# Investigation of Opto-Electronic Properties and Stability of Mixed-Cation Mixed-Halide Perovskite Materials with Machine-Learning Implementation

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mixed-Cation Mixed-Halide Perovskites

## 3. Methods

#### 3.1. Density Functional Theory Calculations

#### 3.2. Assessment of 3D Perovskite Structures, Opto-Electronic Properties and Stability

#### 3.3. Machine-Learning Models

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Qiu, L.; Ono, L.K.; Qi, Y. Advances and challenges to the commercialization of organic–inorganic halide perovskite solar cell technology. Mater. Today Energy
**2018**, 7, 169–189. [Google Scholar] [CrossRef] - Aranda, C.A.; Caliò, L.; Salado, M. Toward Commercialization of Stable Devices: An Overview on Encapsulation of Hybrid Organic-Inorganic Perovskite Solar Cells. Crystals
**2021**, 11, 519. [Google Scholar] [CrossRef] - Kundu, S.; Kelly, T.L. In situ studies of the degradation mechanisms of perovskite solar cells. EcoMat
**2020**, 2, e12025. [Google Scholar] [CrossRef] - Bryant, D.; Aristidou, N.; Pont, S.; Sanchez-Molina, I.; Chotchunangatchaval, T.; Wheeler, S.; Durrant, J.R.; Haque, S.A. Light and oxygen induced degradation limits the operational stability of methylammonium lead triiodide perovskite solar cells. Energy Environ. Sci.
**2016**, 9, 1655–1660. [Google Scholar] [CrossRef] [Green Version] - Aristidou, N.; Eames, C.; Sanchez-Molina, I.; Bu, X.; Kosco, J.; Islam, M.S.; Haque, S.A. Fast oxygen diffusion and iodide defects mediate oxygen-induced degradation of perovskite solar cells. Nat. Commun.
**2017**, 8, 15218. [Google Scholar] [CrossRef] - Yang, J.; Yuan, Z.; Liu, X.; Braun, S.; Li, Y.; Tang, J.; Gao, F.; Duan, C.; Fahlman, M.; Bao, Q. Oxygen- and Water-Induced Energetics Degradation in Organometal Halide Perovskites. ACS Appl. Mater. Interfaces
**2018**, 10, 16225–16230. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Li, M.; Li, H.; Fu, J.; Liang, T.; Ma, W. Recent Progress on the Stability of Perovskite Solar Cells in a Humid Environment. J. Phys. Chem. C
**2020**, 124, 27251–27266. [Google Scholar] [CrossRef] - Xu, F.; Zhang, T.; Li, G.; Zhao, Y. Mixed cation hybrid lead halide perovskites with enhanced performance and stability. J. Mater. Chem. A
**2017**, 5, 11450–11461. [Google Scholar] [CrossRef] - Li, Q.; Zhao, Y.; Zhou, W.; Han, Z.; Fu, R.; Lin, F.; Yu, D.; Zhao, Q. Halogen Engineering for Operationally Stable Perovskite Solar Cells via Sequential Deposition. Adv. Energy Mater.
**2019**, 9, 1902239. [Google Scholar] [CrossRef] - Yang, L.; Xiao, Y.; Han, G.; Chang, Y.; Zhang, Y.; Hou, W.; Lin, J.Y.; Li, H. Enhanced stability and efficiency of perovskite solar cells via bifunctional group passivation with thiosalicylic acid. Org. Electron.
**2020**, 81, 105681. [Google Scholar] [CrossRef] - Stoumpos, C.C.; Cao, D.H.; Clark, D.J.; Young, J.; Rondinelli, J.M.; Jang, J.I.; Hupp, J.T.; Kanatzidis, M.G. Ruddlesden–Popper Hybrid Lead Iodide Perovskite 2D Homologous Semiconductors. Chem. Mater.
**2016**, 28, 2852–2867. [Google Scholar] [CrossRef] - Ortiz-Cervantes, C.; Carmona-Monroy, P.; Solis-Ibarra, D. Two-Dimensional Halide Perovskites in Solar Cells: 2D or not 2D? ChemSusChem
**2019**, 12, 1560–1575. [Google Scholar] [CrossRef] [PubMed] - Meggiolaro, D.; De Angelis, F. First-Principles Modeling of Defects in Lead Halide Perovskites: Best Practices and Open Issues. ACS Energy Lett.
**2018**, 3, 2206–2222. [Google Scholar] [CrossRef] [Green Version] - Brakkee, R.; Williams, R.M. Minimizing Defect States in Lead Halide Perovskite Solar Cell Materials. Appl. Sci.
**2020**, 10, 3061. [Google Scholar] [CrossRef] - Roknuzzaman, M.; Zhang, C.; Ostrikov, K.K.; Du, A.; Wang, H.; Wang, L.; Tesfamichael, T. Electronic and optical properties of lead-free hybrid double perovskites for photovoltaic and optoelectronic applications. Sci. Rep.
