Perovskite single crystals: physical properties and optoelectronic applications

The charge-carrier dissociation of charge carriers is mainly determined by the E_B. For photovoltaic and photodetection applications, a small E_B is preferable to minimize energy loss. The E_B value for the typical perovskite MAPbI₃ varies widely, with reported values ranging from 2 to 75 meV [22, 23, 77, 78]. Optical spectroscopy is a simple and convenient method to measure E_B. As shown in figure 3(b), analyzing optical absorption, Snaith et al estimated the E_B to be in the range of 55 meV for the mixed halide crystal MAPbI_{3 − x} Cl_x [23]. Li et al determined the E_B of the MAPb_x Bi_{1 − x} I₃ single crystal to be ∼10 meV (10 K–150 K) using the temperature dependency of photoluminescence [26]. In addition, Miyata et al proposed that a high magnetic field spectroscopic analysis directly establishes more accurate E_B without the dielectric constant () assumption. This technique estimated the E_B of MAPbI₃ to be just 16 meV at 2 K [78]. These results indicate that halide perovskites are considered a nonexcitonic material, in which excitons dissociate into free charges following illumination, resulting in a photovoltaic effect. However, not all perovskite single crystals have small E_B. The different structures determine different values of E_B in perovskite single crystals.

The dimensionality of the crystal structure has a considerable impact on the E_B. The two-dimensional (2D) perovskite materials (A₂A'_{n − 1}M_n X_{3n + 1}) show a much larger E_B than three-dimensional (3D) materials under quantum and dielectric confinement [79–82]. For instance, the E_B values of 380 meV and 270 meV have been reported for (BA)₂(MA)_{n − 1}Pb_n I_{3n + 1} with n = 1 and 2, respectively [81]. Using low-temperature optical spectroscopy, Blancon et al experimentally determined the E_B drop from 470 meV to 125 meV in the (BA)₂(MA)_{n − 1}Pb_n I_{3n + 1}, with n varying from 1 to 5 [79]. The 2D perovskites have larger E_B, which does not hinder their efficient transport of carriers. A recent study revealed an internal exciton dissociation mechanism in (PEA)₂(MA)_{n − 1}Pb_n I_{3n + 1} (n = 2 − 4) that can convert over 80% of excitons into free carriers in an ultrafast time scale (<1.4 ps) [83]. This provided a reasonable explanation for the excellent performance of 2D perovskites in photoelectric devices.

Moreover, the E_B in perovskites is sensitive to morphology and crystallinity. Grancini et al found that the electron-hole pair interactions are easily influenced by the microstructure of the perovskite [84]. Combining optical spectroscopy and multiscale modeling, they proved that structural disorder and electrostatic potential changes could prevent exciton production in polycrystalline films. This demonstrated that the significant excitonic characteristics of perovskite can only be observed in large single crystals. Recently, using spectrally resolved transient absorption microscopy, the spatial distribution of the exciton in a single-crystal perovskite grain has been directly observed [85]. The results indicated that exciton was more likely to be formed in regions with higher crystallinity, whereas free carriers predominated in the small domain region of the grain.

Carrier mobility (μ), lifetime (τ), and diffusion length (L_D) were critical factors for carrier dynamics, with the diffusion length being defined by both the carrier mobility and lifetime. These basic carrier parameters of halide perovskite single crystals, as reported in the literature, are listed in table 2 [4, 39, 60, 86–89].

Disordered grain boundaries in perovskite polycrystalline films hinder the carriers when transporting from grain to grain and directly affect carrier transport. Researchers have proposed some strategies to improve carrier transport conditions, such as increasing grain size using chlorine doping and controlling grain orientation [90]. perovskite single crystals are free of grain boundaries, contributing to the barrier-free transport of carriers. Meanwhile, charge transport can be affected by defects in perovskites. Under a built-in electric field, free charge carriers move toward the poles within the perovskite layer. However, their trajectories change under Coulomb forces when they encounter scatterers such as phonons and defects, affecting the transport efficiency. Defects in polycrystalline films are concentrated on surfaces and grain boundaries. In a perovskite single crystal without grain boundaries, there are fewer defects. The trap density of the perovskite single crystal (MAPbI₃) was ∼10¹⁰ cm⁻³, which is 6−7 orders lower than that of the polycrystalline film with the same chemical composition [91]. Thus, the perovskite single crystal holds promise for efficient carrier transport.

