Halide Perovskite Single Crystals: Optoelectronic Applications and Strategical Approaches

Halide perovskite is one of the most promising semiconducting materials in a variety of fields such as solar cells, photodetectors, and light-emitting diodes. Lead halide perovskite single crystals featuring long diffusion length, high carrier mobility, large light absorption coefficient and low defect density, have been attracting increasing attention. Fundamental study of the intrinsic nature keeps revealing the superior optoelectrical properties of perovskite single crystals over their polycrystalline thin film counterparts, but to date, the device performance lags behind. The best power conversion efficiency (PCE) of single crystal-based solar cells is 21.9%, falling behind that of polycrystalline thin film solar cells (25.2%). The oversized thickness, defective surfaces, and difficulties in depositing functional layers, hinder the application of halide perovskite single crystals in optoelectronic devices. Efforts have been made to synthesize large-area single crystalline thin films directly on conductive substrates and apply defect engineering approaches to improve the surface properties. This review starts from a comprehensive introduction of the optoelectrical properties of perovskite single crystals. Then, the synthesis methods for high-quality bulk crystals and single-crystalline thin films are introduced and compared, followed by a systematic review of their optoelectronic applications including solar cells, photodetectors, and X-ray detectors. The challenges and strategical approaches for high-performance applications are summarized at the end with a brief outlook on future work.


Introduction
In recent years, there has been blooming development in hybrid organic-inorganic halide perovskite materials as they possess outstanding photoelectronic properties and cost-effective low-temperature solution processability. The synthesis of a hybrid organic-inorganic halide perovskite was first reported several decades ago [1,2]. The significant attention was triggered by the development of hybrid organic-inorganic halide perovskite-sensitized photoelectrochemical cells with a power conversion efficiency (PCE) of 3.8% by Miyasaka and coworkers [3]. The study on perovskite and its derivatives has become a forefront research topic in the field of photovoltaic applications. It has been By tuning the composition and t factor, the characteristics of perovskite vary a lot, providing more opportunities to achieve target parameters. Mixed organic groups [35][36][37], mixed halides [35,38,39], and alloying inorganic cations with organic cations [40] were all reported to have an effect on the tuning properties. It is because of the variable chemical composition and crystal structure that perovskite has excellent photoelectric properties and broad application prospects. Specifically, tunable bandgap is one of the features of perovskite. The replacement of organic cation A shows a significant effect on the tolerance factor t and the crystal structure, as mentioned. The bandgap experiences change with different cations. Perovskite with larger A cations tends to have a wider bandgap due to the interplay of spin−orbit coupling and octahedra tilting [9]. More significantly, the bandgap can be tuned by changing the halide ion X. In the MAPbX3 system, the bandgap varies when changing the X composition. It was reported that by increasing the ratio of I/Br in MAPb(I1−xBrx)3, the bandgap can be tuned from 2.28 eV (Br − only) to 1.58 eV (I − only) [41]. A partial replacement of I − by Br − can slightly increase the bandgap, while still maintain the crystal structure.
Interestingly, even different facets of one single crystal show different properties. This is called the anisotropy phenomenon. It was reported that the (100) and (112) facets of the MAPbI3 single crystal exhibited different ion migration behaviour and defect status [42]. The I − vacancy dominated (100) facet followed n-type behaviour, while the (112) facet displayed p-type behaviour with MA + and Pb 2+ dominance. Another work revealed that stronger ion migration occurred in the (002) facet of MAPbI3 single crystals [43]. The anisotropy phenomenon gives an idea of facet engineering for high-performance applications on favourable facets of single crystals.
Most of the perovskite applications are fabricated based on polycrystalline thin films with several hundred of nanometres. Commonly, vacuum evaporation and solution processing are used to deposit thin films [44]. The quality of thin films largely depends on the fabrication process. Efforts have been made to fabricate conformal and pinhole-free high-quality films. Apart from the technical factor, polycrystalline thin films inherently have low crystallinity, which is reflected in the presence of a large number of grain boundaries and defects that negatively affects the performance of solar cells in terms of PCE and stability. Grain boundary is the interface between two crystallites. It was reported that faster nonradiative recombination and photoluminescence (PL) quenching favourably takes place at the grain boundaries [45], ascribing to faster ion migration and accumulation [46].  3 . The MA + cation is located at the centre of the structure, while surrounded by eight corner-sharing [PbI 6 ] 4− octahedra. Reproduced with permission from [34]. Copyright 2015, Springer Nature.
By tuning the composition and t factor, the characteristics of perovskite vary a lot, providing more opportunities to achieve target parameters. Mixed organic groups [35][36][37], mixed halides [35,38,39], and alloying inorganic cations with organic cations [40] were all reported to have an effect on the tuning properties. It is because of the variable chemical composition and crystal structure that perovskite has excellent photoelectric properties and broad application prospects. Specifically, tunable bandgap is one of the features of perovskite. The replacement of organic cation A shows a significant effect on the tolerance factor t and the crystal structure, as mentioned. The bandgap experiences change with different cations. Perovskite with larger A cations tends to have a wider bandgap due to the interplay of spin−orbit coupling and octahedra tilting [9]. More significantly, the bandgap can be tuned by changing the halide ion X. In the MAPbX 3 system, the bandgap varies when changing the X composition. It was reported that by increasing the ratio of I/Br in MAPb(I 1−x Br x ) 3 , the bandgap can be tuned from 2.28 eV (Br − only) to 1.58 eV (I − only) [41]. A partial replacement of I − by Br − can slightly increase the bandgap, while still maintain the crystal structure.
Interestingly, even different facets of one single crystal show different properties. This is called the anisotropy phenomenon. It was reported that the (100) and (112) facets of the MAPbI 3 single crystal exhibited different ion migration behaviour and defect status [42]. The I − vacancy dominated (100) facet followed n-type behaviour, while the (112) facet displayed p-type behaviour with MA + and Pb 2+ dominance. Another work revealed that stronger ion migration occurred in the (002) facet of MAPbI 3 single crystals [43]. The anisotropy phenomenon gives an idea of facet engineering for high-performance applications on favourable facets of single crystals.
Most of the perovskite applications are fabricated based on polycrystalline thin films with several hundred of nanometres. Commonly, vacuum evaporation and solution processing are used to deposit thin films [44]. The quality of thin films largely depends on the fabrication process. Efforts have been made to fabricate conformal and pinhole-free high-quality films. Apart from the technical factor, polycrystalline thin films inherently have low crystallinity, which is reflected in the presence of a large number of grain boundaries and defects that negatively affects the performance of solar cells in terms of Energies 2020, 13, 4250 4 of 27 PCE and stability. Grain boundary is the interface between two crystallites. It was reported that faster nonradiative recombination and photoluminescence (PL) quenching favourably takes place at the grain boundaries [45], ascribing to faster ion migration and accumulation [46]. Defects are the interruptions of regular patterns. The lattice around the defect is distorted and the periodic potential field is damaged. This kind of deformation will create an energy level in the electronic band. Deep-level defects can act as recombination centres where carriers are captured, and non-radiative recombination happens, resulting in free carrier loss. Generally, grain boundaries and defects are regarded as fatal, and decrease semiconductor properties. Compared with polycrystalline thin films, single crystals have much better crystallinity. The spontaneous crystallisation process ensures single crystals with continuous and rigid crystal lattices [47], so the structure distortion and grain boundaries rarely exist in single crystals as well as fewer defects. High-quality single crystals exhibit several orders of magnitudes lower (10 9 -10 11 cm −3 ) defect density than that of thin films (10 16 -10 18 cm −3 ) [5,48], which is comparable to high crystallinity Si semiconductors [5], suggesting a lower possibility of carrier trapping and recombination. The difference in trap density is also observed in silicon. Disorder in the structure leads to localisation of the states, which appear as band tails within the band gap. These tails are usually described with an exponential density of states [49]. For hybrid organic-inorganic perovskite single crystals, the absence of grain boundaries and high crystallinity in the bulk crystal contribute most to the low trap density. This also allows single crystals to have higher carrier mobility, longer diffusion length, and wider light absorption spectra [21]. Specifically, the MAPbI 3 single crystal was reported to have a surprisingly high carrier diffusion length exceeding 175 µm [4] and a carrier lifetime exceeding 15 µs [50]. An extra-long diffusion length exceeding 380 µm under 1 sun illumination was reported for hybrid CH 3 NH 3 PbI 3x Cl x single crystals [51]. Regarding the thin films, a much shorter diffusion length of~1.7 µm for electrons and up to~6.3 µm for holes was directly observed [52], and the lifetime was dependent on film thickness and the surface defects [53], for which the value varied from 2.8 ns [52] to over 140 ns [54]. This huge difference means that carriers can stay untrapped and unrecombined for a longer time and distance to move to the electrodes in single crystals. Moreover, single crystals exhibit wider absorption spectra and high light absorbance [4,[55][56][57][58]. The Snaith group reported the thickness-dependent light absorptance of MAPbI 3 thin films where about 90% of the incident light could be absorbed with films with a 300-400 nm thickness [59]. The light absorptance further increased to over 99% when the film thickness was over 600 nm. Furthermore, the absorption cut-off of single crystals was located at 850 nm, showing a red shift compared to 800 nm of polycrystalline thin films. It is noteworthy that the perovskite single crystal is an ideal platform to investigate the intrinsic nature of this material, especially for carrier dynamic and mobility [32] because of the superior properties and large dimensions.
Large dimension brings convenience to an intrinsic nature study; however, it also brings challenges to the direct application of single crystals in high performance photovoltaic devices. Though the large thickness can increase the light absorption, it is detrimental for charge separation and collection, which causes a decrease in the external quantum efficiency and thus hinders device performance. To be more specific, photovoltaic applications like solar cells require light-induced carriers to be captured by electrodes to generate voltage across the solar cell and external current. Generally, single crystals are grown in bulk, with thicknesses of several millimetres that far surpasses the carrier diffusion length, while for polycrystalline thin films, it is hundreds of nanometres, so it is much easier for carriers to transport across the cell. Another obstacle is the difficulty of incorporating multilayer devices because the majority of single crystals are free-standing and not attached to any substrate. Therefore, large-area and thin single crystals are highly desired for device fabrications. Recently, researchers have been trying to use the space-confined crystallisation method to grow a single-crystalline thin film with thicknesses ranging from tens of nanometres [27] to hundreds of micrometres [60][61][62]. Using this method, thin single crystalline thin films have been successfully made into devices with vertical structures. A PCE of 21.09% with a maximum FF of 84.3% was achieved by an inverted structural device ITO (indium tin oxide)/poly(triarylamine) (PTAA)/MAPbI 3 single crystal/C60/bathocuproine (BCP)/copper (Cu) based Energies 2020, 13, 4250 5 of 27 on a~20 µm-thick MAPbI 3 single crystal, which performed better than the polycrystalline devices with the same structure (~19% in PCE) [63]. Most recently, a new record of 21.93% was made by the same group using the modified crystallisation process. Remarkable enhancement in the open circuit voltage (V OC ) from 1.08 V (controlled sample) to 1.15 V was observed. The accelerated progress of single-crystalline thin films encourages competition with the polycrystalline counterpart. The chances of surpassing lie in the further improvement of crystal quality and the surface engineering of the device.

