Electron-phonon interactions in halide perovskites
Source abstract
Abstract
Abstract Strong electron-phonon interactions are frequently considered the origin of the unique electrical and optical properties of lead halide perovskites. Electron-phonon interactions induce the formation of a polaron, which is a charge carrier dressed with a phonon cloud. The details of polaron formation are crucial for carrier transport since polaron formation leads to a larger effective mass of a carrier. Several mechanisms have been proposed regarding the physics of polaron formation in halide perovskites, but the details are still under active debate. While the Fröhlich interaction plays an essential role in ionic crystals, we also need to consider the strong phonon anharmonicity of halide perovskites that may lead to the formation of an unconventional polaron. In this review article, we discuss the uniqueness of perovskite semiconductors from the viewpoint of electron-phonon interactions. We review the experimental results and the proposed models concerning the effective carrier mass and carrier mobility. Finally, we briefly explain two physical phenomena related to strong electron-phonon interactions: strong anti-Stokes photoluminescence and slow hot-carrier cooling.
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Research context
OpenAlex topics: Perovskite Materials and Applications · Optical properties and cooling technologies in crystalline materials · Solid-state spectroscopy and crystallography
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References (100+)
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1. Kojima, A., Teshima, K., Shirai, Y. & Miyasaka, T. Organometal halide perovskites as visible-light sensitizers for photovoltaic cells. J. Am. Chem. Soc. 131, 6050–6051 (2009).10.1021/ja809598r ↗
2. Tan, Z. K. et al. Bright light-emitting diodes based on organometal halide perovskite. Nat. Nanotechnol. 9, 687–692 (2014).10.1038/nnano.2014.149 ↗
3. Stranks, S. D. et al. Electron-hole diffusion lengths exceeding 1 micrometer in an organometal trihalide perovskite absorber. Science 342, 341–344 (2013).10.1126/science.1243982 ↗
4. Xing, G. et al. Long-range balanced electron- and hole-transport lengths in organic-inorganic CH3NH3PbI3. Science 347, 344–347 (2013).10.1126/science.1243167 ↗
5. Yamada, Y., Nakamura, T., Endo, M., Wakamiya, A. & Kanemitsu, Y. Photocarrier recombination dynamics in perovskite CH3NH3PbI3 for solar cell applications. J. Am. Chem. Soc. 136, 11610–11613 (2014).10.1021/ja506624n ↗
6. Yamada, Y. et al. Dynamic optical properties of CH3NH3PbI3 single crystals as revealed by one-and two-photon excited photoluminescence measurements. J. Am. Chem. Soc. 137, 10456–10459 (2015).10.1021/jacs.5b04503 ↗
7. Handa, T., Yamada, T., Nagai, M. & Kanemitsu, Y. Phonon, thermal, and thermo-optical properties of halide perovskites. Phys. Chem. Chem. Phys. 22, 26069–26087 (2020).10.1039/D0CP04426A ↗
8. Tahara, H., Aharen, T., Wakamiya, A. & Kanemitsu, Y. Photorefractive effect in organic–inorganic hybrid perovskites and its application to optical phase shifter. Adv. Opt. Mater. 6, 1701366 (2018).10.1002/adom.201701366 ↗