Carrier mobility measures the rate of movement of carriers in semiconductors. The greater the mobility value, the quicker the carrier's transport. Time of flight (ToF), Hall effect, and space charge limited current (SCLC) are the most prevalent mobility testing technologies [39, 86, 87]. Yet, even for identical samples, mobility will vary depending on the measurement procedure. For example, the ToF and SCLC methods are sensitive to traps within bulk materials, but the impacts of surface defects may be insignificant. With a hole mobility of 164 cm² V⁻¹ s⁻¹, the MAPbI₃ single crystal has the highest carrier mobility known to date [4]. Carrier lifetime is the average time photogenerated carriers exist before recombination. MAPbI₃ single crystals attain an extraordinarily extended carrier lifetime due to the absence of grain boundaries.

Long carrier lifetime and high carrier mobility determine the perovskite single crystal's long carrier diffusion distance, which is significant for optoelectronic devices. Specifically for solar cells and self-powered photodetectors, a long carrier diffusion distance is advantageous for minimizing carrier loss during the diffusion process, hence enhancing the quantum efficiency of devices [92, 93]. The longest reported carrier diffusion length exceeds 175 μm, which is several times greater than the absorption depth, allowing single crystals to become ideal materials for optoelectronic devices.

The carrier transport is also influenced by the internal electric field distribution in optoelectronic devices. Ideally, it depends on the energies of band edges and the intentional carrier doping level in the functional layers. Some studies propose to intentionally dope impurities into the perovskite lattice to tune the electron and hole concentrations and achieve the desired band structure. As shown in figure 3(c), Cao et al grew bismuth-doped CH₃NH₃PbI₃ single crystals with Bi³⁺ by partially replacing Pb²⁺. The Hall test results demonstrated that doping with Bi³⁺ ions converted p-type to n-type electric conduction and increased the concentration of hole carriers by four orders of magnitude [26]. However, defects of the perovskite bulk or surface, which are often a form of unintentional doping, disrupt the ideal band arrangement between functional layers and influence the electric field distribution inside the optoelectronic device in an uncontrolled way. In contrast to polycrystalline films, perovskite single crystal has no grain boundary and fewer defects, which endow it with faster carrier mobility and longer carrier lifetime. Most single crystals are grown by the solution method, which causes the precursor solution erosion and the organic ammonium salts escaping on the surface, leading to surface damage and defect formation. The single crystal surface has more defects than the bulk. Surface defects can cause nonradiative recombination and mismatched energy level at the interface of optoelectronic devices. Finding suitable materials and growth method to repair and passivate the surface defects is the focus of future research on single-crystal defects. For example, Osman et al reduced the crystallization temperature of MAPbI₃ single crystal in the ITC to avoid the loss of methylammonium iodide, yielding better quality single crystal with lower defects [94].

