^#is the exciton diffusion length and ^ is the radius of the laser spot. At some distance away from the laser spot ^ ≫ ^#, themodified Bessel function can be approximated byand convolution by the delta-like Gaussian spot leads to ^(^) ∝The value of 1.8μm (0.83μm) was estimated from an asymptotic fit at low excitation power respectively for the n=3 (n=2). The exciton diffusivity +,can then be extracted by combining the exciton diffusion length ^#with the exciton lifetime -,deduced fromPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT TRPL measurements: ^# = .2+,-,. The TRPL signal in the case of the n=3 crystalis better described by a sum of multiexponential components. As the exciton diffusion length is estimated at low excitation power and far away from the laser spot, the relevant exciton lifetime -,to estimate the related exciton diffusivity is the long-time TRPL component -,~3.68ns. A high value of the exciton diffusivity is deduced from the present analysis for the n=3 FA-DJ compound: +,~4.412^3^(. For the n=2 compound, assuming a similar exciton lifetime, a significantly smaller value of the diffusivity is anticipated +,~0.9512^3^(.

[0083] Real-space PL measurements were utilized to study in-plane exciton diffusion lengths of FA-DJ n=3. The real-space landscape shows a PL gradient where the maximum intensity is formed at the excitation position and spreads radially with decreasing intensity, not shown. Radiative recombination from free carriers was spectrally filtered, thus the PL intensity maps show the in-plane transport of excitons near the band edge (1.82 eV) of FA-DJ n=3. The radial symmetry of the diffusion indicates surface homogeneity and unconfined exciton migration within the plane. Significant line shape changes for power dependent profiles of the n=3 exciton diffusion were not observed. To quantify the diffusion length of the FA-DJ perovskite materials, the PL intensity was radially averaged about the excitation center, normalized, then bound by a fitting function for several powers, discussed below. The fit is given by the asymptotic function,.^⁄ ^# , where r is the displacementfrom the center of excitation and the diffusion length, ^#, is the fit parameter. The calculated lower and upper limits for the n=3 diffusion lengths were 1.8 µm and 2.5 µm respectively, longest so far compared to previous reports. Fluence independence of the exciton diffusion for powers ≤1483 µW were observed. At higher laser powers (≥ 2500 µW) exciton-exciton annihilation occurs near r=0 and artificially increases the exciton diffusion. FA-DJ n=2 demonstrated smaller diffusion lengths of 0.83 – 1.5 µm, an expected behavior due to n-dependence typically observed in 2D perovskite materials. Sizeable exciton diffusion lengths are necessary in order to ensure a proper exciton dissociation at the perovskite layer edges in solar cells containing thick and vertically oriented 2D layers.PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT

[0084] The temperature-dependent PL of FA-DJ n=2 and n=3 samples were analyzed by fitting the PL spectra shape with Voigt profiles and extracting their FWHMs as a function of temperature Γ(T). The extracted linewidths are plotted in FIG.16. Based on the gradient of the PL linewidths near T = 0K, the acoustic phonon contribution to the exciton linewidth broadening is minimal (γ9: < 70 μeV / K for n=2, and γ9: <10 μeV / K for n=3, extracted by taking the gradient ^Γ / ^C at T = 0K). Therefore, the exciton-acoustic phonon coupling term (behaves linearly with temperature) is neglected, and the fit of the temperature-dependent PL broadening only considers the inhomogeneous broadening and exciton-longitudinal optical (LO) phonon coupling, which is given by Eqn.1, below. Γ(T) = Γ (^ + ΓFG HIJK / LMN^( Eqn. 1

[0085] Here, Γ^represents the zero-temperature linewidth originating from exciton inhomogeneous broadening, Γ^Orepresents the strength of exciton-LO phonon coupling, and ELO is the corresponding LO phonon energy. The fitted parameters are shown in Table 3, above. The extracted LO phonon energies are for ~8meV n=2 and ~18meV for n=3. This suggests that the strength of the electron-phonon coupling in FA-DJ n=2 and n=3 is not significantly different than the 3D FAPbI3 phase. Nuclear Magnetic Resonance Spectroscopy of Examples 2-5

[0086] To probe the local chemical environments, the disorder and dynamic behaviors of the FA and the 3-AMP cations in the FA-DJ series, Solid-state Magic-Angle Spinning Nuclear Magnetic Resonance (MAS NMR) spectroscopy was used. This technique uses different spin-diffusion mixing times, which allow one to probe immediate H-H proximities at sub-nanometer to middle-range proximities of over a nanometer. The on and off-diagonal 2D peaks in such spectra are due to the chemical shifts and through-space proximities, respectively. Intensities of these latter peaks can be adjusted using spin-diffusion mixing time, which allows the spin magnetization to be transferred between the neighboring proton sites in FA and 3-AMP cations.