9. Wu, L. et al. Perovskite CsPbX3: A promising nonlinear optical material and its applications for ambient all‐optical switching with enhanced stability. Adv. Opt. Mater. 6, 1800400 (2018).10.1002/adom.201800400 ↗
10. Hirori, H. et al. High-order harmonic generation from hybrid organic–inorganic perovskite thin films. APL Mater. 7, 041107 (2019).10.1063/1.5090935 ↗
11. Jang, D. M. et al. Reversible halide exchange reaction of organometal trihalide perovskite colloidal nanocrystals for full-range band gap tuning. Nano Lett. 15, 5191 (2015).10.1021/acs.nanolett.5b01430 ↗
12. Rakita, Y., Cohen, S. R., Kedem, N. K., Hodes, G. & Cahen, D. Mechanical properties of APbX3 (A= Cs or CH3NH3; X= I or Br) perovskite single crystals. MRS Commun. 5, 623–629 (2015).10.1557/mrc.2015.69 ↗
13. Jung, H. S., Han, G. S., Park, N. G. & Ko, M. J. Flexible perovskite solar cells. Joule 3, 1850–1880 (2019).10.1016/j.joule.2019.07.023 ↗
14. Franchini, C., Reticcioli, M., Setvin, M. & Diebold, U. Polarons in materials. Nat. Rev. Mater. 6, 560–586 (2021).10.1038/s41578-021-00289-w ↗
15. Sendner, M. et al. Optical phonons in methylammonium lead halide perovskites and implications for charge transport. Mater. Horiz. 3, 613–620 (2016).10.1039/C6MH00275G ↗
16. Frost, J. M. Calculating polaron mobility in halide perovskites. Phys. Rev. B 96, 195202 (2017).10.1103/PhysRevB.96.195202 ↗
17. Poncé, S., Schlipf, M. & Giustino, F. Origin of low carrier mobilities in halide perovskites. ACS Energy Lett. 4, 456–463 (2019).10.1021/acsenergylett.8b02346 ↗
18. Miyata, K. et al. Large polarons in lead halide perovskites. Sci. Adv. 3, e1701217 (2017).10.1126/sciadv.1701217 ↗
19. Yaffe, O. et al. Local polar fluctuations in lead halide perovskite crystals. Phys. Rev. Lett. 118, 136001 (2017).10.1103/PhysRevLett.118.136001 ↗
20. Miyata, K. & Zhu, X. Y. Ferroelectric large polarons. Nat. Mater. 17, 379–381 (2018).10.1038/s41563-018-0068-7 ↗
21. Guo, Y. et al. Dynamic emission Stokes shift and liquid-like dielectric solvation of band edge carriers in lead-halide perovskites. Nat. Commun. 10, 1175 (2019).10.1038/s41467-019-09057-5 ↗
22. Meggiolaro, D., Ambrosio, F., Mosconi, E., Mahata, A. & De Angelis, F. Polarons in metal halide perovskites. Adv. Energy Mater. 10, 1902748 (2020).10.1002/aenm.201902748 ↗
23. Ghosh, D., Welch, E., Neukirch, A. J., Zakhidov, A. & Tretiak, S. Polarons in halide perovskites: A perspective. J. Phys. Chem. Lett. 11, 3271–3286 (2020).10.1021/acs.jpclett.0c00018 ↗
24. Schilcher, M. J. et al. The significance of polarons and dynamic disorder in halide perovskites. ACS Energy Lett. 6, 2162–2173 (2021).10.1021/acsenergylett.1c00506 ↗
25. Yamada, T., Aharen, T. & Kanemitsu, Y. Up-converted photoluminescence from CH3NH3PbI3 perovskite semiconductors: Implications for laser cooling. Phys. Rev. Mater. 3, 024601 (2019).10.1103/PhysRevMaterials.3.024601 ↗
26. Li, M., Fu, J., Xu, Q. & Sum, T. C. Slow hot-carrier cooling in halide perovskites: Prospects for hot‐carrier solar cells. Adv. Mater. 31, 1802486 (2019).10.1002/adma.201802486 ↗
27. Sekiguchi, F. et al. Enhancing the hot-phonon bottleneck effect in a metal halide perovskite by terahertz phonon excitation. Phys. Rev. Lett. 126, 077401 (2021).10.1103/PhysRevLett.126.077401 ↗