**2019**, 9, 718. [Google Scholar] [CrossRef] [Green Version] - Maiti, A.; Chatterjee, S.; Peedikakkandy, L.; Pal, A.J. Defects and Their Passivation in Hybrid Halide Perovskites toward Solar Cell Applications. Sol. RRL
**2020**, 4, 2000505. [Google Scholar] [CrossRef] - Tao, S.X.; Cao, X.; Bobbert, P.A. Accurate and efficient band gap predictions of metal halide perovskites using the DFT-1/2 method: GW accuracy with DFT expense. Sci. Rep.
**2017**, 7, 14386. [Google Scholar] [CrossRef] - Frost, J.M.; Butler, K.T.; Brivio, F.; Hendon, C.H.; van Schilfgaarde, M.; Walsh, A. Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells. Nano Lett.
**2014**, 14, 2584–2590. [Google Scholar] [CrossRef] [Green Version] - Tenuta, E.; Zheng, C.; Rubel, O. Thermodynamic origin of instability in hybrid halide perovskites. Sci. Rep.
**2016**, 6, 37654. [Google Scholar] [CrossRef] [Green Version] - Ivanov, I.; Steparuk, A.; Bolyachkina, M.; Tsvetkov, D.; Safronov, A.; Zuev, A. Thermodynamics of formation of hybrid perovskite-type methylammonium lead halides. J. Chem. Thermodyn.
**2018**, 116, 253–258. [Google Scholar] [CrossRef] - Juarez-Perez, E.J.; Ono, L.K.; Uriarte, I.; Cocinero, E.J.; Qi, Y. Degradation Mechanism and Relative Stability of Methylammonium Halide Based Perovskites Analyzed on the Basis of Acid–Base Theory. ACS Appl. Mater. Interfaces
**2019**, 11, 12586–12593. [Google Scholar] [CrossRef] [Green Version] - Zhang, Y.Y.; Chen, S.; Xu, P.; Xiang, H.; Gong, X.G.; Walsh, A.; Wei, S.H. Intrinsic Instability of the Hybrid Halide Perovskite Semiconductor CH3NH3PbI3. Chin. Phys. Lett.
**2018**, 35, 036104. [Google Scholar] [CrossRef] [Green Version] - Senocrate, A.; Kim, G.Y.; Grätzel, M.; Maier, J. Thermochemical Stability of Hybrid Halide Perovskites. ACS Energy Lett.
**2019**, 4, 2859–2870. [Google Scholar] [CrossRef] [Green Version] - Ciccioli, A.; Latini, A. Thermodynamics and the Intrinsic Stability of Lead Halide Perovskites CH3NH3PbX3. J. Phys. Chem. Lett.
**2018**, 9, 3756–3765. [Google Scholar] [CrossRef] [PubMed] - Li, Z.; Xu, Q.; Sun, Q.; Hou, Z.; Yin, W.J. Thermodynamic Stability Landscape of Halide Double Perovskites via High-Throughput Computing and Machine Learning. Adv. Funct. Mater.
**2019**, 29, 1807280. [Google Scholar] [CrossRef] - Park, H.; Ali, A.; Mall, R.; Bensmail, H.; Sanvito, S.; El-Mellouhi, F. Data-driven enhancement of cubic phase stability in mixed-cation perovskites. Mach. Learn. Sci. Technol.
**2021**, 2, 025030. [Google Scholar] [CrossRef] - Wu, T.; Wang, J. Deep Mining Stable and Nontoxic Hybrid Organic–Inorganic Perovskites for Photovoltaics via Progressive Machine Learning. ACS Appl. Mater. Interfaces
**2020**, 12, 57821–57831. [Google Scholar] [CrossRef] - Le Corre, V.M.; Sherkar, T.S.; Koopmans, M.; Koster, L.J.A. Identification of the dominant recombination process for perovskite solar cells based on machine learning. Cell Rep. Phys. Sci.
**2021**, 2, 100346. [Google Scholar] [CrossRef] - Workman, M.; Zhi Chen, D.; Musa, S.M. Machine Learning for Predicting Perovskite Solar Cell Opto-Electronic Properties. In Proceedings of the 2020 International Conference on Data Analytics for Business and Industry: Way Towards a Sustainable Economy (ICDABI), Sakheer, Bahrain, 26–27 October 2020; pp. 1–5. [Google Scholar] [CrossRef]
- Tao, Q.; Xu, P.; Li, M.; Lu, W. Machine learning for perovskite materials design and discovery. Npj Comput. Mater.
**2021**, 7, 23. [Google Scholar] [CrossRef] - Bidikoudi, M.; Kymakis, E. Novel approaches and scalability prospects of copper based hole transporting materials for planar perovskite solar cells. J. Mater. Chem. C
**2019**, 7, 13680–13708. [Google Scholar] [CrossRef] [Green Version] - Kim, E.B.; Akhtar, M.S.; Shin, H.S.; Ameen, S.; Nazeeruddin, M.K. A review on two-dimensional (2D) and 2D-3D multidimensional perovskite solar cells: Perovskites structures, stability, and photovoltaic performances. J. Photochem. Photobiol. C Photochem. Rev.
**2021**, 48, 100405. [Google Scholar] [CrossRef] - Gholipour, S.; Ali, A.M.; Correa-Baena, J.P.; Turren-Cruz, S.H.; Tajabadi, F.; Tress, W.; Taghavinia, N.; Grätzel, M.; Abate, A.; De Angelis, F.; et al. Globularity-Selected Large Molecules for a New Generation of Multication Perovskites. Adv. Mater.
