Halide perovskites (HPs) have garnered enormous interest in the past decade, owing to the low-cost solution preparation^[1−3], the easily adjustable bandgap^{[4, 5]}, and extraordinary optoelectronic properties^[6−11]. HPs have a generic structure of ABX₃, whereas A denotes organic ammonium or cesium cation (CH₃NH₃⁺, H₂NCHNH₂⁺, Cs⁺), B is divalent metal cation (Pb²⁺, Sn²⁺), and X is halide anion (Cl⁻, Br⁻, I⁻). The diversiform compositions lead to easily tailored bandgap and consequently altered properties, giving a broad range of candidates with excellent optical absorption coefficients and optoelectronic properties. It is no exaggeration that the past decade has witnessed the booming development of these promising HPs. The certified energy conversion efficiency of single-junction perovskite-based solar cells has reached 26.7%^[12], exhibiting the capability for further advancement to exceed silicon-based solar cells. Besides, the external quantum efficiency (EQE) of perovskite light-emitting diodes exceeds 30%^[13], and multifunctional photodetectors have been widely constructed^[14−16]. All of these applications demonstrate the remarkable potential of HPs as active layers for optoelectronic devices.

Among diverse A-site and X-site substituted HP systems, formamidinium lead iodide (FAPbI₃) is of utmost importance. α-FAPbI₃ possesses extraordinary optical and electrical properties^[17] with a decent bandgap (1.48 eV) close to the theoretical value of the single-junction solar cell (1.39 eV)^[18], exhibiting high efficiency up to 25.6%^[19]. Despite its outstanding performance as an active material, α-FAPbI₃ is plagued by the issues of the diversiform phases of FAPbI₃, including α-, β-, γ-, and δ-phase^[20]. As shown in Fig. 1, β- and γ-phase are both low-temperature tetragonal phases, which are presented below 285 and 140 K, respectively^[21]. While the δ-phase is thermodynamically stable at room temperature, α-FAPbI₃ would convert to the δ-FAPbI₃ regardless of the storage environment at room temperature^[22]. α-FAPbI₃ is a cubic system with corner-sharing octahedrons, whereas δ-FAPbI₃ is a hexagonal system with face-sharing octahedrons, the molecular volume increases by only 2.2% from α- to δ-phase transition, resulting in the good coexistence between these two phases at room temperature^[23]. Regrettably, due to the non-perovskite 1D hexagonal structure of δ-FAPbI₃, the potential barrier for self-trapping in the low-dimension structures is significantly reduced, resulting in self-trapped states under strong electron−phonon coupling^[24]. Thus, δ-FAPbI₃ is photo-inactive and electronic insulating (bandgap of ~2.88 eV), and the power conversion efficiency of δ-FAPbI₃-based solar cells is only 0.2%−0.7%^{[25, 26]}.

As a result of the stark contrast efficiencies of these two phases, the non-functional δ-phase is always treated as a "trashy" parasitic phase during the formation of α-FAPbI₃^[27]. Thus, the major challenge for FAPbI₃ is to suppress the phase transition from the photoactive black α-phase to the yellow δ-phase, and a great number of strategies have been proposed. For solution-processed FAPbI₃-based films, A-site incorporation with smaller inorganic Cs⁺ or organic MA⁺ and B-site incorporation with Br⁻ was widely demonstrated as an effective approach to suppress the transformation from the black phase to the yellow phase at room temperature^{[28, 29]}. This strategy can be attributed to the reduced electron−phonon coupling strength by restricting FA⁺ cation motion^[30−32], leading to larger charge carrier mobility, lower non-radiative electron−hole recombination rate, and thus facilitating the charge carrier collection process^[31].

Every coin has two sides, is δ-FAPbI₃ perovskite thoroughly impractical? To ponder this impediment from another perspective, could the δ-FAPbI₃, with unique electronic insulating properties, act as electrical insulating layers and thus use the phase transition between α- and δ-phase to manipulate electron insulation to conduction? In this review, the drastically distinct structure and associated properties of α- and δ-phase are firstly compared, looking forward to clarifying the origin of the nature of electronic insulating δ-FAPbI₃. Secondly, the phase transition from α- to δ-phase is an intricate process, which can be attributed to factors such as temperature, pressure (internal/external pressure), humidity, etc. Thus, different characteristics and mechanisms related to phase transition are systematically presented, giving a comprehensive summary and profound insight into the process. Meanwhile, strategies for promoting and preventing phase transitions utilizing different means are also provided. Finally, combined with some novel δ-phase applications reported so far and the above analysis of properties and phase transition mechanisms, we hope to give some insights into the further functionalized application of δ-FAPbI₃. In a word, we are looking forward to giving a roundabout strategy to exploit the "trashy" δ-FAPbI₃ and providing more possibilities for the application of FAPbI₃-based perovskite.

