Synthesis and numerical simulation of formamidinium-based perovskite solar cells: a predictable device performance at NIS-Egypt

Formamidinium lead triiodide (δ-FAPbI3)-based perovskite solar cells showed remarkable potential as light harvesters for thin-film photovoltaics. Herein, the mechanochemical synthesis of δ-FAPbI3, MAPbI3, and mixed-cation FA1−xMAxPbI3 with (x = 0.3, 0.5, and 0.7) perovskite materials were prepared as a novel green chemistry method for scaling up production. Crystallinity, phase identification, thermal stability, optoelectronic properties, and nanoscale composition are discussed. The results demonstrated that the prepared mixed-cation samples are enhanced in the visible absorption region and are consistent with previous works. The crystal structure of δ-FAPbI3 was altered to a cubic structure due to the change in FA-cation. Moreover, the performance of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta$$\end{document}δ-FA-based perovskites was investigated using the Solar Cell Capacitance Simulator (SCAPS-1D) software. The validity of the device simulation was confirmed by comparing it to real-world devices. The photovoltaic characteristics and impact of absorber thickness on device performance were explained. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta$$\end{document}δ-FA-based solar cell with a 50% MA-doped molar ratio shows a better performance with an efficiency of 26.22% compared to 8.43% for δ-FAPbI3. The outcome results of this work confirm the beneficial effect of mixed cations on device operation and advance our knowledge of the numerical optimization of perovskite-based solar cells.

, indicating superior semiconducting properties and promising perovskite material for high-performing single-junction photovoltaic applications compared to MAPbI 3 . Despite these advantages, the black-colored cubic α-FAPbI 3 is found to be metastable at ambient temperature 13,18 . The FA + replacement with MA + perovskite is preferred to FAI because it has a long charge diffusion and an optimal output bandgap, which is comparable to ideal performance 13 . Therefore, as reported by Boucle et al. 19 , the mixed organic cation (FA + /MA + ) strategy is extremely useful in stabilizing the α-FAPbI 3 , simultaneously suppressing the yellow δ-FAPbI 3 phase, which is unsuitable for photovoltaic applications. This combination of cations quenches the spontaneous phase change from black to yellow or δ-phase, as shown later 20,21 . Due to its controlled stoichiometric ratios, a mix-cation perovskite has been suggested as an effective strategy to enhance stability and boost the PCE compared to mono-cation perovskite 13 . In particular, the incorporation of commonly known organic FA + /MA + into the A site cation is now well established to achieve more stable and efficient photocurrent generation as compared to their pure counterparts 22 . However, to our knowledge, no studies have been conducted to fully investigate their physical, chemical, and optoelectronic properties.
In this work, two different types of δ-FA-based and a control powder sample of pristine MAPbI 3 perovskite active layers are synthesized using a mechanochemically solvent-free solid-state reaction based on grinding method: (i) pristine δ-phase FAPbI 3 , (ii) FA 1−x MA x PbI 3 , where x = 0.3, 0.5, and 0.7. To address the drawbacks of pure MAPbI 3 and pure δ-FAPbI 3 , we utilized MAPbI 3 as crystal seeds to modulate the growth of δ-FAPbI 3 crystals and form a high-quality mixed-cation perovskite material FA 1−x MA x PbI 3 with large grain size, good crystallinity, fewer defects, and higher PCE. To know the influence of MA + cation addition on δ-FAPbI 3 , crystallinity, vibrational structure, element composition, morphology, thermal stability, and optical spectra are presented. More specifically, simulations of the device's electrical responses are performed using the Solar Cell Capacitance Simulator (SCAPS-1D) software, allowing us to discuss the influence of perovskite composition and evaluate the influences of material characteristics on the device performances of a solar cell. The influence of device parameters, such as the thickness of the absorber layer, spectral response, and external quantum efficiency, are highlighted in this study. As far as our literature review extends, this is the first report enlightening the correlation between green synthesis and SCAPS-1D simulated formamidinium organic cation-based perovskites solar devices, especially on pristine δ-phase FAPbI 3 , FA 0.7 MA 0.3 PbI 3 , FA 0.5 MA 0.5 PbI 3 , and FA 0.3 MA 0.7 PbI 3 . As a consequence, it would be meaningful for promising studies of perovskite-based optoelectronic devices.