[0087] FIG. 17 shows thespectra of 3D α-FAPbI3and FA-DJ, i.e., (3- AMP)PbI4 (n=1), (3-AMP)(FA)Pb2I7 (n=2), and (3-AMP)(FA)2Pb3I10 (n=3) phases. For 3-AMP cations in n=1, the broad distribution of1H peaks in the 1-5 ppm range arePATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT due to the -NCH2-, -CH2- and CH moieties of the cyclic piperidinium groups (circles), and the -NH2+and NH groups produce peaks at 7.1 and 7.4 (triangles) ppm, respectively. In the case of the n=2 and n=3 compounds, additional peaks at 7.4 and 8.1 ppm can be related to the FA cation by comparison to the spectrum for pure 3D α- FAPbI3. A partial overlap of the signatures of NH2groups associated with both FA and 3-AMP cations are observed in the [6 – 9] ppm chemical shift range for n=2 and n=3. The FA-DJ n=2 and n=3 phases exhibit in addition relative displacements, Δδ (NH2+) = 0.2 ppm (vertical dashed line) for the NH2groups of the 3-AMP cations. The peaks corresponding to the1H of the NH2(squares) sites of FA and the1H of the NH / NH2(triangles) sites of 3-AMP are better resolved for n=2 than they are for n=3. This fact together with the observed relative displacements (Δδ (NH2+)), suggests a difference in the local chemical environment for the cations in n=2 and n=3 phases. The relative displacement of the NH2+peak (triangle) between the 3-AMP n=1 and the n=2 and n=3 FA-DJ phases clearly indicate a significant difference in the local chemical environment upon the addition of FA cations into the A-sites for n=2 and n=3.

[0088] To gain further insight into the local packing interactions and the connection between the FA cations located in the perovskite backbone and the 3-AMP cations in the interlayer, 2Dspin diffusion experiments were carried out on FA-DJ n=1, n=2, and n=3, not shown. A short mixing time of 50 ms allows the magnetization exchange between all1H sites in 3-AMP cations in (n=1) phase, and a similar trend was observed for the FA-DJ n=2 and FA-DJ n=3 phases, whereby the peaks corresponding to intra- and intermolecular interactions of the A-site cations and the spacer cations between themselves are detected. The intermolecular interactions between FA(CH) are especially prominent, indicating very close proximity between the CH sites of the A- site cations. The n=3 phase, in contrast to the n=2 phase, exhibits off-diagonal peaks corresponding to interactions between FA and 3-AMP. By increasing the diffusion mixing time to 500 ms, the diffusion length of the magnetization is increased within the phases which allows for the detection of H-H proximities at much longer distances. For 2D FA-DJ (n=2) and FA-DJ (n=3), the off-diagonal peaks between the1H sites in FA+and the 3-AMP+cations corroborate the dynamical interactions between the A-site cations and spacer cations in 2D layered structures. From the XRD displacement parameters, it is known that the apical iodines located at the edges and in direct contactPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT with FA and 3-AMP cations exhibit a higher degree of disorder than the iodines located in the inner layers of the perovskite backbone. Analysis of Polymorphous Cubic FAPbI3 Compared to Example 3

[0089] The pair distribution functions (PDFs) were calculated for polymorphous cubic FAPbI3and tetragonal FA-DJ n=2. Atomic contributions from the FA or spacer molecules were excluded from the calculations. Compared to the idealized PDFs obtained from the average atomic positions related to the high-symmetry cubic Pm3m or tetragonal P4 / mmm crystallographic structures, the peaks of the PDFs of the polymorphous structures are shifted and broadened, FIG. 18a and FIG. 18b. These effects arise from a distribution of locally disordered unit cells within the polymorphous networks. This approach allows accounting for the random distribution of atomic positions related to slow relaxational motions (Raman scattering, FIG. 15) by adding thermal disorder due to lattice vibrations (anharmonic phonons) at 300 K, the PDFs are further broadened, yielding a better comparison with measured PDFs, FIG. 18c and FIG.18d.