Despite the recent controversy about the distorted tetragonal structure of α-FAPbI₃^[33], α-FAPbI₃ is still widely recognized as a cubic structure with Pm$\overline{3}$m symmetry, while δ-FAPbI₃ is accepted as 1D hexagonal P6₃mc^{[22, 34]}, as can be seen from XRD patterns with different periodic alignments in Fig. 2(a). The phase transition from α- to δ-FAPbI₃ is also accompanied by the main Raman peak redshifted from 135 to 111 cm⁻¹ due to the different vibration modes of FA molecules (Fig. 2(b))^[17]. It has been discovered that there exist contrasting properties between α- and δ-FAPbI₃, for instance, δ-FAPbI₃ exhibits thermodynamic stable at room temperature with lager bandgap, but the chain-like structure in δ-FAPbI₃ obstructs electron transport compared to α-FAPbI₃. The strong electron−phonon coupling in this 1D structure easily lead to self-trapped excitons (STEs)^{[35, 36]}, which induces an elastic distortion of the surrounding lattice and further captures the photogenerated electrons. Owing to the more stable self-trapped state, the electron−phonon coupling in δ-FAPbI₃ would further deteriorate the electrical properties, which can explain the electronically isolated states in the δ-phase^[37].

Electron−phonon coupling refers to the interaction between charge carriers and lattice vibrations (phonons), where charge carriers dressed by phonons induce the formation of polarons, setting a fundamental limit to charge carrier mobility without extrinsic scattering off impurities or interfaces^[38]. Electron−phonon coupling is an aggregation of various mechanisms, where the Fröhlich interaction is expected to dominate in ionic crystals as HPs at room temperature, and the phonon anharmonicity may also form unconventional polaritons, which causes phonon overdamping and may have a strong impact on the physical properties, especially electron−phonon interactions^[39]. Fröhlich interaction refers to the long-range interaction of electric fields generated by longitudinal optical (LO) phonons with electrons^[40], which is the dominant source of PL linewidth broadening^{[41, 42]}. As presented in Eq. (1):

1$\Gamma \left(T\right)={\Gamma }_{\text{0}}+{\Gamma }_{\text{LO}}={\Gamma }_{\text{0}}+\frac{{\gamma }_{\text{LO}}}{{\text{e}}^{E_{\text{LO}}/kT}-1},$

where Г₀ is a temperature-independent inhomogeneous broadening term as a result of disorder and/or imperfections, Г_LO is a homogeneous broadening term attributed to longitudinal optical (Fröhlich) scattering, γ_LO is coupling strength and E_LO is an energy representative of longitudinal optical phonon. The temperature-dependent steady-state PL spectrum and the extracted full width at half-maximum (FWHM) of FAPbI₃ (here refers to the alpha phase) are shown in Figs. 2(c) and 2(d), and the well-fitted PL linewidth to Eq. (1) indicates that the existence of Fröhlich coupling in α-FAPbI₃ like other HPs, and the dominant contribution to the homogeneous linewidth broadening attributes to the Fröhlich coupling between charge carriers and LO phonons^[38]. Meanwhile, it is found the substitution of organic cations in HPs has relatively little effect on the Fröhlich interaction compared to the substitution of inorganic frameworks^[43]. Many studies have also found that doping Cs^+[30], (CH₃)₂NH₂⁺ (abbreviated as DMA) cation^[31], and Br⁻ anion^{[31, 32]} restrict FA⁺ cation motion by restraining the structural fluctuations of the lattice, exhibiting reduced electron−phonon coupling strength and suppressed ionic migration, which is conducive to larger charge carrier mobility, lower non-radiative recombination rate, and better stability than pure α-FAPbI₃.