28. Yang, Y. et al. Observation of a hot-phonon bottleneck in lead-iodide perovskites. Nat. Photon 10, 53–59 (2016).10.1038/nphoton.2015.213 ↗
29. Yamada, Y., Endo, M., Wakamiya, A. & Kanemitsu, Y. Spontaneous defect annihilation in CH3NH3PbI3 thin films at room temperature revealed by time-resolved photoluminescence spectroscopy. J. Phys. Chem. Lett. 6, 482–486 (2015).10.1021/jz5026596 ↗
30. Nie, W. et al. Light-activated photocurrent degradation and self-healing in perovskite solar cells. Nat. Commun. 7, 11574 (2016).10.1038/ncomms11574 ↗
31. Mahata, A., Meggiolaro, D. & De Angelis, F. From large to small polarons in lead, tin, and mixed lead–tin halide perovskites. J. Phys. Chem. Lett. 10, 1790–1798 (2019).10.1021/acs.jpclett.9b00422 ↗
32. Li, Z. et al. Stabilizing perovskite structures by tuning tolerance factor: formation of formamidinium and cesium lead iodide solid-state alloys. Chem. Mater. 28, 284–292 (2016).10.1021/acs.chemmater.5b04107 ↗
33. Poglitsch, A. & Weber, D. Dynamic disorder in methylammoniumtrihalogenoplumbates (II) observed by millimeter‐wave spectroscopy. J. Chem. Phys. 87, 6373–6378 (1987).10.1063/1.453467 ↗
34. Onoda-Yamamuro, N., Matsuo, T. & Suga, H. Dielectric study of CH3NH3PbX3 (X = Cl, Br, I). J. Phys. Chem. Solids 53, 935–939 (1992).10.1016/0022-3697(92)90121-S ↗
35. Yamada, Y., Yamada, T. & Kanemitsu, Y. Free carrier radiative recombination and photon recycling in lead halide perovskite solar cell materials. Bull. Chem. Soc. Jpn. 90, 1129–1140 (2017).10.1246/bcsj.20170208 ↗
36. Marronnier, A. et al. Anharmonicity and disorder in the black phases of cesium lead iodide used for stable inorganic perovskite solar cells. ACS nano 12, 3477–3486 (2018).10.1021/acsnano.8b00267 ↗
37. Quarti, C. et al. The Raman spectrum of the CH3NH3PbI3 hybrid perovskite: interplay of theory and experiment. J. Phys. Chem. Lett. 5, 279–284 (2013).10.1021/jz402589q ↗
38. La-o-Vorakiat, C. et al. Phonon mode transformation across the orthohombic–tetragonal phase transition in a lead iodide perovskite CH3NH3PbI3: a terahertz time-domain spectroscopy approach. J. Phys. Chem. Lett. 7, 1–6 (2016).10.1021/acs.jpclett.5b02223 ↗
39. Leguy, A. M. et al. Dynamic disorder, phonon lifetimes, and the assignment of modes to the vibrational spectra of methylammonium lead halide perovskites. Phys. Chem. Chem. Phys. 18, 27051–27066 (2016).10.1039/C6CP03474H ↗
40. Nagai, M. et al. Longitudinal optical phonons modified by organic molecular cation motions in organic-inorganic hybrid perovskites. Phys. Rev. Lett. 121, 145506 (2018).10.1103/PhysRevLett.121.145506 ↗
41. Ferreira, A. C. et al. Direct evidence of weakly dispersed and strongly anharmonic optical phonons in hybrid perovskites. Commun. Phys. 3, 48 (2020).10.1038/s42005-020-0313-7 ↗
42. Fröhlich, H. Electrons in lattice fields. Adv. Phys. 3, 325–361 (1954).10.1080/00018735400101213 ↗
43. Röseler, J. A new variational ansatz in the polaron theory. Phys. Status Solidi (b) 25, 311 (1968).10.1002/pssb.19680250129 ↗
44. Devreese, J. T. in Encyclopedia of Physics. 2 3rd edn (eds Lerner, R. G. & Trigg, G. L.) 2004-2027 (Wiley-VCH, Berlin, Germany, 2005).
