Polarons in perovskite solar cells: effects on photovoltaic performance and stability

Organic–inorganic hybrid perovskites manifest unique photophysical properties in terms of their long carrier lifetime, low recombination rate, and high defect tolerance, enabling them to be promising candidates in optoelectronic devices. However, such advanced properties are unexpected in perovskite materials with moderate charge mobility. Recent investigations have revealed that these appealing properties were endowed due to the formation of large polarons in the perovskite crystals, resulting from the coupling of photogenerated carriers and a polarized crystal lattice, which largely affected the carrier-transport dynamics and structural stability of perovskite solar cells (PSCs). In this review, first the crystal structure of the perovskite lattice and the formation mechanism of polarons are elucidated. Then, the modulation of polaron states in PSCs, including large polaron stabilization, polaron-facilitated charge transport, hot-carrier solar cells, and polaron-related stability issues such as polaron-induced metastable defects, polaronic strain, and photostriction are systematically investigated. Finally, the prospect of further understanding and manipulating polaron-related phenomena, working toward highly efficient and stable PSCs, is suggested.


Introduction
Emerging organic lead-halide perovskites have captured worldwide research attention since their first attempted inclusion in solid-state photovoltaics in 2012 [1], and recent rapid achievements have endued perovskite solar cells (PSCs) as one of the most appealing candidates for the future energy supply because of their high efficiency and relatively low production cost. Studies at the forefront of investigations on PSCs have been dedicated from a material science and optical point of view, and have regulated perovskite crystallization, designed charge-transport materials, passivated interfacial and bulk defect states [2][3][4], and managed light propagation and distribution within multilayered devices [5,6] to improve their power-conversion efficiency and long-term durability, resulting in efficiency exceeding 25% with remarkable operational lifetimes [7]. However, in-depth understanding of the photophysical properties in perovskite materials, such as photocharge generation and transport dynamics, has lagged far behind, restricting the further development of PSCs from efficiency approaching the Shockley-Queisser limit and prolonged stability, which would fulfill commercial requirements [8,9].
The achievement of superior power-conversion efficiency in PSCs is mainly attributed to the unique optoelectronic properties of perovskite materials, such as long diffusion length (>1 µm) [10] and charge-carrier lifetime (⩾1 µs) [11], low trap defect density (10 9 -10 10 cm −3 ) [12] and exciton-binding energy (2-26 meV) [13], and high defect tolerance [14]. However, these properties are unexpected for materials like perovskites, which have a modest charge-carrier mobility in the range of ∼100 cm 2 V −1 s −1 [15]. Several mechanisms have been established to explain the origin of these attractive photophysical properties in perovskite materials [16]. Notably, perovskites are considered a type of ferroelectric material because of the rotational dipolar organic cations, and spontaneous polarization of the perovskite lattice from the disordered phase to the ordered phase can occur under a critical temperature [17,18]. The as-formed built-in electric field from lattice polarization can promote the spatial separation of electrons and holes and screen their Coulomb interaction in the ferroelectric domains, leading to suppressed charge recombination and enhanced carrier lifetime [19,20]. The presence of a ferroelectric phase in perovskite materials has recently been confirmed by direct experimental evidence [21]. In addition, owing to the constituent heavy atoms (i.e. Pb, I), perovskite materials manifest strong spin-orbit coupling [22], which can facilitate spin splitting in the band edges and largely affect their photophysical properties [23,24]. In particular, Rashba spin splitting allowed for the formation of spin-forbidden recombination channels or an indirect bandgap in perovskite materials [25], resulting in a long charge-carrier lifetime and slow carrier recombination [24,26]. However, the above mechanisms cannot explain the moderate mobility in perovskite materials.
Recently, the moderate mobility and low recombination rates in perovskite materials have been correlated via the concept of polarons, which refers to electron-phonon coupling [27][28][29][30]. It has been realized that the molecule rotation of organic cations and the vibration of the soft inorganic sublattice largely affect the charge carrier transport dynamic. The strong electron-phonon interaction within polarons generates pseudo-free dressed carriers, which can screen the carriers from defect states to prevent nonradiative recombination and trapping, leading to a prolonged charge-carrier lifetime and diffusion length [30][31][32]. Moreover, polarons were also found in conjugated organic semiconductors such as charge-transport materials in PSCs, which can promote charge extraction from the device and hence improve device performance [33,34]. In addition, the formation of polarons has been employed to explain some stability issues in PSCs owing to the generated polaronic gradients and metastable defects, which majorly affect the phase stability and charge transport [35,36]. Therefore, the presence of polarons in PSCs has a great influence on device performance and photostability, which merits more investigations, including the understanding of their formation mechanism and the development of polaron manipulation, working toward high-performance PSCs [37,38].
In this review, the fundamental basics of the crystal structure and lattice vibration of perovskite materials are briefly introduced, and the formation mechanism of polarons within perovskites and their effect on charge-transport dynamics are then elucidated. Based on that, the presence of polarons in PSCs and their effect on device performance and stability are systematically reviewed. At the end, prospects on further understanding and modulating polarons in PSCs are proposed.