However, it is still hard to explain the different performance between α- and δ-FAPbI₃ (Fig. 3(a)) with only different Fröhlich coupling, due to the similar phonon densities of states in these FAPbI₃ phases (Fig. 3(b)). Thus, a more complex electron−phonon coupling process exists in electronically isolated δ-FAPbI₃, and the anharmonic effects in δ-FAPbI₃ should be taken into consideration^[33]. The 1D distorted face-sharing PbX₆ octahedrons could result in anharmonic electron−phonon coupling^{[35, 45]}. The self-trapping is strongly related to the dimensionality of materials, and in three-dimensional materials there is a potential barrier that needs to be overcome to initiate the self-trapping process. However, in low-dimensional materials, the potential barrier for self-trapping is weakened or disappears, and thus STEs are more easily observed, e.g., as the number of quasi-two-dimensional HP layers decreases (i.e., the dimensionality is closer to two-dimensionality), the intensity of STEs increases, as shown in Fig. 3(c)^[24]. Therefore, the lower-dimensional 1D structure of δ-FAPbI₃ gives rise to the low potential barrier for self-trapping like CsPbI₃^[45] and TMAPbI₃^[35] with a similar 1D structure, resulting in strong STEs and poor electrical performance because of anharmonic electron−phonon coupling^[24]. As a result of the existence of STEs, the captured photogenerated excitons then release energy in the form of luminescence, and the multiple broadband photoluminescence (PL) emission of δ-FAPbI₃ can be seen, as compared with that of α-FAPbI₃ in Fig. 3(d)^[37]. Based on the above analysis, we believe that the origin of the different properties of α- and δ-FAPbI₃ is due to the STEs caused by anharmonic electron−phonon coupling in the low-dimensional δ-FAPbI₃.

It becomes more reasonable to explain the contrasting properties between α- and δ-FAPbI₃ after considering STEs in δ-FAPbI₃ due to anharmonic electron−phonon coupling. The different coupling effects between electrons and phonons of these two phases in the microscopic perspective can also be manifested in the macroscopic properties. Owing to the confinement of electrons and phonons in δ-FAPbI₃, it exhibits significantly reduced electronic and thermal properties compared to the α-phase. Firstly, relative permittivity is the ratio of a material’s permittivity to vacuum permittivity and is widely used to describe and compare the electronic properties of different materials. Due to the different coupling effects and structural arrangements of α- and δ-FAPbI₃, these two phases exhibit greatly different relative permittivity, as shown in Figs. 4(a)−4(c). Regardless of varying temperature cycles, the real part of the permittivity measured at 100 kHz from δ-FAPbI₃ to α-FAPbI₃ undergoes a rapid increase, approximately a twofold increase from 20 to about 50^[46]. Since the electronic mobility at room temperature is typically governed by phonon scattering via electron−phonon coupling^[47], the carrier mobility of δ-FAPbI₃ is even about 20 times lower than that of α-FAPbI₃^{[5, 48]}, which also explains the additional electron transport limitations present in δ-FAPbI₃, such as the anharmonic electron−phonon coupling mentioned above.

Meanwhile, the δ-phase also exhibits lower thermal transport properties, since the thermal conductivity is related to the crystal structure through phonon properties. The thermal conductivity (k) consists of two parts: electronic and phononic/lattice contributions, as expressed as follows:

2$k=k_{\text{e}}+k_{\text{ph}}=L\sigma T+\frac{1}{3}{C}_{\text{ph}}{v}_{\text{g}}\Lambda ,$

where k_e is electron thermal conductivity (according to the Wiedemann−Franz law k_e = LσT), L is the Lorenz constant, σ is electrical conductivity, T is temperature, and k_ph is phonon thermal conductivity, where C_ph is the volumetric phonon heat capacity, v_g is the average phonon group velocity, and $\Lambda$ is the mean free path of phonon. Owing to the low carrier concentration of non-metallic HPs, the electronic contribution is negligible, and the phononic contribution dominates the total thermal conductivity, expressed as^[49]:

3$k=\frac{1}{3}{C}_{\text{ph}}{v}_{\text{g}}\Lambda .$

The ultralow thermal conductivity (less than 1 W∙K⁻¹∙m⁻¹) of HPs can be related to the enhanced anharmonic phonon−phonon scattering due to the highly overlapped phonon branches^{[50, 51]}. Considering the lifetime of acoustic phonons (~ps) is orders of magnitude larger than the sub-picosecond lifetime of optical phonons, it could be concluded that acoustic phonons dominate the thermal transport, and the mean free path of acoustic phonons is in the range of 20−200 Å^[52].