Experimental
Materials. High-purity PbI 2 (99.999% trace metals basis, yellow powder), MAI with a purity of more than (≥ 99%, anhydrous, white powder), and FAI (99.99% trace metals basis, powder) were purchased from Sigma-Aldrich Company Ltd. All the chemicals were used without further purification.
To prepare MAPbI 3 material using the green mechanochemical synthesis approach, the high-pure precursors were weighed into a mortar (made of Zirconia to eliminate precursor contamination effectively) in stoichiometric amounts and ground together with a pestle for 50-60 min by hand at room temperature. Consequently, the black-colored MAPbI 3 appeared by blending 2.9 g of yellow powder (PbI 2 ) (1 mol) with 1.0 g of (1 mol) MAI white powder, yielding a total of 3.9 g mixture using a solvent-free solid-state approach until a magnificent structure was obtained. Correspondingly, the dark-yellow δ-phase FAPbI 3 was prepared by adding 2.68 g of PbI 2 (1 mol) with 1.0 g of FAI white powder (1 mol), yielding a total weight of 3.68 g mixture. As shown in Fig. 1, pure δ-FAPbI 3 has not been synthesized successfully using this method in ambient conditions because black Techniques. The crystallographic properties of the prepared samples and their phase identification were performed using an Empyrean PANalytical X-ray diffractometer (XRD) with a Cu anode x-ray source (Cu K α1 , 1.54060 Å). Raman spectra were collected on a WITec alpha300 instrument using a laser with a 532 nm excitation wavelength at 0.1 mW laser power and an acquisition time of 5 s. The attenuated total reflectance was used to generate Fourier transform infrared (FT-IR) spectra (ATR) configuration (Platinum ATR diamond, Bruker Co.) in the range of 400 to 4000 cm −1 . The elemental compositions and valence states of perovskite compositions were determined by using the Thermo Scientific™ K-Alpha™ XPS system. The measurements were conducted using a fully integrated, small-spot size of 400 µm with depth profiling capabilities with a base pressure of 10-9 m bar in the spectrometer and sample handler. The X-ray source is a monochromatic Al-Kα with an excitation energy of 1486.71 eV ranging from − 10 to 1350 eV, and a full-spectrum pass energy of 200 eV at a narrow spectrum of 50 eV. The microstructure of perovskite powders and elemental composition were characterized by using a field-emission scanning electron microscope (FE-SEM) and a dispersive energy X-ray (EDX) (Zeiss, Sigma 500 VP, Germany). The thermal stability of the present compositions was further confirmed by thermogravimetric and differential thermal analyses using a Shimadzu DTG-60H and Shimadzu TGA-50H in an interval from 28 to 800 °C at a heating rate of 10 °C min −1 under N 2 gas with a flow rate of 30 ml min −1 . The sample was placed in an Al 2 O 3 crucible, and approximately 5 mg of the powder was used for each experiment. UV-vis/NIR spectrophotometer (Jasco V-570, Japan) coupled with an integrating spherical reflectance unit (ISN) in the wavelength range  nm was used to investigate the UV-vis absorbance and diffuse reflectance spectra of several perovskite samples at ambient temperature. A 50 W xenon lamp measured the photoluminescence (PL) spectra at room temperature (Shimadzu RF-5301PC, Kyoto, Japan). All of the data was gathered at room temperature.

Results and discussions
Characterization. X-ray diffraction (XRD). Figure 2a,b presents the XRD patterns of pure MAPbI 3 and FA 1−x MA x PbI 3 with (x = 0.3, 0.5, and 0.7). By investigating the powder XRD spectra of MAPbI 3 , the MAPbI 3 structure is tetragonal as a symmetry group with I4/cm (108) space group, and the unit cell parameters are; a = b = 8.8718 Å, c = 12.6617 Å 23 . The preferred orientation along the (211) plane appeared, and the signature diffraction intensity peak of PbI 2 in the (002) direction at 13.927˚ was observed with the highest peak. For the tetragonal structure, the reflection peaks of (211) and (310) planes were misaligned with the cubic structure, 10  www.nature.com/scientificreports/ which would be useful for optimizing the cubic and tetragonal phases. The crystal structure is in good agreement with the previously published reports 24 as well as JCPDS standard no. 96-451-8044. The XRD examination confirms high crystallinity and pure perovskite tetragonal MAPbI 3 crystal structure. In comparison with MAPbI 3 perovskite, δ-FA-based compounds have received less attention, despite their potential. It is mainly because of the unstable nature of the pure δ-FAPbI 3 perovskite phase and its spontaneous evolution into its yellow hexagonal polymorph (δ-phase), which has made the studies delicate. Therefore, we start this study by first inspecting the structural behavior of the yellow δ-phase of FAPbI 3 , which has a hexagonal P63/mmc symmetry 25 . In turn, the FA 1-x MA x PbI 3 structures with a molar ratio of (x = 0.3, 0.5, 0.7) have a crystalline cubic phase of Pm-3 m (221) space group, as displayed in Fig. 2b. The unit cells were refined to be a = b = c = 6.3146 Å.
