Exploring A‐Site Cation Variations in Dion–Jacobson Two‐Dimensional Halide Perovskites for Enhanced Solar Cell Applications: A Density Functional Theory Study

The exceptional photophysical and electronic properties of 2D hybrid perovskites possess potential applications in the field of solar energy harvesting. The present work focuses on the two systems, exhibiting the Dion–Jacobson phase of 2D perovskite consisting of methylammonium (MA) and formamidinium (FA) cations at A‐site and 3‐(aminomethyl)pyridinium (3AMPY) as ring‐shaped organic spacer. Altering A‐site cations creates a distortion of inorganic layers and hydrogen bond interactions. It has been noted that the angles of Pb–I–Pb and I–Pb–I are more symmetric (close to 180°) for (3AMPY)(MA)Pb2I7 compared to (3AMPY)(FA)Pb2I7 and result in increase of bandgap from 1.51 to 1.58 eV. This further leads to a significant difference in Rashba splitting energy under the influence of spin‐orbit coupling effects, where the highest splitting (36 meV) is calculated for conduction band edge of the (3AMPY)(FA)Pb2I7, suggesting the promising applications toward spintronics. The calculated absorption spectra cover the range from 300 to 450 nm, indicating significant optical activity of 2D (3AMPY)(MA)Pb2I7 and (3AMPY)(FA)Pb2I7 in the visible and ultraviolet regions, which bodes well for their application in advanced optoelectronic devices. The bandgap and high absorption coefficients present more than 30% of theoretical power conversion efficiency for both systems, as calculated from the spectroscopic‐limited maximum efficiency.


Introduction
[3] These materials have found extensive utilization in various domains, such as solar cells where single junction devices have achieved efficiencies surpassing 25%. [4]dditionally, they have been employed in light-emitting diodes (LEDs) and have shown promising features for lasing applications. [5]These exhibit an octahedral crystalline structure, commonly denoted by the conventional formula ABX 3 .Within this structure, the cation A represents methylammonium (CH 3 NH 3 þ , MA), formamidinium (HC(NH 2 ) 2 þ , FA), and cesium (Cs þ ).Here, the corner-sharing inorganic framework is maintained through three A-site cations solely. [6]The divalent metal ion B is denoted by Pb 2þ or Sn 2þ , while X represents a halide anion, including bromide (Br À ), chloride (Cl À ), or iodide (I À ). [3]9] One challenge related to metal halide perovskites pertains to

H. L. Kagdada Department of Mechanical Engineering Indian Institute of Technology Bombay Mumbai, Maharashtra 400076, India
The exceptional photophysical and electronic properties of 2D hybrid perovskites possess potential applications in the field of solar energy harvesting.The present work focuses on the two systems, exhibiting the Dion-Jacobson phase of 2D perovskite consisting of methylammonium (MA) and formamidinium (FA) cations at A-site and 3-(aminomethyl)pyridinium (3AMPY) as ring-shaped organic spacer.Altering A-site cations creates a distortion of inorganic layers and hydrogen bond interactions.It has been noted that the angles of Pb-I-Pb and I-Pb-I are more symmetric (close to 180°) for (3AMPY)(MA)Pb 2 I 7 compared to (3AMPY)(FA)Pb 2 I 7 and result in increase of bandgap from 1.51 to 1.58 eV.This further leads to a significant difference in Rashba splitting energy under the influence of spin-orbit coupling effects, where the highest splitting (36 meV) is calculated for conduction band edge of the (3AMPY)(FA)Pb 2 I 7 , suggesting the promising applications toward spintronics.The calculated absorption spectra cover the range from 300 to 450 nm, indicating significant optical activity of 2D (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 in the visible and ultraviolet regions, which bodes well for their application in advanced optoelectronic devices.The bandgap and high absorption coefficients present more than 30% of theoretical power conversion efficiency for both systems, as calculated from the spectroscopic-limited maximum efficiency.their environmental stability, specifically their vulnerability to moisture. [10,11]][14][15][16] These systems replace the A cation with a larger organic cation to mitigate the issue.To accommodate a larger cation within the structure, the three-dimensional (3D) structures must undergo a breakdown to form their low-dimensional