Microscopically, effective thermal conduction is the transfer of excess kinetic energy of carriers to the surroundings in an irreversible manner, which can be categorized into three stages: the scattering of carrier−phonon (Frӧhlich interaction), the attenuation from high-frequency optical phonons to low-frequency acoustic phonons and the propagation of acoustic phonons to the far-field region^[50]. Therefore, the stronger electron−phonon coupling in material severely restricts the thermal conduction and results in lower thermal conductivity, which has been reported in metals^[53], metal−nonmetal interfaces^[54], and semimetals^[55−57]. In our previous work, the thermal diffusivity of δ-FAPbI₃ (α = k/ρc, where ρ is density and c is specific heat capacity) is about two-thirds of that of α-phase^[44]. It is worth mentioning that due to the strict requirements of the test instrument on the sample size and surface flatness, it is not a single crystal in situ test, but a test of pressed crystallite tablets. However, the yellow δ-FAPbI₃ will transition to the different phase under pressure. The actual "δ-phase" tablet tested is a mixture of the multi-phases, which can be intuitively seen from the single-crystal and tablet color comparisons in Fig. 4(d), so it is reasonable to believe that the real thermal transport properties of δ-FAPbI₃ should be further lower.

Although α-FAPbI₃ and δ-FAPbI₃ can coexist well at room temperature, the α-phase is metastable and would gradually transition to the thermodynamically stable δ-phase. As shown in Fig. 5(a), the lower Gibbs free energy in δ-FAPbI₃ results in the inevitable α-to-δ phase transition, mainly aroused from the entropy contribution of the organic cation^[58]. At high temperatures, the FA⁺ cation has an isotropic orientation with a large entropy value, stabilizing the cubic structure. In contrast, as the temperature decreases, the FA⁺ cation acquires a strong preferred orientation in the hexagonal phase with a lower entropy value (Fig. 5(b))^[59]. Thus, α- to δ-FAPbI₃ transition is a Gibbs free energy (chemical potential) reduction process, and the driving force of the α-to-δ phase transition can be attributed to the internal tensile strain in the α-FAPbI₃ unit cells. As presented in Fig. 5(c), strain-free α-FAPbI₃ films rapidly transform to δ-FAPbI₃, while the strained α-FAPbI₃ films show striking long-term stability, which is stable for at least 360 days after growth^[60]. The driving force of the α-to-δ phase transition is thought to be the internal tensile strain in the unit cell, which induces the formation of vacancies and the subsequent phase transition, whereas, the films under compressive strain effectively neutralize the effect of the internal tensile strain, which is key to the stabilization of α-FAPbI₃. What’s more, this strain could even effectively changes the crystal structure, reduces the bandgap and increases the hole mobility of α-FAPbI₃. In addition to the internal strain, the external pressure can also affect the process of phase transition as illustrated in Fig. 5(d)^[22]. During compression from 0.1 to 6.59 GPa, the structural transition of the cubic α-FAPbI₃ follows the sequence Pm$\overline{3}$m to P4/mbm to Im$\overline{3}$ to partially amorphous, whereas the δ-FAPbI₃ converts to the orthorhombic Cmc2₁ structure between 1.26 and 1.73 GPa. Conversely, the phase transition can also be recovered during the decompression process.

To obtain the photoactive α-FAPbI₃ from the thermodynamically stable δ-phase, elevating the temperature is the most direct and widely used strategy. As illustrated in Fig. 6(a), at temperatures greater than 150 °C, the δ-phase would completely transition to the black α-FAPbI₃ within a few minutes. Therefore, Steele et al.^[61] proposed to apply direct-laser-writing on the δ-FAPbI₃ surface to realize micro-area δ-to-α transition, utilizing the transient high temperature (>150 °C) of the focused laser beam, as shown in Fig. 6(b). This strategy gives a controlled and convenient way to achieve micro-region phase transitions from δ-FAPbI₃ to α-FAPbI₃. Provided that the heat generated by the laser beam is sufficient to achieve the phase transition, the higher the laser power the smaller the minimum irradiation time required, and the phase transition can be realized within a few seconds of the focused laser sweep (Fig. 6(c)). When the required laser irradiation time is small enough, a patterned phase change region can be achieved by controlling the laser movement via the direct-laser-writing displacement stage. But too much laser power can also increase the phase transition region, as shown in Fig. 6(d). By choosing an appropriate laser power to balance the phase transition time and line array width, the α-FAPbI₃ line array can be constructed on the δ-FAPbI₃ host by controlling the focused laser using a displacement stage. However, due to the limitations of laser power and focusing lenses to realize surface temperatures greater than 150 °C, the smallest achievable micro-region width is still a few microns^{[44, 61]}. This customizable micro-region hybrid α-/δ-FAPbI₃ can take full advantage of the different properties of these two phases for functional sensing, which will be introduced in the next Section.