**2017**, 29, 1702005. [Google Scholar] [CrossRef] - Kieslich, G.; Sun, S.; Cheetham, A.K. Solid-state principles applied to organic–inorganic perovskites: New tricks for an old dog. Chem. Sci.
**2014**, 5, 4712–4715. [Google Scholar] [CrossRef] - Shannon, R.D. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. Sect. A
**1976**, 32, 751–767. [Google Scholar] [CrossRef] - Raifuku, I.; Chiang, Y.H.; Hou, C.H.; Li, M.H.; Lin, C.F.; Lin, P.Y.; Shyue, J.J.; Chen, P. Formamide iodide: A new cation additive for inhibiting δ-phase formation of formamidinium lead iodide perovskite. Mater. Adv.
**2021**, 2, 2272–2277. [Google Scholar] [CrossRef] - D’Annibale, A.; Panetta, R.; Tarquini, O.; Colapietro, M.; Quaranta, S.; Cassetta, A.; Barba, L.; Chita, G.; Latini, A. Synthesis, physico-chemical characterization and structure of the elusive hydroxylammonium lead iodide perovskite NH3OHPbI3. Dalton Trans.
**2019**, 48, 5397–5407. [Google Scholar] [CrossRef] - Akbulatov, A.F.; Frolova, L.A.; Anokhin, D.V.; Gerasimov, K.L.; Dremova, N.N.; Troshin, P.A. Hydrazinium-loaded perovskite solar cells with enhanced performance and stability. J. Mater. Chem. A
**2016**, 4, 18378–18382. [Google Scholar] [CrossRef] - Han, Q.; Bae, S.H.; Sun, P.; Hsieh, Y.T.; Yang, Y.M.; Rim, Y.S.; Zhao, H.; Chen, Q.; Shi, W.; Li, G.; et al. Single Crystal Formamidinium Lead Iodide (FAPbI3): Insight into the Structural, Optical, and Electrical Properties. Adv. Mater.
**2016**, 28, 2253–2258. [Google Scholar] [CrossRef] [PubMed] - Ma, D.; Dai, N.; Lan, Y. Solution Route to Single-Crystalline Ethylammonium Lead Halide Microstructures. ChemistrySelect
**2019**, 4, 2174–2180. [Google Scholar] [CrossRef] - Kim, Y.; Bae, C.; Jung, H.S.; Shin, H. Enhanced stability of guanidinium-based organic-inorganic hybrid lead triiodides in resistance switching. APL Mater.
**2019**, 7, 081107. [Google Scholar] [CrossRef] [Green Version] - Becker, M.; Wark, M. Organic Cation Substitution in Hybrid Perovskite CH3NH3PbI3 with Hydroxylammonium (NH3OH+): A First-Principles Study. J. Phys. Chem. C
**2018**, 122, 3548–3557. [Google Scholar] [CrossRef] - Li, W.G.; Rao, H.S.; Chen, B.X.; Wang, X.D.; Kuang, D.B. A formamidinium–methylammonium lead iodide perovskite single crystal exhibiting exceptional optoelectronic properties and long-term stability. J. Mater. Chem. A
**2017**, 5, 19431–19438. [Google Scholar] [CrossRef] - Xiao, Z.; Wang, Q.; Wu, X.; Wu, Y.; Ren, J.; Xiong, Z.; Yang, X. Efficient light-emitting devices based on mixed-cation lead halide perovskites. Org. Electron.
**2020**, 77, 105546. [Google Scholar] [CrossRef] - Wang, Y.; Zhang, T.; Li, G.; Xu, F.; Wang, T.; Li, Y.; Yang, Y.; Zhao, Y. A mixed-cation lead iodide MA
_{1-x}EA_{x}PbI3 absorber for perovskite solar cells. J. Energy Chem.**2018**, 27, 215–218. [Google Scholar] [CrossRef] [Green Version] - Liu, D.; Li, Q.; Wu, K. Ethylammonium as an alternative cation for efficient perovskite solar cells from first-principles calculations. RSC Adv.
**2019**, 9, 7356–7361. [Google Scholar] [CrossRef] [Green Version] - Wang, R.T.; Liu, E.E.; Xu, A.F.; Yang, L.W.; Chen, J.Y.; Xu, G. Ethylammonium Lead Iodide Formation in MAPbI3 Precursor Solutions by DMF Decomposition and Organic Cation Exchange Reaction. Crystals
**2020**, 10, 162. [Google Scholar] [CrossRef] [Green Version] - Jodlowski, A.D.; Roldán-Carmona, C.; Grancini, G.; Salado, M.; Ralaiarisoa, M.; Ahmad, S.; Koch, N.; Camacho, L.; de Miguel, G.; Nazeeruddin, M.K. Large guanidinium cation mixed with methylammonium in lead iodide perovskites for 19% efficient solar cells. Nat. Energy
**2017**, 2, 972–979. [Google Scholar] [CrossRef] [Green Version] - Tsarev, S.; Boldyreva, A.G.; Luchkin, S.Y.; Elshobaki, M.; Afanasov, M.I.; Stevenson, K.J.; Troshin, P.A. Hydrazinium-assisted stabilisation of methylammonium tin iodide for lead-free perovskite solar cells. J. Mater. Chem. A
**2018**, 6, 21389–21395. [Google Scholar] [CrossRef] - Yu, S.; Liu, H.; Wang, S.; Zhu, H.; Dong, X.; Li, X. Hydrazinium cation mixed FAPbI3-based perovskite with 1D/3D hybrid dimension structure for efficient and stable solar cells. Chem. Eng. J.
