Theoretical Explorations of Self-trapped Excitons in Halide Perovskites Towards Efficient Broadband Photoluminescence

Halide perovskites have attracted extensive attention in recent decades due to their advanced optoelectronic properties in the field of photoluminescence and functional devices. In particular, the broadband white-light photoluminescence that was recently observed in halide perovskite materials reveals their potential to be the next generation single-source solid-state broadband phosphors. According to the current research progress, these intriguing broadband emissions are widely attributed to the formation of self-trapped excitons (STEs). Currently, although the generation of STEs in halide perovskites can be promoted experimentally through atomic substitution, the detailed formation mechanisms of STEs are still obscure. Besides, the current evaluation methods of STEs are mainly based on traditional spectral experiments, which is not conducive to the high-throughput determination and screening of potential STEs materials. Therefore, to better understand and modulate the STEs effect, this thesis mainly focuses on the STEs in halide perovskites from three aspects: (1) atomic substitution effects in halide perovskites, (2) detailed mechanism regarding the formation of STEs in double halide perovskites (DHPs), and (3) machine learning (ML) assisted prediction of STEs.

Experimental doping and composition modification have been applied to modulate the STEs effects of halide perovskites in many studies. However, the specific role of these atomic substitutions in influencing the development of STE effects through the regulation of the inherent physical characteristics of halide perovskites remains uncertain. Therefore, investigating the atomic substitution effects in halide perovskites is a crucial initial step in understanding the mechanisms behind STEs formation and can provide valuable insights for guiding future material engineering endeavors. In this thesis, based on density functional theory (DFT) calculations, we have processed valuable research on the atomic substitution effects of halide perovskite materials regarding their optoelectronic as well as vibrational properties. The optoelectronic properties of these materials are mainly determined by the bonding and orbital characteristics between the halogen and B-site metal atoms. Therefore, the atomic substitutions induced variation of orbital and bonding characteristics will regulate the energy band offsets and change the corresponding optoelectronic performance. In addition, the atomic substitution effects can also influence the conversation of phonons by regulating the phonon band structure. Based on the phonon band structure and visualized vibration modes, we have further confirmed that the B-site metal-halogen octahedrons are the main vibrational source of halide perovskite materials. This study has discussed the detailed atomic substitution effects in halide perovskites and provided significant research guidance for the design of functional materials in a timely manner.

This thesis has also presented our study regarding the formation mechanism of STEs in DHPs. In general, DHPs have exhibited impressive potential for the STEs photoluminescence, although the physical nature of STEs is still ambiguous. Therefore, we have conducted theoretical research on a series of DHPs Cs₂B¹B²Cl₆ (B¹ = Na⁺, K⁺; B² = Al³⁺, Ga³⁺, In³⁺) regarding their properties related to STEs, including electronic structure, excitonic characteristics, electron-phonon coupling intensity, and geometrical configuration. For electronic structure, the flat valence band edges of these DHPs suggest the presence of heavy localized holes. These heavy holes provide the localized center for the generation of STEs. For excitonic properties, these materials show much higher exciton binding energies than typical halide perovskites. Their extremely short Bohr radius of excitons reflects that their quantum confinement is comparable to the size of one single lattice. For the electron-phonon coupling effect, we have revealed the more intense carrier-phonon coupling effects in Ga-series DHPs by applying the Feynman polaron theory and Fröhlich coupling constant. After investigating the nuclear coordinate diagrams, we have calculated the Huang–Rhys factors of our DHPs and Cs₂NaGaCl₆ shows a high value as 36.21. Moreover, the intense carrier-phonon coupling effect has further influenced the geometry configurations of B-site metal-halogen octahedrons. Based on the analysis of phonon characteristics and vibration modes, we have confirmed that the Jahn-Teller distortion within the octahedrons caused by the self-trapping process of holes after excitation is the original source of STEs. This work improves the understanding of the optoelectronic nature of STEs and offers effective evidence for uncovering their formation mechanisms.

On the other hand, despite our attempts to unravel the generation process of STEs, the comprehensive interpretation of their detailed origin is still in its early stages. The exact role of different B-site metal atoms in DHPs in influencing the STEs has not been discussed yet. In addition, the lack of effective STEs databases further hinders the efficient discovery and screening of advanced optoelectronic materials with strong STEs effects. Therefore, the ML-assisted prediction of STEs in DHPs has also been highlighted in this thesis to show a new methodology accelerating the screening and determination of potential STEs materials. In this study, we have built a systematic database describing the STEs effects in DHPs by connecting the DFT calculations and ML technology for the first time. After the continuous iterative optimization and screening, we have successfully trained the predictive ML-model for the target physical parameters. The output correlation factors (CFs) reveal the various influence of two B-site metal atoms on DHPs. In detail, the B¹ atoms are more suitable for tuning the electron-phonon coupling strength, while the B² atoms mainly affect the electronic transfer and phonon patterns. Besides, we have further trained the predictive ML-model for the Huang-Rhys factors in DHPs. By applying the predicted effective phonon frequency data, we have realized the effective predictions of the Huang-Rhys factors in DHPs under the balance of satisfying accuracy and acceptable calculation loadings. Based on the theoretical calculations, this work supplies an efficient approach to analyze and explore the STEs effects in DHPs, offering new strategies for the efficient large-scale screening of significant optoelectronic candidates.