Crystal structure and lattice vibration of perovskite
Perovskite is a class of crystalline material with a common chemical formula of ABX 3 , as shown in figure 1(a), in which the As are monovalent cations (i.e. formamidinium (FA + ), methylammonium (MA + ), Cs + ), B bivalent metals (i.e. Pb 2+ , Sn 2+ ), and X halide ions (i.e. I − , Br − , Cl − ), respectively. The crystal lattice can be viewed as two interpenetrating sublattices of corner-sharing octahedral BX − 3 and A + cations, in which the BX − 3 framework dominates the electronic configuration of perovskite materials and the cations determine the structural deformation. Specifically, the valence and conduction band of perovskite materials originate from the electronic configuration of the inorganic lead-halide framework, enabling the properties to be comparable to inorganic semiconductors. Moreover, the mechanical properties of perovskite materials are determined by the connectivity of B-X bonds and their interaction with cations, leading to a relatively low Young's modulus and soft nature [39], which is similar to organic semiconductors. Therefore, perovskite materials manifest a crystalline solid and liquid-like behavior [32]. Particularly, the halides can move perpendicularly to the lead-lead axis with a strong anharmonic shape [40][41][42] (figure 1(b)), and the organic cations (e.g. MA + , FA + ) can tumble within the soft BX − 3 cage because of their charge anisotropy (figure 1(c)) [43], largely affecting the local polarization and charge-carrier transport [44]. The structural variation of the crystal lattice can be characterized by Raman or near infrared spectra in a specific frequency region, as shown in figure 1(d) [45].

Polaron size in perovskite
Polarons are defined as a type of charged quasiparticle, which are likely formed in polarizable materials because of the coupling of excess charges (i.e. electrons or holes) with ionic vibrations [46]. Specifically, in a perovskite lattice, an injected charge carrier can induce reorientation of the polar A-cations and structural vibration of the BX − 3 sublattice to minimize the Gibbs free energy of the local lattice, and hence form a polarization cloud that accompanies along the carrier propagation. According to the spatial size of the polarization cloud, the polarons can be classified into small and large polarons, referring to the polaron radius close to approximately one single lattice constant and multiple unit cells, respectively [35].  [43], with permission from Springer Nature. (d) Charge-injection-induced structural variation as calculated from the near infrared spectra. Adapted with permission from [45]. Copyright (2019) American Chemical Society.

Small polarons
Small polarons are short-range carrier-phonon interactions, and their formation in perovskite materials is attributed to the cation rearrangement with dipoles toward Pb atoms and system equilibrium with lattice distortion to maintain the dipole direction [47]. Thus, the polaron-binding energy is determined by the volumetric strain of the inorganic sublattice and rotational degrees of freedom of the A-cations [47], which increase as the lattice structure is distorted [48]. Small polarons transport within perovskite crystals in an incoherent motion via phonon hopping, in which the carrier is partially delocalized by thermally driven atomic distortion. Thereby, the mobility of small polarons is relatively low with typical values smaller than 1 cm 2 V −1 s −1 , which increases as the temperature increases owing to the heat-accelerated lattice distortion [46]. Small polarons are prone to accumulate charges within the perovskite lattice and induce deep-level traps within the bandgap. Moreover, the presence of point defects in the perovskite lattice can further facilitate the formation of small polarons, which largely reduce carrier mobility and promote charge-defect recombination, leading to detrimental effects on the device performance of the corresponding PSCs [49].