**2021**, 403, 125724. [Google Scholar] [CrossRef] - Saliba, M.; Matsui, T.; Seo, J.Y.; Domanski, K.; Correa-Baena, J.P.; Nazeeruddin, M.K.; Zakeeruddin, S.M.; Tress, W.; Abate, A.; Hagfeldt, A.; et al. Cesium-containing triple cation perovskite solar cells: Improved stability, reproducibility and high efficiency. Energy Environ. Sci.
**2016**, 9, 1989–1997. [Google Scholar] [CrossRef] [Green Version] - Stoddard, R.J.; Rajagopal, A.; Palmer, R.L.; Braly, I.L.; Jen, A.K.Y.; Hillhouse, H.W. Enhancing Defect Tolerance and Phase Stability of High-Bandgap Perovskites via Guanidinium Alloying. ACS Energy Lett.
**2018**, 3, 1261–1268. [Google Scholar] [CrossRef] - Boziki, A.; Mladenović, M.; Grätzel, M.; Rothlisberger, U. Why choosing the right partner is important: Stabilization of ternary CsyGUAxFA(1-y-x)PbI3 perovskites. Phys. Chem. Chem. Phys.
**2020**, 22, 20880–20890. [Google Scholar] [CrossRef] - Ono, L.K.; Juarez-Perez, E.J.; Qi, Y. Progress on Perovskite Materials and Solar Cells with Mixed Cations and Halide Anions. ACS Appl. Mater. Interfaces
**2017**, 9, 30197–30246. [Google Scholar] [CrossRef] [Green Version] - Zarick, H.F.; Soetan, N.; Erwin, W.R.; Bardhan, R. Mixed halide hybrid perovskites: A paradigm shift in photovoltaics. J. Mater. Chem. A
**2018**, 6, 5507–5537. [Google Scholar] [CrossRef] - McGovern, L.; Futscher, M.H.; Muscarella, L.A.; Ehrler, B. Understanding the Stability of MAPbBr3 versus MAPbI3: Suppression of Methylammonium Migration and Reduction of Halide Migration. J. Phys. Chem. Lett.
**2020**, 11, 7127–7132. [Google Scholar] [CrossRef] [PubMed] - Pistor, P.; Burwig, T.; Brzuska, C.; Weber, B.; Fränzel, W. Thermal stability and miscibility of co-evaporated methyl ammonium lead halide (MAPbX3, X = I, Br, Cl) thin films analysed by in situ X-ray diffraction. J. Mater. Chem. A
**2018**, 6, 11496–11506. [Google Scholar] [CrossRef] - Knight, A.J.; Borchert, J.; Oliver, R.D.J.; Patel, J.B.; Radaelli, P.G.; Snaith, H.J.; Johnston, M.B.; Herz, L.M. Halide Segregation in Mixed-Halide Perovskites: Influence of A-Site Cations. ACS Energy Lett.
**2021**, 6, 799–808. [Google Scholar] [CrossRef] [PubMed] - Soler, J.M.; Artacho, E.; Gale, J.D.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. The SIESTA method for ab initio order- N materials simulation. J. Phys. Condens. Matter
**2002**, 14, 2745. [Google Scholar] [CrossRef] [Green Version] - Ceperley, D.M.; Alder, B.J. Ground State of the Electron Gas by a Stochastic Method. Phys. Rev. Lett.
**1980**, 45, 566–569. [Google Scholar] [CrossRef] [Green Version] - Latini, A.; Gigli, G.; Ciccioli, A. A study on the nature of the thermal decomposition of methylammonium lead iodide perovskite, CH3NH3PbI3: An attempt to rationalise contradictory experimental results. Sustain. Energy Fuels
**2017**, 1, 1351–1357. [Google Scholar] [CrossRef] - Scikit-Learn. Available online: https://scikit-learn.org (accessed on 15 July 2021).
- TensorFlow. Available online: https://www.tensorflow.org/ (accessed on 15 July 2021).
- Keras. Available online: https://keras.io/ (accessed on 15 July 2021).
- Brunetti, B.; Cavallo, C.; Ciccioli, A.; Gigli, G.; Latini, A. On the Thermal and Thermodynamic (In)Stability of Methylammonium Lead Halide Perovskites. Sci. Rep.
**2016**, 6, 31896. [Google Scholar] [CrossRef] [PubMed] - Valenzano, V.; Cesari, A.; Balzano, F.; Milella, A.; Fracassi, F.; Listorti, A.; Gigli, G.; Rizzo, A.; Uccello-Barretta, G.; Colella, S. Methylammonium-formamidinium reactivity in aged organometal halide perovskite inks. Cell Rep. Phys. Sci.
**2021**, 2, 100432. [Google Scholar] [CrossRef] - Nazarenko, O.; Kotyrba, M.R.; Yakunin, S.; Aebli, M.; Rainò, G.; Benin, B.M.; Wörle, M.; Kovalenko, M.V. Guanidinium-Formamidinium Lead Iodide: A Layered Perovskite-Related Compound with Red Luminescence at Room Temperature. J. Am. Chem. Soc.
**2018**, 140, 3850–3853. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**(