The current demands for stable and efficient broadband emitters are ever-growing and halide perovskites are increasingly becoming one of the most promising candidates for the next-generation photoluminescence. Improving the corresponding overall performance of optoelectronic devices depends on the in-depth understanding of their functional materials. Different from the numerous attempts existing on traditional experimental approaches, the supporting theoretical analyses for intrinsic mechanisms are insufficient. In this thesis, all the aforementioned works have focused on the unique STEs effects in halide perovskites. Systematic research based on theoretical calculations has been conducted to ascertain reasonable interpretations and strategies for decoding the formation mechanism of STEs. These necessary investigations of essential STEs principles provide support for the subsequent research in the field of broadband photoluminescence and future sustainable energy systems.

1 Stoumpos C. C. & Kanatzidis M. G. The Renaissance of Halide Perovskites and Their Evolution as Emerging Semiconductors. Accounts Chem. Res., 2015, 48, 2791-2802.
2 Akbulatov A. F., Martynenko V. M., Frolova L. A. et al. Intrinsic thermal decomposition pathways of lead halide perovskites APbX
3. Solar Energy Materials and Solar Cells, 2020, 213, 110559.3 Usiobo O. J., Kanda H., Gratia P. et al. Nanoscale mass-spectrometry imaging of grain boundaries in perovskite semiconductors. Journal of Physical Chemistry C, 2020, 124, 23230-23236.
4 Yun S., Zhou X., Even J. et al. Theoretical treatment of CH3NH3PbI3 perovskite solar cells. Angewandte Chemie International Edition, 2017, 56, 15806-15817.
5 A decade of perovskite photovoltaics. Nature Energy, 2019, 4, 1-1.6 Kojima A., Teshima K., Shirai Y. et al. Organometal halide perovskites as visible-light sensitizers for photovoltaic cells. J. Am. Chem. Soc., 2009, 131, 6050.7 Wei H. T., Fang Y. J., Mulligan P. et al. Sensitive X-ray detectors made of methylammonium lead tribromide perovskite single crystals. Nature Photonics, 2016, 10, 333.8 Tan Z. K., Moghaddam R. S., Lai M. L. et al. Bright light-emitting diodes based on organometal halide perovskite. Nature Nanotechnology, 2014, 9, 687-692.9 Wong A. B., Lai M. L., Eaton S. W. et al. Growth and anion exchange conversion of CH3NH3PbX3 nanorod arrays for light-emitting diodes. Nano Letters, 2015, 15, 5519-5524.10 Zhu H. M., Fu Y. P., Meng F. et al. Lead halide perovskite nanowire lasers with low lasing thresholds and high quality factors. Nature Materials, 2015, 14, 636-U115.11 Chen Y. S., Manser J. S. & Kamat P. V. All solution-processed lead halide perovskite-BiVO4 tandem assembly for photolytic solar fuels production. J. Am. Chem. Soc., 2015, 137, 974-981.12 National Renewable Energy Laboratory. Best Research-Cell Efficiency Chart, (2024).13 Serafettin D., Ahmet Nuri O., Mustafa C. et al. in Nanostructured Solar Cells (ed Das Narottam) Ch. 13 (IntechOpen, 2017).14 Targhi F. F., Jalili Y. S. & Kanjouri F. MAPbI3 and FAPbI3 perovskites as solar cells: Case study on structural, electrical and optical properties. Results in Physics, 2018, 10, 616-627.15 Goldschmidt V. M. Die Gesetze der Krystallochemie. Naturwissenschaften, 1926, 14, 477-485.16 Xiao Z. W. & Yan Y. F. Progress in theoretical study of metal halide perovskite solar cell materials. Adv. Energy Mater., 2017, 7, 20.17 Hong K., Le Q. V., Kim S. Y. et al. Low-dimensional halide perovskites: review and issues. Journal of Materials Chemistry C, 2018, 6, 2189-2209.18 Igbari F., Wang Z.-K. & Liao L.-S. Progress of lead-free halide double perovskites. Adv. Energy Mater., 2019, 9, 1803150.19 Li J., Wang H. & Li D. Self-trapped excitons in two-dimensional perovskites. Frontiers of Optoelectronics, 2020, 13, 225-234.20 Hu T., Smith M. D., Dohner E. R. et al. Mechanism for broadband white-light emission from two-dimensional (110) hybrid perovskites. J. Phys. Chem. Lett., 2016, 7, 2258-2263.21 Wu B., Ning W., Xu Q. et al. Strong self-trapping by deformation potential limits photovoltaic performance in bismuth double perovskite. Science Advances, 2021, 7, eabd3160.22 Arend H., Huber W., Mischgofsky F. H. et al. Layer perovskites of (CnH2n+1NH3)2MX4 and NH3(CH2)mNH3MX4 families with M=Cd, Cu, Fe, Mn or Pd and X=Cl or Br - importance, solubilities and simple grouth techniques. J. Cryst. Growth, 1978, 43, 213-223.23 Willett R. D. Crystal structure of (NH4)2CuCI4. J. Chem. Phys., 1964, 41, 2243.24 Willett R. D., Liles O. L. & Michelso.C. Electronic absorption spectra of monomeric Copper(2) chloride species and electron spin resonance spectrum of square-planar CuCl42-ion. Inorg. Chem., 1967, 6, 1885.25 