To assess the effects of mixed-organic cations, the (010) plane is selected. It is observed that as the MA proportion increases, the peak positions of the XRD spectra shift slightly towards a higher angle. Because the crystal lattice size of MAPbI 3 is smaller than that of δ-FAPbI 3 ; thus, according to the Bragg equation, a higher content of MA cation FA 1−x MA x PbI 3 will result in a shift of the XRD peaks towards a higher angle 26 ; as shown in Fig. 2a. Furthermore, the full width at half maximum (FWHM) narrows as the proportion of MA increases until x = 0.7, and then becomes wider further as the proportion of MA increases; this indicates slight differences in the crystal domain size of our samples. According to the Scherrer equation, the purer the organic cations, the larger the crystal domain. By comparing the characteristics of the XRD data of these samples, we can conclude that the FA and MA molecules are distributed uniformly within the materials. Because the molecular sizes of FA and MA are different, the strain will be induced at the boundaries between them and distributed uniformly within the crystals. The uniformly distributed strains account for the final pure cubic phase after the organic cations are mixed.
Raman measurements. Raman spectra of the investigated samples are displayed in Fig. 3a. The Raman spectra of the MAPbI 3 powder revealed the features of rocking motion, Pb-I-Pb, bending Pb-I stretching, and the multifaceted vibration modes of the CH 3 NH 3 cation. The peaks of the MAPbI 3 powder are situated at 71.4, 97.5, and 109 cm −1 , as illustrated in Fig. 3b. Notably, there are shifts in the peaks that happened for the perovskite based on FA cation, which indicated the change in the lattice of the phase transition. According to Lu et al. 27 , the Pb-I stretching forms to B 3 g symmetries, which mainly represent vibration information about the inorganic components in the material, were attributed to the peaks at 97.5 and 109 cm −1 . The translational modes of the organic cation CH 3 NH 3 in MAPbI 3 are connected to the peak at 71.4 cm −1 .
FT-IR analysis. FT-IR spectra of the pure MAPbI 3 and FA 1−x MA x PbI 3 with (x = 0.0, 0.3, 0.5, and 0.7) perovskites were studied between 400 and 4000 cm −1 . The structure and vibrational peaks ascribed to the substituents of perovskite materials are shown in Fig. 3b. In general, the -CH of the alkyl group displayed bending bands at 1250 and 1468 cm −1 for all samples, which is consistent with the symmetric bending mode of the CH 3 and CH 2 groups. The asymmetric and symmetric stretching modes of CH 2 were also attributed to two significant peaks at 2920 and 2970 cm −1 . Stretching vibration is seen in the C-N bands between 960 and 971 cm −1 for MAPbI 3 and FA 1−x MA x PbI 3 with (x = 0.0, 0.3, 0.5, and 0.7) perovskites. The CH 3 rocking vibration is responsible for the IR bands at 671 and 906 cm −1 . The NH 3+ rocking vibration was situated at 1249-1260 cm −1 for all samples. Furthermore, broadband has been seen at 3300-3500 cm −1 , which has been linked to the amine groups -NH. In the infrared, the NH 3+ bands vibrate asymmetrically at 3170 cm −1 . The asymmetrical deformation vibration of NH 3+ is linked to the bands at 1608 cm −1 . The NH 3+ scissoring vibration is linked to the bands at 1467 and 1465 cm −128,29 .