**a**) Organic cations used in perovskite structures (A and A’); (

**b**) The pattern of presentation in each of the figures below. We will show multiple compositions of mixed-cation and mixed-halide perovskites: three binary mixtures of cations (three composite circles, each with 16 dots, corresponding to the indicated proportions of A and A’), three binary halogen mixtures (dots on the circles) and four ternary halogen mixtures (dots within the circles). The middle dot corresponds to equal halogen proportions. The colors are set to encode the magnitude of the different quantities (measures of optical absorption and stability).

**Figure 2.**(

**a**) Minimum and (

**b**) maximum bond length distribution for mixtures of halogens, expressed in [Å], using the RGB encoding: iodine (red), bromide (green) and chlorine (blue).

**Figure 3.**Classification of 3D perovskite structures of formula A${}_{x}$A’${}_{1-x}$PbX${}_{y}$X’${}_{z}$X”${}_{3-y-z}$ based on Pb-X bond length statistics: feasible (yellow dots) and likely infeasible (black dots) 3D structures. A and A’ index the rows and columns, respectively. Each matrix element, except the ones on the secondary diagonal, has the representation given in Figure 1b. Two criteria have been considered (marked by shaded areas): ${f}_{\mathrm{bl}}=10$% deviations (upper left triangle) and ${f}_{\mathrm{bl}}=5$% deviations (lower right triangle) from the smallest or the largest Pb-X bond lengths as established for MAPbX${}_{3}$ perovskites.