45. Yamada, Y. et al. Polaron masses in CH3NH3PbX3 perovskites determined by landau level spectroscopy in low magnetic fields. Phys. Rev. Lett. 126, 237401 (2021).10.1103/PhysRevLett.126.237401 ↗
46. Sumi, H. & Toyozawa, Y. Urbach-Martienssen rule and exciton trapped momentarily by lattice vibrations. J. Phys. Soc. Jpn. 31, 342–358 (1971).10.1143/JPSJ.31.342 ↗
47. Toyozawa, Y. Optical Processes in Solids (Cambridge University Press, Cambridge, UK, 2003).10.1017/CBO9780511615085 ↗
48. Neukirch, A. J. et al. Polaron stabilization by cooperative lattice distortion and cation rotations in hybrid perovskite materials. Nano Lett. 16, 3809–3816 (2016).10.1021/acs.nanolett.6b01218 ↗
49. Cody, G. D., Tiedje, T., Abeles, B., Brooks, B. & Goldstein, Y. Disorder and the optical-absorption edge of hydrogenated amorphous silicon. Phys. Rev. Lett. 47, 1480 (1981).10.1103/PhysRevLett.47.1480 ↗
50. Yamada, Y., Nakamura, T., Endo, M., Wakamiya, A. & Kanemitsu, Y. Near-band-edge optical responses of solution-processed organic–inorganic hybrid perovskite CH3NH3PbI3 on mesoporous TiO2 electrodes. Appl. Phys. Express 7, 032302 (2014).10.7567/APEX.7.032302 ↗
51. Yamada, T., Handa, T., Yamada, Y. & Kanemitsu, Y. Light emission from halide perovskite semiconductors: bulk crystals, thin films, and nanocrystals. J. Phys. D: Appl. Phys. 54, 383001 (2021).10.1088/1361-6463/ac0e58 ↗
52. Yamada, T., Aharen, T. & Kanemitsu, Y. Near-band-edge optical responses of CH3NH3PbCl3 single crystals: photon recycling of excitonic luminescence. Phys. Rev. Lett. 120, 057404 (2018).10.1103/PhysRevLett.120.057404 ↗
53. Wolf, C., Kim, J. S. & Lee, T. W. Structural and thermal disorder of solution-processed CH3NH3PbBr3 hybrid perovskite thin films. ACS Appl. Mater. Interfaces 9, 10344–10348 (2017).10.1021/acsami.6b15694 ↗
54. Ledinsky, M. et al. Temperature dependence of the urbach energy in lead iodide perovskites. J. Phys. Chem. Lett. 10, 1368–1373 (2019).10.1021/acs.jpclett.9b00138 ↗
55. Kajino, Y. et al. Anti-Stokes Photoluminescence from CsPbBr3 Nanostructures Embedded in a Cs4PbBr6 Crystal. Phys. Rev. Mater. 6, L043001 (2022).10.1103/PhysRevMaterials.6.L043001 ↗
56. Miyata, A. et al. Direct measurement of the exciton binding energy and effective masses for charge carriers in organic–inorganic tri-halide perovskites. Nat. Phys. 11, 582–587 (2015).10.1038/nphys3357 ↗
57. Galkowski, K. et al. Determination of the exciton binding energy and effective masses for methylammonium and formamidinium lead tri-halide perovskite semiconductors. Energy Environ. Sci. 9, 962–970 (2016).10.1039/C5EE03435C ↗
58. Yang, Z. et al. Impact of the halide cage on the electronic properties of fully inorganic cesium lead halide perovskites. ACS Energy Lett. 2, 1621–1627 (2017).10.1021/acsenergylett.7b00416 ↗
59. Peeters, F. M. & Devreese, J. T. Energy levels of two-and three-dimensional polarons in a magnetic field. Phys. Rev. B 31, 3689 (1985).10.1103/PhysRevB.31.3689 ↗
60. Peeters, F. M. & Devreese, J. T. Magneto-optical absorption of polarons. Phys. Rev. B 34, 7246 (1986).10.1103/PhysRevB.34.7246 ↗
61. Puppin, M. et al. Evidence of large polarons in photoemission band mapping of the perovskite semiconductor CsPbBr3. Phys. Rev. Lett. 124, 206402 (2020).10.1103/PhysRevLett.124.206402 ↗
62. Haken, H. Zur quantentheorie des mehrelektronensystems im schwingenden gitter. Z. Phys. 146, 527–554 (1956).10.1007/BF01333179 ↗
63. Klingshirn, C. F. Semiconductor Optics 4th edn (Springer, Berlin, Germany, 2012).10.1007/978-3-642-28362-8 ↗