Kitazawa N. Compositional modulation of two-dimensional layered perovskite (RNH3)2Pb(Cl,Br,I)4 and its optical properties. Jpn. J. Appl. Phys. Part 1 - Regul. Pap. Short Notes Rev. Pap., 1996, 35, 6202-6207.26 Kitazawa N. Excitons in two-dimensional layered perovskite compounds: (C6H5C2H4NH3)2Pb(Br,I)4 and (C6H5C2H4NH3)2Pb(Cl,Br)4. Mater. Sci. Eng. B-Solid State Mater. Adv. Technol., 1997, 49, 233-238.27 Yan J., Qiu W., Wu G. et al. Recent progress in 2D/quasi-2D layered metal halide perovskites for solar cells. Journal of Materials Chemistry A, 2018, 6, 11063-11077.28 Fakharuddin A., Shabbir U., Qiu W. et al. Inorganic and layered perovskites for optoelectronic devices. Adv. Mater., 2019, 31, 1807095.29 Smith M. D., Connor B. A. & Karunadasa H. I. Tuning the Luminescence of Layered Halide Perovskites. Chem. Rev., 2019, 119, 3104-3139.30 Stoumpos C. C., Cao D. H., Clark D. J. et al. Ruddlesden–Popper hybrid lead iodide perovskite 2D homologous semiconductors. Chemistry of Materials, 2016, 28, 2852-2867.31 Turck V., Rodt S., Stier O. et al. Effect of random field fluctuations on excitonic transitions of individual CdSe quantum dots. Phys. Rev. B, 2000, 61, 9944-9947.32 Han D., Shi H., Ming W. et al. Unraveling luminescence mechanisms in zero-dimensional halide perovskites. Journal of Materials Chemistry C, 2018, 6, 6398-6405.33 Zhou C. K., Tian Y., Yuan Z. et al. Highly efficient broadband yellow phosphor based on zero-dimensional tin mixed-halide perovskite. Acs Applied Materials & Interfaces, 2017, 9, 44579-44583.34 Zhou C., Lin H., Tian Y. et al. Luminescent zero-dimensional organic metal halide hybrids with near-unity quantum efficiency. Chem. Sci., 2018, 9, 586-593.35 Smith M. D., Jaffe A., Dohner E. R. et al. Structural origins of broadband emission from layered Pb-Br hybrid perovskites. Chem. Sci., 2017, 8, 4497-4504.36 Kovalenko M. V., Protesescu L. & Bodnarchuk M. I. Properties and potential optoelectronic applications of lead halide perovskite nanocrystals. Science, 2017, 358, 745-750.37 Filip M. R. & Giustino F. Computational screening of homovalent lead substitution in organic–inorganic halide perovskites. The Journal of Physical Chemistry C, 2016, 120, 166-173.38 Ye J., Byranvand M. M., Martínez C. O. et al. Defect passivation in lead-halidep perovskite nanocrystals and thin films: toward efficient LEDs and solar cells. Angewandte Chemie International Edition, 2021, 60, 21636-21660.39 Luo J., Wang X., Li S. et al. Efficient and stable emission of warm-white light from lead-free halide double perovskites. Nature, 2018, 563, 541-545.40 Zhao X. G., Yang D. W., Ren J. C. et al. Rational design of halide double perovskites for optoelectronic applications. Joule, 2018, 2, 1662-1673.41 Knox R. S. in Collective Excitations in Solids (ed Baldassare Di Bartolo) 183-245 (Springer US, 1983).42 Mueller T. & Malic E. Exciton physics and device application of two-dimensional transition metal dichalcogenide semiconductors. npj 2D Materials and Applications, 2018, 2, 29.43 Muljarov E. A., Tikhodeev S. G., Gippius N. A. et al. Excitons in self-organized semiconductor-insulator superlattices - PBI-based perovskite compounds. Phys. Rev. B, 1995, 51, 14370-14378.44 Ishihara T., Takahashi J. & Goto T. Optical properties due to electronic transitions in two-dimensional semiconductors (CnH2n+1NH3)2PbI4. Phys. Rev. B, 1990, 42, 11099-11107.45 Klein J., Kampermann L., Mockenhaupt B. et al. Limitations of the Tauc plot method. Advanced Functional Materials, 2023, 33, 2304523.46 Smith M. D. & Karunadasa H. I. White-light emission from layered halide perovskites. Accounts Chem. Res., 2018, 51, 619-627.47 Yuan Z., Kardynal B. E., Stevenson R. M. et al. Electrically driven single-photon source. Science, 2002, 295, 102-105.48 Zhang B.-B., Wang F., Xiao B. et al. Self-trap-state-adjustable photoluminescence of quasi-one-dimensional RbPbI3 and Cs substitutional counterparts. Journal of Materials Chemistry C, 2020, 8, 12108-12112.49 Martin M. Exciton self‐trapping in rare‐gas crystals. The Journal of Chemical Physics, 1971, 54, 3289-3299.50 Fu M., Ehrat F., Wang Y. et al. Carbon dots: a unique fluorescent cocktail of polycyclic aromatic hydrocarbons. Nano Letters, 2015, 15, 6030-6035.51 Guo Q., Zhao X., Song B. et al. Light emission of self-trapped excitons in inorganic metal halides for optoelectronic applications. Adv. Mater., 2022, 34, 2201008.52 Sui X., Gao X., Wu X. et al. Zone-folded longitudinal acoustic phonons driving self-trapped state emission in colloidal CdSe nanoplatelet superlattices. Nano Letters, 2021, 21, 4137-4144.53 Gautier R., Paris M. & Massuyeau F. Exciton self-trapping in hybrid lead halides: role of halogen. J. Am. Chem. Soc., 2019, 141, 12619-12623.54 Smith M. D., Jaffe A., Dohner E. R. et al. Structural origins of broadband emission from layered Pb–Br hybrid perovskites. Chem. Sci., 2017, 8, 4497-4504.55 Xu Z., Jiang X., Cai H.