However, whether utilizing pure α-FAPbI₃ or hybrid α-/δ-FAPbI₃, the stability issue needs to be first considered, both in terms of phase and material stability. The phase stability of different forms of α-FAPbI₃ varies significantly. Due to undesirable surface and interfacial defects in spin-coated films, the α-FAPbI₃ films would completely transition to δ-phase within a few hours or a few days^[62−66], thus additives and alloying/doping engineering has been proposed to suppress the α-to-δ phase transition^[20]. In contrast, α-FAPbI₃ single crystals exhibit greater stability, taking about one month to fully phase transition to the δ-phase, which can be attributed to the well-arranged lattice inside effectively inhibits the entry of water and oxygen molecules. As a result, the α-FAPbI₃ line array constructed on δ-FAPbI₃ single crystal through direct-laser-writing was maintained for nearly three weeks in an unencapsulated air environment, where the temperature is between 20−25 °C and the relative humidity is between 40%−55%^[44]. Although the α-to-δ phase transition is spontaneous, humidity accelerates the process^[23], and excessive humidity results in the degradation of HPs, where H₂O molecules irreversibly decompose FAPbI₃ into precursors accompanied by FA⁺ molecules dissolved in water or lost as gas^[46]. Due to the water absorption of FA⁺ molecules, α-FAPbI₃ and δ-FAPbI₃ exhibit close material stability.

Because of the poor electrical transmission and narrower light absorption range, δ-FAPbI₃ has been treated as "trash", and a variety of strategies have been proposed to suppress the α-to-δ phase transition^{[26, 29]}. Although δ-FAPbI₃ is difficult to be applied to optoelectronic devices as an active layer material alone, its special properties can be utilized to assist the photoactive α-FAPbI₃ layer for functional applications, and the comparison of α-FAPbI₃ and δ-FAPbI₃ from phase transition to application is shown in Table 1. In this Section, we will introduce the potential application of α/δ-FAPbI₃ based on their special properties, hoping to change the stereotype of uselessness for δ-FAPbI₃.

It was found that the presence of nanoscale inclusions of δ-FAPbI₃ in α-FAPbI₃ thin films work as barriers, while α-FAPbI₃ behave as quantum wells, these hybrid structure leads to quantum confinement effects^[67]. As shown in Fig. 7(a), the absorption spectra of FAPbI₃ thin films exhibit oscillatory features as a result of the quantum confinement effects, and the length scale of confinement is estimated to be 10−20 nm. Even the width of δ-phase barriers is less than 10% of the potential wells and the height of barriers is less than 100 meV, the periodic δ-phase superlattice could still cause absorption peaks at higher energies. The energies of above-bandgap oscillatory peaks change with temperature according to the inverse square of the intrinsic lattice parameter, and with peak index in a quadratic manner^[68]. This phenomenon suggests a controlled strategy to change the confinement potential in FAPbI₃ by properly manipulating the phase distribution. Utilizing the instantaneous high temperature of the focused laser, direct-laser-writing can act on the δ-phase to achieve the α-phase transition in specific micro-regions^[61]. Therefore, customized hybrid α/δ-FAPbI₃ structures can be constructed with suitable laser power and displacement speed. Although there is no quantum confinement effect in this macroscopic hybrid structure, where micron-scale α-FAPbI₃ is surrounded by δ-FAPbI₃, the interior of δ-FAPbI₃ has more restricted carrier and phonon transport than α-FAPbI₃ due to stronger electron−phonon coupling and macroscopically exhibits restricted electrical and thermal transport properties. Given this, we propose to utilize hybrid α/δ-FAPbI₃ structure constructed by direct-laser-writing to achieve low-crosstalk terahertz sensing. Terahertz is an electromagnetic radiation between infrared and microwave, with a special wavelength (3 mm−30 μm) that gives it many intriguing properties, such as the ability to penetrate the vast majority of materials, non-ionizing photonic properties, and correspondence to many molecular vibrational frequencies^[69]. Therefore, terahertz sensing has a wide range of applications including non-destructive imaging, security inspection, molecular identification, etc.^[70−72]. However, terahertz waves of several meV energy are susceptible to room temperature thermal noise and often requires additional cryogenic devices, and conventional infrared antenna detectors are limited by their reliance on structures with nonlinear optics and materials with nonlinear electronics. To avoid delicate device architecture design^{[73, 74]} or cryogenic cooling systems^{[75, 76]} in detecting weak terahertz photons (0.41 to 41 meV)^[77], the photo-thermal effect based on HPs has been widely used in room-temperature terahertz sensing^[78−81]. This far below-bandgap photo−thermal response could be realized based on the characteristic terahertz absorption due to Pb−X bonds’ vibration and the extremely low thermal transport performance of HPs, which convert terahertz wave into thermal energy, easily accumulate heat to raise the temperature, and the temperature rise alters the material resistance (bolometric effect) and electric potential (Seebeck effect), producing the thermal-induced electrical response. Although a single terahertz detection unit can be realized in this way, wavelength-dependent diffraction of terahertz causes inevitable thermal/electrical crosstalk limiting the improvement of detection accuracy. In general, thermal crosstalk is caused by heat diffusion from adjacent pixels, which further leads to electrical crosstalk in the photo−thermal detector arrays.