64. Dong, Q. et al. Electron-hole diffusion lengths> 175 μm in solution-grown CH3NH3PbI3 single crystals. Science 347, 967–970 (2015).10.1126/science.aaa5760 ↗
65. Shrestha, S. et al. Assessing temperature dependence of drift mobility in methylammonium lead iodide perovskite single crystals. J. Phys. Chem. C. 122, 5935–5939 (2018).10.1021/acs.jpcc.8b00341 ↗
66. Saidaminov, M. I. et al. High-quality bulk hybrid perovskite single crystals within minutes by inverse temperature crystallization. Nat. Commun. 6, 7586 (2015).10.1038/ncomms8586 ↗
67. Shi, D. et al. Low trap-state density and long carrier diffusion in organolead trihalide perovskite single crystals. Science 347, 519–522 (2015).10.1126/science.aaa2725 ↗
68. Song, Y. et al. Efficient lateral-structure perovskite single crystal solar cells with high operational stability. Nat. Commun. 11, 274 (2020).10.1038/s41467-019-13998-2 ↗
69. Bari, M. et al. Room-temperature synthesis, growth mechanisms and opto-electronic properties of organic–inorganic halide perovskite CH3NH3PbX3 (X = I, Br, and Cl) single crystals. CrystEngComm. 23, 3326–3339 (2021).10.1039/D0CE01690J ↗
70. Valverde-Chávez, D. A. et al. Intrinsic femtosecond charge generation dynamics in single crystal CH3NH3PbI3. Energy Environ. Sci. 8, 3700–3707 (2015).10.1039/C5EE02503F ↗
71. Semonin, O. E. et al. Limits of carrier diffusion in n-type and p-type CH3NH3PbI3 perovskite single crystals. J. Phys. Chem. Lett. 7, 3510–3518 (2016).10.1021/acs.jpclett.6b01308 ↗
72. Chen, Y. et al. Extended carrier lifetimes and diffusion in hybrid perovskites revealed by Hall effect and photoconductivity measurements. Nat. Commun. 7, 12253 (2016).10.1038/ncomms12253 ↗
73. Yamada, Y., Hoyano, M., Akashi, R., Oto, K. & Kanemitsu, Y. Impact of chemical doping on optical responses in bismuth-doped CH3NH3PbBr3 single crystals: carrier lifetime and photon recycling. J. Phys. Chem. Lett. 8, 5798–5803 (2017).10.1021/acs.jpclett.7b02508 ↗
74. Wang, Q. et al. Morphological and chemical tuning of lead halide perovskite mesocrystals as long-life anode materials in lithium-ion batteries. CrystEngComm 21, 1048–1059 (2019).10.1039/C8CE01779D ↗
75. Rao, H. S., Li, W. G., Chen, B. X., Kuang, D. B. & Su, C. Y. In situ growth of 120 cm2 CH3NH3PbBr3 perovskite crystal film on FTO glass for narrowband‐photodetectors. Adv. Mater. 29, 1602639 (2017).10.1002/adma.201602639 ↗
76. Lin, C. H. et al. Metal contact and carrier transport in single crystalline CH3NH3PbBr3 perovskite. Nano Energy 53, 817–827 (2018).10.1016/j.nanoen.2018.09.049 ↗
77. Musiienko, A. et al. Deep levels, charge transport and mixed conductivity in organometallic halide perovskites. Energy Environ. Sci. 12, 1413–1425 (2019).10.1039/C9EE00311H ↗
78. Tang, W. et al. Substitutional doping of hybrid organic–inorganic perovskite crystals for thermoelectrics. J. Mater. Chem. A 8, 13594–13599 (2020).10.1039/D0TA03648J ↗
79. Kimura, T., Matsumori, K., Oto, K., Kanemitsu, Y. & Yamada, Y. Observation of high carrier mobility in CH3NH3PbBr3 single crystals by AC photo-Hall measurements. Appl. Phys. Express 14, 041009 (2021).10.35848/1882-0786/abf02b ↗
80. Wei, H. et al. Dopant compensation in alloyed CH3NH3PbBr3− xClx perovskite single crystals for gamma-ray spectroscopy. Nat. Mater. 16, 826 (2017).10.1038/nmat4927 ↗
81. Liu, X. et al. Charge transport behavior in solution-grown methylammonium lead tribromide perovskite single crystal using α particles. J. Phys. Chem. C. 122, 14355–14361 (2018).10.1021/acs.jpcc.8b03512 ↗
82. Wei, H. et al. Sensitive X-ray detectors made of methylammonium lead tribromide perovskite single crystals. Nat. Photonics 10, 333–339 (2016).10.1038/nphoton.2016.41 ↗