-p. et al. Toward a general understanding of exciton self-trapping in metal halide perovskites. The Journal of Physical Chemistry Letters, 2021, 12, 10472-10478.56 Liang M., Lin W., Zhao Q. et al. Free carriers versus self-trapped excitons at different facets of Ruddlesden–Popper two-dimensional lead halide perovskite single crystals. The Journal of Physical Chemistry Letters, 2021, 12, 4965-4971.57 Li S., Luo J., Liu J. et al. Self-Trapped Excitons in All-Inorganic Halide Perovskites: Fundamentals, Status, and Potential Applications. The Journal of Physical Chemistry Letters, 2019, 10, 1999-2007.58 Wang X., Meng W., Liao W. et al. Atomistic mechanism of broadband emission in metal halide perovskites. The Journal of Physical Chemistry Letters, 2019, 10, 501-506.59 Wang H., Wang C., Sun M. et al. Insight into efficient photoluminescence regulation mechanism by lattice distortion and Mn2+ doping in organic-inorganic hybrid perovskites. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 2023, 299, 122821.60 Zhou G., Jiang X., Molokeev M. et al. Optically modulated ultra-broad-band warm white emission in Mn2+-doped (C6H18N2O2)PbBr4 hybrid metal halide phosphor. Chemistry of Materials, 2019, 31, 5788-5795.61 Chen J., Li Y., Yin Z. et al. Phase transition and rapid temperature response of lead-free perovskite Cs–Cu–I nanocrystals enabled by their size. Journal of Materials Chemistry C, 2023, 11, 13030-13038.62 Dohner E. R., Hoke E. T. & Karunadasa H. I. Self-assembly of broadband white-Light emitters. J. Am. Chem. Soc., 2014, 136, 1718-1721.63 Dohner E. R., Jaffe A., Bradshaw L. R. et al. Intrinsic white-light emission from layered hybrid perovskites. J. Am. Chem. Soc., 2014, 136, 13154-13157.64 Cortecchia D., Neutzner S., Kandada A. R. S. et al. Broadband emission in two-dimensional hybrid perovskites: the role of structural deformation. J. Am. Chem. Soc., 2017, 139, 39-42.65 Yu J. C., Kong J. T., Hao W. et al. Broadband extrinsic self-trapped exciton emission in Sn-doped 2D lead-halide perovskites. Adv. Mater., 2019, 31, 9.66 Han Y., Yin J., Cao G. et al. Exciton self-trapping for white emission in 100-oriented two-dimensional perovskites via halogen substitution. ACS Energy Letters, 2022, 7, 453-460.67 Tao S., Ohtani N., Uchida R. et al. Relaxation dynamics of photoexcited excitons in rubrene single crystals using femtosecond absorption spectroscopy. Physical Review Letters, 2012, 109.68 Yangui A., Garrot D., Lauret J. S. et al. Optical investigation of broadband white-light emission in self-assembled organic-inorganic perovskite (C6H11NH3)2PbBr4. Journal of Physical Chemistry C, 2015, 119, 23638-23647.69 Kobitski A. Y., Zhuravlev K. S., Wagner H. P. et al. Self-trapped exciton recombination in silicon nanocrystals. Phys. Rev. B, 2001, 63.70 Vial J. C., Bsiesy A., Gaspard F. et al. Mechanisms of visible-light emission from electrooxidized porous silicon. Phys. Rev. B, 1992, 45, 14171-14176.71 Li S. R., Luo J. J., Liu J. et al. Self-trapped excitons in all-Inorganic halide perovskites: fundamentals, status, and potential applications. J. Phys. Chem. Lett., 2019, 10, 1999-2007.72 Zhang Y., Mollick S., Tricarico M. et al. Turn-on fluorescence chemical sensing through transformation of self-trapped exciton states at room temperature. ACS Sensors, 2022, 7, 2338-2344.73 Li X., Liu A., Wang Z. et al. Boosting self-trapped exciton emission from Cs3Cu2I5 nanocrystals by doping-enhanced exciton-phonon coupling. Nano Research, 2023, 16, 10476-10482.74 Ye S., Xiao F., Pan Y. X. et al. Phosphors in phosphor-converted white light-emitting diodes: Recent advances in materials, techniques and properties. Materials Science and Engineering: R: Reports, 2010, 71, 1-34.75 Bowers M. J., McBride J. R. & Rosenthal S. J. White-light emission from magic-sized cadmium selenide nanocrystals. J. Am. Chem. Soc., 2005, 127, 15378-15379.76 Li J. Z., Wang J., Ma J. Q. et al. Self-trapped state enabled filterless narrowband photodetections in 2D layered perovskite single crystals. Nat. Commun., 2019, 10, 10.77 Lao X., Yang Z., Su Z. et al. Luminescence and thermal behaviors of free and trapped excitons in cesium lead halide perovskite nanosheets. Nanoscale, 2018, 10, 9949-9956.78 Machulin V. F., Motsnyi F. V., Smolanka O. M. et al. Effect of temperature variation on shift and broadening of the exciton band in Cs3Bi2I9 layered crystals. Low Temperature Physics, 2004, 30, 964-967.79 McCall K. M., Stoumpos C. C., Kostina S. S. et al. Strong electron-phonon coupling and self-trapped excitons in the defect halide perovskites A3M2I9 (A = Cs, Rb; M = Bi, Sb). Chemistry of Materials, 2017, 29, 4129-4145.80 Zhang L., Sun C., He T. et al. High-performance quasi-2D perovskite light-emitting diodes: from materials to devices. Light: Science & Applications, 2021, 10, 61.81 Yue L., Yan B., Attridge M. et al. Light absorption in perovskite solar cell: Fundamentals and plasmonic enhancement of infrared band absorption. Solar Energy, 2016, 124, 143-152.82 Leng J., Wang T., Tan Z.