counterparts.Examples of such structures include hollow perovskites, denoted by (en) AMX 3 , [17] (hea)-AMX3, [18] and (tea)AMX3 [19] (where "en" represents ethylenediammonium, "hea" represents hydroxyethylammonium, and "tea" represents thioethylammonium).][22] The 2D perovskites have demonstrated encouraging efficacy in solar cells [15,[23][24][25][26] and LEDs. [27,28]heir remarkable stability is a key characteristic, attributable to their water-resistant properties, reduced ion migration, and the ability to tune their optoelectronic properties.][22] As a result, they can be considered as naturally occurring quantum well systems.In this analogy, the organic spacer acts as the barrier, while the inorganic layer functions as the well.The height of the barrier can be adjusted by modifying the dielectric constant of the organic spacer. [21]oncerning 2D halide perovskites oriented along the (100) crystallographic plane, four distinct types have been observed and studied experimentally.These types include 1) the RuddlesdenÀPopper (RP) phase, denoted as A ' 2 A nÀ1 M n X 3nþ1 , [29] 2) the DionÀJacobson (DJ) phase represented by A ' A nÀ1 M n X 3nþ1 , [30] 3) the alternating cations interlayer (A and A 0 ) in the interlayer space known as A 0 A n M n X 3nþ1 , [31,32] and 4) those incorporating alkyl diammonium cations (DC), specifically (NH 3 C m H 2m NH 3 )-(CH 3 NH 3 ) nÀ1 Pb n I 3nþ1 . [33]In the DJ phase, represented as case (2) above, the structure comprises monoammonium cation spacers (NH3 þ ), which are present at only one end of the spacer cation.In contrast, alkyl DC spacers feature NH 3 þ cations at both ends of the spacer.This key difference leads to the formation of electrostatic connections between the inorganic slabs that extend out of the plane.Consequently, the DC spacers impart greater rigidity and, by extension, enhanced stability to the perovskite structure.The RP phases are characterized by the presence of monovalent cations that can conveniently interlock between neighboring inorganic layers.Further, this results in a nonuniform arrangement where the stacked layers are shifted by half a unit cell (1/2, 1/2 displacements) relative to each other.This particular class of 2D perovskites is prominent in terms of the number of known members and holds a dominant position within the 2D perovskite family.The DJ phases exhibit the presence of compact divalent þ2 cations amid the layers, resulting in an eclipsed stacking arrangement (0, 0, displacements).These DJ phases are relatively recent additions to the family of halide perovskites, with only a limited number of known examples (mostly lacking thorough structural characterization), particularly for members with n > 2. [34][35][36][37] For linear DC, when the chain length is long enough, they have a tendency to adopt staggered configurations where the extended chain assumes an inclined alignment in the middle of the inorganic sheets. [33]This effect has been observed, for instance, when the chain length is as short as four carbons.In such cases, the inorganic layers exhibit a slight offset, often leading to out-of-plane deformation of the octahedra due to the presence of robust hydrogen bonding. [14,38]Furthermore, DJ phases of halide perovskites exhibit hydration under the humid environment. [11,39]However, such hydration could be reversed and recently, Dučinskas et al. unraveled that the absorption of pristine and dehydrated DJ phase of perovskite shows similar behavior through the generation of Pb-I layer during the postsynthetic annealing process. [11]Additionally, the impact of longer chain of alkyl components reveals the improved stability against the moisture. [40]When transitioning from linear DCs to shorter cyclic DCs, such as x-(aminomethyl)piperidinium (AMP) (x = 3 and 4), there is a preference for the formation of DJ phases.This preference arises due to the reduction in the distance between the inorganic layers as a result of using shorter cations. [30]In recent times, there has been a renewed interest in the structural chemistry of DJ oxide perovskites, driven by predictions that these structures can exhibit ferroelectricity [31,32] through specific material design principles. [33]lthough DJ perovskites are abundant in oxide materials, [34,41] AMP organic spacer-based DJ phases are largely unexplored in hybrid halide perovskites.