Synthesis Methods of Perovskite Single Crystals
In the middle of the twentieth century, scientists started synthesizing perovskite single crystals. In 2015, Zhipeng Lian and coworkers synthesised MAPbI 3 single crystals by the bottom-seeded solution growth (BSSG) method, and first fabricated single-crystal based photodetectors on the (100) facet [64], where the superiority of the perovskite single crystals was revealed. Compared with polycrystalline thin film photodetectors, their devices showed a 10 2 times higher responsivity and 10 3 times higher response speed, greatly encouraging the exploration of single crystals.
To obtain high quality single crystals, several solution-processed crystallisation methods have been developed, mainly in three categories of the antisolvent vapor-assisted crystallisation (AVC) method, solution temperature-lowering (STL) method, and inverse temperature crystallisation (ITC) method. The fundamental mechanisms of these methods are to create supersaturation in the precursor, modulate the solubility, and induce crystallisation. Researchers are keeping the optimizing crystallisation process toward a low temperature-process and controlled nucleation based on these methods to obtain larger-sized high-quality single crystals.

Antisolvent Vapor-Assisted Crystallisation (AVC) Method
During perovskite thin film deposition, antisolvents are commonly used to accelerate crystallisation and improve film quality [65,66]. The mechanism is to use the large solubility difference of perovskite in different solvents. For common solvents like dimethyl sulfoxide (DMSO), dimethylformamide (DMF), and gamma-butyrolactone (GBL), MAPbI 3 dissolves well, while in antisolvents like chlorobenzene (PhCl), diethyl ether (Et 2 O), and dichloromethane (DCM), MAPbI 3 shows low solubility. In the process of thin film deposition, the perovskite precursor is firstly spin coated on substrates followed immediately by the deposition of the antisolvent. Antisolvents induce fast nucleation and crystallisation, increasing the grain sizes and film uniformity. In addition to low solubility, the antisolvent is required to be highly volatile and can dissolve well in the chosen solvent to make sure the efficient diffusion into the solvent. Based on this strategy, Bakr's group first developed the AVC method to grow single crystals [5]; Figure 2a illustrates the AVC process for single crystals. The same molar ratio of MAI and PbI 2 are dissolved in solvent gamma-butyrolactone (GBL) to get the precursor solution. In a closed environment, the open vial containing precursor solution is covered with a large vessel with antisolvent dichloromethane (DCM). When the vapor of the antisolvent mixes with the precursor solution, the solubility of the target crystals reduces, thus crystallisation is promoted [55]. Crystals slowly grow along with the gradual diffusion of the antisolvent. The MAPbBr 3 and MAPbI 3 crystals shown in Figure 2b were obtained within one week of crystallisation. Figure 2c shows a modified AVC setup where a temperature controller and a flow controller are used to ensure a stable environment and continuous antisolvent diffusion for high-quality and large single crystals [67]. A large MAPbBr 3 single crystal over 50 mm in size was grown with this modified method (Figure 2d) after over-15-day synthesis. Compared with conventional temperature-tuning crystallisation methods, the AVC method avoids the temperature-dependent phase transitions, and the disturbance of convective currents; it also prevents the potential lattice disorder due to the solvation of MA + during the crystal growth. However, the crystal growth rate is relatively low.