Large polarons
Large polarons in perovskite are characterized by low binding energy (<k B T) and large effective mass, in which the charge carrier can overcome the binding energy and coherently move across multiple lattice units. The reorientation of cations and the oscillation of the inorganic framework within large polarons tends to localize but also facilitate carrier transport. Different from small polarons, the mobility of large polarons is significantly increased with values in the order of 10 3 cm 2 V −1 s −1 and exhibits a converse trend as the temperature increases because of thermal-enhanced carrier scattering [46]. The strength of electron-phonon coupling within perovskite materials can be described by the dimensionless Fröhlich coupling constant α [50]: where e is the elementary charge, h is the Plank constant, c is the speed of light, m e * is the effective mass, ω LO is the angular frequency of the coupled longitudinal-optical (LO) phonon, and ε ∞ and ε 0 are the optical and static dielectric constants, respectively. The values of α were calculated to be located in the range of 1.1-2.7 in perovskite materials, indicating intermediate-to-large polarons [23,29,51].

Evidence of polaron formation in perovskite
The formation of polarons in perovskite materials was first confirmed in MAPbBr 3 single crystal by employing time-resolved optical Kerr effect (TR-OKE) spectroscopy [28]. As shown in figure 2(a), the MAPbBr 3 exhibited broadband and featureless TR-OKE responses when using nonresonant pump photon energy (1.85 eV), which is similar to a typical liquid, indicating structural flexibility of the inorganic PbBr 3 − sublattice. Upon preresonant photon energy (approaching the bandgap) excitation, energy-dependent slow responses (>1 ps) were clearly observed (figure 2(a)) because of the coupling of nuclear motion to electronic transitions, which were assigned to the Pb-Br-Pb bending within the organic sublattice, as confirmed by the low frequency (<100 cm −1 ) responses in the corresponding Fourier spectra (figure 2(b)). In contrast, these features disappeared upon above-bandgap (2.30 eV) excitation, indicating the interaction of nuclei and photogenerated carriers (the formation of polarons) [28]. The perovskite lattice structure under neutral and electron polaron states was further calculated by using density function theory to study the structural dynamics upon polaron formation [52]. In a polaron state, the A-cations were reoriented with dipoles toward the Pb, and the octahedral PbX − 3 geometry was also deformed to minimize the Gibbs free energy of the local lattice. As illustrated in figure 2(d), the vibration of the PbX − 3 sublattice involves skeletal and in-plane bending and stretching along the z-axis of the X-Pb-X bonds , and the most significant structure variations were the elongation of the Pb-X bond lengths and the tilting of the X-Pb-X angles [52]. The vibration of the inorganic sublattice was further confirmed by experimental measurement by using time-domain Raman spectroscopy [52] and a terahertz-electromagnetic probe [53].
In order to investigate the effect of different cations on polaron formation, the TR-OKE transient spectra of perovskites with different cations (i.e. CsPbBr 3 , MAPbBr 3 , FAPbBr 3 ) were compared, as detailed in figure 2(c). Specifically, the CsPbBr 3 manifested (1) instantaneous (∼70 fs) and (2) ultrafast (∼140 fs) responses, which were ascribed to the polarization-induced inertial reorientation of the inorganic sublattice. Different from CsPbBr 3 , two additional long-time responses appeared in MAPbBr 3 and FAPbBr 3 , which were correlated to (3) local-interaction-induced rotational motion (<1 ps) and (4) diffusive rotation (1 ∼ 2 ps) of the liquid-like molecular cations [32]. Therefore, polaron formation in perovskites is dominantly dependent on the photocarrier-induced deformation of the inorganic PbBr − 3 lattice, irrespective of the type of cations, and the cations differed from the formation time in Br-based perovskites [28]. In contrast, the polaron-formation time is irrespective of cation motion and similar values were measured for lead-iodide perovskites (e.g. CsPbI 3 , FAPbI 3 , MAPbI 3 ) [54], while it should be noticed that the type of cations affect polaron mobility because of the interaction of the cation dipole within the polaron [29].
Moreover, the perovskite films exhibited high values (∼10 3 ) of low-frequency dielectric constants in the dark, which linearly increased as a function of light intensity (figure 3(a)), resulting in a giant dielectric constant (∼10 6 ) under 1 sun irradiation [55]. This dramatic enhancement of dielectric response was attributed to photocarrier-induced structural fluctuation of the perovskite lattice, and the enlarged dielectric constant can effectively screen the Coulomb attraction between the electrons and holes and facilitate charge transport. Meanwhile, similar to other inorganic semiconductors, the mobility in perovskite materials presents a strong temperature dependence and follows a power law µ ∼ T −3/2 (figure 3(b)) [56], which indicates that the carrier scattering is majorly dominated by temperature-induced lattice vibration other than defect scattering. These experimental observations are direct hints of the correlation between the phonon modes and the carrier dynamics [55,56].
In addition, the presence of large polarons can be proven by measuring the effective mass and charge mobility. For instance, the effective mass was calculated according to the following function: where m * is the effective mass, e is the elementary charge, λ is the mean-free path, k B is the Boltzmann constant, T is the kelvin temperature, and µ is the carrier mobility. As roughly estimated from the above equation, the room-temperature effective mass in perovskites was hundreds or thousands (10-300 m e ) times heavier than the mass of a single-particle band (0.1 m e ), suggesting the presence of large polarons [30]. However, such an estimation was contradicted with some numerical evidence as well as actual experimental measurements of the band mass in perovskites [57][58][59], and the evidence of polaron formation obtained through band masses is still under debate [60]. Indeed, some polaron behaviors have been clearly observed in perovskite materials, which can be rationally explained by a classical polaron model. However, prototypical perovskites manifested unusually large lattice displacement at room temperature because of their relatively low phonon energies compared with typical inorganic crystal materials (e.g. Si, GaAs), leading to a failed interpretation of all photophysical properties of the perovskites using a standard polaron model [38]. For instance, some recent theory work found that mobilities obtained in the Fröhlich polaron model are disparate from several experimental findings, including their magnitudes and temperature dependencies [38,61,62]. To explain the unusual charge-carrier transport and light-absorption properties of the perovskite materials, the dynamic disorder concept was implemented by considering the charge and lattice fluctuations [63].