In this study, we explore the fundamental characteristics of the DJ phase within quasi-2D perovskites, focusing on the influence of A-site cation variations.While researchers have shown a significant interest in methylammonium (MA)-based cations, formamidinium (FA)-containing 2D perovskites have exhibited noteworthy optoelectronic and photovoltaic traits when combined with various organic spacers. [42]Additionally, the challenge of creating quasi-2D DJ phases in perovskites, using AMP as organic spacers and MA as the A-site cation, becomes apparent when compared to their counterparts based on FA cations.Consequently, our present work serves as a demonstration of the effects stemming from the replacement of MA with FA cations on the structural, electronic, and optical properties of quasi-2D lead halide perovskites.Furthermore, we conducted simulations to assess the power conversion efficiency of these systems, employing the spectroscopy limited maximum efficiency (SLME) method.

Methodology
In our study, we conducted structural relaxation computations using density functional theory (DFT) with the Quantum Espresso software. [43]We adopted the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for exchange-correlation functional.Full-relativistic effects were accounted for using norm-conserving pseudopotentials. [44]The basis set was comprised of plane waves extended up to 80 Ry, and Brillouin zone sampling was achieved with a 1 Â 6 Â 6 Monkhorst-Pack grid.The Broyden-Fletcher-Goldfarb-Shanno method was employed to find the ground state of the structures, [45] and van der Waals interactions were included through Grimme's DFT-D2 method. [46]For electronic minimization, we set a convergence criterion of 10 À8 Ry, while ionic positions were optimized with force and energy criteria of 10 À3 eV Å À1 and 10 À4 Ry, respectively.Additionally, we computed the frequency-dependent real part of the dielectric constants (ε 1 ) using the Kramer-Kronig formalism, while the imaginary part (ε 2 ) was derived from the momentum matrix of occupied and unoccupied states within the Brillouin zone, adhering to selection rules.This comprehensive computational methodology provided a thorough understanding of the material properties under investigation.

Structural Properties
The interpretation of the electronic and optical properties of 2D halide perovskites is revealed from the detailed structural analysis as a function of A-site cations.In general, halide perovskite materials consist softness in their crystal structure, which can be significantly altered through various strategies such as inorganic layer thickness, change of organic spacers, and variation in the A-site cations located inside the inorganic cage, thereby, providing full control of tailoring the physical properties.Unlike RP phase of 2D perovskite (where large organic chains form the bridge between inorganic layers), the DJ phase contains short organic spacers such as ring-shaped organic molecules, which reduce the distance between inorganic layers and enhance the rigidity of the structure. [41]Considered structures of DJ phase of quasi-2D halide perovskites (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 are illustrated in Figure 1.The full structures are presented in Figure S1, Supporting Information.Both the systems exhibit the monoclinic structure and the structural parameters are listed in Table 1.It is observed that the calculated lattice parameters for MA-based quasi-2D DJ phase of perovskite are in good agreement with the previously reported experimental values. [41]he aromatic (aminomethyl)pyridinium (3AMPY) organic spacer