Solution Temperature-Lowering (STL) Method
The STL method is a classic crystallisation method that creates supersaturation by lowing the temperature. It is suitable to grow perovskite in the HX-based precursor solution, because its solubility greatly decreases as the temperature goes down. Figure 3a gives the solubility curve of MAPbI3 in HI solution. Briefly, Pb(CH3COOH)2•3H2O and MAI are dissolved in a HI aqueous solution at 60 °C, then the temperature is cooled to 45 °C at a slow rate of 0.1-0.5 °C per hour [68]. Consequently, single crystals with a 10 mm size can be harvested [69] (Figure 3b). STL method was further optimised by fixing seed crystals in different positions in the vessel with the top seeded solution growth (TSSG) method and the bottom seeded solution growth (BSSG) method. Figure 3c,d illustrates the setup of the two methods. For BSSG, first, small seed crystals with a millimetre scale were obtained by the STL method. Nice seeds were picked out and put in the bottom of the vial with fresh precursor for further growth. This step is repeated until the targeted size was attained. For TSSG, nice small seeds were fixed on a substrate that is immersed in the top half of the precursor. The bottom half of the vial containing precursor and seed crystals is heated in an oil bath while the top half is air cooled to remove the heat and create a temperature gradient [4]. Low temperature at the top induces the crystallisation, at the same time, the bottom continuously provides ions by convection [32]. Large size single crystals can be obtained by STL under the strict control of temperature, but the growth rate is relatively low (2 mm per day). Irregular crystals and MA4PbI6•2H2O by-products will be formed if the temperature drops too fast or decreases below 40 °C. Formic acid was reported to be effective in accelerating the STL crystallisation and promoting a higher quality of MAPbI3 single crystals [70]. A crystal of 9 mm in length was obtained by 3-day direct growth without seed.

Solution Temperature-Lowering (STL) Method
The STL method is a classic crystallisation method that creates supersaturation by lowing the temperature. It is suitable to grow perovskite in the HX-based precursor solution, because its solubility greatly decreases as the temperature goes down. Figure 3a gives the solubility curve of MAPbI 3 in HI solution. Briefly, Pb(CH 3 COOH) 2 ·3H 2 O and MAI are dissolved in a HI aqueous solution at 60 • C, then the temperature is cooled to 45 • C at a slow rate of 0.1-0.5 • C per hour [68]. Consequently, single crystals with a 10 mm size can be harvested [69] (Figure 3b). STL method was further optimised by fixing seed crystals in different positions in the vessel with the top seeded solution growth (TSSG) method and the bottom seeded solution growth (BSSG) method. Figure 3c,d illustrates the setup of the two methods. For BSSG, first, small seed crystals with a millimetre scale were obtained by the STL method. Nice seeds were picked out and put in the bottom of the vial with fresh precursor for further growth. This step is repeated until the targeted size was attained. For TSSG, nice small seeds were fixed on a substrate that is immersed in the top half of the precursor. The bottom half of the vial containing precursor and seed crystals is heated in an oil bath while the top half is air cooled to remove the heat and create a temperature gradient [4]. Low temperature at the top induces the crystallisation, at the same time, the bottom continuously provides ions by convection [32]. Large size single crystals can be obtained by STL under the strict control of temperature, but the growth rate is relatively low (2 mm per day). Irregular crystals and MA 4 PbI 6 ·2H 2 O by-products will be formed if the temperature drops too fast or decreases below 40 • C. Formic acid was reported to be effective in accelerating the STL crystallisation and promoting a higher quality of MAPbI 3 single crystals [70]. A crystal of 9 mm in length was obtained by 3-day direct growth without seed.

Inverse Temperature Crystallisation (ITC) Method
The ITC method was first proposed in 2015 by Bakr's group, and is now the most commonly used method for lead halide perovskite single crystal synthesis [56,71]. In certain solvents, the solubility of perovskite shows retrograde behaviour, which decreases as the temperature increases, and keeping the precursor at high temperature can promote crystallisation. For MAPbI3, MAPbCl3 and MAPbBr3, GBL, DMSO, and DMF are suitable solvents in the ITC method, respectively. The solubility of perovskite in the corresponding solvent for the ITC method is illustrated in Figure 4a-d. The mechanism is that, at low temperature, the perovskite forms complexes with the solvent, exhibiting high solubility. As the temperature increases, the bonds break, perovskite molecules are freed, and the solubility drops. This method is applied to formamidinium and methylammonium lead halide perovskites [23,71] as well as mixed halide perovskite [72]. The synthesis procedure of the ITC method is quite simple. Taking the crystallisation of MAPbI3 single crystals as an example, 1 M of PbI2 and MAI are dissolved in GBL at a 45 °C to form a saturated precursor, which is then heated to 80-130 °C. The precursor is kept at a specific temperature for several hours, and MAPbI3 on a millimetre scale can be obtained. Repeated seeded growth is conducted to harvest large crystals. Figure 4e gives an illustration of the ITC method. The growth rate of MAPbI3 was calculated to be 3 mm 3 h −1 for the first hour and exponentially increased for the following hours (Figure 4f), one order of magnitude faster than other methods [23,69]. ITC is simple to operate and fast in growth, but the growth rate is hard to control, consequently inducing more defects.

Inverse Temperature Crystallisation (ITC) Method
The ITC method was first proposed in 2015 by Bakr's group, and is now the most commonly used method for lead halide perovskite single crystal synthesis [56,71]. In certain solvents, the solubility of perovskite shows retrograde behaviour, which decreases as the temperature increases, and keeping the precursor at high temperature can promote crystallisation. For MAPbI 3 , MAPbCl 3 and MAPbBr 3 , GBL, DMSO, and DMF are suitable solvents in the ITC method, respectively. The solubility of perovskite in the corresponding solvent for the ITC method is illustrated in Figure 4a-d. The mechanism is that, at low temperature, the perovskite forms complexes with the solvent, exhibiting high solubility. As the temperature increases, the bonds break, perovskite molecules are freed, and the solubility drops. This method is applied to formamidinium and methylammonium lead halide perovskites [23,71] as well as mixed halide perovskite [72]. The synthesis procedure of the ITC method is quite simple. Taking the crystallisation of MAPbI 3 single crystals as an example, 1 M of PbI 2 and MAI are dissolved in GBL at a 45 • C to form a saturated precursor, which is then heated to 80-130 • C. The precursor is kept at a specific temperature for several hours, and MAPbI 3 on a millimetre scale can be obtained. Repeated seeded growth is conducted to harvest large crystals. Figure 4e gives an illustration of the ITC method. The growth rate of MAPbI 3 was calculated to be 3 mm 3 h −1 for the first hour and exponentially increased for the following hours (Figure 4f), one order of magnitude faster than other methods [23,69]. ITC is simple to operate and fast in growth, but the growth rate is hard to control, consequently inducing more defects.