X-ray photoelectron spectroscopy (XPS). The XPS measurements were employed on MAPbI 3 , δ-FAPbI 3 , and FA 0.7 MA 0.3 PbI 3 perovskite samples to investigate the interaction of FA/MA organic-organic species. In addition, XPS confirmed the elemental composition after precisely small incorporation of MA material and understand-  Figure 4a depicts the broad-range XPS survey spectrum of a typical MAPbI 3 perovskite, which reveals peaks at binding energies of 402.49 eV and 284.80 eV, respectively, matching the photoelectron peaks of N 1 s and C 1 s. Moreover, the doublet peaks of I and Pb are found with concomitant spin-orbit splitting at 619.29 eV and 138.45 eV, respectively. As a consequence, the presence of C, N, Pb, and I components in the produced powder is revealed by this broad energy spectrum, which is consistent with the earlier report 30 , illustrating the purity and complete conversion of MAPbI 3 perovskite. Besides, the structure is also elucidated by the elements including C, N, Pb, and I based on the spectrum of the FA 1-x MA x PbI 3 with x = (0.0 and 0.3) . According to the intensity reliance of core levels, the I 4d and Pb 5d may precisely detect the I/Pb proportions in the samples since they are the same kind of orbital. Because their binding energies are identical, the observed electrons come from the same probing depth. Unfortunately, oxygen sits on the crystal surface for the sample of x = 0.3 may be due to the decontamination during XPS measurements. Table 1 shows the main quantification results, including atomic concentrations of the core levels extracted from XPS survey spectra of MAPbI 3    www.nature.com/scientificreports/ were deconvoluted with the CasaXPS program using a non-linear least-squares fitting procedure. The surface atomic percentages were determined using the manufacturer's sensitivity factors from the relevant peak regions. The narrow scan XPS spectra of the I 3d, O 1 s, and Pb 4f. regions for δ-FAPbI 3 , MAPbI 3 , and MA-doped with 0.3 are described in Fig. 4a-c. For δ-FAPbI 3 , the deconvoluted XPS spectra of the core level I 3d doublets of 3d 3/2 and 3d 5/2 at 619.30 and 630.75 eV, respectively, corresponding to the I 3 charge, are illustrated in Fig. 4b. According to previous studies 31 , the lower binding component of I 3d situated at 619.30 eV is assignable to triiodide I 3 − and the existence of oxidized species of iodine at the surface, which generates the I 2+ cation and the iodate anion (IO 2 ), might be indicated by the extra widening signal at 622.3 eV. The characteristic peak separation of the associated spin-orbit splitting is determined at 4.88 eV. Correspondingly, for MAPbI 3 , the same figure shows the XPS spectra of I 3d, where two peaks were observed at 619.29 and 630.76 eV, which are characteristic of 3d 5/2 and 3d 3/2 , respectively, indicating the presence of I in the (−1) state. Accordingly, an insignificant shift of ∼0.01 eV is observed for I 3d spectrum in δ-FAPbI 3 , which might correspond to a relative effect of the local chemical environment. Additionally, for FA 0.7 MA 0.3 PbI 3 , the XPS measurement shows two peaks also for I 3d 5/2 and 3d 3/2 doublets spectra at 618.98 eV and 630.44 eV, respectively. Consequently, a slightly significant shift of ∼0.3 eV is observed for I 3d spectrum, which might correspond to a relatively high oxidation level. As illustrated in Fig. 4c for FA 0.7 MA 0.3 PbI 3 , the O 1 s core level was observed at 532.62 eV. The presence of O 1 s core level was found due to an oxidation level as mentioned before, or the effect of the local chemical environment.
Finally, for the Pb 4f. core level, in the case of δ-FAPbI 3 , there are two intense peaks located at 138.49 eV and 143.34 eV, corresponding to 4f 7/2 and 4f 5/2 , respectively, with a distinct peak separation of 4.88 eV, indicating the presence of Pb +2 that could be ascribed to the Pb-I bond in perovskite 32 , as shown in Fig. 4d. At lower binding energies, the prepared material exhibits two additional peaks reflecting the presence of metallic Pb (0) , which is frequently detected in XPS spectra of halide perovskites 33 . Similarly, for a perovskite with MAPbI 3 and mixed-cations of the FA 0.7 MA 0.3 PbI 3 , the Pb 4f. spectrum slightly shifts negatively to up 0.32 eV with higher binding energies.