**Figure 4.**Representative opto-electronic properties. The band structures are indicated for (

**a**) MAPbI${}_{3}$, (

**b**) MAPbBr${}_{3}$, (

**c**) MAPbCl${}_{3}$. The absorption coefficients are depicted comparatively for the different halogens and cations in (

**d**,

**e**), respectively. The spectral solar irradiance ($\mathcal{S}I$) is also represented.

**Figure 5.**Distribution of solar spectrum integrated absorption, measured by ${f}_{\mathrm{a}}$ index, for two different values of the absorber layer width, ${d}_{1}=300$ nm (upper left triangle) and ${d}_{2}=600$ nm (lower right triangle). Significant variations due to halogen proportions are observed, while smaller contributions due to cation mixtures are visible, with particular enhancements for FA, EA and GA binary mixtures.

**Figure 7.**Absorption-stability (${f}_{\mathrm{a}}-{f}_{\mathrm{s}}$) maps demonstrating individual contributions from the organic cations and halogens, established for the intrinsic degradation mechanism. Stability enhancements are observed for mixtures containing FA and GA, while large proportions of FM is detrimental. The halogens significantly influence the absorption in accordance with their concentrations (${f}_{\mathrm{a}}^{\mathrm{I}}>{f}_{\mathrm{a}}^{\mathrm{Br}}>{f}_{\mathrm{a}}^{\mathrm{Cl}}$), while Br brings a shift towards higher formation energies.

**Figure 8.**Regression data obtained using ANN models: (

**a**) optical absorption index ${f}_{\mathrm{a}}$; (

**b**,

**c**) stability indices for the intrinsic/extrinsic mechanisms, ${f}_{\mathrm{s}}^{(i/e)}$; (

**d**,

**e**) minimum/maximum bond lengths.

**Table 1.**A-site cations considered here used to form 3D mixed-halide perovskites. The Goldschmidt tolerance factor is calculated for each halogen type. The listed cation effective radii (except FM) were adopted from Kieslich et al. [34]. The ionic radii of the constituent elements are ${R}_{\mathrm{eff}}^{\mathrm{Pb}}=119$, ${R}_{\mathrm{eff}}^{\mathrm{I}}=220$, ${R}_{\mathrm{eff}}^{\mathrm{Br}}=196$, ${R}_{\mathrm{eff}}^{\mathrm{Cl}}=188$, ${R}_{\mathrm{eff}}^{\mathrm{N}}=146$, ${R}_{\mathrm{eff}}^{\mathrm{O}}=135$, adopted from Shannon [35]. All ionic radii are given in [pm] units.

A-Cations | MA | FA | EA | GA | FM | HA | HZ |
---|---|---|---|---|---|---|---|

Formula | CH${}_{3}$NH${}_{3}$ | CH(NH${}_{2}$)${}_{2}$ | (CH${}_{3}$CH${}_{2}$)NH${}_{3}$ | (NH${}_{2}$)${}_{3}$C | NH${}_{3}$COH | NH${}_{3}$OH | NH${}_{3}$NH${}_{2}$ |

3D? | yes | yes | yes | yes | no ${}^{1}$ | no ${}^{2}$ | no ${}^{3}$ |

${R}_{\mathrm{eff}}$ | 217 | 253 | 274 | 278 | 254 ${}^{*}$ | 216 | 217 |

${T}_{\mathrm{f}}$ (I) | 0.91 | 0.99 | 1.03 | 1.04 | 0.99 ${}^{*}$ | 0.91 | 0.91 |

${T}_{\mathrm{f}}$ (Br) | 0.93 | 1.01 | 1.06 | 1.06 | 1.01 ${}^{*}$ | 0.92 | 0.93 |

${T}_{\mathrm{f}}$ (Cl) | 0.94 | 1.02 | 1.07 | 1.08 | 1.03 ${}^{*}$ | 0.94 | 0.94 |

**Table 2.**Selection of 10 best candidates with the goal of optimizing: (a) absorption index ${f}_{\mathrm{a}}$; (b) stability index ${f}_{\mathrm{s}}$; both ${f}_{\mathrm{a}}$ and ${f}_{\mathrm{s}}$ , with values larger than 0.65. The intrinsic degradation mechanism has been considered.