83. Liu, Y. et al. A 1300 mm2 ultrahigh‐performance digital imaging assembly using high‐quality perovskite single crystals. Adv. Mater. 30, 1707314 (2018).10.1002/adma.201707314 ↗
84. Pospisil, J. et al. Density of bulk trap states of hybrid lead halide perovskite single crystals: temperature modulated space-charge-limited-currents. Sci. Rep. 9, 3332 (2019).10.1038/s41598-019-40139-y ↗
85. Duijnstee, E. A. et al. Understanding dark current-voltage characteristics in metal-halide perovskite single crystals. Phys. Rev. Appl. 15, 014006 (2021).10.1103/PhysRevApplied.15.014006 ↗
86. Le Corre, V. M. et al. Revealing charge carrier mobility and defect densities in metal halide perovskites via space-charge-limited current measurements. ACS Energy Lett. 6, 1087–1094 (2021).10.1021/acsenergylett.0c02599 ↗
87. Yamada, T. et al. Fast free‐carrier diffusion in CH3NH3PbBr3 single crystals revealed by time‐resolved one‐and two‐photon excitation photoluminescence spectroscopy. Adv. Electron. Mater. 2, 1500290 (2016).10.1002/aelm.201500290 ↗
88. Yamada, T., Yamada, Y., Nakaike, Y., Wakamiya, A. & Kanemitsu, Y. Photon emission and reabsorption processes in CH3NH3PbBr3 single crystals revealed by time-resolved two-photon-excitation photoluminescence microscopy. Phys. Rev. Appl. 7, 014001 (2017).10.1103/PhysRevApplied.7.014001 ↗
89. Yang, Y. et al. Low surface recombination velocity in solution-grown CH3NH3PbBr3 perovskite single crystal. Nat. Commun. 6, 7961 (2015).10.1038/ncomms8961 ↗
90. Zhang, Z. & Saparov, B. Charge carrier mobility of halide perovskite single crystals for ionizing radiation detection. Appl. Phys. Lett. 119, 030502 (2021).10.1063/5.0057411 ↗
91. Stillman, G. E., Waife, C. M. & Dimmock, J. O. Hall coefficient factor for polar mode scattering in n-type GaAs. J. Phys. Chem. Solids 31, 1199 (1970).10.1016/0022-3697(70)90122-8 ↗
92. Mishchenko, A. S. et al. Polaron mobility in the “beyond quasiparticles” regime. Phys. Rev. Lett. 123, 076601 (2019).10.1103/PhysRevLett.123.076601 ↗
93. Alvar, M. S., Blom, P. W. & Wetzelaer, G. J. A. Space-charge-limited electron and hole currents in hybrid organic-inorganic perovskites. Nat. Commun. 11, 4023 (2020).10.1038/s41467-020-17868-0 ↗
94. Jin, H. et al. It’s a trap! On the nature of localised states and charge trapping in lead halide perovskites. Mater. Horiz. 7, 397–410 (2020).10.1039/C9MH00500E ↗
95. Stoumpos, C. C., Malliakas, C. D. & Kanatzidis, M. G. Semiconducting tin and lead iodide perovskites with organic cations: phase transitions, high mobilities, and near-infrared photoluminescent properties. Inorg. Chem. 52, 9019–9038 (2013).10.1021/ic401215x ↗
96. Chung, I. et al. CsSnI3: semiconductor or metal? High electrical conductivity and strong near-infrared photoluminescence from a single material. High hole mobility and phase-transitions. J. Am. Chem. Soc. 134, 8579–8587 (2012).10.1021/ja301539s ↗
97. Gunawan, O. et al. Carrier-resolved photo-Hall effect. Nature 575, 151–155 (2019).10.1038/s41586-019-1632-2 ↗
98. Ng, H. M., Doppalapudi, D., Moustakas, T. D., Weimann, N. G. & Eastman, L. F. The role of dislocation scattering in n-type GaN films. Appl. Phys. Lett. 73, 821 (1998).10.1063/1.122012 ↗
99. Yang, X., Xu, C. & Giles, N. C. Intrinsic electron mobilities in CdSe, CdS, ZnO, and ZnS and their use in analysis of temperature-dependent Hall measurements. J. Appl. Phys. 104, 073727 (2008).10.1063/1.2996032 ↗
100. Sheik-Bahae, M. & Epstein, R. I. Optical refrigeration. Nat. Photonics 1, 693–699 (2007).10.1038/nphoton.2007.244 ↗