Morphology and EDX analysis. FE-SEM is used to test the morphology of the samples. The FE-SEM images of the δ-FAPbI 3 , MAPbI 3 , and FA 1−x MA x PbI 3 with (x = 0.3, 0.5, and 0.7) perovskite samples are displayed in Fig. 5a-e. Both pure δ-FAPbI 3 and MAPbI 3 showed perovskite structures with homogenous particle distribution. After adding 30% MA, tiny particles accumulated with enhancement in the grain size of the particles (see Fig. 5c). By increasing the doping of MA by 50% and 70%, the shape appears like large rocks, and some small circular rocks are scattered on it, but the small rocks seem to merge with the large ones, and that high doping can explain this has integrated with the particles of δ-FAPbI 3 effectively, see Fig. 5d-e. SEM images demonstrate that the FA 0.5 MA 0.5 PbI 3 has the largest crystal size, indicating that the perovskite has few grain boundary defects, which is beneficial to solar cell applications. Furthermore, some articles claim that FA 1−x MA x PbI 3 perovskites showed increased crystallinity after MA ions were incorporated into the δ-FAPbI 3 crystal structure, which has a favorable influence on photovoltaic industries 34 . The dispersive energy X-ray (EDX) analysis was performed for more investigations, as seen in Fig. 6a-e. The analysis confirms the elemental compositions and purity of the as-prepared samples, as revealed in Table 2. The EDX results agree with the molar ratio of the elemental analysis to precisely determine the metal ratios stoichiometry of the as-prepared materials.
Thermogravimetric analysis. To investigate the thermal stability of the as-prepared perovskites, thermogravimetric analysis (TGA) was performed under nitrogen flow from room temperature to 800 °C. The TGA and derivative thermogravimetric (DTA) results showed that MAPbI 3 , δ-FAPbI 3 , and FA 1−x MA x PbI 3 perovskites decomposed before melting at the temperature range of 338.2-409.3 °C 25 , as revealed in Fig. 7a-e a small weight loss (≤ 3%) for the samples was detected may be due to the evaporation of the atmospheric moisture in the first stage. The decomposition temperature also gradually increases with the increase in MAPbI 3 content, thereby indicating that MAPbI 3 can increase the thermal stability of perovskites, which is good for device stability based on FA 1−x MA x PbI 3 . No mass loss was detected for δ-FAPbI 3 when the sample was heated in nitrogen until it reached 346.9 °C, see Fig. 7a. From 346.9 to 407.6 °C, the composition began to decompose through a weight loss matching FAI and PbI 2 . On the other hand, FAI begins to evaporate at a lower temperature of 278 °C for the typical precursor mixture of FAI and PbI 2 owing to the decomposition of the unreacted free FAI to FA + , resulting in a weight loss equivalent to the loss of HI molecules. In the second stage, steady weight loss was detected for both compounds up to 600 °C, corresponding to the transition of PbO 2 caused by the molecule being degraded in the air. Figure 7b depicts the thermal stability of MAPbI 3 until 338.2 °C, after which it loses 27.2% of its initial weight at 516.5 °C. It shows that MAPbI 3 decomposes into solid PbI 2 , along with the evolution of gaseous NH 3 and CH 3 I 35 . Decomposition of other MAPbI 3 perovskite samples may produce gaseous CH 3 NH 2 and HI, leading to the loss of their structural and optoelectronic properties. Similarly, Fig. 7c-f shows that loss varies from 371.9 to 409.3 °C depending on the level of MA-doping (i.e., x = (0.3, 0.5, 0.7)). Consequently, at x = 0.3, no mass loss until 371.9 °C before degradation to 23.6% of its initial weight at 548.8 °C, as illustrated in Fig. 7c. By increasing the doping level by 50% and 70%, the thermal stability of the samples is increased to 337.1 °C and 342.0 °C, respectively, as displayed in Fig. 7d-e. Therefore, the TGA data presented in this figure show that the addition of CH 3 NH 3 to FA/MA mixed perovskites can actually improve their thermal stability, which is surprising considering the volatility of CH 3 NH 3 . One possible explanation for this observation is that the CH 3 NH 3 molecules may interact with the perovskite lattice and stabilize its crystal structure. Previous studies have shown that CH 3 NH 3 molecules can form hydrogen bonds with the halide ions in the perovskite lattice, which can enhance its stability against thermal degradation. Another possible explanation is that the CH 3 NH 3 molecules may act as a passivation agent, reducing the number of defects and trap states in the perovskite film. This can improve the charge transport properties of the film and enhance its overall performance and stability. To further investigate these  www.nature.com/scientificreports/ observations, additional experiments and analyses, such as XRD, FTIR and PL spectroscopy, are performed to examine the crystal structure and optoelectronic properties of the perovskite films with and without CH 3 NH 3 addition. Overall, TGA studies reveal the thermodynamic phase purity of the synthesized δ-FAPbI 3 , and mixed FA/MA perovskites. They show high stability at ambient temperature, which is beneficial for long-term storage and commercialization. The surprising improvement in thermal stability observed in the study with CH 3 NH 3 addition to FA/MA mixed perovskites opens up new avenues for the development of more stable and durable perovskite solar cells.