Optoelectronic Applications of Perovskite Single Crystals
Perovskite, as one of the most promising candidates of next-generation semiconductor materials, has demonstrated a wide range of device applications. As the most widely studied application of perovskite, the perovskite single junction solar cell has achieved a PCE over 80% of the theoretical value. Researchers are now focusing on modifying the interfaces between the perovskite with electron transport layers and hole transport layers. On the other hand, the development of another potential application, perovskite photodetectors and X-ray detectors, is still in its early stage. Optimisations on single crystals with low trap density and high crystallinity are still desirable. As mentioned, the exploration of high-performance photodetectors with perovskite single crystals is quite encouraging. Ye reported a perovskite photodetector exhibiting a high detectivity of 1.8 × 10 15 Jones and a response time of 68.9 μs with high quality cuboid MAPbI3 single crystals. The X-ray detector made with the same material showed a sensitivity of 969.9 μC Gy −1 cm −2 under −1 V bias, which went as high up to 6218 μC Gy −1 cm −2 under −13 V bias. In the following part, some representative applications are summarised.

Perovskite Single Crystal for Solar Cells
Efficient carrier transport plays a dominant role in the performance of solar cells, which requires carriers to travel across the light-absorb layer to the electrodes. For bulk single crystals, the mm-scale thickness did not match the μm-scale carrier diffusion length, leading to incompatibility with the vertically multi-layer solar cell structure. Furthermore, free-standing bulk single crystals have a small aspect ratio that is not suitable for device fabrications. Therefore, controlling the thickness of single crystals down to at least the μm-scale is one of the prerequisites for high-performance solar cells. Efforts have been made to grow large-area single crystals directly on substrates. Here, the major fabrication methods of single-crystalline thin films and solar cell applications are summarised.
The top-down method is a universal and easily applicable method to prepare single-crystalline thin films, especially large-area thin films, from bulk single crystals by mechanical slicing [57] and grinding [73]. Liu et al. reported the fabrication of large-area single-crystalline thin films from a series

Optoelectronic Applications of Perovskite Single Crystals
Perovskite, as one of the most promising candidates of next-generation semiconductor materials, has demonstrated a wide range of device applications. As the most widely studied application of perovskite, the perovskite single junction solar cell has achieved a PCE over 80% of the theoretical value.
Researchers are now focusing on modifying the interfaces between the perovskite with electron transport layers and hole transport layers. On the other hand, the development of another potential application, perovskite photodetectors and X-ray detectors, is still in its early stage. Optimisations on single crystals with low trap density and high crystallinity are still desirable. As mentioned, the exploration of high-performance photodetectors with perovskite single crystals is quite encouraging. Ye reported a perovskite photodetector exhibiting a high detectivity of 1.8 × 10 15 Jones and a response time of 68.9 µs with high quality cuboid MAPbI 3 single crystals. The X-ray detector made with the same material showed a sensitivity of 969.9 µC Gy −1 cm −2 under −1 V bias, which went as high up to 6218 µC Gy −1 cm −2 under −13 V bias. In the following part, some representative applications are summarised.