[0090] The phonon spectral functions in the frequency range 0 – 10 meV were calculated for polymorphous cubic FAPbI3 and FA-DJ n=2, not shown. In this range, the spectrum is dominated by vibrations of the inorganic network. Polymorphism in both cases induce coupled optical vibrations, reducing the phonon correlation length and lifetimes. The enhanced broadening observed for FA-DJ n=2 was related to quantum confinement and the disconnection of the perovskite backbone along the stacking axis, leading essentially to weaker elastic constants and surface-like optical modes. Nonetheless, the phonon spectral function calculated for FA-DJ n=2 exhibits similar phonon frequencies and quasiparticle peak positions to those calculated for FAPbI3. It is expected that these features will converge in the bulk limit.

[0091] The valence band maximum (VBM) and conduction band minimum (CBM) density of states (DOS) of polymorphous FA-DJ n=2 and FAPbI3 were calculated for 300 K, not shown. Both the VBM and CBM of FA-DJ n=2 exhibit a similar band broadening than the corresponding single electronic states of FAPbI3. The PL linewidth (FIG.16) is not directly related to the smearing of the electronic density of states but to the effect of the imaginary part of the electron-phonon self-energy on resonant excitonicPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT states. From the real part of the electron-phonon self-energy, the calculations for the phonon-induced band gap renormalization [Δεg (T)] demonstrate a stronger electron- phonon coupling effect in FAPbI3. In particular, the calculations yield a band gap opening of Δεg (300 K) = 120 meV for FAPbI3, while Δεg (300 K) = 33 meV for FA- DJ n=2, i.e.4 times smaller. Physical Properties of Comparative 2D Perovskite Materials Compared to Examples 3 & 4

[0092] In order to perform a physical comparison with previous studies on 2D multilayered RP perovskite materials, with PEA and BA cations in the interlayer ((BA)2(MA)n-1PbnI3n+1 and (PEA)2(MA)n-1PbnI3n+1, with n=1-3, shown in FIG. 19 and FIG. 20, the diffusivity for FA-DJ n=2 and n=3 was estimated. PEA refers to phenethylammonium and mF-PEA refers to 3-fluorophenethylammonium. The estimated diffusivity for FA-DJ n=3 (+,~4.412^3^() is the largest obtained so far for 2D perovskite materials, sizeably larger than the previous record value reported for (mF-PEA)2PbI4(+,~1.912^3^(). A reliable theoretical framework and microscopic interpretation of the intrinsic exciton diffusivity in 2D multilayered perovskite materials does not exist yet. It has thus been proposed to correlate the observed exciton diffusivity to various experimental results, related to structural distortions including in- plane and out of plane perovskite octahedra tilt angles, exciton–phonon coupling strength estimated from temperature dependent PL broadening and average atomic displacements. Small values for the last two parameters were interpreted as signatures of a reduced exciton-phonon coupling strength and a large lattice stiffness due to the presence of a rigid cation. This was the main explanation given for the sizeably larger exciton diffusivities in PEA-RP n=1 2D perovskite materials by comparison to (BA)2PbI4. Following this proposition, large values of the PL broadening and atomic displacement parameters in the present work may indicate that the exciton coupling strengths are much larger for FA-DJ perovskite materials (ΓLO =50meV for FA-DJ n=3, compared to 14.96 meV for PEA-RP n=3 and 22.25 meV for BA-RP n=3). However, as shown by the simulations, polymorphism is important in FA-DJ perovskite materials. This effect is known to lead to a smearing of both vibrational and electronic dispersion. Therefore, PL broadening and atomic displacement parameters are not expected to bePATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT solely related to the exciton coupling strength but are additionally increased by polymorphism.