Absorption Index (${\mathit{f}}_{\mathbf{a}}$) | Stability Index (${\mathit{f}}_{\mathbf{s}}$) | Both ${\mathit{f}}_{\mathbf{a}}$ and ${\mathit{f}}_{\mathbf{s}}$ |
---|---|---|

EA${}_{0.25}$GA${}_{0.75}$PbI${}_{3}$ | GAPbBr${}_{2.25}$Cl${}_{0.75}$ | EA${}_{0.25}$GA${}_{0.75}$PbI${}_{3}$ |

${f}_{\mathrm{a}}=0.81$ and ${f}_{\mathrm{s}}=0.77$ | ${f}_{\mathrm{a}}=0.26$ and ${f}_{\mathrm{s}}=0.97$ | ${f}_{\mathrm{a}}=0.81$ and ${f}_{\mathrm{s}}=0.77$ |

GAPbI${}_{2.25}$Cl${}_{0.75}$ | GAPbI${}_{0.75}$Br${}_{1.50}$Cl${}_{0.75}$ | GAPbI${}_{2.25}$Cl${}_{0.75}$ |

${f}_{\mathrm{a}}=0.77$ and ${f}_{\mathrm{s}}=0.83$ | ${f}_{\mathrm{a}}=0.48$ and ${f}_{\mathrm{s}}=0.94$ | ${f}_{\mathrm{a}}=0.77$ and ${f}_{\mathrm{s}}=0.83$ |

EAPbI${}_{3}$ | GAPbCl${}_{3}$ | EA${}_{0.25}$GA${}_{0.75}$PbI${}_{2.25}$Br${}_{0.75}$ |

${f}_{\mathrm{a}}=0.77$ and ${f}_{\mathrm{s}}=0.54$ | ${f}_{\mathrm{a}}=0.13$ and ${f}_{\mathrm{s}}=0.94$ | ${f}_{\mathrm{a}}=0.75$ and ${f}_{\mathrm{s}}=0.80$ |

EA${}_{0.75}$GA${}_{0.25}$PbI${}_{3}$ | GAPbI${}_{3}$ | GA${}_{0.75}$HZ${}_{0.25}$PbI${}_{3}$ |

${f}_{\mathrm{a}}=0.76$ and ${f}_{\mathrm{s}}=0.63$ | ${f}_{\mathrm{a}}=0.58$ and ${f}_{\mathrm{s}}=0.93$ | ${f}_{\mathrm{a}}=0.73$ and ${f}_{\mathrm{s}}=0.73$ |

FA${}_{0.25}$EA${}_{0.75}$PbI${}_{2.25}$Cl${}_{0.75}$ | GAPbI${}_{2.25}$Br${}_{0.75}$ | EA${}_{0.50}$GA${}_{0.50}$PbI${}_{2.25}$Br${}_{0.75}$ |

${f}_{\mathrm{a}}=0.75$ and ${f}_{\mathrm{s}}=0.51$ | ${f}_{\mathrm{a}}=0.56$ and ${f}_{\mathrm{s}}=0.93$ | ${f}_{\mathrm{a}}=0.73$ and ${f}_{\mathrm{s}}=0.69$ |

EA${}_{0.25}$GA${}_{0.75}$PbI${}_{2.25}$Br${}_{0.75}$ | FA${}_{0.25}$GA${}_{0.75}$PbI${}_{1.50}$Br${}_{1.50}$ | FA${}_{0.50}$GA${}_{0.50}$PbI${}_{3}$ |

${f}_{\mathrm{a}}=0.75$ and ${f}_{\mathrm{s}}=0.80$ | ${f}_{\mathrm{a}}=0.59$ and ${f}_{\mathrm{s}}=0.91$ | ${f}_{\mathrm{a}}=0.72$ and ${f}_{\mathrm{s}}=0.75$ |

EAPbI${}_{2.25}$Br${}_{0.25}$ | FA${}_{0.25}$GA${}_{0.75}$PbI${}_{0.75}$Br${}_{2.25}$ | EA${}_{0.25}$GA${}_{0.75}$PbI${}_{1.50}$Br${}_{1.50}$ |

${f}_{\mathrm{a}}=0.75$ and ${f}_{\mathrm{s}}=0.52$ | ${f}_{\mathrm{a}}=0.55$ and ${f}_{\mathrm{s}}=0.91$ | ${f}_{\mathrm{a}}=0.71$ and ${f}_{\mathrm{s}}=0.79$ |

EA${}_{0.50}$GA${}_{0.50}$PbI${}_{3}$ | FA${}_{0.25}$GA${}_{0.75}$PbI${}_{3}$ | EA${}_{0.75}$GA${}_{0.25}$PbI${}_{3}$ |

${f}_{\mathrm{a}}=0.75$ and ${f}_{\mathrm{s}}=0.41$ | ${f}_{\mathrm{a}}=0.66$ and ${f}_{\mathrm{s}}=0.90$ | ${f}_{\mathrm{a}}=0.71$ and ${f}_{\mathrm{s}}=0.66$ |

GA${}_{0.75}$HZ${}_{0.25}$PbI${}_{3}$ | FA${}_{0.25}$GA${}_{0.75}$PbBr${}_{2.25}$Cl${}_{0.25}$ | FAPbI${}_{3}$ |