is vertically stacked along the a-direction of the crystal structure and separates the inorganic layers.Further, it is to be noted that inorganic layers are periodically expanded through corners of the octahedral configuration for both structures toward the band c-direction.Furthermore, the hydrogen bond between A-site cations and inorganic layers (H 2 N-H þ … I À ) plays a vital role in the modification of the physical properties of 2D halide perovskites as well as the distortion in the inorganic cage.A stronger hydrogen bond from the spacer cation is observed for (3AMPY)(FA)Pb 2 I 7 , compared to that of (3AMPY)(MA)Pb 2 I 7 .The arrangement and positions of A-site cations, such as FA and MA, play a pivotal role in influencing the distortion of the inorganic octahedral geometry within the perovskite structure.We can observe this distortion through the measurement of angles, specifically the Pb-I-Pb and I-Pb-I angles, which exhibit lower values in the case of the FA-based perovskite structure (as outlined in Table 1).Consequently, in the (3AMPY)(FA) Pb 2 I 7 configuration, the top layer of iodine atoms displays a more pronounced tilt toward the spacer cation.This results in the formation of stronger hydrogen bonds compared to the (3AMPY)(MA)Pb 2 I 7 structure, with important implications for the material properties and behavior.As shown in Figure 1, the minimum distance of H 2 N-H…I (from NH 3 þ of spacer cation) is 2.52 Å for (3AMPY)(MA)Pb 2 I 7 , while the same is reduced to 2.45 Å in (3AMPY)(FA)Pb 2 I 7 .Further, the geometries and position of the MA and FA cations and their interactions with the iodine influence the distortions in inorganic octahedra.The distortion in the PbI 6 octahedra is characterized by the Pb-I-Pb angle in vertical and horizontal direction of the inorganic cage.For the case of MA cation, the vertical or axial angle Pb-I-Pb is 165.44°, while it is reduced to 153.57°, and 160.52°.It has been noted that the calculated axial angle is in good agreement with the experimental observation. [41]Moreover, the Pb-I-Pb in horizontal direction, which is also the angle between corner-sharing octahedral, is found to be 153.32°for(3AMPY)(MA)Pb 2 I 7 (See Figure 1).In contrast, the same angles in the cage of inorganic layers are calculated as 162.40°and 161.79°for (3AMPY)(FA)Pb 2 I 7 .In the octahedra geometry, the lowest I-Pb-I angle is 173.88°and168.40°for (3AMPY)(MA) Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 , respectively.This suggests that replacing A-site cation with MA molecule the octahedral structure becomes more symmetric compared to the FA cation.Such change in inorganic layers plays an important role in the electronic as well as optical properties of 2D halide perovskite materials.

Electronic Properties
We conducted band structure calculations for considered 2D halide perovskites, namely, (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 , aiming to gain insights into the energy level dispersion across the high symmetry points of the Brillouin zone (BZ).In contrast, the VB is predominantly influenced by contributions from iodine p orbitals.Interestingly, (3AMPY)(FA)Pb 2 I 7 exhibits a CB dominated by cationic contributions, which sets it apart from (3AMPY)(MA)Pb 2 I 7 and other conventional hybrid metal halide perovskites.Through this comprehensive examination of the PDOS, we gain a better understanding of the factors influencing the bandgap values in these perovskite materials, paving the way for further advancements in tuning their electronic properties for potential applications in solar cell performance and other optoelectronic devices.