To address the unavoidable thermal crosstalk and subsequent electrical crosstalk as a result of the terahertz diffraction, the hybrid α/δ-FAPbI₃ single-crystal detector array was utilized to realize low-crosstalk terahertz detection. α-FAPbI₃ single crystal with excellent optoelectronic performance was used as the active layer, while δ-FAPbI₃ single crystal was used as the α-phase spacer layer, utilizing its more restricted thermal transport properties and carrier mobility to reduce the thermal and electrical crosstalk. Based on the bolometric effect, the α-FAPbI₃ terahertz detector achieves a responsivity of 34.3 μA∙W⁻¹, a noise equivalent power of 5.3 × 10⁻¹⁰ W∙Hz^−1/2, and a specific detectivity of 1.4 × 10⁷ Jones to 0.1 THz at 200 V∙mm⁻¹. Since the δ-FAPbI₃ spacer layer effectively blocks the thermal and electrical signals to reduce the crosstalk, the crosstalk of the nearest-neighbor and next-nearest-neighbor detection units in the two-phase coexisting α/δ-FAPbI₃ is reduced from −5.35 and −12.38 dB to −17.60 and −21.53 dB, respectively (Figs. 7(b) and 7(c)). Therefore, the proof-of-concept imaging to terahertz using the δ-FAPbI₃ spacing layer also has sharper contrast, as shown in Figs. 7(d) and 7(e).

In addition to reducing photo−thermal crosstalk, the hybrid α/δ-FAPbI₃ constructed by direct-laser-writing is also ideally suited to enable polarization detection. Tian et al.^[82] etched a micro-grating on α-FAPbI₃ film using direct-laser-writing, where uniform grating structure in perovskite films can be obtained without visible damages around the grating. As can be seen in the enlarged SEM image, the perovskite grain size increases in the valley where the laser scanned, which indicates that fs laser may help grain growth with better crystallinity and contribute to carrier transport and optoelectronic efficiency (Fig. 8(a)). The photodetectors achieved polarized responses due to the anisotropy conferred by the triangular grating on the film surface under a rotating linearly polarized light (Fig. 8(b)). It is worth noting that the polarization originates exclusively from the arrayed grating structure, where the ridges and valleys of the grating are composed of homogeneous α-FAPbI₃. As a result, the measurement of α-FAPbI₃ photodetectors with micro-grating shows that the highest and smallest photocurrent appear at 0° and 90° polarization directions, respectively, exhibiting a linear polarization of 0.97 under light intensity of 37.8 mW∙cm⁻², demonstrating that unidirectional perovskite triangular grating arrays with potential for polarization detection (Fig. 8(c)). Linear sensitivity also indicates the increased polarization detection performance with micro-grating, and the linear sensitivity of α-FAPbI₃ photodetector with micro-grating (258.4 nA per degree) is superior to that of the pristine α-FAPbI₃ photodetector (189.2 nA per degree) under light intensity of 37.8 mW∙cm⁻². Although only the change in film morphology of α-FAPbI₃ has been utilized in this work to achieve polarization detection, it is reasonable to speculate that if δ-FAPbI₃ with different (lower) optoelectronic properties are utilized as spacer grating for α-FAPbI₃ as described above, the anisotropic light absorption and electrical transport properties superimposed on the anisotropic structure will further increase the polarization sensitivity. But honestly speaking, the current focused laser spot in direct-laser-writing is still too large, and the width of the realized grating is about 10 μm, which is still far from the wavelength of visible light about hundreds of nanometers. Thus, the polarization effect will be further enhanced if the size of the focused laser spot can be further reduced to construct a nanoscale grating or the detection band can be tuned to the micron-scale.