[0093] Moreover, it was observed in PEA and BA-RP perovskite materials that the replacement of MA cations by FA cations leads to an increase of exciton diffusivities, attributed to the increased lattice stiffness of the structures containing FA. The beneficial effect of FA cations is partially explaining the large exciton diffusivities observed herein. Next, it is also necessary to consider the effect of the increase as well of quantum well thickness (n). BA-based 2D perovskite materials undergo a clear increase of exciton diffusivities from n=1 to n=3, which correlates to the reduction of the octahedra tilt angles, when the system comes closer to the reference 3D perovskite materials. By comparison, the PEA-RP perovskite materials exhibit the opposite trend, with larger octahedra tilt angles for the n=3 compound than for the BA-based one. This second aspect is also important for the n=3 FA-DJ compound, which exhibits both a large exciton diffusivity and vanishing octahedra tilt angles. Analytical Methods for Examples 1-6

[0094] 1D X-ray diffraction measurements: The measurements were conducted using a Rigaku Smartlab II X-Ray diffractometer with Cu(Kα) radiation (λ = 1.5406 Å), running at 40 kV and 44 mA.

[0095] Single crystal structure measurements: Intensity data of a black plate single crystal of thick-layered perovskite material containing 3-AMP were collected at 293 K. A suitable single crystal with dimensions of ~0.1×0.1×0.02 mm3was mounted on a MiTeGen loop with Paratone oil on a STOE StadiVari diffractometer equipped with an AXO Ag Kα micro-focus sealed Xray A-MiXS source (λ = 0.560834 Å), running at 65 kV and 0.68 mA, and a Dectris Pilatus3 R CdTe 300K Hybrid Photon Counting detector. Data reduction was performed with the CrysAlisPro software using a spherical absorption1 correction. The structure was solved with the ShelXT structure solution program using the Intrinsic Phasing solution method and by using Olex2 as the graphical interface. The model was refined with ShelXL using least squares minimization.

[0096] Absorbance measurements: The optical absorbance measurements were conducted using a broad-band light source (Thorlabs Solis-3C) focused onto the samplePATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT with a 50 μm beam size. The transmitted spectrum was collected by optical fiber and then sent to the spectrometer (Andor Kymera 328i) and CCD (Andor iDus 416). The measurement was conducted on thin KCSC crystals.

[0097] Photoluminescence measurements: The photoluminescence (PL) spectroscopy of FA-DJ 2D perovskite materials was measured based on a lab-built confocal microscopy system. The sample was photo-excited at 480nm using a supercontinuum pulsed laser (repetition rate 78MHz, temporal width ~50ps, NKT Photonics) spectral selected at 480nm. The laser was focused onto the sample through a 50x objective (0.42 NA) with ~ 1 µm beam size, yielding an excitation intensity of 3.6×104 mW / cm2. The PL data was collected from 500 to 950 nm (1.3-2.4eV) by a spectrometer (Andor Kymera 328i) and a CCD camera (Andor iDus 416). For room temperature PL measurements, the sample was kept and measured at ambient condition. For temperature-dependent PL spectroscopy, the sample was kept under vacuum (10-4to 10-5torr) in a closed-cycle cryostat (Advanced Research Systems) with sample temperature range from 6.5K to 300K using a temperature controller (Lakeshore). The excitation intensity was kept the same for all temperature ranges.

[0098] The temperature-dependent reflectance measurements were carried out in the same microscopy system, with the broad-band white light source (Thorlabs Solis-3C) focused on the sample guided by a beam splitter. The reflected spectra were normalized by reflectance of silver mirror on the sample plane.

[0099] 1D and 2D NMR Measurements: The 2D RP and DJ materials were separately packed into 1.3 mm (outer diameter) zirconia rotors fitted with VESPEL caps without any further sample pretreatment. Solid-state MAS NMR experiments were conducted on a 21.1 T (1H, 900 MHz) Bruker AVANCE-NEO spectrometer using a double resonance 1.3 mm H-X probehead. Unless specified, the MAS frequency was 50 kHz in all ssNMR experiments. The 1D1H MAS NMR spectra were acquired by co-addition of 16 transients, where the relaxation delays were optimized to ensure the quantitate analysis of peak integrals. The spin-lattice relaxation time (T1) values are determined from saturation recovery measurements and analyses. All 2D1H-1H spin diffusion NMR experiments were acquired using three-pulse noesy-like sequence under fast MAS with 50 ms of mixing time. A rotor-synchronized increment of 20 s was applied to detect 400 t1 increments. The1H experimental shift was calibrated with respect toPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT neat TMS using adamantane as an external reference (1H resonance, 1.82 ppm). All spectra were processed using Bruker Topspin 4.1 inbuilt package.