-K. et al. Tuning the emission wavelength of lead halide perovskite NCs via size and shape control. ACS Omega, 2022, 7, 565-577.83 Sajid S., Elseman A. M., Huang H. et al. Breakthroughs in NiOx-HTMs towards stable, low-cost and efficient perovskite solar cells. Nano Energy, 2018, 51, 408-424.84 Wimmer E., Najafabadi R., Young G. A. et al. Ab initio calculations for industrial materials engineering: successes and challenges. Journal of Physics: Condensed Matter, 2010, 22, 384215.85 Nørskov J. K., Abild-Pedersen F., Studt F. et al. Density functional theory in surface chemistry and catalysis. Proceedings of the National Academy of Sciences, 2011, 108, 937-943.86 Benbarrad T., Salhaoui M., Kenitar S. B. et al. Intelligent machine vision model for defective product inspection based on machine learning. Journal of Sensor and Actuator Networks, 2021, 10, 7.87 Penumuru D. P., Muthuswamy S. & Karumbu P. Identification and classification of materials using machine vision and machine learning in the context of industry 4.0. Journal of Intelligent Manufacturing, 2020, 31, 1229-1241.88 Deng L. & Li X. Machine learning paradigms for speech recognition: an overview. IEEE Transactions on Audio, Speech, and Language Processing, 2013, 21, 1060-1089.89 Nassif A. B., Shahin I., Attili I. et al. Speech recognition using deep neural networks: a systematic review. IEEE Access, 2019, 7, 19143-19165.90 Scher S. & Messori G. Predicting weather forecast uncertainty with machine learning. Quarterly Journal of the Royal Meteorological Society, 2018, 144, 2830-2841.91 Singh N., Chaturvedi S. & Akhter S. in 2019 International Conference on Signal Processing and Communication (ICSC). 171-174.92 Chen B., Chen R. & Huang B. Machine learning-accelerated development of perovskite optoelectronics toward efficient energy harvesting and conversion. Adv. Energy Sustainability Res., 2023, 4, 2300157.93 Zhou J., Huang B., Yan Z. et al. Emerging role of machine learning in light-matter interaction. Light: Science & Applications, 2019, 8, 84.94 Mattsson A. E., Schultz P. A., Desjarlais M. P. et al. Designing meaningful density functional theory calculations in materials science - a primer. Modelling and Simulation in Materials Science and Engineering, 2005, 13, R1.95 Togo A. & Tanaka I. First principles phonon calculations in materials science. Scripta Materialia, 2015, 108, 1-5.96 Wei J., Chu X., Sun X.-Y. et al. Machine learning in materials science. InfoMat, 2019, 1, 338-358.97 Schleder G. R., Padilha A. C. M., Acosta C. M. et al. From DFT to machine learning: recent approaches to materials science–a review. Journal of Physics: Materials, 2019, 2, 032001.98 Wang Z., Yang M., Xie X. et al. Applications of machine learning in perovskite materials. Advanced Composites and Hybrid Materials, 2022, 5, 2700-2720.99 Gao Z., Zhang H., Mao G. et al. Screening for lead-free inorganic double perovskites with suitable band gaps and high stability using combined machine learning and DFT calculation. Applied Surface Science, 2021, 568, 150916.100 Zhai X., Ding F., Zhao Z. et al. Predicting the formation of fractionally doped perovskite oxides by a function-confined machine learning method. Communications Materials, 2022, 3, 42.101 Schmidt J., Shi J., Borlido P. et al. Predicting the Thermodynamic Stability of Solids Combining Density Functional Theory and Machine Learning. Chemistry of Materials, 2017, 29, 5090-5103.102 Liu H., Cheng J., Dong H. et al. Screening stable and metastable ABO3 perovskites using machine learning and the materials project. Computational Materials Science, 2020, 177, 109614.103 Yang X., Li L., Tao Q. et al. Rapid discovery of narrow bandgap oxide double perovskites using machine learning. Computational Materials Science, 2021, 196, 110528.104 Bloch F. Über die quantenmechanik der elektronen in kristallgittern. Zeitschrift für Physik, 1929, 52, 555-600.105 Born M. & Oppenheimer R. Zur Quantentheorie der Molekeln. Annalen der Physik, 1927, 389, 457-484.106 Møller C. & Plesset M. S. Note on an approximation treatment for many-electron systems. Physical Review, 1934, 46, 618-622.107 Parr R. G. Density-functional theory of atoms and molecules, Oxford University Press, 1989.108 Rousseau D. L., Bauman R. P. & Porto S. P. S. Normal mode determination in crystals. Journal of Raman Spectroscopy, 1981, 10, 253-290.109 Fox M. Optical properties of solids, New York : Oxford University Press, 2 edn, 2010.110 Fröhlich H. Electrons in lattice fields. Advances in physics, 1954, 3, 325-361.111 Schultz T. D. Slow electrons in polar crystals: self-energy, mass, and mobility. Physical Review, 1959, 116, 526-543.112 Feynman R. P. Slow electrons in a polar crystal. Physical Review, 1955, 97, 660-665.113 Huang K., Rhys A. & Mott N. F. Theory of light absorption and non-radiative transitions in F-centres. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1950, 204, 406-423.114 Xu S. Huang-Rhys factor and its key role in the interpretation of some optical properties of solids. Acta Physica Sinica, 2019, 68, 166301-166301-166301-166311.115 Pedregosa F., Varoquaux G., Gramfort A. et al. Scikit-learn: machine learning in Python. Journal of Machine Learning Research, 2011, 12, 2825-2830.116 Mao L., Wu Y., Stoumpos C. C. et al. Tunable white-light emission in single-cation-templated three-layered 2D perovskites (CH3CH2NH3)4Pb3Br10–xClx. J. Am. Chem. Soc., 2017, 139, 11956-11963.117 Yangui A., Pillet S., Lusson A. et al. Control of the white-light emission in the mixed two-dimensional hybrid perovskites (C6H11NH3)2[PbBr4−xIx]. Journal of Alloys and Compounds, 2017, 699, 1122-1133.118 Jain A., Ong S. P., Hautier G. et al. Commentary: The Materials Project: A materials genome approach to accelerating materials innovation. 2013, 1, 011002.119 Segall M. D., Lindan P. J. D., Probert M. J. et al. First-principles simulation: ideas, illustrations and the CASTEP code. Journal of Physics: Condensed Matter, 2002, 14, 2717-2744.120 Fischer T. H. & Almlof J. General methods for geometry and wave function optimization. The Journal of Physical Chemistry, 1992, 96, 9768-9774.121 Perdew J. P., Burke K. & Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett, 1996, 77, 3865-3868.122 Monkhorst H. J. & Pack J. D. Special points for Brillouin-zone integrations. Phys. Rev. B, 1976, 13, 5188-5192.123 Hamann D. R., Schlüter M. & Chiang C. Norm-conserving pseudopotentials. Physical Review Letters, 1979, 43, 1494-1497.124 Baroni S., Giannozzi P. & Testa A. Greens-function approach to linear response in solids. Physical Review Letters, 1987, 58, 1861-1864.125 Ferdani D. W., Pering S. R., Ghosh D. et al. Partial cation substitution reduces iodide ion transport in lead iodide perovskite solar cells. Energy & Environmental Science, 2019, 12, 2264-2272.126 Aziz A., Aristidou N., Bu X. et al. Understanding the enhanced stability of bromide substitution in lead iodide perovskites. Chemistry of Materials, 2020, 32, 400-409.127 Brik M. G. Comparative first-principles calculations of electronic, optical and elastic anisotropy properties of CsXBr3 (X=Ca, Ge, Sn ) crystals. Solid State Communications, 2011, 151, 1733-1738.128 Rajeswarapalanichamy R., Amudhavalli A., Padmavathy R. et al. Band gap engineering in halide cubic perovskites CsPbBr3−yIy (y = 0, 1, 2, 3) – a DFT study. Materials Science and Engineering: B, 2020, 258, 114560.129 Ghaithan H. M., Alahmed Z. A., Qaid S. M. H. et al. Density functional study of cubic, tetragonal, and orthorhombic CsPbBr3 perovskite. ACS Omega, 2020, 5, 7468-7480.130 Afsari M., Boochani A., Hantezadeh M. et al. Topological nature in cubic phase of perovskite CsPbI3: by DFT. Solid State Communications, 2017, 259, 10-15.131 Tao S., 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, 14386-14389.132 Bose S. K., Satpathy S. & Jepsen O. Semiconducting CsSnBr3. Phys. Rev. B, 1993, 47, 4276-4280.133 Zheng J. C., Huan C. H. A., Wee A. T. S. et al. Electronic properties of CsSnBr3: studies by experiment and theory. Surface and Interface Analysis, 1999, 28, 81-83.134 Chabot J. F., Cote M. & Briere J. F. Ab initio study of the electronic and structural properties of CsSnI3 perovskite, Natl Research Council Canada, 2003.135 Yuan Y., xu R., Xu H.