Polaron-associated carrier dynamics in perovskites
The charge-carrier dynamics in perovskite materials can be analyzed by terahertz time-domain spectroscopy [28,29,64]. As demonstrated in figure 4(a), photogenerated carriers undergo a sequential hot-carrier cooling and polaron-formation process upon above-bandgap excitation, which delays the rise rate of photoconductivity increase compared to that of resonant excitation [54]. It was noted in figure 4(b) that the timescales of photoconductivity rise were around ∼1.5 ps, which indicates that the photoconductivity is dominated by carrier thermalization rather than photocarrier generation, which is in the range of hundreds of femtoseconds [65,66].
Moreover, the rise of photoconductivity is independent of temperature upon on-gap excitation, suggesting temperature-independent polaron-formation time (τ pol ). Polaron formation under on-gap excitation is ascribed to thermally driven LO phonons at Debye temperatures, which is below 140 K for tetragonal FAPbI 3 and MAPbI 3 [51,67]. The interaction strength between the carrier and LO phonon is mainly determined by the inorganic Pb-I sublattice. In contrast, the carrier-cooling time (τ cool ) is strongly dependent on excitation energy and temperature upon above-bandgap energy excitation. Particularly, the cooling time increases as the excitation energy increases and the temperature decreases. Moreover, the cooling rates depend on the types of cation from which the high energy optical phonons are generated, following an order of Cs < MA < FA in lead-iodide perovskites [54].

Polaron modulation for high-performance PSCs
The power-conversion efficiency of a solar cell is intimately dependent on a multistep charge-carrier dynamic process, including light harvesting, photocarrier generation, carrier transport, and collection at respective electrodes, in which the above-bandgap photon energy and nonradiative recombination of oppositely charged carriers (electrons and holes) are main energy losses, restricting the efficiency of solar cells. As aforementioned, the formation of large polarons in a perovskite layer can lead to giant dielectric constants and can screen the Coulomb attractive interaction between electrons and holes, resulting in a low recombination rate [55]. Moreover, polarons can lower HC relaxation, enabling the possibility to extract high-energy carriers from perovskite materials [69][70][71]. In addition, large polarons were also observed in conjugated organic materials, which can be used to facilitate charge extraction in PSCs as grain boundary passivators [34] or a charge transport layer [33]. Therefore, the modulation of polarons in perovskites and organic charge-transport materials is expected to eliminate energy losses in PSCs.