[0100] Low-frequency Raman measurements: Raman spectroscopy measurements were carried out using a diode laser module stabilized by volume holographic grating (VHG) filter, operating at 830nm (Coherent Ondax THz-Raman). The excitation laser was introduced into a home-built microscope and focused onto the sample using a microscope objective (Nikon ELWD 20x, NA 0.45). Typical laser power on sample surface was 2.4 mW. The light retro-reflected from the sample was routed back into the laser module which integrates a set of VHG notch filters. The Rayleigh scattered light was attenuated by the VHG filter set. The remaining Raman scattered light was subsequently fiber coupled into a spectrometer (Princeton Instruments Iso-Plane 320), dispersed by a 1200 grooves / mm grating, and captured by a thermoelectrically cooled CCD camera (PIXIS-BRX400). Typical integration time was 100s.

[0101] PL Diffusion measurements: Montana Instruments Cryostation, with attached turbo pump, was employed to maintain a high vacuum environment (10-4to 10-5Torr) during room temperature (295 K) measurements. An objective with 100x magnification and 0.9 NA focused a 532 nm continuous-wave laser onto the samples with a resulting beam diameter (D4σ) of ~ 0.6 µm. A neutral density filter was placed in the beam path, before the objective, to modulate the laser power for the power-dependent measurements. Laser contributions from the reflected PL were blocked with a 550 nm long-pass filter, installed before the detector. Additionally, free carrier diffusion contributions were removed with a 700 nm short-pass filter for both n=2 and n=3 FA- DJ perovskite materials. Subsequent real-space emission images of the sample surface were acquired using an EMCCD camera in low electron multiplication mode. An n- type GaAs wafer was used for calibration of measurements and to confirm reliability of analysis.

[0102] Time-resolved PL: The TRPL spectrum of DJ n=3 sample was acquired with a lab-built confocal microscopy system. The sample was photo-excited using a 50-ps- pulsed super-continuum laser (NKT Photonics, repetition rate tuned at 39MHz) spectral selected at 480 nm. The excitation laser was focused onto the sample with ~ 1 µm beam size and average excitation intensity of 1.8×104 mW / cm2. The emission was collected using PicoQuant HydraHarp 400 time-correlated single photon counting systemPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT combined with an Avalanche Photo-Diode (MPD-SPAD). The emission was spectrally filtered through a spectrograph (Andor Kymera 328i) to remove laser excitation. During TRPL measurement, the sample was kept under vacuum (10-4to 10-5torr) in a closed- cycle cryostat and maintained at cryogenic temperature (T = 6.5K). Computational Methods

[0103] DFT calculations for obtaining the PDF, phonon spectral functions, and DOS were performed using the Quantum Espresso (QE) software. A kinetic energy cutoff of 120 Ry, the PBEsol approximation, and optimized norm-conserving Vanderbilt pseudopotentials were used. To obtain the polymorphous structures known methods were used. 2x2x2 and 2x2x1 supercells of the primitive cells of cubic FAPbI3 and (3- AMP)FAPb2I7 containing 96 and 164 atoms, respectively, were employed. Geometry optimizations in supercells were performed by allowing the nuclear coordinates to relax and keeping the lattice constants fixed to their experimental values.3x3x3 and 3x3x2 uniform k-grids were employed to sample the Brillouin Zone of polymorphous cubic FAPbI3and (3-AMP)FAPb2I7. Geometry optimizations and phonon calculations (see below) were performed using scalar relativistic pseudopotentials, neglecting the effect of spin-orbit coupling.