${f}_{\mathrm{a}}=0.73$ and ${f}_{\mathrm{s}}=0.73$ | ${f}_{\mathrm{a}}=0.43$ and ${f}_{\mathrm{s}}=0.89$ | ${f}_{\mathrm{a}}=0.69$ and ${f}_{\mathrm{s}}=0.70$ |

GA${}_{0.50}$FM${}_{0.50}$PbI${}_{3}$ | EA${}_{0.25}$GA${}_{0.75}$PbBr${}_{2.25}$Cl${}_{0.25}$ | EA${}_{0.50}$GA${}_{0.50}$PbI${}_{1.50}$Br${}_{1.50}$ |

${f}_{\mathrm{a}}=0.73$ and ${f}_{\mathrm{s}}=0.27$ | ${f}_{\mathrm{a}}=0.23$ and ${f}_{\mathrm{s}}=0.89$ | ${f}_{\mathrm{a}}=0.69$ and ${f}_{\mathrm{s}}=0.70$ |

**Table 3.**The ${R}^{2}$ coefficient of determination, measuring the accuracy of the test sets, in the case of MLS, RF and ANN methods. For MLS and RF, 10 distinct partitions of the train-test sets were employed yielding the minimum, maximum and average ${R}^{2}$. The ANN models confirm the performance attained by the previous two methods.

Training: | 50 Samples | 100 Samples | 200 Samples |
---|---|---|---|

Data: | Method: min. max. av. | Method: min. max. av. | Method: min. max. av. |

${f}_{\mathrm{a}}$ | MLS: 0.69 0.77 0.74 | MLS: 0.74 0.79 0.77 | MLS: 0.77 0.79 0.78 |

RF : 0.61 0.75 0.69 | RF : 0.70 0.76 0.73 | RF : 0.73 0.77 0.75 | |

ANN: 0.82 | |||

${f}_{\mathrm{s}}^{\left(\mathrm{i}\right)}$ | MLS: 0.90 0.91 0.91 | MLS: 0.92 0.93 0.92 | MLS: 0.92 0.93 0.92 |

RF : 0.78 0.85 0.82 | RF : 0.85 0.90 0.88 | RF : 0.89 0.92 0.90 | |

ANN: | ANN: 0.92 | ||

${f}_{\mathrm{s}}^{\left(\mathrm{e}\right)}$ | MLS: 0.92 0.93 0.93 | MLS: 0.93 0.94 0.94 | MLS: 0.94 0.94 0.94 |

RF : 0.70 0.81 0.77 | RF : 0.81 0.87 0.85 | RF : 0.87 0.91 0.89 | |

ANN: | ANN: 0.95 | ||

${l}_{\mathrm{min}}$ | MLS: 0.43 0.56 0.48 | MLS: 0.51 0.60 0.56 | MLS: 0.55 0.60 0.58 |

RF : 0.81 0.87 0.84 | RF : 0.83 0.86 0.85 | RF : 0.84 0.86 0.85 | |

ANN: 0.84 | |||

${l}_{\mathrm{max}}$ | MLS: 0.12 0.31 0.23 | MLS: 0.11 0.33 0.28 | MLS: 0.27 0.38 0.32 |

RF : 0.16 0.37 0.31 | RF : 0.17 0.42 0.33 | RF : 0.20 0.42 0.35 | |

ANN: 0.43 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Filipoiu, N.; Mitran, T.L.; Anghel, D.V.; Florea, M.; Pintilie, I.; Manolescu, A.; Nemnes, G.A.
Investigation of Opto-Electronic Properties and Stability of Mixed-Cation Mixed-Halide Perovskite Materials with Machine-Learning Implementation. *Energies* **2021**, *14*, 5431.
https://doi.org/10.3390/en14175431

**AMA Style**

Filipoiu N, Mitran TL, Anghel DV, Florea M, Pintilie I, Manolescu A, Nemnes GA.
Investigation of Opto-Electronic Properties and Stability of Mixed-Cation Mixed-Halide Perovskite Materials with Machine-Learning Implementation. *Energies*. 2021; 14(17):5431.
https://doi.org/10.3390/en14175431

**Chicago/Turabian Style**

Filipoiu, Nicolae, Tudor Luca Mitran, Dragos Victor Anghel, Mihaela Florea, Ioana Pintilie, Andrei Manolescu, and George Alexandru Nemnes.
2021. "Investigation of Opto-Electronic Properties and Stability of Mixed-Cation Mixed-Halide Perovskite Materials with Machine-Learning Implementation" *Energies* 14, no. 17: 5431.
https://doi.org/10.3390/en14175431