Optoelectronic properties. UV-visible spectroscopy is a non-destructive analytical chemistry technique used for determining the quantitative composition of transition metal ions and highly conjugated organic molecules 36 . The optical properties of δ-FAPbI 3 , MAPbI 3 , and FA 1−x MA x PbI 3 with (x = 0.3, 0.5, and 0.7) were studied by measuring the absorbance and reflectance spectra of the synthesized powders within 200-1000 nm wavelength range. The spectra of all samples are presented in Fig. 8a,b. The absorption edge is shifted positively from 573 nm for δ-FAPbI 3 to 866 nm for (FA-MA) mixed cation with molar ratio of 30%. After adding 50% of MA, the absorption edge still increases to 874 nm and decreases to 868 nm for 70% molar ratio. The optical absorption of δ-FAPbI 3 has partially covered the visible region. Nevertheless, for MAPbI 3 and FA 1−x MA x PbI 3 , the optical absorption covers the entire visible as well as near IR regions. Consequently, the MA-doped samples have higher absorption in the visible range compared to the typical MAPbI 3 . In addition, the optical bandgap energy (E g ) of the as-prepared samples was estimated from diffuse reflectance UV-vis data and the Kubelka-Munk equation as shown in the following formulae 24 : (1)   where R, α, and S denote reflected light, absorption, and scattering coefficients, respectively. The value n equals 0.5 or 2 depending on direct or indirect bandgaps. Figure 8b shows the E g values of 2.288 eV and 1.547 eV for δ-FAPbI 3 and MAPbI 3 samples, respectively, which is in good consistency with previous reports 37 . Besides, FA 1−x MA x PbI 3 with x = (0.3, 0.5, 0.7), the values of E g are 1.480 eV,1.472 eV, and 1.486 eV, respectively. Therefore, we observed that the FA 1−x MA x PbI 3 powders have the highest absorbance intensity and the broadest absorbance spectrum, followed by the MAPbI 3 and δ-FAPbI 3 perovskites, which have the narrowest absorbance spectrum.
In addition, as illustrated in Fig. 8b, it is possible to state that the energy bandgap for MA-doped with x = 0.5 is smaller than that of the others, implying its suitable applications for solar cells.
Photoluminescence analysis. Photoluminescence (PL) measurements were conducted at room temperature for MAPbI 3 and FA 1−x MA x PbI 3 , as shown in Fig. 9. The measurement excitation source is a diode laser with a power of 10 mW that operates at 660 nm. For pure MAPbI 3 , single-peak emission appears at ~ 800 nm, whereas for the mixed-organic cation perovskites, single emission peak appears at the wavelength range from 834 to 842 nm positions. Stokes shifts are very small for all samples; this indicates the recombination of free excitons 38 . The FWHM of PL spectra for pure and mixed-organic cation perovskites is narrow (~ 7 nm) due to the excitonphonon interaction. The PL peak positions for mixed organic cation perovskite materials shift positively as the is widely regarded as the most realistic modeling and simulation technique for various types and structures of metal halide perovskite solar cells. One of the drawbacks of SCAPS-1D that we have encountered is the inability to generate the dark J-V curves and the failure to account for reflection at interfaces, which causes an underestimation of the short-circuit current density (J sc ) 40 . In this work, the SCAPS-1D simulator was also used to predict and optimize the optoelectronic performance of our synthesized materials, as well as to investigate the impact of the absorber thickness on the device performance 41 . We employed the values of measured energy band gaps obtained from the above-mentioned mechanochemical synthesis approach as input parameters in SCAPS to simulate the performance of perovskite devices. It seems to be a significant gap between the energy band gap of perovskite powders and thin-film devices. Hence, as stated later, we assume three interface layers to analog the real devices by increasing the defect densities as input variables.