[0104] Doubly Screened Hybrid: Density functional based calculations were performed with the projector augmented wave potentials as implemented in the VASP code. The energy cut-off for the expansion of the wave-functions is set at 450 eV, and spin-orbit coupling interactions were taken into account for all calculations. To maintain the symmetry of the structures, the organic moieties were replaced with Cs atoms that were placed at the position of the N-atoms. This replacement does not affect the electronic structure, as evidenced by comparing the band structures, and that no symmetry is broken (i.e., the space group remains the same as the experimentally observed). Furthermore, to include the effect of polymorphism in the structures, a calculation of a 2x2x2 super-cell of FAPbI3 (poly-FAPbI3) which include the FA molecules was performed. To overcome the well-known band-gap underestimation of DFT, a doubly screened hybrid exchange-correlation functional was employed. The ε∞ was calculated from first-principles (details below) for all compounds and ε-1∞ is the mixing parameter for the long range, while the exact exchange is used for the short range. For the employed model dielectric function, a screening length parameter μ value of 1.05PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT was used on FAPbI3. For the calculations of the exact exchange uniform Γ-centered k- point grids of 4x4x2 for the layered materials, and 6x6x6 (2x2x2) for the mono-FAPbI3and poly- FAPbI3 were used, respectively.

[0105] Calculation of ε∞: The density functional perturbation theory (DFPT) was used to calculate the dielectric constant of the n=1,2,3,4, mono-FAPbI3and poly-FAPbI3compounds. Γ-centered k-point grids of 12x12x4, 12x12x4, 10x10x4,10x10x4, 20x20x20 and 6x6x6 were used, respectively. Local field effects were included at the DFT level. For the layered materials, the organic spacers were replaced with N atoms, to avoid artifacts due to the different dielectric screening. A capacitor stack model was used to extract the ε∞ of the inorganic slab layer from the DFPT calculation. The final ε∞ for the materials are given in Table 4, above.

[0106] Phonons and PDF: The phonons of the polymorphous structures were calculated by means of finite differences using the zeroth order iteration of the anharmonic special displacement method (A-SDM). PDFs of the polymorphous structures were evaluated as (eqn) by replacing the delta function with a Gaussian of width 0.035 Å, see Eqn.2.

[0107] Here, κ is the atom index and τκκ’ defines the distance between atom κ and κ’. To include the effect of thermal vibrations in the PDFs, the thermally displaced configurations in 10x10x10 and 20x20x1 supercells were employed. The configurations were generated using the A-SDM at essentially no cost, as it takes advantage of Fourier interpolation of the phonons in the reciprocal space.

[0108] Phonon Spectral Functions: Phonon spectral functions were calculated using the phonon unfolding technique as implemented in the ZG package of EPW. 663 and 787 equally-spaced q-points were employed for (3-AMP)FAPb2I7 and FAPbI3, respectively, and 12 × 12 × 12 g-grid of reciprocal lattice vectors to ensure convergence of the spectral weights.

[0109] DOS at Finite Temperatures: Electronic structure calculations for the DOS were performed using fully relativistic pseudopotentials, including the effect of spin-orbit coupling. To calculate the DOS at the VBM and CBM for 300 K, the A-SDM was used. In the A-SDM, anharmonic phonons computed for the polymorphous structures arePATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT used to generate thermally displaced configurations, which capture the effect of electron-phonon coupling on the electronic structure when combined with DFT calculations. To obtain the DOS of polymorphous FAPbI3 and (3-AMP)FAPb2I7 at 300 K, 10 configurations of supercell size 4x4x4 (768 atoms) and 4x4x1 (656 atoms) were used, respectively. 1x1x1 and 1x1x2 grids were used to sample the Brillouin zone of these supercells. The phonon-induced band gap renormalization, Δεg, with respect to the band gap of the polymorphous structure at static-equilibrium was determined by taking the average renormalization over the 10 configurations.

[0110] Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from this invention. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims.

Claims

PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT CLAIMS What is claimed:

1. A two-dimensional perovskite material comprising: a layered material having the formula (I) (A′)(A)n-1MnX3n+1, wherein A′ is an organic cation selected from the group consisting of butyl ammonium, 3-(aminomethyl)piperidium (3-AMP), 4-(aminomethyl)piperidium, and combinations thereof, A is a perovskitizer-cation selected from the group consisting of formamidinium (FA), guanidinium (GA), dimethylamine, cesium, and combinations thereof, M is a divalent metal selected from the group consisting of Pb, Ge, Sn, Cu, and combinations thereof, X is a halide selected from the group consisting of I, Br, Cl, F, and combinations thereof, and n is greater than or equal to 2; wherein the layered material comprises alternating layers of a first type and a second type, wherein the first type comprises the organic cation (A′) and the second type comprises a hybrid anion having the formula (II) (A)n-1MnX3n+1.