Perovskite Single Crystal for Solar Cells
Efficient carrier transport plays a dominant role in the performance of solar cells, which requires carriers to travel across the light-absorb layer to the electrodes. For bulk single crystals, the mm-scale thickness did not match the µm-scale carrier diffusion length, leading to incompatibility with the vertically multi-layer solar cell structure. Furthermore, free-standing bulk single crystals have a small aspect ratio that is not suitable for device fabrications. Therefore, controlling the thickness of single crystals down to at least the µm-scale is one of the prerequisites for high-performance solar cells. Efforts have been made to grow large-area single crystals directly on substrates. Here, the major fabrication methods of single-crystalline thin films and solar cell applications are summarised.
The top-down method is a universal and easily applicable method to prepare single-crystalline thin films, especially large-area thin films, from bulk single crystals by mechanical slicing [57] and  3 and MAPb((Br y I 1−y ) 3 mixed halide perovskite bulk single crystals by diamond-wire sawing [57]. They optimised the coolant solution, the sawing speed, and the feeding rate of the slicing machine to cut a 113 mm × 58 mm × 52 mm-large MAPbI 3 single crystal into wafers with thicknesses of 190, 380, and 570 µm. The as-cut wafers were characterised to have a high quality with a low trap density of 2.1 × 10 8 cm −3 , a low hole concentration of 6.1 × 10 9 cm −3 , a high carrier mobility of 41 cm 2 V −1 s −1 , and high absorption onset of 910 nm. Wafers were made into solar cells with an Au/ITO/Spiro-MeOTAD/perovskite-wafer/PCBM/LiF/Ag/Au structure. The best device had a open circuit voltage (V OC ) of 1.15 V and short current density (J SC ) of 20.02 mAcm −2 , and interestingly, minor hysteresis between the reverse scan and forward scan. However, the efficiency was as low as 4%. It is speculated that the slicing process can cause damage on the wafer surface including high roughness and surface defects. Oxygen and moisture could intrude on the surface during the slicing process, resulting in surface degradation, at the same time, coolant solution could cause partial dissolution of the crystal. Moreover, top-down method can hardly produce wafers with thicknesses below 50 µm, which is still too thick for efficient carrier transport. The poor contact between the HTL, ETL, and the wafer could be another obstacle for high performance.
Later, a universal top-down approach that combined mechanical slicing and wet etching was developed by Yan's group [74]. Large thick single crystals were first wire-cut into wafers in 200-µm thicknesses. The thin wafers were then immersed in unsaturated mother liquor for wet etching by controlling the immersion conditions (time, temperature, and concentration), and the thickness of the wafers could be reduced to as low as 15 µm, as shown in Figure ??a. The combined process preserves the surface properties of the original large single crystal without obvious degradation and maintains the crystallinity, but still, the thickness of the thin wafers cannot be reduced below micron-scale and the thin wafers had relatively small area. They did not report the application of solar cells in this literature. However, this method is promising to synthesize single-crystalline thin films without damaging the surface properties for high-performance solar cells.
The cavitation-triggered asymmetrical crystallisation (CTAC) strategy was first reported by Bakr's group for the growth of monocrystalline MAPbBr 3 films on various substrates including silicon wafers, ITO-coated glass, FTO-coated (FTO: fluorine-doped tin oxide) glass, and sputter-coated metal on silicon [75]. Ultrasonic pulse with antisolvent vapor diffusion was introduced to a low supersaturated precursor to generate cavities, where the formation and collapse can release energy to overcome the nucleation barrier and promote symmetric crystal growth near the substrate by high-speed fluid jets, as demonstrated in Figure ??b. By regulating the rate and time, the film thickness was controlled from one up to several tens of micrometres, however, the larger the thickness, the weaker the performance. Their ETL and HTL-free devices of ITO/MAPbBr 3 (4 µm)/Au had a PCE of over 5%, which was improved to 6.5% with a single p-n-junction-based structure of FTO/TiO 2 /MAPbBr 3 (1 µm)/Au that exhibited a high V OC of 1.4 V. The dark and illuminated J-V curves for the two samples are as in Figure ??c,d. This work gives an insight of the design of rational device structures.
Breakthroughs on single-crystal solar cells were attained using space-confined solution-process method. It was first developed by Liu et al. to fabricate single-crystalline thin film photodetector devices using an ultrathin geometry-defined dynamic-flow reaction system [76], as shown in Figure ??e. Substrates are separated by different spacers; a peristaltic pump continuously provides fresh precursor with dynamic flow into the middle layer. Single crystalline wafers (thinnest to 150 µm) are obtained in the interspace. Later in 2017, Huang and co-workers reported MAPbI 3 single crystal growth on poly(triarylamine) (PTAA) coated ITO substrates for high-performance solar cells [8]. The hydrophobicity of PTAA weakens the solvent-substrate interaction, thus promoting the solvent diffusion, which benefits the in-plane crystallisation, as shown in Figure 6a. They studied thickness-dependent performance and concluded that, theoretically, single crystals with a 200 µm thickness can reach the highest PCE (Figure 6b), however, from the experiment, the 10 µm-thick crystal displayed the best performance. This is due to the inconsistent of the carrier diffusion length of the bulk single crystal and the single-crystalline thin film. The hole and electron diffusion length were 24.7 and 13.6 µm, respectively, in this report, far shorter than those reported values of the bulk crystals. The resultant devices of ITO/PTAA/MAPbI 3 (10 µm)/phenyl-C61-butyric acid methyl ester (PCBM)/C60/bathocuproine (BCP)/copper (Cu) had the best PCE of 16.1%, which was increased to 17.8% with a J SC of 21.0 mA cm −2 , a V OC of 1.08 V, and a FF of 78.6% by surface passivation of MAI. Later in 2019, Bakr's group fabricated a solar cell with a similar method, but was conducted in a N 2 -filled environment, which had a J SC of 23.46 