One-dimensional planar n-i-p perovskite devices (FTO/IL 1 /TiO 2 /IL 2 /Perovskites/IL 3 /Spiro-OMeTAD/Au) were simulated using SCAPS-1D software. The device configuration and energy band diagram are illustrated in Fig. 10a,b. Three very thin interface layers (IL 1 , IL 2 , and IL 3 ) have been introduced in the model to mimic the defective interface between the absorber layer and transport layers. where ε is permittivity, q is the electron charge, G is generation rate, D is diffusion coefficient, ψ is electrostatic potential, ξ is the electric field, p(x), n(x), p t (x), p n (x) are free holes, free electrons, trapped holes, and trapped electrons, respectively. N + d stands for ionized donor-like doping concentration and N − a refers to ionized acceptorlike doping concentration. x is the direction along the thickness.
The optical bandgap energy of the light-harvesting materials (active layers) is obtained from our experimental absorption spectra measurements, which strongly influence the photovoltaic performance of these cells, according to Shockley and Queisser 48 . Basic parameters used to perform simulation work gathered from various experimental and theoretical published works are summarized in Table 3 [49][50][51][52][53][54][55] , to firstly validate and verify our software 50,56 . The values for the defects in active layers used to simulate the work, as well as the considered interface defect density in the device simulation, is presented in Table 4. The absorption coefficient spectra ( α ) of all layers is calculated in SCAPS-1D via α = A α (E − E g ) 1/2 and the prefactors A α was assumed to be (4) dp n dt = G p − p n − p n0 τ p − p n µ p dξ dx − µ p ξ dp n dx + D p d 2 p n dx 2 (5) dn p dt = G n − n p − n p0 τ n + n p µ n dξ dx + µ n ξ dn p dx + D n d 2 n p dx 2 www.nature.com/scientificreports/ 10 5 . This assumption was used as in many previous studies on perovskite-based solar cells 50 . In this simulation model, ideal perovskite devices are meticulously optimized without considering R series and R shunt resistances. This impractical step is a key factor in determining the maximum limit of device performance achieving highly stable photovoltaic performance parameters when considering optimal operation 51 . To validate and verify our simulated model, the recently reported experimental works for the similar planar n-i-p structure (FTO/TiO 2 /FAPbI 3 or MAPbI 3 /Spiro-OMeTAD/Au) obtained by Michael Grätzel et. al. 57 and NREL cell efficiency data 7 , respectively, are compared to those obtained by SCAPS-1D. Table 5 shows the validated photovoltaic characteristics of solar cell devices reported in the literature and our simulated SCAPS. The thickness of the FTO, ETL, absorber, and HTL layers are chosen to be 100 nm, 50 nm, 800 nm, and 50 nm, respectively. The comparative current-voltage (J-V) characteristic data are shown in Table 4 with the four performance indicators, open circuit voltage (V OC ), short circuit current density (J SC ), fill factor (FF), and efficiency ( η ). Comparing the data, it is confirmed that our Table 3. Electrical properties of the materials used in our simulated structures [49][50][51][52][53][54][55] .  Electron thermal velocity, ν th(n) (cm s        Fig. 11b. Figure 11c shows the spectral power responsivity in A/W for all simulated devices 60 . Due to the use of two wide and narrow bandgap absorber layers, the optical absorption edge of the device shifts from 540 nm to more than 840 nm. It can be seen that a preferable quantum efficiency in the visible wavelength range was obtained for the perovskite structures. The absorption edge of FA-based devices is about 300 nm higher than FAPbI 3 structure which is due to the light absorption of the latter that has a lower bandgap of 2.288 eV compared to ~ 1.5 eV.
In conclusion, the champion perovskite solar cell based on FA 0.5 MA 0.5 PbI 3 absorber layer with a thickness of 800 nm has achieved the highest PCE of 26.22% compared to other devices 61,62 . Based on it, this device has a good application prospect in the solar cell field.