][49] To understand the phenomena, we employed the spin-orbit coupling effects (SOC), and the calculated band edges are presented in Figure 2b (full band structure considering SOC effects are presented in Figure S3, supporting information).In-depth observation of band edges in SOC bands reveals that the parabolic band is depicting splitting into the two bands within the energy and momentum space.Such splitting of bands near the zone center suggests Rashbatype splitting as the presence of noncentrosymmetric configuration of inorganic layers in both systems, attributed to their major contribution to the band edges.The calculated splitting energy for CBM (VBM) of (3AMPY)(FA)Pb 2 I 7 along Γ-Y and Γ-U is 36 (16) and 24 (8) meV.In contrast, (3AMPY)(MA)Pb 2 I 7 exhibits a very little splitting of 8 and 19.3 meV along Γ-Y direction of BZ for CBM and VBM, respectively.The difference in Rashba splitting energy between the considered systems is directly attributed to the structural changes with MA and FA cation in 2D DJ phase of halide perovskites.However, from PDOS analysis it should be noted that band edges are not contributed from the A-site or spacer cations, and therefore, it is pointed out that the fluctuation in splitting energy is probed indirectly by the A-site cations.Here, the structural fluctuations for the FA cation-based perovskites are quite higher than that of the MA cation, which perhaps in turn the greater amount of local electric field between organic cations and inorganic layer [50] and results in large value of splitting for (3AMPY)(FA)Pb 2 I 7 compared to (3AMPY)(MA)Pb 2 I 7 .The splitting of band edges in the presence of SOC probes the indirect bandgap of 1.06 and 1.08 eV for (3AMPY)(MA) Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 .Such indirect bandgap with the splitting of energy might be beneficial for the performance of perovskite solar cells, via slowing down the charge recombination process. [14,50,51]urthermore, the bands near the edges demonstrate high dispersion, indicating a high mobility of the photogenerated carriers.In the VBs of both materials, the energy levels also exhibit significant dispersion throughout the Brillouin zone.However, a noteworthy distinction arises in the CB edge of (3AMPY)(MA)Pb 2 I 7 .Here, the CB edge shows lower dispersion, primarily due to its constitution of the organic spacer cation.The presence of organic cations leads to a downward shift of the flat organic bands, potentially stemming from the stabilization of cationic molecular orbitals.Compared to the lead-iodide moiety in the VB edge, the organic cations have lower dielectric nature, which could result in a flat CB for photoexcited electrons.Consequently, this flat CB may lead to the generation of lowmobility electrons.The comprehensive analysis of the band structure provides valuable insights into the electronic characteristics of these perovskite materials, aiding in our understanding of their potential applications in optoelectronic devices and guiding further research for enhanced device performance.

Optical Properties
For optical parameters, we considered a range of photon energy values spanning from 0 to 30 eV, oriented along the directions of the electric vector (E).The dielectric function, ε(ω), can be expressed as ε(ω) = ε 1 (ω) þ iε 2 (ω), where the imaginary part ε 2 (ω) is directly obtained from the electronic band structure using the optical matrix elements.4] To meet the conditions stipulated by the equations above, the following relationships must hold: where n and k represent the refractive index and extinction coefficient, respectively.These values can be derived from the dielectric function ε(ω) as follows: and Furthermore, the absorption coefficient α(ω) can be computed by k(ω) where λ 0 and k, respectively, are the velocity of light and extinction coefficient in a vacuum.
In Figure 3, we present the optical response of the complex dielectric function, ε(ω), for both (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 , including real and imaginary parts.The imaginary part, ε 2 (ω), plays a crucial role in understanding the interband transitions within the material.The distinctive features observed in ε 2 (ω) are directly associated with interband transitions, indicating the absorption of radiation by electrons in the occupied VBs located below the Fermi level.On a different aspect, the real part of the dielectric function, ε 1 (ω), provides valuable insights into the electronic polarizability of the material, which can be analyzed using the Clausius-Mossotti relation. [55]n this studied energy range, we can safely neglect other polarizability contributions, such as ionic and dipolar effects, due to the inertia of the atomic cores and molecules.The comprehensive analysis of ε(ω) in both its real and imaginary components aids in understanding the optical properties and electronic behavior of these 2D halide perovskite materials.By unraveling the interband transitions and electronic polarizability, we can gain deeper insights into their potential applications in optoelectronic devices and photonics.
The optical behavior of incident light interacting with (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 demonstrates a significant degree of anisotropy within the energy range spanning from infrared (IR) to vacuum ultraviolet (UV) (E < 13 eV).However, at higher energies, an isotropic response is observed.The static dielectric constants (at zero frequency limit), ε 1 (0), are measured as 4.4 and 4.12 for (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 , respectively.Remarkably, in the high-energy region between 7 and 11 eV, negative values appear in the real part of the dielectric function.This intriguing characteristic suggests the presence of a metallic character in both (3AMPY)(MA) Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 within the X-ray region of the electromagnetic spectrum.Additionally, this negative response of ε 1 (ω) signifies the absence of light transmission in the deep X-ray region, thus indicating the lack of optical transparency in the energy range of approximately 7-11 eV.The thorough analysis of the optical response provides valuable insights into the materials' unique properties and behavior across different energy regimes.The observed anisotropy, metallic character, and absence of optical transparency in specific energy ranges contribute to our understanding of the potential applications of these 2D halide perovskite materials in optoelectronic devices and photonics.