-T. et al. Nature of the band gap of halide perovskites ABX3 (A = CH3NH3, Cs; B = Sn, Pb; X = Cl, Br, I): first-principles calculations. Chinese Physics B, 2015, 24, 116302.136 Sutton R. J., Filip M. R., Haghighirad A. A. et al. Cubic or orthorhombic? Revealing the crystal structure of metastable black-phase CsPbI3 by theory and experiment. ACS Energy Letters, 2018, 3, 1787-1794.137 Dutta A., Dutta S. K., Das Adhikari S. et al. Phase-stable CsPbI3 nanocrystals: the reaction temperature matters. Angewandte Chemie International Edition, 2018, 57, 9083-9087.138 Motta C., El-Mellouhi F., Kais S. et al. Revealing the role of organic cations in hybrid halide perovskite CH3NH3PbI3. Nat. Commun., 2015, 6, 7026.139 Harrison J. F. On the role of the electron density difference in the interpretation of molecular properties. The Journal of Chemical Physics, 2003, 119, 8763-8764.140 Sanchez-Portal D., Artacho E. & Soler J. M. Projection of plane-wave calculations into atomic orbitals. Solid State Communications, 1995, 95, 685-690.141 Mulliken R. S. Electronic population analysis on LCAO–MO molecular wave functions. The Journal of Chemical Physics, 1955, 23, 1833-1840.142 Amudhavalli A., Rajeswarapalanichamy R., Padmavathy R. et al. Electronic structure and optical properties of CsPbF3-yIy (y=0, 1, 2) cubic perovskites. Acta Physica Polonica A, 2021, 139, 692-697.143 de L. Kronig R. On the theory of dispersion of X-rays. J. Opt. Soc. Am., 1926, 12, 547-557.144 Stenzel O. The physics of thin film optical spectra, Springer Cham, 2 edn, 2016.145 Jackson J. D. Classical electrodynamics, Wiley, 3rd edition edn, 1999.146 Alù A., Silveirinha M. G., Salandrino A. et al. Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern. Phys. Rev. B, 2007, 75, 155410.147 Edwards B., Alù A., Young M. E. et al. Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide. Physical Review Letters, 2008, 100, 033903.148 Sun Q., Xu Y., Zhang H. et al. Optical and electronic anisotropies in perovskitoid crystals of Cs3Bi2I9 studies of nuclear radiation detection. Journal of Materials Chemistry A, 2018, 6, 23388-23395.149 Zygmanski P. & Sajo E. A self-powered thin-film radiation detector using intrinsic high-energy current. Medical Physics, 2016, 43, 4-15.150 Tanner D. B. Optical effects in solids, Cambridge University Press, 2019.151 Yang L.-M., Ravindran P., Vajeeston P. et al. Formation of an intermediate band in isoreticular metal–organic framework-993 (IRMOF-993) and metal-substituted analogues M-IRMOF-993. Journal of Materials Chemistry, 2012, 22, 16324-16335.152 Pérez-Osorio M. A., Milot R. L., Filip M. R. et al. Vibrational properties of the organic–inorganic halide perovskite CH3NH3PbI3 from theory and experiment: factor group analysis, first-principles calculations, and low-temperature infrared spectra. The Journal of Physical Chemistry C, 2015, 119, 25703-25718.153 Kashikar R., Khamari B. & Nanda B. R. K. Second-neighbor electron hopping and pressure induced topological quantum phase transition in insulating cubic perovskites. Physical Review Materials, 2018, 2, 124204.154 Guo P., Xia Y., Gong J. et al. Polar fluctuations in metal halide perovskites uncovered by acoustic phonon anomalies. ACS Energy Letters, 2017, 2, 2463-2469.155 Marronnier A., Lee H., Geffroy B. et al. Structural instabilities related to highly anharmonic phonons in halide perovskites. The Journal of Physical Chemistry Letters, 2017, 8, 2659-2665.156 Amudhavalli A., Padmavathy R., Rajeswarapalanichamy R. et al. First-principles study of structural and optoelectronic properties of CsSnI3−yFy (y = 0, 1, 2, 3) perovskites. Indian Journal of Physics, 2020, 94, 1351-1359.157 Yang J., Wen X., Xia H. et al. Acoustic-optical phonon up-conversion and hot-phonon bottleneck in lead-halide perovskites. Nat Commun, 2017, 8, 14120-14120.158 Fu J., Xu Q., Han G. et al. Hot carrier cooling mechanisms in halide perovskites. Nat. Commun., 2017, 8, 1300.159 Kohn W. Image of the Fermi surface in the vibration spectrum of a metal. Physical Review Letters, 1959, 2, 393-394.160 Sun M. & Huang B. Phonon evidence of Kohn anomalies in nanogenerator ZnO. Nano Energy, 2019, 59, 626-635.161 Martin R. M. Electronic structure: basic theory and practical methods, Cambridge University Press, 2004.162 Satta J., Melis C., Carbonaro C. M. et al. Raman spectra and vibrational analysis of CsPbI3: a fast and reliable technique to identify lead halide perovskite polymorphs. Journal of Materiomics, 2021, 7, 127-135.163 Hamermesh M. Group theory and its application to physical problems, Dover Publications, 1989.164 Wei W., Li W., Butler K. T. et al. An unusual phase transition driven by vibrational entropy changes in a hybrid organic–inorganic perovskite. Angew. Chem. Int. Ed, 2018, 57, 8932-8936.165 Xiao Z., Meng W., Wang J. et al. Searching for promising new perovskite-based photovoltaic absorbers: the importance of electronic dimensionality. Materials Horizons, 2017, 4, 206-216.166 Yin W., Yang J., Kang J. et al. Halide perovskite materials for solar cells: a theoretical review. Journal of Materials Chemistry A, 2015, 3, 8926-8942.167 Gong M., Sakidja R., Goul R. et al. High-performance all-Inorganic CsPbCl3 perovskite nanocrystal photodetectors with superior stability. ACS Nano, 2019, 13, 1772-1783.168 Gray