2. The two-dimensional perovskite material of claim 1, wherein the layered material has a tetragonal crystal structure with space group symmetry P4 / mmm.

3. The two-dimensional perovskite material of claims 1 or 2, wherein n is in the range of from 2 to 10.

4. The two-dimensional perovskite material of any one of the preceding claims, wherein the layered material has a lattice mismatch between the first type and second type of 10% or less.

5. The two-dimensional perovskite material of any one of the preceding claims, wherein the layered material is linear and has an equatorial M-X-M angle ranging from 160 to 180 °C.PATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT 6. The two-dimensional perovskite material of any one of the preceding claims, wherein the layered material has the formula (III) (3-AMP)(FA)n-1PbnI3n+1and n is 2, 3, or 4.

7. The two-dimensional perovskite material of claim 6, wherein the layered material has an interlayer distance ranging from 3.8 to 7 Å.

8. The two-dimensional perovskite material of any one of the preceding claims, wherein the layered material has a band gap of from about 1.6 eV to 2.0 eV.

9. The two-dimensional perovskite material of any one of the preceding claims, wherein the layered material is a film.

10. A device comprising the film of claim 9, wherein the device is an electronic or optoelectronic device.

11. The device of claim 10, wherein the device is a solar cell.

12. A method of making a two-dimensional perovskite material, the method comprising: mixing a divalent metal source and a salt containing a perovskitizer-cation in a halogen acid solution, forming a first suspension, stirring the suspension at an elevated temperature of from about 100 °C to 400 °C, adding a solution comprising an organic cation and an acid to the suspension, forming a mixture, cooling the mixture to a temperature of from about 80 °C to 120 °C at a cooling rate of 0.01 to 200 °C / s, to form crystals, and filtering and drying the crystals to obtain a two-dimensional perovskite material.

13. The method of claim 12, wherein the two-dimensional perovskite material has the formula (I) (A′)(A)n-1MnX3n+1, wherein A′ is an organic cation selected from the group consisting of butyl ammonium, 3-(aminomethyl)piperidium (3-AMP), 4- (aminomethyl)piperidium, and combinations thereof, A is a perovskitizer-cation selected from the group consisting of formamidinium (FA), guanidinium, dimethylamine, cesium, and combinations thereof, M is a divalent metal selected from the group consisting of Pb, Ge, Sn, Cu, and combinations thereof, X is a halide selectedPATENT APPLICATION ATTORNEY DOCKET NO.17500-265WO1 CLIENT REF. NO.2024-072-PCT from the group consisting of I, Br, Cl, F, and combinations thereof, and n is greater than or equal to 2.

14. The method of claim 12 or 13, wherein the halogen acid is selected from the group consisting of hydroiodic acid, hydrochloric acid, hydrobromic acid, hydrofluoric acid, and combinations thereof.

15. The method of any one of claims 12-14, wherein the salt containing a perovskitizer- cation is selected from the group consisting of FACl, FABr, FAI, GACl, GABr, GAI, CsBr, CsCl, CsI, and combinations thereof.

16. The method of any one of claims 12-15, wherein the divalent metal source is selected from the group consisting selected from the group consisting of PbI2, PbCl2, PbBr2, PbO, and combinations thereof.

17. The method of any one of claims 12-16, wherein the solution comprising the organic cation and the acid comprises an acid selected from the group consisting of H3PO2, HI, HCl, HBr, HF, and combinations thereof.

18. The method of any one of claims 12-17, wherein the first suspension further comprises H3PO2.

19. The method of any one of claims 12-18, wherein the two-dimensional perovskite material has the formula (III) (3-AMP)(FA)n-1PbnI3n+1and n is 2, 3, or 4.

20. The method of claim 19, wherein the two-dimensional perovskite material is free of δ- phase formamidinium lead iodide (FAPbI3).

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