Different from the incorporation of other ions into thin films to stabilize FAPbI₃, some concepts have also been proposed about the application of δ-FAPbI₃ to stabilize α-FAPbI₃ phase^[83−85]. Unlike traditional bypassing of δ-FAPbI₃ phase formation by altering the reaction pathway^[86], it was found that the existence of δ-FAPbI₃ in α-FAPbI₃ films can stabilize the α-phase, accompanied by the enhancement and modulation of the NIR emission blueshift to 780 nm^[87]. Ma et al. found that with the molar ratio of FAI/PbI₂ increases, the colloidal size in precursor solution gradually decreases, and more coordination effects can be aroused from excess FAI in the precursor solution, causing the formation of large colloids. Once the size of the colloidal particles reaches a sufficiently low value, the total free energy of δ-FAPbI₃ (including surface and bulk) may be equal to or even higher than that of α-FAPbI₃, thus promoting the formation of α-FAPbI₃ at lower annealing temperatures and the formation of α/δ phase junctions. Therefore, the α/δ phase junction could be formed through stoichiometrically modified precursors (FAI/PbI₂ = 1.2), as shown in Fig. 9(a). High resolution transmission electron microscopy (HRTEM) in Fig. 9(b) clearly displays a junction structure, where the lattice fringes with spacing of 3.17 and 2.38 Å are indexed to the (222) plane of α-FAPbI₃ and the (031) plane of δ-FAPbI₃, respectively. The well aligned α/δ-FAPbI₃ junction has energy levels between those of α-FAPbI₃ and δ-FAPbI₃ (Fig. 9(c)), and possesses not only structural stability but also long-term stability against humidity. This stable and controllable α/δ phase junction provides an example of how δ-FAPbI₃ should be applied^[87].

Moreover, Zhang et al.^[88] found that photo-inactive δ-FAPbI₃ could formed in situ on the black phase (FAMAPbI₃) surface, which serves as a surface water−oxygen barrier and reduces the surface defect density. As illustrated in Fig. 9(d), after the two-step spin-coating of the FAMAPbI₃ thin film, FAI/IPA solution was then spin-coated on the surface, where the excess PbI₂ on the pristine film would react with FAI to form a δ-FAPbI₃ layer. The formed δ-FAPbI₃ mainly distributed on the surface and at grain boundaries, which could not only act as a surface barrier to improve the stability of perovskite films, but also reduce the surface defect density to suppress the trap-assisted recombination. What’s more, the introduce of δ-FAPbI₃ on FAMAPbI₃ surface gives rise to a type-Ⅰ band alignment at the interface, which efficiently hinder the electron transfer to hole transporting layer (HTL) and inhibit the nonradiative recombination. Thus, the performance of solar cells based on this bilayered δ-FAPbI₃/perovskite films has greatly improved compared to the pristine perovskite films, with power conversion efficiency (PCE) increased from 21.05% to 23.10%, short-circuit current (J_sc) increased from 25.0 to 25.3 mA∙cm⁻², open-circuit voltage (V_oc) increased from 1.12 to 1.16 V, as shown in Figs. 9(e) and 9(f). In addition, the evolution of PCE for the device based on bilayered δ-FAPbI₃/perovskite films exhibit long-term stability (Fig. 9(g)), attributing to the stable δ-FAPbI₃ locates at grain boundaries protecting the perovskite films from the moisture penetration.

Besides, Mandal et al.^[89] used well-crystallised δ-FAPbI₃ single crystals as an intermediate phase for the formation of high-quality α-FAPbI₃ to prepare high-performance solar cells. As shown in Fig. 10(a), δ-FAPbI₃ single crystals are firstly precipitated utilizing anti-solvent, and then dissolved in solution to be spin-coated as films, which would further phase transition during annealing to form a high-quality α-FAPbI₃ films. As shown in Fig. 10(b), the 1D hexagonal δ-FAPbI₃ single crystals precipitated using anti-solvents exhibit excellent crystalline. Due to the reduced trap states in δ-FAPbI₃ single crystals, the solar cells based on intermediate δ-FAPbI₃ single crystals has larger V_oc and J_sc (1.16 V and 24.62 mA∙cm⁻², respectively) with a champion PCE of 22.61%, compared to solar cells’ PCE of 21.58% based on intermediate δ-FAPbI₃ powder (Fig. 10(c)). It is noteworthy that such devices prepared by intermediate δ-FAPbI₃ single crystals and powder show excellent long-term stability, as shown in Fig. 10(d). Although the δ-phase itself may not directly serve as a good optoelectronic active layer, high-performance devices can still be prepared through phase transition from the δ-phase to the α-phase, and this use of thermodynamic stable δ-FAPbI₃ with good crystallinity provides a new strategy for its application.