In 2016, Huang et al reported the first sensitive x-ray detector constructed from a 2 mm thick MAPbBr₃ single crystal [28]. As shown in figure 8(a), the x-ray detector-based structure of Au/MAPbBr₃/C60/BCP/Au attained a charge collection efficiency of 16.4% for 50 keV x-rays at a near-zero bias condition, enabling the direct conversion of high-energy x-ray flux into collectible charges. Thus, the devices achieved a low detectable x-ray dose rate of 0.5 μGy_air s⁻¹ and a sensitivity of 80 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻². Using solution-grown perovskite single crystals with a simple surface treatment can provide unexpectedly exceptional x-ray detection performance, indicating its potential utility in high-energy ray detection. Using brominated (3-aminopropyl) triethoxysilane molecules as a bonding agent, they developed a mechanically and electrically robust connection between MAPbBr₃ single crystals and silicon substrates in 2017 (figure 8(b)) [120]. The dipole of the bonding molecule decreased the dark current of the device while retaining signal intensity. The Si-integrated detectors showed a very low detectable x-ray dose rate of <0.1 μGy_air s⁻¹ and a high sensitivity of 2.1 × 10⁴ μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² when exposed to 8 keV x-rays, which were superior to the state-of-the-art commercial α-Se x-ray detectors. In 2020, Fang et al grew high-quality MAPbBr₃ single crystals at room temperature by separating the solvent from the perovskite precursors using silicone oil [29]. Figure 8(c) shows the schematic of liquid-diffused, separation-induced crystallization (LDSC) of MAPbBr₃ single crystals (LDSC-MAPbBr₃). LDSC-MAPbBr₃ exhibited a carrier lifetime of approximately 1 μs and a low trap density of 4.4 × 10⁹ cm⁻³ compared to ITC-fabricated MAPbBr₃. The 2 mm thick LDSC-MAPbBr₃ single-crystal detectors demonstrated a sensitivity of 184.6 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² and a measurable x-ray dose rate of 1.2 μGy_air s⁻¹ at −4 V. In 2021, x-ray detectors fabricated from FAPbBr₃ single crystals could maintain high performance and stability at high operating temperatures [121]. FAPbBr₃ single crystals maintained an excellent mobility lifetime product (1.1 × 10⁻² cm²) and a low electron trap density of (5.0 ± 0.2) × 10⁹ cm⁻³. The detectors based on the Ga/FAPbBr₃/Au structure can detect a minimum detectable dose rate of 0.3 μGy_air s⁻¹ with a sensitivity of 130 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² under 0.5 V mm⁻¹ electric field for 23.8 keV x-rays.

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Additionally, compared to MAPbBr₃ single crystals, MAPbI₃ has promising applications in x-ray detection because of its higher μτ product and atomic number Z. Typically, nonrectangular dodecahedrons of the MAPbI₃ single crystal limited the fabrication of flat-panel devices. Choy et al found the preferred growth of the (100) facet over the (110) facet in a halogen-rich precursor, which facilitated the synthesis of cuboid MAPbI₃ single crystals (figure 9(a)) [122]. The cube shape imparts favorable geometry for device fabrication. Based on the (100) plane of MAPbI₃, cuboid MAPbI₃-based x-ray detectors exhibited a high sensitivity of 968.9 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² under a −1 bias. The crystal quality of active materials is the key to improving the performance of semiconductor electron devices. Density functional theory simulations suggested that mixing bigger ions with smaller MA⁺ at the A-site could reduce the interstitial defects and electron-phonon coupling strength of MAPbI₃. As illustrated in figure 9(b), partial MA⁺ substitution with DMA⁺ (DMA = dimethylammonium) and GA⁺ (GA = guanidinium) produced DMAMAPbI₃ and GAMAPbI₃ single crystals [123]. Electrical characterizations confirmed that the alloyed GAMAPbI₃ single crystal displayed improved charge collection efficiency and suppressed shallower defect density compared to the pristine MAPbI₃ single crystal. Finally, the GAMAPbI₃-based x-ray detectors demonstrated a sensitivity of 2.3 × 10⁴ μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² and a detectable x-ray dose rate of 16.9 μGy_air s⁻¹, which was superior to the pristine MAPbI₃-based devices (2.5 × 10³ μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻²). Later, numerous methods of fabricating high-quality crystals were presented. In the growing process of crystals, the growth rate of crystals reduces with time as the solute concentration drops below the level of supersaturation. This disrupts crystal growth and results in single crystals with imperfect structural perfection. Xu et al employed a continuous-mass transport process (CMTP) approach to solve this problem. The schematic illustration of the CMTP approach is shown in figure 9(c) [124]. This approach can uninterruptedly provide raw materials in the precursor solution for maintaining the MAPbI₃ single crystal's steady growth at a constant growth rate. The CMTP-fabricated MAPbI₃ exhibits a lower defect density (4.5 × 10⁹ cm⁻³) and a higher mobility-lifetime product (1.6 × 10⁻³ cm² V⁻¹), allowing it to achieve ultrahigh x-ray detection performance comparable to that of a high-quality CdZnTe device. In 2021, Huang et al found that 3‐(decyldimethylammonio)‐propane‐sulfonate inner salt (DPSI) as an additive in the precursor solution can help to maintain the same crystal growth rate during the late period of growth, as shown in figure 9(d) [125]. Meanwhile, DPST additives interacting with Pb²⁺ and undercoordinated Pb can limit the probability of bonding or stacking incorrect ions, greatly enhancing the crystal quality. Finally, the devices showed a sensitivity of 2.6 × 10⁶ μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² and a detectable x-ray dose rate of 5.0 μGy_air s⁻¹ for 60 kVp x-rays. However, 3D perovskite materials have lower E_B and faster charge transport, which is not conducive to the accumulation and amplification of x-ray signals. In this regard, 2D perovskite materials have better adaptability.