Stabilization of large polarons in perovskite layers
It has been established from theoretical predictions and experimental observations that both small and large polarons can be generated in perovskite materials [16]. However, the presence of small polarons in perovskite materials is believed to cause deep-level traps and structure distortion, which is detrimental for the performance of corresponding PSCs [72]. In contrast, large polarons beneficially contribute to the prolonged carrier lifetime and diffusion length, which are expected to promote the efficiency of PSCs [16,46]. Given the experimental evidence, large polarons are more likely observed in perovskite single crystals than in perovskite thin films [53], in FA-and MA-based perovskite than in Cs-based perovskites [32], and in Br-based perovskite than in I-based perovskite. Therefore, the chemical composition is desirable to stabilize large polarons in PSCs.

Compositional engineering
As it has been established that the band configurations of perovskite materials are majorly dominated by the inorganic Pb-X sublattice, the A cations have a negligible impact on their optoelectronic properties [4,44]. Recent investigations have found that the A cations, such as their length, dipole moment, etc, can largely affect the formation of polarons [30,54]. For instance, small polarons are prone to form in MAPbI 3 and the magnitude of polaron-binding energy is dependent on the type of cations. Specifically, the binding energies have been calculated to be 1.3 and 0.6 eV for electron and hole polarons in MAPbI 3 , respectively, which are reduced to 0.9 and 0.3 eV in CsPbI 3 because of the smaller dipole moment of Cs + compared to MA + . The polaron-binding energy can be further reduced when employing FA + as A-site cations, which is attributed to the restricted rotation of large FA cations within the lattice [47,73]. Thus, the polaron-binding energy of iodide-based perovskites with different cations follows an order of MA > Cs > FA because of the restricted cationic reorientation in Cs-and FA-based perovskites [73], and the corresponding hole-spin density distribution was calculated, as seen in figures 5(a)-(c), respectively. Therefore, alloying FA and Cs into MA-based perovskites allows the electron and hole polaron-binding energy to be minimized [74], which is ascribed to the reduced lattice symmetry and suppressed cationic reorientation (figure 5(d)), and perovskites with mixed cations exhibit high resistance against structure distortion particular to Pb-I bonds in the octahedral framework [75]. Moreover, Br-based perovskites present tighter polaron binding than that of I-based perovskites, and the substitution of Pb by Sn can further reduce the polaron-binding energy [73].
Polaron mobility is another tunable parameter in perovskite materials via compositional engineering, as it is known that polaron mobility is correlated with carrier scattering time, which is determined by carrier-lattice interaction. The substitution of Pb or I by lighter Sn or Br, respectively, in the inorganic cage can improve the carrier mobility of perovskites due to the increased phonon vibrational frequencies [76,77]. For instance, when the perovskite composition of (FAPbI 3 ) 0.85 (MAPbBr 3 ) 0.15 (denoted as FA0.85) was changed to (FAPbI 3 ) 0.95 (MAPbI 3 ) 0.05 (denoted as FA0.95), the polaron mobility can be enhanced by 30% from 8-15 to 10-18 cm 2 V −1 s −1 [78]. As was analyzed from the terahertz spectrum, the co-substitution of the A-and X-site of FAPbI 3 by MA + and Br − , respectively, can reduce carrier scattering time because of the reduced structural distortion and cation dipole-polaron coupling in FA0.95 compared to that in FA0.85, contributing to the increase of polaron mobility and retarded carrier-phonon cooling in FA0.95. Moreover, the polaron mobility of inorganic CsPbI 3 was measured to be 270 ± 44 cm 2 V −1 s −1 , which is around one magnitude higher than that of organic hybrid perovskite in terms of MAPbI 3 and FAPbI 3 (25-75 cm 2 V −1 s −1 ) [51,79]. Therefore, the increased polaron mobility of perovskites based on Cs-and alloyed cations is indicative of the effect of polarons on charge-transport dynamics, and rational composition engineering can modulate the polaron dynamics in resultant perovskites, resulting in outstanding power-conversion efficiency of PSCs.