mA cm −2 , a V OC of 1.076 V, a FF of 83.5%, and a PCE of 21.09% [63]. Figure 6c illustrates the cell structure and band energy of each layer of ITO/PTAA/MAPbI 3 (20 µm)/C60/bathocuproine (BCP)/Cu. It was speculated that the easy-to-oxidize I − may result in I 3 − trimers that form deep-level defects [77,78], which the N 2 environment can prevent. Most recently, a new record of a PCE of 21.93% with a J SC of 23.68 mA cm −2 , a V OC of 1.144 V, and a FF of 81% was made by Bakr's group using the same device configuration [26]. They optimised the composition of the precursor solvent to a solvent mixture of propylene carbonate (PC) and γ-butyrolactone (GBL) for low-temperature crystallisation for high-quality single crystal thin film. The addition of PC reduced 45% of the solubility of MAPbI 3 , but still kept the retrograde solubility behaviour, so that a single crystal could be obtained at the lower temperature at 90 • C, which alleviated the escape of MAI from the crystal lattice (Figure 6d,e), consequently, improving crystallinity and performance. An improvement of over 1% on PCE was achieved by lowering the crystallisation temperature, as shown in Figure 6f.  [63]. Figure 6c illustrates the cell structure and band energy of each layer of ITO/PTAA/MAPbI3 (20 μm)/C60/bathocuproine (BCP)/Cu. It was speculated that the easy-to-oxidize I − may result in I3 − trimers that form deep-level defects [77,78], which the N2 environment can prevent. Most recently, a new record of a PCE of 21.93% with a JSC of 23.68 mA cm −2 , a VOC of 1.144 V, and a FF of 81% was made by Bakr's group using the same device configuration [26]. They optimised the composition of the precursor solvent to a solvent mixture of propylene carbonate (PC) and γbutyrolactone (GBL) for low-temperature crystallisation for high-quality single crystal thin film. The addition of PC reduced 45% of the solubility of MAPbI3, but still kept the retrograde solubility behaviour, so that a single crystal could be obtained at the lower temperature at 90 °C, which alleviated the escape of MAI from the crystal lattice ( Figure 6d,e), consequently, improving crystallinity and performance. An improvement of over 1% on PCE was achieved by lowering the crystallisation temperature, as shown in Figure 6f. (SEM) image of the monocrystalline film; 3-6, illustrations of the cavity formation and collapse of the CTAC mechanism on a microscopic scale; dark and illuminated J-V curves of (c) ITO-based and (d) FTO/TiO 2 -based monocrystalline solar cells, respectively, the inset depicts an illustration of the device architecture. Reproduced with permission from [75]. Copyright 2016, WILEY-VCH.
(e) Schematic diagrams of the ultrathin geometry-defined dynamic-flow reaction system. Two flat glass slides are separated apart by two spacers (Si wafers, stainless-steel foils, wires, etc.) to form a microreactor in which the single crystal wafer is formed. Reproduced with permission from [76]. Copyright 2016, WILEY-VCH.
Energies 2020, 13, x FOR PEER REVIEW 11 of 27 of the device architecture. Reproduced with permission from [75]. Copyright 2016, WILEY-VCH. (e) Schematic diagrams of the ultrathin geometry-defined dynamic-flow reaction system. Two flat glass slides are separated apart by two spacers (Si wafers, stainless-steel foils, wires, etc.) to form a microreactor in which the single crystal wafer is formed. Reproduced with permission from [76]. Copyright 2016, WILEY-VCH.  There are also some cases of lateral-structure solar cells. Dong and coworkers simply deposited two symmetrical gold electrodes with a spacing of 50 µm on the top surface of a single crystal, forming an Au/MAPbI 3 /Au structure, and this device is shown in Figure 6g. When a high electrical field of 1 Vµm −1 was applied in the device, reversible shape changing was observed, which was likely due to the slipping between the weakly bonded (100) planes to relieve the accumulated strain. The slipping induced defect and grain boundaries in the crystal act as a high-speed channel for ion migration, resulting in self-doping, thus, after the electrical poling, the symmetry of the device was broken into a lateral p-i-n structure solar cell. This process is illustrated in Figure 6h. The device exhibited a J SC of 2.28 mA cm −2 and a V OC of 0.82 V under 0.25 sun. The PCE was hindered by the poling-induced high trap density as 1.88%. Later in 2019, the same group used the surface tension assisted growth method to synthesize single-crystalline thin films with a large aspect ratio and fabricate lateral-structure solar cells [79]. As illustrated in Figure 6i, in brief, by controlling the solvent evaporation of the precursor, nuclei favourably form at the centre of the solution top surface due to fast evaporation at the centre and float at the air-solution interface with the support from surface tension. Then, the thin crystals grow along the lateral direction along with evaporation. The as-grown wafers have a lateral size in centimetres and a thickness of tens of micrometres as well as wider light absorbance and prolonged carrier lifetime. The best lateral solar cell of Au/MAPbI 3 /C60/BCP/Au had a J SC of 5.06 mAcm −2 , V OC of 0.66 V, FF of 44%, and PCE of 5.9% under 0.25 sun without poling treatment (Figure 6j). For the lateral-structure solar cells, surface treatment is highly desired to reduce the surface trap density because surface defects would significantly limit the carrier diffusion length at the near surface region. The carrier diffusion length is expected to be over 50 µm, as this is the normal gap between two electrodes. Song reported that surface passivation by MAI on the MAPbI 3 single crystal is effective in improving the solar cell efficiency, which increases the surface potential and encourages better energy band alignment of the device, as shown in Figure 6k. The PCE of devices based on the passivated single crystal exceeded 11% (Figure 6l), and the operation stability was enhanced to 200 h without degradation.
Though the PCE of the single-crystal solar cell was improved to 21.93%, there is still a huge gap between the single-crystal devices and polycrystalline counterparts (25.2%). It is worth noting that single-crystal solar cells still suffer from the significant surface trap density, despite the low trap density in the bulk. Moreover, the lattice mismatching between the perovskite and deposited layer requires optimisation by interface engineering.