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Compared to 3D perovskites, 2D perovskites have a wider bandgap, better structural stability and larger E_B. In 2020, 2D perovskite, BDAPbI₄ (BDA=NH₃C₄H₈NH₃), single crystals were synthesized (figure 10(a)) [126]. The introduction of BDA²⁺ allows for the flexible control of the distance between adjacent inorganic layers to generate strong electrostatic interactions. Enhancing the structural stability and effective charge transport of BDAPbI₄ single crystals is advantageous. The BDAPbI₄-based x-ray detector showed a sensitivity of 242 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² with a measurable x-ray dose rate as low as 430 nGy_air s⁻¹. By aligning the benzene rings in the same orientation, Wei et al introduced fluorine atoms to PEA⁺ ions to enhance supramolecular interactions between organic spacers [127]. As shown in figure 10(b), strong interactions blocked the ion migration paths to stabilize and tune the electronic properties of (F-PEA)₂PbI₄ single crystals. The (F-PEA)₂PbI₄ single-crystal detector showed a remarkable sensitivity of 3402 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² to 120 keV. Meanwhile, the lowest detected x-ray dosage rate was 23 nGy_air s⁻¹. Zhao et al have recently demonstrated for the first time how the halide-modulated molecular assembly affects the structure and characteristics of 2D perovskite single crystals [128]. Using an amidino-based organic spacer (3AP, 3-amidinopyridine), 2D (3AP)PbX₄ (X=Cl, Br, and I) single crystals were effectively synthesized. Figure 10(c) depicts the images and crystalline structures of 2D (3AP)PbX₄ (X=Cl, Br, and I) single crystals. Parallel and antisymmetric 3AP cations are placed between two inorganic layers. The halide transformation from I to Br and Cl resulted in greater Pb − X − Pb angles and a stronger hydrogen interaction, inhibiting ion migration in single crystals. The (3AP)PbCl₄ exhibited an x-ray photoresponse with sensitivity up to 791.8 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² and a low detection limit of 1.54 μGy_air s⁻¹.Owing to the toxicity of Pb, perovskite-based products containing Pb have been controversial. However, x-ray detection still have absorption coefficient requirements. It is necessary to study non-lead perovskite materials that meet the radiation detection requirements.

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Bi is considered the most promising element to replace Pb in halide perovskite because its atomic radius is similar to Pb. Tang et al reported for the first time in 2017 the use of Cs₂AgBiBr₆ single crystals in fabricating x-ray detectors [129]. Under a 5 V bias, the detector exhibited a high sensitivity of 105 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² and a low detection limit of 59.7 nGy_air s⁻¹. The Ag⁺/Bi³⁺ disordering considerably affected the poor structural stability of the Cs₂AgBiBr₆ double perovskite, resulting in poor photoelectric properties. Roeffaers et al studied the temperature dependence of the photophysical properties of Cs₂AgBiBr₆ at room and liquid nitrogen (LN₂T) temperatures [130]. By cooling Cs₂AgBiBr₆ to LN₂T, lattice defects induced by structural distortion were considerably reduced, resulting in enhanced free-carrier transporting efficiency (figure 10(d)). Therefore, the x-ray detectors exhibited better performance with a sensitivity of 988 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² near LN₂T than at room temperature, which was 316 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻². Fan et al found that phenylethylamine bromide (PEABr) enables the in situ regulation of the alternatively ordered arrangement of Ag⁺ and Bi³⁺ ions in the Cs₂AgBiBr₆ single crystal [131]. The experimentally established and the enhanced ordering extent of the [BiX₆]³⁻ and [AgX₆]⁵⁻ octahedral can inhibit the formation of self-trapped excitons, contributing to the carrier drift distance. As shown in figure 11(a), the corresponding detectors based on PEA-Cs₂AgBiBr₆ exhibit a very high sensitivity of 288.8 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻², which was two times greater than that of the reference Cs₂AgBiBr₆ (165.6 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻²).