The imaginary part of the dielectric constant plays a crucial role in understanding the optical properties, and in this study, we report the calculated ε 2 (ω) for (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 [see Figure 3].Due to the similarity in the electronic band structure of these systems, we observe nearly identical line shapes in ε 2 (ω).The prominent peaks in both (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 are primarily attributed to electron transitions from the hybridized bonding between Pb and I 2p states, leading to an absorption behavior.The dominant part of these spectra arises from the electronic transitions between the VB and CB. Figure 3c,d illustrates the behavior of the imaginary part of the dielectric function, ε 2 (ω), representing the radiation absorbed by the compound, with main peaks located at 3.2 and 3.3 eV for (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 , respectively.Notably, ε 2 (ω) remains at zero until absorption begins after the photon energy reaches the bandgap energy, which serves as the threshold for a direct optical transition.The dielectric function ε 2 (ω) signifies the fundamental absorption edge, occurring at 1.2 and 1.4 eV for (3AMPY)(MA) Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 , respectively, correspond to the energy thresholds at which electrons begin to transfer from the VB to the CB.As they mark the onset of absorption within a transition region, these absorption edges are somewhat lower in energy than the bandgap values themselves.The observed peaks in the spectra result from various electronic transitions between occupied and unoccupied states, with some being associated with near-band transitions and low-energy peaks.
It is important to note that these peaks are not only due to interband transitions between direct and indirect bands, but also a result of the hybridized π and σ bonding-antibonding nature of the p orbitals.Overall, the comprehensive analysis of ε 2 (ω) provides valuable insights into the optical absorption behavior of these 2D halide perovskite materials, shedding light on their electronic structure and potential applications in optoelectronic devices and photovoltaics.
To explore the potential of these compounds for photovoltaic applications, we conducted a comprehensive study of their absorption coefficients across the entire spectrum range, from IR to extreme UV.The absorption coefficient of a material defines its ability to absorb light or solar radiation within a specific energy range.In Figure 4, we present the absorption coefficients of (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 monolayers up to 30 eV (converted to wavelength (nm)).The absorption coefficient quantifies the number of electromagnetic waves with a particular energy that can penetrate the material before being absorbed.When the bandgap of a material is lower than the energy of the incident solar radiation, the material can absorb photons through direct and indirect electronic transitions, which are associated with interband transitions.The absorption threshold occurs at nearly the same value as that of the imaginary parts of the dielectric function.Remarkably, our results reveal that (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 show effective photovoltaic conversion capabilities.Therefore, we have evaluated the power conversion efficiency using SLME method, where the efficiency has been calculated using bandgap, absorption coefficients, and the thickness of light-absorbing material. [56]he calculated SLME for both systems is presented in Figure 4b.It is to be noted that the difference between direct and indirect bandgap in (3AMPY)(MA)Pb 2 I 7 is miserable and below room temperature energy and therefore, here we have considered the direct bandgap for the SLME calculation.Both systems show excellent power conversion efficiency more than 30% at layer thickness of light-absorbing material in the range of micrometer, which is originated from the high absorption coefficients and lower bandgap values.Furthermore, in the literature, we found that Li et al. [41] reported experimental efficiency data for the MA-based quasi-2D DJ phase of halide perovskites, specifically achieving a 9.29% efficiency for (3AMPY)(MA) 3 Pb 4 I 13 (a four-layered Pb-I perovskite).Discrepancies in efficiency might arise from the limitations of DFT-PBE calculations, resulted in of the bandgap from the experimental result.Further, during the experiments, several factors such as device quality, surrounding environment, humidity, etc., are difficult to consider for complex structures like perovskite structures.Perhaps, the trends of the properties might be unaltered and still explain the fundamental phenomena that occurred in optical and electronic properties.Here, we believe that the absorption characteristics indicate that these materials are promising candidates for photovoltaic applications due to their ability to efficiently absorb incident photons within the solar spectrum.By investigating the absorption coefficients across a broad energy range, we gain valuable insights into the materials' suitability for solar energy conversion and potential contributions to the advancement of photovoltaic technologies.