Molecular passivation
Large polarons can be introduced into perovskite films by molecular passivation. For example, aromatic molecules, e.g. porphyrin and monoamine Cu porphyrin (CuP), are prone to self-assemble into supramolecules upon thermal treatment ( figure 6(a)). The strong interaction between amine groups and the central metals of the adjacent molecules can affect the dipole direction, leading to the formation of homogeneously large polarons in the formed supramolecules (CuP-S2), which was confirmed by electron paramagnetic resonance and Raman spectroscopy. As the porphyrin molecules were doped into the perovskite, CuP-S2 with a gradient electric field was formed at the grain boundaries, as illustrated in figures 6(b) and (c), which can act as a continuous pathway for hole extraction across the perovskite grain boundaries and effectively suppress nonradiative recombination. Consequently, a champion efficiency up to 24.2% of the device based on porphyrin-modified perovskites was achieved, as shown in figure 6(d), and the T 80 lifetime was elongated to 3000 h under constant light illumination and an environmental temperature of 65 • C condition (figure 6(e)) [34].

Polarons in hole transport layer
Polarons can be generated in organic materials consisting of periodic structures, in terms of conjugated polymers of poly(3-hexylthiophene-2,5-diyl) (P3HT) [80], poly(triarylamine) (PTAA) [33], etc, and small molecules of spiro-OMeTAD [81,82], porphyrin [34], etc, if the charge carriers are strongly associated with the vibrational modes of components in the organics. Parameters in terms of crystallinity, chain length, molecular weight and so forth of the organics determine their interchain interaction with the charge [80]. For example, the increase of conjugation chain length of P3HT can significantly enhance the polaron delocalization, and hence improve its charge mobility [80]. In the case of PTAA, the doping of high-molecular weight PTAA can enhance the polaron delocalization. Particularly, the doping of PTAA can partially oxide the polymer and thereby affect the polarity of the adjacent chains. Moreover, the increase of molecular weight can restrict the vibration of the PTAA chains. Accordingly, the combined effect of delocalized polarons and improved charge mobility can significantly promote charge transport through the PTAA layer. In addition, the increase of molecular weight can dramatically boost the thermal stability of the PTAA. As a result, 17% efficiency of solar modules (43 cm 2 ) based on high-molecular weight PTAA was obtained, and 90% of the initial performance was maintained after 800 h aging at 85 • C [33].  . Energy diagram and work mechanism of hot-carrier solar cells, which consist of a hot-carrier absorber, energetically narrow selective contact, and electrodes. Adapted from [70] with permission from the Royal Society of Chemistry.

Toward HC solar cells
One of the major thermodynamic limits for energy conversion in a solar cell is the loss of above-bandgap (hot) photon energy, which is a femtosecond process in most photovoltaic materials [8]. As illustrated in figure 7, the concept of an HC solar cell is proposed to reduce hot energy loss by extracting HCs immediately prior to their cooling. Particularly, the hot electrons and holes with a temperature higher than the lattice (e.g. T e > T L , T h > T L ) generated at the photoactive layer are extracted through energy-selective contacts. The extracted HCs can retain their high-energy states and increase the chemical potential from ∆µ of a conventional device to c eh of an HC device, as illustrated in figure 7. Therefore, HC solar cells enable the absorption of a wide range of photon energy and increase the open circuit voltage. A theoretical efficiency up to 67% can be achieved in single-junction HC solar cells, which is approaching the limit of infinite tandem cells [65,71].
Perovskite materials manifest an ultralong HC lifetime and slow charge-recombination process, which can be utilized in the realization of HC solar cells [29,65,83]. To reach truly high performance HC PSCs, the HCs should reach a charge transport layer before their cooling, so the perovskite layer should be electrically thin and optically thick. In this regard, the crystal quality and chemical composition of perovskite thin films should be intensively engineered to retard the HC relaxation. For example, Cs-based perovskite (i.e. CsPbI 3 ) exhibited a slower cooling time than that of FA-and MA-based perovskites (i.e. FAPbI 3 , MAPbI 3 ), which is attributed to the reduced HC-phonon coupling in Cs-based perovskite [84] and the lowest cooling rates [54]. The doping of alkali ions (e.g. K + , Cs + , Rb + ) into (MAFA)Pb(BrI) 3 can markedly prolong the HC lifetime to above 10 ps with a diffusion length of over 100 nm because of the facilitated lattice strain relaxation and passivation of vacancy defects [85]. Moreover, the control of point defects (e.g. introducing interstitial iodide defects and eliminating vacancies defects) within the MAPbI 3 lattice can largely retard the hot-electron cooling, which was attributed to the reduced band degeneracy and weakened HC-phonon interaction [86]. In addition, HC lifetime is found to be proportional to light intensity, so a suitable concentrator or light management can be developed to enhance the carrier density within the perovskite layer to prolong the lifetime [66]. However, the exact origin and underlying mechanism (e.g. phonon bottleneck [66], auger heating [87], large polaron [32], etc) for such a long HC lifetime in perovskite materials are not well understood or are still under debate [4]. Furthermore, the design of charge-transport materials, which should present a narrow band pass with energy levels to selectively extract HCs without interrupting cold carriers, is another challenge to the realization of truly HC solar cells [69][70][71].