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In addition to Cs₂AgBiBr₆ single crystals, some double perovskites are fabricated for higher x-ray performance. Yang et al fabricated an (NH₄)₃Bi₂I₉ single-crystal x-ray detector [132]. The devices demonstrated high sensitivity (8.2 × 10³ μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻²) and a low detection limit (55 nGy_air s⁻¹). In 2020, Liu et al synthesized large-sized Cs₃Bi₂I₉ single crystals via a nucleation-controlled solution method [133]. The nucleation-controlled method is realized by refining the precursor solution. The detector based on the Cs₃Bi₂I₉ single crystal showed a sensitivity of 1146.7 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻². Meanwhile, Cs₃Bi₂I₉ single crystals showed an excellent thermodynamic, stability-assured x-ray detector with a stable response at a temperature of 100 °C for a long time under continuous x-ray illumination and a high electric field (63.4 μGy_air s⁻¹, 50 V mm⁻¹), as shown in figure 11(b).

Recently, Zhao et al synthesized metal-free halide perovskite single crystals, such as DABCO-NH₄Br₃ (DABCO=N-N'-diazabicyclo[2.2.2] octonium) [75], and MDABCO-NH₄I₃ (MDBACO=methyl-N'-diazabicyclo[2.2.2] octonium) [76], as shown in figure 11(c). The environmentally friendly, metal-free halide perovskites can be fabricated from an aqueous solution and are fully degradable when rinsed with water. DABCO-NH₄Br₃, for instance, showed very high charge diffusion lengths (tens of μm), contributing to a sensitivity of up to 173 μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm⁻² for a 29 keV x-ray.

As shown in table 5, perovskite single-crystal x-ray detectors achieved impressive performance, and that stability and environmental friendliness have gradually been resolved through the continuous development of material systems, issues [28, 29, 75, 76, 120–123, 125–139]. However, the solution method has the drawbacks of limited size and high time cost, which hinder the preparation of large area detectors and their commercial applications. A vapor-phase epitaxy deposition is a potential solution. For example, Liu et al Grown large-scale thin CsPbBr₃ single crystal film on sapphire substrate via chemical vapor deposition.

Table 5. Key parameters of perovskite single crystal-based x-ray detectors.