The thickness of the absorber layer has the most crucial parameter and has a remarkable influence on the solar cell performance. Hence, in this modeling, we focus only on the impact of variation of thickness on the photovoltaic performance (i.e., V OC , J SC , FF, and PCE) of the above-mentioned devices. Keeping all electrical parameters constant as listed in Table 3, the thickness of all five simulated devices is varying from 0.05 to 2.0 µm . The results of this variation in thickness are illustrated in Fig. 12a-d. As shown in Fig. 12a, the simulation results illustrate that with absorber thickness increasing, open-circuit voltage (V OC ) increases up to 0.2 µm . Beyond this thickness, V OC starts to decrease slightly, except for Ds (A) device is continuously increasing. In the V OC increase stage, the hole-electron recombination is lower with thinner absorber layers, keeping the dark saturation current (I 0 ) at a low level. As a consequence, different excess carrier concentrations are a benefit to generate a higher lightgenerated current (I L ) and promote the rising of V OC . However, in the V OC decrease stage, the thicker absorber tends to raise I 0 to a higher level and provides more opportunity for carrier recombination, resulting in a sharp decrease in V OC . On the other hand, Fig. 12b indicates that with absorber thickness increasing, short-current density (J SC ) is continuously increasing. In the thin perovskite layer, the charge carrier diffusion length is greater than the thickness, and most of the extra carriers can reach both electrodes and generate power. The increase in thickness causes more light absorption and more extra carrier concentration, which brings J SC values to upraise. Therefore, by increasing the photogenerated carriers, the value of J SC increases. Moreover, for FA-based devices, the fill factor continuously drops from 86.45 to 81.07% with the thickness varying from 0.5 to 0.9 µm , see Fig. 12c.
The MAPbI 3 -based device, D S (B), fill factor has quite a similar behavior except that it was continuously decreased with increasing thickness. Moreover, D s (A) device has a reverse bell-like-shape behavior, FF% sharply decreased until it reaches 83.37% at a thickness of 1.15 µm , then, exponentially increasing with the increasing of the layer thickness. The fill Factor is considered as an ability to deliver available power to a load generated by a cell, in other words, internal power depletion. In thicker absorbers, the internal power depletion enhances and causes a reduction of the fill factor. Figure 12d shows that the PCE% characteristic of all structures follows the same trend and is particularly identical from 0.05 to 1.2 μm of the absorber layer thickness except for device D S (A). As observed in Fig. 12d, D S (A) device has a very low efficiency compared to other devices due to its bandgap energy being very high (E g = 2.288 eV). Besides, by increasing the absorber thickness in the solar cell, the PCE increases until it reaches nearly 800 nm. After that, it slightly impacts the PV parameters in the (0.8-2.0) μm regime.

Conclusions
In this work, we demonstrated a novel and promising green chemical strategy for producing δ-FAPbI 3 , MAPbI 3, and δ-FA-based perovskite materials using a mechanochemical synthesis technique. The results showed that the obtained mixed-cation FA 1−x MA x PbI 3 with (x = 0.3, 0.5, and 0.7) perovskites using this strategy have achieved excellent crystallinity and purity as evidenced by different characterization techniques such as XRD, SEM-EDX, FTIR, XPS, and Raman spectroscopy. TGA measurements showed the thermal stability of the prepared samples within the range from 346.9 to 409.3 °C, depending on the rate of doping. The absorbance of light proved that FA 1-x MA x PbI 3 perovskites were boosted in the visible region and are in good agreement with recently published works. Furthermore, with a molar ratio of 50%, the bandgap energy for the mixed-structured perovskite (FA 0.5 MA 0.5 PbI 3 ) was reduced to 1.472 eV, compared to 2.288 and 1.547 eV for δ-FAPbI 3 and MAPbI 3 , respectively. Numerical simulation using SCAPS-1D software was proposed to predict the effect of hybrid organiccation perovskites on the performance of solar cell devices. The simulation model was successfully verified by comparing it with FA-based solar cells performance parameters reported in recent literature. The variation of absorber layer thickness on the device performance was also investigated, indicating that an optimal thickness range exists from 0.8 to 2.0 µm for preparing efficient solar cells. It was evidenced that the proposed planar n-i-p perovskite device (FTO/IL 1 /TiO 2 /IL 2 /FA 0.5 MA 0.5 PbI 3 /IL 3 /Spiro-OMeTAD/Au) shows a better performance with an efficiency of 26.22% compared to 8.43 eV for FAPbI 3 -based solar cell.

Data availability
All data generated or analyzed in this study are available from the corresponding authors upon any reasonable request.