The yellow-phase δ-FAPbI₃ and black-phase α-FAPbI₃ have poor and good electrical transmission characteristics, respectively, and can be used as off and on elements in circuits. Therefore, it is possible to utilize the δ-to-α phase transition induced by an increase in temperature and pressure, and the circuit is set from off to on to realize the detection of temperature and pressure. Without the phase transition triggers, the transitioned α-FAPbI₃ (on) still spontaneously transitions to the thermodynamically stable δ-FAPbI₃ (off), enabling self-recovering temperature and pressure detection. If issues such as the recovery rate of α-to-δ phase transitions, and reversible phase transitions under pressure can be guaranteed are resolved, α/δ-FAPbI₃ will enable promising self-recovering temperature and pressure detection^[22]. Also, the poorly electrically conductive δ-FAPbI₃ can inhibit the excess carriers in α-FAPbI₃ to retard the degradation of FAPbI₃^[90]. By and large, based on the fact that δ-FAPbI₃ is very different from α-FAPbI₃ and is easy to transition between each other, there is still much room for exploration from the preparation of the δ-phase to the functional applications.

In this review, in response to the problem of thermodynamically stable δ-FAPbI₃ at room temperature limiting the development of α-FAPbI₃, we present a fresh perspective on the δ-FAPbI₃ with worse optoelectronic performance. Although the unavoidable phase transition from α- to δ-FAPbI₃ at room temperature makes the δ-phase interferes with the optical response and electrical transport of α-phase active layers, the unique properties of δ-FAPbI₃ can also be used to realize functional applications in combination with α-FAPbI₃. For example, we have utilized the much lower thermal and electrical transport properties of δ-FAPbI₃ as spacer layers for α-FAPbI₃ to reduce the crosstalk of photothermal terahertz detection. Therefore, we wish to provide another perspective on δ-FAPbI₃ in this work to change the traditional view that δ-FAPbI₃ is useless trash, and thus advance the development of FAPbI₃ material systems.

Firstly, the two phases’ internal carrier and phonon dynamics are comprehensive analyses to explain the contrast properties between α- and δ-FAPbI₃. α-FAPbI₃ is the cubic structure with corner-sharing octahedrons, while δ-FAPbI₃ is the 1D hexagonal structure with face-sharing octahedrons. The 1D distorted face-sharing PbX₆ octahedrons of δ-FAPbI₃ give rise to the anharmonic electron−phonon coupling and leads to STEs under anharmonic electron−phonon coupling because the low-dimensional structure reduces the potential barrier for self-trapping. Therefore, due to the restricted internal carrier and phonon transport, δ-FAPbI₃ exhibits significantly reduced electronic and thermal properties compared to the α-phase, where the carrier mobility of δ-phase is about 5% and the thermal diffusion coefficient is two-thirds as compared to the α-phase. Secondly, several strategies for controlled phase transitions between α- and δ-FAPbI₃ are presented. Factors affecting the phase transitions include temperature, pressure (internal/external pressure), humidity, etc., some of which can lead to reversible phase transitions. For example, using the instantaneous high temperatures (>150 °C) of the focused laser in direct-laser-writing, the micro-region phase transition from δ-FAPbI₃ to α-FAPbI₃ can be achieved. Finally, some functional applications of δ-FAPbI₃ in combination with α-FAPbI₃ are given and analyzed according to previous reports and our experience.

For the multi-phase FAPbI₃, applications at room temperature are still dominated by the α- and δ- phases rather than the low-temperature β- and γ-phase. The internal electron−phonon coupling of the intrinsically low-dimensional δ-FAPbI₃ always limits its optoelectronic properties, while α-FAPbI₃ with excellent optoelectronic properties is also limited by the spontaneous phase transition due to the thermodynamic instability at room temperature. Therefore, follow-up ideas should still consider the complementary roles of α- and δ-FAPbI₃ and utilize the mixed phases for functional applications, especially the phase stabilizing and the electrical and thermal spacing effect of δ-FAPbI₃ on α-FAPbI₃. In conclusion, we hope to introduce δ-FAPbI₃ from another perspective and provide some insights into its unique properties, in the hope of advancing the following application of multi-phase FAPbI₃.