Materials	Sensitivity (μC ${\text{Gy}}_{{\text{air}}}^{ - 1}$ cm−2)	Lowest detectable x-ray dose rate (μGyair s−1)	Devise structure	References
MAPbBr3	80	0.5	Au/perovskite/C60/BCP/Ag or Au	[28]
Si-integrated MAPbBr3	2.1 × 104	<0.1	Si/perovskite/C60/BCP/Au	[120]
MAPbBr3	184.6	<1.2	InGa/C70/perovskite/Au	[29]
FAPbBr3	130	0.3	Ga/perovskite/Au	[121]
MAPbI3	968.9	—	Au/Cr/perovskite/Cr/Au	[122]
GA- MAPbI3	2.3 × 104	1.7 × 10−2	Ga/perovskite/Au	[123]
MAPbI3	5.2 × 106	0.1 × 10−3	Au/BCP/C60/perovskite/MoO3/Au	[134]
MAPbI3	(2.6 ± 0.4) × 106	(5.0 ± 0.7) × 10−3	Cr/Oxysalt/perovskite/Oxysalt/C60/BCP/Cr	[125]
MAPbX3 cascade single crystal	1.6	—	Gd or Ag/perovskite/Au	[135]
BDAPbI4	242	0.43	Au/perovskite/Au	[126]
(F-PEA)2PbI4	3402	2.3 × 10−2	Au/perovskite/C60/BCP/Cr	[127]
(3AP)PbX4	791.8	1.54	Au/perovskite/Au	[128]
DABCO-NH4Br3	173	4.960	Au/perovskite/Au	[75]
MDABCO-NH4I3	1997 ± 80	—	Au/perovskite/Au	[76]
[(CH3)3NH]MnCl3	295	0.90	Au/perovskite/Au	[136]
Cs2AgBiBr6	105	6.0 × 10−2	Au/perovskite/Au	[129]
Cs2AgBiBr6	988	—	Au/perovskite/Au	[130]
PEA- Cs2AgBiBr6	288.8	—	Ga/perovskite/Ga	[131]
Cs2AgBiBr6 wafers	250	95.3 × 10−3	Au/perovskite/Au	[137]
(NH4)3Bi2I9	8.2 × 103	55 × 10−3	Au/perovskite/Au	[132]
Cs3Bi2I9	1652.3	0.130	Au/perovskite/Au	[133]
Rb3Bi2I9	159.7	8.32	Au/perovskite/Au	[138]
(4,4-difluoropiperidinium)4 AgBiI8	188	3.13	Au/perovskite/Au	[139]

The bandgap of the MAPbCl₃ perovskite is approximately 2.9 eV, making it an appropriate active layer material for UV light detectors. In 2015, Bakr et al developed a centimeter-sized MAPbCl₃ single crystal using the ITC method and fabricated a UV light photodetector for the first time (figure 12(a)) [60]. The device exhibited UV light sensitivity with a spectrum responsivity of 46.9 mA W⁻¹, detectivity of 1.2 × 10¹⁰ Jones, and fast response speed of 24 ms under an applied bias of 15 V and 365 nm UV illumination (1 W cm⁻²). Although the rapid growth rate of the ITC method enables the formation of enormous single crystals in a matter of hours, high-temperature growth results in a substantial number of single-crystal defects. A novel, two-step, thermal procedure, high-quality MAPbCl₃ has been developed. This method involves two growth processes: lower-temperature nucleation and higher-temperature crystallization [142]. The fabricated MAPbCl₃ single crystal has a lower defect density (∼7.9 × 10⁹ cm⁻³) than the ITC-grown MAPbCl₃ crystals. As a result, the responsivity and detectivity of the detector employing the optimized MAPbCl₃ crystal were increased to 3730 mA W⁻¹ and 9.97 × 10¹¹ Jones at 415 nm, respectively. In addition, the devices exhibited a quick response time of 130 ns. Bakr et al reported the fabrication of a photodetector with the structure ITO/MAPbCl₃/spiro-OMeTAD/Au using an μm-thick MAPbCl₃ single crystal [143]. Their photodetectors showed an excellent self-powered character without consuming external power, ascribed to a p-n junction at the interfaces of perovskite/Spiro-OMeTAD. As shown in figure 12(c), the detectors exhibit a high specific detectivity of 6 × 10¹² Jones, a responsivity of 134 mA W⁻¹, and 42.9% EQE when illuminated by 400 nm light.

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Single crystals of 2D perovskite (PEA)₂PbBr₄ have a bandgap width of Eg = 2.91 eV, making them also ideal for use in UV photodetectors. Liu et al synthesized a large-size (PEA)₂PbBr₄ single crystal using the controlled evaporation method [62]. With a bias of 10 V, the fabricated detector-based (PEA)₂PbBr₄ exhibited responsivity, detectivity, and rapid response rates of 31.48 mA W⁻¹, 1.55 × 10¹³ Jones, and 0.4 ms, respectively, when illuminated by a 365 nm LED (figure 12(b)). Subsequently, Zhou et al developed a gas-liquid interface crystalline route to grow a BA₂PbBr₄ (BA=CH₃CH₂CH₂CH₂NH₃ ⁺) single crystal [64]. The nucleation energy barrier difference between the solution surface and volume gave the precursor molecules a higher chemical potential in the initial state at the gas-liquid interface, resulting in a crystal nucleus at this interface. Moreover, a thin crystal will preferentially grow along the side parallel to the surface of the solution under the buoyancy and surface tension effect. Under 400 nm illumination and a 4 V bias, BA₂PbBr₄ thin crystals exhibited a heightened UV light response with an efficient responsivity of 45 mA W⁻¹ and a detectivity of ∼10¹² Jones.