Perovskite Single Crystals for Photodetectors
A photodetector is a sensor of light that presents in a large variety of equipment for light imaging sensing, process control, and security purposes. It converts an indecipherable light signal into an electrical signal with a semiconductor that displays the photovoltaic effect or photoconductivity with an external voltage. The key parameters that describe the performance of a photodetector are dark current density (J d ), external quantum efficiency (EQE), responsivity (R), specific detectivity (D*), linear dynamic range (LDR), and response speed (rise time τ r and fall time τ f ).
Perovskite single crystal-based photodetectors feature high R and D* for their extraordinary characteristics. In 2015, Lian first revealed the better capability of perovskite single crystals over thin films for photodetectors [64]. The centimetre-scale MAPbI 3 single crystals grown by the BSSG method were made into planar-type photodetectors on (100) facet. Simple devices with two interdigitated Au electrodes with channel width of 20 µm were fabricated, as illustrated in Figure 7a. Under the lowest detectable light intensity (2.12 nW cm −2 ), a high R of 953 AW −1 and EQE of 2.22 × 10 5 % were measured at 1 V bias, with a LDR of 76 dB, τ r of 74 µs, and τ f of 58 µs. Under a relative strong light source of 1 mWcm −2 , the single crystal photodetector showed 100 times higher R ( Figure 7b) and EQE, and 10 3 times faster response speed than their polycrystalline-based devices. Lian's work encouraged researches to apply high-quality single crystals for high-performance photodetectors.
The carrier dynamic of perovskite makes it ideal for the light-absorb layer. The generation of the electron-hole pair happens in several picoseconds and the free carrier concentration remains high at the microsecond scale [80], while the recombination that reduces the carriers is relatively slow at several microseconds. Fast generation and low recombination assure a fast response (low τ r and τ f ). Additionally, the carrier mobility, lifetime, and diffusion lengths of perovskite single crystals were surprisingly high. Carrier lifetime exceeding 15 µs [50] and a diffusion length exceeding 175 µm [4] were detected. This means that carriers can stay untrapped and unrecombined for an adequate time and distance to move to the electrodes. Meanwhile, the defect density in the perovskite single crystals was as low as 10 9 cm −3 , comparable to that of high crystallinity Si semiconductors [5], suggesting a lower possibility of carrier trapping and power loss. These properties guarantee highly efficient collection, giving rise to an outstanding photocurrent, EQE, D*, and R. In particular, high-quality single crystals have more chances in performance breakthroughs. Ye reported MAPbI 3 single crystal-based photodetectors with an ultrahigh detectivity. High-quality crystals were obtained by modifying the ITC method by dissolving the seeds back to the precursor prior to heating up for regrowth [81]. The impurities at the surface dissolve at low temperature, so the mismatch between the nucleus and seed surface is diminished to avoid gap defect formation, thus improving crystallinity. The as-obtained cuboid MAPbI 3 single crystals had a low trap density of 1.14 × 10 9 cm −3 . The resultant photodetectors had the best performance of R of 2.6 × 10 4 mAW −1 , EQE of 5700%, and D* of 1.8 × 10 15 Jones under 550 nm illumination at −1 V bias. Recently, a highly sensitive photodetector with an ultra-high R of 1017.1 AW −1 was reported [82]. A MAPbBr 3 single crystalline thin film (2.25 µm in thickness) was integrated with a monolayer of graphene vertically. The difference in Fermi level between the two materials pushes holes from the graphene to the perovskite side and results in electron doping in the graphene side. This charge transfer induces a built-in field that helps the efficient separation of light-generated electron-hole pairs as well as suppressing carrier recombination in the perovskite layer. Figure 7c illustrates the energy band bending of the integration. At 3 V bias, the resultant photodetector (the device structure is illustrated in Figure 7d  By tuning the composition of halide, perovskite can achieve detection in different wavelength ranges. Visible-blind UV detection was reported using a large band gap material: MAPbCl3 single crystals [56]. MAPbBr3 and MAPbI3 single crystals showed strong near infrared photo responses below their optical gaps due to surface defect induced sub-gap absorption, enabling near infrared detection [83]. Fang et al. reported highly narrowband photodetectors with a vertical structure using mixed halide perovskite thick single crystals [15]. Changing the halide ratio Cl/Br and thus bandgap, the response spectral can be tuned from blue to red. Together with the "charge collection narrowing effect" and the assistance of applied voltage, response spectral with a full-width at half-maximum (FWHM) below 20 nm was achieved, as shown in Figure 7e,f. Long-wavelength light that penetrates deeper into the bulk crystal generates carriers closer to the rear electrode, which can be more easily collected, while the short-wavelength light generates carriers in the near surface region where strong surface-charge recombination happens. Therefore, charge collection in the short wavelength is limited. However, this band narrowing is at the expense of the device performances, R, and response speed due to severe carrier recombination.
2D single crystals with large organic groups and special quantum well structure also play an important part in the development of perovskite photodetectors. Wang systematically studied the effect of the number of metal halide monolayer sheets, n, on the performance of simple planer-type devices with Au/perovskite single crystal/glass, based on BAnMAn−1PbnI3n+1 (BA + : butylammonium, C4H9NH3 + ; n = 1, 2, 3, 4 and ∞) single crystals [36], as illustrated in Figure 8a. With a thinner quantum well thickness, significant reductions in Jd, τr, and τf were observed. However, on the contrary, the photocurrent, R, and D* experienced a negative effect (Figure 8b,c). For instance, when n = 1, that is 2D BA2PbI4, the dark current was measured as 6 × 10 −13 A at 0.8 V, whilst under 200 μW/cm 2 at a 1 V bias, the on/off ratio (current under light to dark current) was 10 4 , D* was 1.6 × 10 13 Jones, τr was 1.7 By tuning the composition of halide, perovskite can achieve detection in different wavelength ranges. Visible-blind UV detection was reported using a large band gap material: MAPbCl 3 single crystals [56]. MAPbBr 3 and MAPbI 3 single crystals showed strong near infrared photo responses below their optical gaps due to surface defect induced sub-gap absorption, enabling near infrared detection [83]. Fang et al. reported highly narrowband photodetectors with a vertical structure using mixed halide perovskite thick single crystals [15]. Changing the halide ratio Cl/Br and thus bandgap, the response spectral can be tuned from blue to red. Together with the "charge collection narrowing effect" and the assistance of applied voltage, response spectral with a full-width at half-maximum (FWHM) below 20 nm was achieved, as shown in Figure 7e,f. Long-wavelength light that penetrates deeper into the bulk crystal generates carriers closer to the rear electrode, which can be more easily collected, while the short-wavelength light generates carriers in the near surface region where strong surface-charge recombination happens. Therefore, charge collection in the short wavelength is limited. However, this band narrowing is at the expense of the device performances, R, and response speed due to severe carrier recombination.
2D single crystals with large organic groups and special quantum well structure also play an important part in the development of perovskite photodetectors. Wang systematically studied the effect of the number of metal halide monolayer sheets, n, on the performance of simple planer-type devices with Au/perovskite single crystal/glass, based on BA n MA n−1 Pb n I 3n+1 (BA + : butylammonium, C 4 H 9 NH 3 + ; n = 1, 2, 3, 4 and ∞) single crystals [36], as illustrated in Figure 8a. With a thinner quantum well thickness, significant reductions in J d , τ r , and τ f were observed. However, on the contrary, the photocurrent, R, and D* experienced a negative effect (Figure 8b,c). For instance, when n = 1, that is 2D BA 2 PbI 4 , the dark current was measured as 6 × 10 −13 A at 0.8 V, whilst under 200 µW/cm 2 at a 1 V bias, the on/off ratio (current under light to dark current) was 10 4 , D* was 1.6 × 10 13 Jones, τ r was 1.7 µs, and τ f was 3.9 µs. For pure 2D materials, the controlled evaporation method was used to grow large-area (>200 mm 2 ) 2D (PEA) 2 PbBr 4 single crystals (PEA + : phenethylammonium, C 8 H 9 NH 3 + ) [84]. Figure 8d shows the photo of the large 2D single crystal. The metal/crystal/metal device had an extremely low J d of 10 −13 A, large ON/OFF current ratio of 10 5 , D* of 10 13 Jones, and fast response speed of 0.4 ms. Figure 8e,f demonstrates the dark current noise at various frequencies and light intensity-dependent R and D* data of the device fabricated with their 2D single crystals. Moreover, 2D perovskite material exhibited excellent stability over 3D perovskite. The single crystal in this work showed no degradation for up to four months under 45% of relative humidity. The comparison of 2D single-crystal and 3D single-crystal photodetectors reflects the effect of the quantum well structure. The insulating organic layers constrain the carriers in the inorganic layers. The carrier diffusion is greatly suppressed in both in-plain [85] and out-of-plain directions [86], leading to a low dark current, but also a low photocurrent. The long alkyl chains bring in additional resistances, consequently, low photoconduction and device performance. Still, 2D single crystals are highly promising for its high formation energy of defects and the suppression of ion migration. Chances lie in the effective use of the structure's advantages. More fundamental study is desired to pave the way for 2D single crystal applications.
Energies 2020, 13, x FOR PEER REVIEW 15 of 27 μs, and τf was 3.9 μs. For pure 2D materials, the controlled evaporation method was used to grow large-area (>200 mm 2 ) 2D (PEA)2PbBr4 single crystals (PEA + : phenethylammonium, C8H9NH3 + ) [84]. Figure 8d shows the photo of the large 2D single crystal. The metal/crystal/metal device had an extremely low Jd of 10 −13 A, large ON/OFF current ratio of 10 5 , D* of 10 13 Jones, and fast response speed of 0.4 ms. Figure 8e,f demonstrates the dark current noise at various frequencies and light intensitydependent R and D* data of the device fabricated with their 2D single crystals. Moreover, 2D perovskite material exhibited excellent stability over 3D perovskite. The single crystal in this work showed no degradation for up to four months under 45% of relative humidity. The comparison of 2D single-crystal and 3D single-crystal photodetectors reflects the effect of the quantum well structure. The insulating organic layers constrain the carriers in the inorganic layers. The carrier diffusion is greatly suppressed in both in-plain [85] and out-of-plain directions [86], leading to a low dark current, but also a low photocurrent. The long alkyl chains bring in additional resistances, consequently, low photoconduction and device performance. Still, 2D single crystals are highly promising for its high formation energy of defects and the suppression of ion migration. Chances lie in the effective use of the structure's advantages. More fundamental study is desired to pave the way for 2D single crystal applications.