Conclusion
In this study, we conducted a comprehensive first principlesbased DFT investigation on the structural, electronic, optical, and solar cell efficiency properties of 2D halide perovskites, specifically in the DJ phases of (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 .The electronic energy bandgaps at equilibrium lattice constants indicate their potential as materials for various optoelectronic applications.The optical analysis further revealed maximum absorption with an absorption coefficient of approximately 10 6 cm À1 .The optical absorption spectrum shows the highest absorption capacity within the visible range of the electromagnetic spectrum for considered structure.Additionally, we explored the solar cell applications of these materials by determining their solar cell parameters using the SLME model.Impressively, the (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 monolayers demonstrated efficiency values of 30% and 31.4%,respectively.These results signify their excellent potential as absorber layers in solar cells, making them promising candidates for practical implementation.In conclusion, our DFT predictions offer valuable insights for future theoretical and experimental studies of perovskite-type halides, especially in their advanced applications as absorber layers in high-efficiency solar cells.The combination of structural, electronic, optical, and solar cell efficiency analyses enhances our understanding of these 2D halide perovskites, opening new avenues for their utilization in cutting-edge optoelectronic devices and renewable energy technologies.

Figure 1 .
Figure 1.Ball and stick models of structures of (3AMPY)(MA)Pb 2 I 7 (left side) and (3AMPY)(FA)Pb 2 I 7 (right side).The color code of atoms is presented in the middle panel.To clear visualization of the bond angles and bond lengths, the radius of the Pb and I sphere is reduced.

Figure 2
illustrates the band structure plots obtained using the PBE method.For (3AMPY)(MA)Pb 2 I 7 , the valence band maximum (VBM) and conduction band maximum (CBM) are located at Γ and Y point of the first BZ, which results in the indirect bandgap.For (3AMPY)(FA)Pb 2 I 7 perovskites, a direct bandgap at the zone center is observed.However, the indirect and direct bandgap of (3AMPY)(MA)Pb 2 I 7 is 0.019 eV, which is even less than the room temperature energy.Therefore, at room temperature, there is a possibility of a direct bandgap for (3AMPY)(MA) Pb 2 I 7 .The calculated bandgap values for (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 are 1.51 and 1.58 eV, respectively.Among (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 , the former possesses slightly smaller bandgap that can be attributed to its more ideal Pb-I-Pb bond angle of %160°as compared to 154°in (3AMPY)(FA)Pb 2 I 7 .The bandgap properties of the materials are influenced by the structural distortions of the ring and the interlayer distance.Subsequently, to gain insights into these bandgap values, we conducted an in-depth analysis of the perovskites' partial density of states (PDOS) (FigureS2, Supporting Information) and explored the elemental contributions to the valence band (VB) and conduction band (CB).We observed that both (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 exhibit a minor presence of cationic states near the CB edge, while the carbon components are noticeably distant from the VB edge.In the case of (3AMPY)(MA)Pb 2 I 7 and (3AMPY)(FA)Pb 2 I 7 , the carbon components are positioned at energy levels 1.5 and 2.2 eV above their respective CB edges.

Figure 2 .
Figure 2. a) Electronic band structure without considering the spin-orbit coupling (SOC) effects and b) with consideration of SOC effect the splitting of band edges along U-Γ-Y high symmetry path of BZ.

Table 1 .
Crystal structure parameters such as lattice constants and distortion angles of inorganic layers in considered systems.