Notably, the ferroelectric photovoltaic effect has been observed in 2D perovskite materials. This effect can separate electron-hole pairs via the spontaneous, polarization-induced, built-in electric field, making self-powered photodetection possible [65, 144]. Based on this, Yang et al fabricated a self-powered UV photodetector using a PMA₂PbCl₄ monocrystalline sheet [65]. When illuminated by UV light, a built-in ferroelectric field of PMA₂PbCl₄ can generate and separate photoinduced carriers, forming a stable photocurrent (figure 12(d)). Meanwhile, spontaneous polarization and bound charges decreased with the increasing irradiation temperature, generating a positive output pyroelectric current. At zero bias, the devices exhibited a responsivity of 9000 mA W⁻¹ and a detectivity of 1.01 × 10¹¹ Jones for 320 nm UV light.

As shown in table 6, the detection performance of single-crystal solar-blind UV detectors has gradually improved, but the detection wavelength range is only focused in the near ultraviolet region [60–65, 142–147]. Detecting the deep ultraviolet region remains a challenge for future research. One possible solution is to broaden the band gap of perovskite single crystals through designedly doping or component engineering. Luo et al reported a wide band gap 2D perovskite ferroelectric, (isobutylammonium)₂(methylamium)Pb₂C_l7, achieved photoresponse under 266 nm illumination [148].

In 2015, Huang et al reported the first photodetector based on a halide perovskite single crystal [1]. The spectral response of the resulting MAPbBr_{3 − x} Cl_x and MAPbI_{3 − x} Br_x mixed halide perovskite was continuously tunable from blue to red (figure 13(a)). With these single crystals, the photodetector exhibited constantly tunable ultra-narrow photodetection in the visible region, with a full-width, half-maximum of <20 nm for the EQE peak. Although the devices had low detectivity compared to commercial InGaAs photodetectors, they can be further improved by optimizing the quality of the single crystals. A planar-type photodetector based on the (100) facet of a MAPbI₃ single-crystal bulk was fabricated in the same year [149]. Due to the excellent properties of the MAPbI₃ single crystal, the performance of the detectors was considerably enhanced compared to their polycrystalline film counterparts. With a 1 V bias, even devices with a simple structure (Au/perovskite/Au) exhibited a high R-value of 953 A W⁻¹ and an EQE of 222 000%. Meanwhile, the transient photocurrent measurement demonstrated the quick response speed (74 μs/58 μs) of the photodetector. Liu et al sliced a large-sized MAPbI₃ single crystal to a millimeter-thick, single-crystalline wafer via the crystal-slicing method and integrated ∼100 photodetectors on a piece of wafer, as shown in figure 13(b) [69].

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Optimizing the crystal growth is critical to improving the detector's performance. By investigating the crystal nucleation and growth dynamics, Liu et al summarized an LTGC strategy to generate high crystalline MAPbBr₃ [66]. As shown in figure 13(c), the MAPbBr₃ single crystal synthesized using the low-temperature strategy showed a long carrier lifetime (∼900 ns), high carrier mobility (81 ± 5 cm² V⁻¹ s⁻¹), and low trap density (6.2 ± 2.7 × 10⁹ cm⁻³), and its photodetectors achieved a high responsivity and detectivity of 16 A W⁻¹ and 6 × 10¹³ Jones, respectively, under 525 nm illumination at 4 V bias. Notably, they designed an imaging assembly comprised of 729 pixel array sensors that can accurately distinguish the projected optical patterns on the imaging components. A new study was conducted on the nucleation and growth dynamics of the LTGC strategy [41]. The single-crystal growth model can be divided into three primary regions: the unsaturated, oversaturated, and optimized growth regions, separated by the solubility curve (S-T curve) and nucleation curve (N-T curve). At the optimized growth region, crystallization occurs solely on the existing nucleation seed, but there is not enough energy to exceed the nucleation energy to form a new crystal nucleus and limit extraneous nucleation. In addition to preventing the extraneous nucleation of single crystals, the formation of high-quality crystals also requires an appropriate development rate. As illustrated in figure 13(d), single crystals exhibit excellent electrical properties when the optimal growth temperature and heating rate are selected. These excellent optoelectronic properties were further translated into the highest sensor performance, including a high responsivity of 55.7 A W⁻¹, EQE of 13 453%, detectivity of 8 × 10¹³ Jones, and response time of 15.8 μs.