Effect of polarons on device stability of PSCs
Carrier-phonon coupling within perovskite crystals is accompanied with cation reorientation, lattice deformation, etc, which can create some metastable defects, polaronic strain, and photostriction in PSCs, largely undermining their photostability.

Polaron-induced metastable defects
As seen in figure 8(a), PSCs suffer from a fast photocurrent decay upon light illumination and recovery when resting in the dark, which seriously undermines their operational stability [35]. Such light-induced performance degradation and recovery in PSCs was attributed to polaron-induced metastable defects in perovskite layers, as illustrated in figure 8(b). As was evidenced from the increase of dielectric constants (figure 8(c)) and Raman scattering in the region of 135-210 cm −1 , the cation (i.e. MA + ) vibration within the crystal lattice was slowed down or even frozen after light illumination, which was ascribed to the coupling of photogenerated carriers to the local lattice. Polaron-induced distortions [88] of the symmetric structure and local field fluctuation can act as deep-level metastable defects, as confirmed by the absorption increase at the near infrared wavelength region ( figure 8(d)), leading to a fast photocurrent decay in PSCs; the long-term slow degradation process is attributed to the slow mobility and accumulation of small polarons [35]. Therefore, light-induced performance decay can be recovered by resting in the dark or can be significantly suppressed by reducing the activation energy for structure vibration. For instance, the switch between day-night or operating at low-temperature (e.g. 0 • C) conditions can extend the operational stability of PSCs.

Photostriction
Owing to the phonon-lattice coupling, perovskite materials demonstrate strong light-matter interaction. In the case of photoexcited MAPbI 3 , the generation of charge carriers can weaken the binding between the amine group of organic cations and the iodide from the inorganic framework because of the reduced electron density of I as the charge transfers from the valence band maximum of Pb 6s-I 5p to the conduction band minimum of Pb 6p [89]. The weakened interaction promotes the rotational degree of freedom of MA and straightens the Pb-I-Pb bond, leading to a giant photostriction, as illustrated in figures 9(a) and (b) [89]. It was realized that the straightening of the Pb-I-Pb bond can reduce the migration energy barrier of the water molecules at the crystal surface and promote water adsorption (figures 9(c) and (d)). The reason was ascribed to the enhanced electron density of Pb after photostriction, which can easily be attacked by the O of moisture molecules, leading to increased moisture sensitivity [90]. Moreover, photostriction is a self-accelerated process because the straightening of Pb-I-Pb bonds can improve photon absorption and further speed up photostriction, leading to inferior stability of PSCs in an ambient environment [90,91].
However, there is still debate about the photostrictive effect in perovskite materials since both lattice contraction and expansion were experimentally observed under low-and high-intensity light illumination, respectively [92,93]. For instance, a lattice-contraction effect was observed in MAPbBr 3 , and its correlation with cation rotation was confirmed by Raman measurements. Particularly, the Raman peak of the MAPbBr 3 was blueshifted from 317.5 to 328.2 cm −1 upon light illumination, which corresponds to the MA + rotation along the C-N axis, indicating a direct correlation between the cation rotation and photostriction due to the strong electron-phonon coupling [94].  Adapted from [90] with permission from the Royal Society of Chemistry.