M. B., Hariyani S., Strom T. A. et al. High-efficiency blue photoluminescence in the Cs2NaInCl6: Sb3+ double perovskite phosphor. Journal of Materials Chemistry C, 2020, 8, 6797-6803.169 Zeng R., Zhang L., Xue Y. et al. Highly efficient blue emission from self-trapped excitons in stable Sb3+-doped Cs2NaInCl6 double perovskites. The Journal of Physical Chemistry Letters, 2020, 11, 2053-2061.170 Noculak A., Morad V., McCall K. M. et al. Bright blue and green luminescence of Sb(III) in double perovskite Cs2MInCl6 (M = Na, K) matrices. Chemistry of Materials, 2020, 32, 5118-5124.171 Saeed Y., Amin B., Khalil H. et al. Cs2NaGaBr6: a new lead-free and direct band gap halide double perovskite. RSC Advances, 2020, 10, 17444-17451.172 Munro J. M., Latimer K., Horton M. K. et al. An improved symmetry-based approach to reciprocal space path selection in band structure calculations. npj Computational Materials, 2020, 6, 112.173 Baroni S., Giannozzi P. & Testa A. Green's-function approach to linear response in solids. Physical Review Letters, 1987, 58, 1861-1864.174 Hutter J. Excited state nuclear forces from the Tamm-Dancoff approximation to time-dependent density functional theory within the plane wave basis set framework. The Journal of chemical physics, 2003, 118, 3928-3934.175 Baranowski M. & Plochocka P. Excitons in metal-halide perovskites. 2020, 10, 1903659.176 Umari P., Mosconi E. & De Angelis F. Relativistic GW calculations on CH3NH3PbI3 and CH3NH3SnI3 perovskites for solar cell applications. Scientific Reports, 2014, 4, 4467.177 Brivio F., Butler K. T., Walsh A. et al. Relativistic quasiparticle self-consistent electronic structure of hybrid halide perovskite photovoltaic absorbers. Phys. Rev. B, 2014, 89, 155204.178 Protesescu L., Yakunin S., Bodnarchuk M. I. et al. Nanocrystals of cesium lead halide perovskites (CsPbX3, X = Cl, Br, and I): novel optoelectronic materials showing bright emission with wide color gamut. Nano Letters, 2015, 15, 3692-3696.179 Hellwarth R. W. & Biaggio I. Mobility of an electron in a multimode polar lattice. Phys. Rev. B, 1999, 60, 299-307.180 Iaru C. M., Brodu A., van Hoof N. J. J. et al. Fröhlich interaction dominated by a single phonon mode in CsPbBr3. Nat. Commun., 2021, 12, 5844.181 Rashba Ė. I. & Sturge M. D. Excitons : selected chapters, North-Holland Pub. Co., 1987.182 Huang K., Rhys A. & Mott N. F. Theory of light absorption and non-radiative transitions in F-centres. 1950, 204, 406-423.183 Pan F., Li J., Ma X. et al. Free and self-trapped exciton emission in perovskite CsPbBr3 microcrystals. RSC Advances, 2022, 12, 1035-1042.184 Yu P. Y. Fundamentals of semiconductors physics and materials properties, Springer, 4th edn, 2010.185 Chen B., Sun M., Chen R. et al. Atomic substitution effects of inorganic perovskites for optoelectronic properties modulations. EcoMat, 2022, e12201.186 Halcrow M. A. Jahn–Teller distortions in transition metal compounds, and their importance in functional molecular and inorganic materials. Chemical Society Reviews, 2013, 42, 1784-1795.187 Hao F., Stoumpos C. C., Cao D. H. et al. Lead-free solid-state organic–inorganic halide perovskite solar cells. Nature Photonics, 2014, 8, 489-494.188 Noel N. K., Stranks S. D., Abate A. et al. Lead-free organic–inorganic tin halide perovskites for photovoltaic applications. Energy & Environmental Science, 2014, 7, 3061-3068.189 Liao W., Zhao D., Yu Y. et al. Lead-free inverted planar formamidinium tin triiodide perovskite solar cells achieving power conversion efficiencies up to 6.22%. Adv. Mater., 2016, 28, 9333-9340.190 Slavney A. H., Hu T., Lindenberg A. M. et al. A bismuth-halide double perovskite with long carrier recombination lifetime for photovoltaic applications. J. Am. Chem. Soc., 2016, 138, 2138-2141.191 Meng W., Wang X., Xiao Z. et al. Parity-forbidden transitions and their impact on the optical absorption properties of lead-free metal halide perovskites and double perovskites. The Journal of Physical Chemistry Letters, 2017, 8, 2999-3007.192 Segall M. D., Philip J. D. L., Probert M. J. et al. First-principles simulation: ideas, illustrations and the CASTEP code. Journal of Physics: Condensed Matter, 2002, 14, 2717.193 Holden N. E., Coplen T. B., Böhlke J. K. et al. IUPAC periodic table of the elements and isotopes (IPTEI) for the education community (IUPAC technical report). Pure and Applied Chemistry, 2018, 90, 1833-2092.194 Baranowski M. & Plochocka P. Excitons in metal-halide perovskites. Adv. Energy Mater., 2020, 10, 1903659.195 Chen B., Chen R. & Huang B. Strong electron–phonon coupling induced self-trapped excitons in double halide perovskites. Adv. Energy Sustainability Res., 2023, 2300018.