2D perovskite materials with narrow bandgap can also be used as active material for visible photodetectors. Large organic cations, such as PEA⁺ (PEA=C₆H₅C₂H₄NH₃), can inhibit the formation of shallow impurities during crystallization. The x-ray diffraction patterns and optical images of PEA₂PbI₄·(MAPbI₃)_{n − 1} (n = 1, 2, 3) single crystals are depicted in figure 14(a). (PEA)₂PbI₄·(MAPbI₃)_{n − 1} (n = 1, 2, and 3) exhibited self-doping concentrations that were three orders of magnitude lower than those of 3D hybrid perovskites. The corresponding photodetectors showed a detectivity of 1.1 × 10¹³ and a responsivity of 0.15 A W⁻¹ for an n value of 1. Using an induced peripheral crystallization approach, large, area-flexible (PEA)₂PbI₄ single crystals have been created to meet the needs of flexible wearable electronic device design [150]. Figure 14(b) demonstrates that plate-like (PEA)₂PbI₄ crystals achieved a large area exceeding 2500 mm² and a controlled micron-thickness maximum bending angle greater than 190°. As an application in flexible photodetectors, the highest R, EQE, and D* are measured to be 98.17 A W⁻¹, 26 500%, and 1.62 × 10¹⁵ Jones, respectively, at 460 nm wavelength and 4 V bias. Based on the anisotropy of the crystal, they also found that the carrier-carrying performance of the (100) facet of (PEA)₂PbI₄ is superior to the (010) facet [151]. Figure 14(c) illustrates that, according to a series of electrical performance measurements, the average carrier life, trap density, and μτ measurement along the (001) facet are superior to those along the (010) facet. Hence, the device on the (001) plane exhibits a very high R of 139.6 A W⁻¹, an EQE of 37 719.6%, a D* of 1.89 × 10¹⁵ Jones, and a rapid response speed of 21 μs/37 μs.

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Additionally, scientists have developed various 2D perovskite single crystals, such as (BA)_n (MA)_{n − 1}Pb_n I_{3n + 1} (n = 1, 2, 3,4, and ∞) [152], BDAPbI₄ [153], and demonstrated their application in a single-crystal photodetector. For (BA)_n (MA)_{n − 1}Pb_n I_{3n + 1}, reducing the thickness of the quantum well can effectively limit the charge transfer. As shown in figure 14(d), the excellent charge transporting behavior will allow the devices based on (BA)_n (MA)_{n − 1}Pb_n I_{3n + 1} to exhibit the highest on/off ratio of ∼10⁴ and the lowest dark current of ∼10⁻¹³A as an n value of 1. However, the thinner quantum wells enlarged the E_B energy of 2D materials, limiting the detectivity and responsivity of photodetectors. At n = ∞, the detectors achieved the highest detectivity of 2.4 × 10¹³ Jones and a responsivity of 38 A W⁻¹. Perovskite single crystals vis-light detectors have been realized excellent performance such as high responsivity and ultrafast response speed (see table 7) [1, 41, 66–69, 71, 72, 86, 112, 149–159]. In the future, the research direction of single crystal vis-light detectors will gradually shift from improving performance to functional development to achieve the building of multi-functional, high-performance, and multimode optical detector systems, such as polarized light detections [160] and spectrometers [161, 162].