Polaronic strain
Light-induced phase segregation is likely to happen in hybrid perovskites with mixed halides (e.g. Br/I), largely undermining the photovoltaic performance in the resultant PSCs [95]. The formation of highly coupled polarons can promote phase separation in mixed-halide perovskites [36,72,96]. Particularly, halide ions such as I − and Br − are randomly distributed in the as-deposited mixed MAPb(I 0.1 Br 0.9 ) 3 perovskite films, as demonstrated in figure 10(a). Upon photoexcitation, electron-hole pairs with a small binding energy (0.03 eV) are generated, which are quickly separated into free carriers (i.e. electrons and phonons). The polar cations (i.e. MA + ) are reoriented to localize the carriers because of the strong carrier-phonon interaction, leading to the formation of polarons with a diameter of 8 nm and a binding energy of 0.08 eV [96]. The deformation of the local lattice can generate polaronic strain [97], which can increase with exposure time and further reduce the activation energy for ions migration [98,99]. Polaronic strain was primarily formed at low bandgap (high I concentration) regions under low-intensity light irradiation, which causes strain gradients and stabilizes the polaron within I-rich regions, segregating the mixed perovskites into I-rich and Br-rich domains ( figure 8(b)). Such phase separation issues can be recovered as the release of strain by relaxing the perovskite film in the dark for a certain time [96]. In contrast, upon high-intensity light illumination, the polaronic strain filed from Br-rich domains overlaps with that from I-rich regions and the strain gradients disappear, leading to the homogenous remixing of halides with eliminated phase separation, as shown in figure 10(b) [72]. Recently, polaronic strain in perovskites has been experimentally visualized by real-time characterizations according to crystal structural variations [97].
To prevent phase segregation in hybrid perovskites, strategies should be dedicated to reducing carrier-phonon interaction. For example, substituting organic cations (MA + , FA + ) with Cs + [96] or doping Cs + into mixed I/Br perovskite films [74,100] can effectively mitigate halide ions segregation and boost the photostability of mixed-hybrid perovskites. The improved stability was attributed to the less polarity of Cs + , which significantly reduces carrier-phonon coupling.

Conclusions and perspectives
In summary, the specific ionic and soft nature of perovskite crystal structures enable long-range coupling between photogenerated carriers and the polarized crystal lattice in organic-inorganic hybrid perovskites. The presence of large polarons is effective in protecting the photogenerated carriers from scattering with the trap states, resulting in prolonged carrier lifetime and reduced nonradiative recombination in perovskite materials, and hence high performance of the resultant PSCs. However, the strong coupling between the carriers and ionic lattice can parasitically create metastable defects, photostriction, and polaronic strain, leading to inferior photostability of PSCs. Pioneering investigations have proven that rational engineering of the chemical composition and crystal quality of perovskite materials is effective in modulating the polaron state in the perovskite layer, leading to improved efficiency and stability of PSCs.
However, the formation mechanism of polarons in perovskite materials and their effect on carrier dynamics still lack solid understanding. Prospects for further understanding the role of polarons in the realization of highly efficient and stable PSCs should focus on the following aspects. First, fundamental understanding about the influence of defect states, chemical composition, crystal quality, and some other external parameters such as light illumination, heat, electric field, etc, on polaron formation and transport need to be explored with the assistance of computational simulations, machine learning, advanced characterizations, and rational experimental design. Moreover, direct correlation of the parameters of polarons (e.g. binding energy, mobility, coherence length, lifetime, etc) with photovoltaic metrics and the long-term stability of the corresponding PSCs could provide great insight for further modulation of polaron formation, working toward highly efficient and stable PSCs. For instance, a thorough understanding of the origin of extended HC lifetime could facilitate the design of perovskite materials or nanostructures for the realization of truly high performance HC solar cells. In addition, the correlation between polaron transport and local strain in perovskite lattices needs to be explored, and some other types of polarons, such as ferroelectric polarons and excitons polarons, need further theoretical and experimental investigations.

Data availability statement
No new data were created or analyzed in this study.