Perovskite Single Crystals for X-Ray Detectors
X-ray detectors absorb high-energy X-ray photons and convert them into charges. Briefly, the working mechanism involves two process. One is the photoelectric effect process, where multiple carriers are generated by one X-ray photon due to its high energy. The other process is the Compton scattering, where the incident photon passes energy to the electrons by scattering in the specific angle.

Perovskite Single Crystals for X-ray Detectors
X-ray detectors absorb high-energy X-ray photons and convert them into charges. Briefly, the working mechanism involves two process. One is the photoelectric effect process, where multiple carriers are generated by one X-ray photon due to its high energy. The other process is the Compton Energies 2020, 13, 4250 16 of 27 scattering, where the incident photon passes energy to the electrons by scattering in the specific angle. The carriers are collected by electrodes, producing a signal current for further analysis. Conventional Si or Ge semiconductor-based or scintillator-based (such as NaI) X-ray detectors have the disadvantages of low energy resolution, high cost, and narrow operating temperature range. The newly developed materials such as CdZnTe, HgI, and TlBr still cannot meet the requirements of both low price and high detection efficiency and energy resolution, while perovskite single crystals provide opportunities for high sensitivity, high resolution radiation detectors.
The key operation factors for X-ray detectors are the X-ray attenuation coefficient, µτ product (where µ is the carrier mobility and τ is the carrier lifetime), sensitivity, detection limit, EQE, and responsivity R. Attenuation coefficient is the fraction of the intensity of the incident beam that is scattered and absorbed by per unit distance of the material. The strong penetration capability of X-ray requires a thicker semiconductor for charge generation. High attenuation coefficient benefits sufficient photon absorption with a small thickness, so the carriers will be generated across the semiconductor and be easily collected. The attenuated photons will be exported as the signal current [87]. At the same time, a lower dose of X-ray is required for detection using high-attenuation materials, ensuring a safer operating environment for technicians. The attenuation coefficient is proportional to Z 4 /E 3 , where Z is the atomic number of the material and E is the energy of the X-ray photon. Figure 9a illustrates the thickness-dependent attenuation efficiency of different materials [88]. From the figure, the 2 mm-thick MAPbBr 3 crystal is enough to attenuate almost 100% of the X-ray due to the heavy Pb (Z of 82). The 2D perovskite material (NH 4 ) 2 Bi 2 I 9 exhibits higher attenuation with heavy Bi (Z = 83) and I (Z = 53). The µτ product is the average diffusion and drift distance under per unit of the electric field, it also means that under a given electric field, the charge collection efficiency will be higher, which can be calculated from the Hecht equation where I is the photocurrent; I 0 is the saturated photocurrent; L is the thickness of the material thickness; V is the bias voltage; and s is the surface recombination velocity. As mentioned, the perovskite single crystal has excellent carrier dynamics of large carrier mobility µ and long carrier lifetime τ as a semiconductor, enabling sufficient charge collection and a larger µτ product. As X-rays are high energy radiation, strict regulations are applied to the effective dose and accelerating potential, especially for medical use like computed tomography (CT). The X-ray beam aims at the human body and is attenuated to different degrees. The penetrated photons are detected and reveal localised information. As the radiation exposure is of high risk of developing cancer, the dose for each CT scan should be as low as possible. The detection limit explains the minimum dose rate for detection, meanwhile, sensitivity decides the resolution of the resultant image. The two work together to realize a high-quality image. Wei and coworkers first reported a highly sensitive X-ray detector made of MAPbBr 3 single crystals [17]. They passivated the crystal surface by UV-O 3 treatment for 20 min to oxidize the surface defects by hydroxyl bonds between the hydrogen and lead atoms. The passivated perovskite showed a longer radiative recombination lifetime, reduced trap density, and high µτ product of 1.2 × 10 −2 cm 2 V −1 . The X-ray device based on a 2 mm-thick MAPbBr 3 single crystal had a sensitivity of 80 µC Gy air −1 cm −2 and a detection limit of 0.5 µGy air s −1 .
Later in 2017, they overcame the limitations of device noise and charge collection by alloying p-type doped MAPbBr 3 and n-type doped MAPbCl 3 into MAPbBr 2.94 Cl 0.06 [89]. The resultant X-ray detector with the structure of Cr/MAPbBr 3-x Cl x /C60/bathocuproine (BCP)/Cr had a high sensitivity of 8.4 × 10 4 µC Gy air −1 cm −2 , which is about 4000-fold higher than that of commercial α-Se X-ray detectors, with a detection limit of 7.6 nGy air s −1 . The dose rate-dependent current density is shown in Figure 9d. Zhuang et al. reported an innovative 2D layered perovskite single crystal, (NH 4 ) 3 Bi 2 I 9 , with a high µτ product of 1.1 × 10 −2 cm 2 V −1 [88]. Due to the suppressed carrier diffusion, 2D perovskite is always inferior to 3D for the µτ product, where it is interesting for (NH 4 ) 3 Bi 2 I 9 to have such high mobility. As they explained, the absence of the Bi 2 I 9 3− cluster dimer in the (NH 4 ) 3 Bi 2 I 9 structure is beneficial to delocalize the electron band, implying potentially better carrier mobility [90]. Unsurprisingly, the X-ray detector exhibited a sensitivity of 0.8 × 10 4 µC Gy air −1 cm −2 , a detection limit of 210 nGy air s −1 much lower than the upper limit for medical diagnosis (5.5 µGy air s −1 ). ensuring a safer operating environment for technicians. The attenuation coefficient is proportional to Z 4 /E 3 , where Z is the atomic number of the material and E is the energy of the X-ray photon. Figure  9a illustrates the thickness-dependent attenuation efficiency of different materials [88]. From the figure, the 2 mm-thick MAPbBr3 crystal is enough to attenuate almost 100% of the X-ray due to the heavy Pb (Z of 82). The 2D perovskite material (NH4)2Bi2I9 exhibits higher attenuation with heavy Bi (Z = 83) and I (Z = 53). The μτ product is the average diffusion and drift distance under per unit of the electric field, it also means that under a given electric field, the charge collection efficiency will be higher, which can be calculated from the Hecht equation where I is the photocurrent; I0 is the saturated photocurrent; L is the thickness of the material thickness; V is the bias voltage; and s is the surface recombination velocity. As mentioned, the perovskite single crystal has excellent carrier dynamics of large carrier mobility μ and long carrier lifetime τ as a semiconductor, enabling sufficient charge collection and a larger μτ product. Reproduced with permission from [89]. Copyright 2017, Springer Nature.

Strategical Approaches for Advancing Perovskite Single Crystal-Based Applications and Recommendations
There is no doubt that perovskite single crystals featuring superior optical properties are promising for photovoltaics. However, with regard to device performance, the single crystal drops behind the polycrystalline thin film counterpart, even though it holds advanced crystallinity. Herein, several innovative approaches and optimisation strategies are summarised, followed by the existing challenges.

Synthesis Process
Defects are interruptions of regular patterns in crystals due to the misplacement of atoms and lattice mismatching. All defects create electron transition levels in the forbidden region. Deep-level traps are located near the centre of the forbidden gap, which can work as the recombination centres that trap carriers, resulting in non-radiative recombination. Non-radiative recombination is fatal for the performance of photovoltaic applications as the trapped carriers are lost, cannot reach and be collected by electrodes, and generate an external current. High-quality single crystals exhibit a several orders of magnitudes lower (10 9 -10 11 cm −3 ) defect density than that of thin films (10 16 -10 18 cm −3 ), which is dominated by the synthesis process. However, the conventional crystallisation methods of AVC, STL, and ITC are adapted from methods for other materials, so an optimisation of the process is called for.
A stable environment is critical for crystallisation. The factors include temperature, vibration, humidity, etc. The supersaturation state, a metastable state of the solution, would collapse due to sudden disturbance, resulting in massive nucleation and lattice distortion. The low-temperature-gradient crystallisation (LTGC) method aims at eliminating the negative influence of the quick temperature change in the conventional ITC method [91]. When heating up the solution to induce supersaturation, the heating rate was as low as 2 • C per day. A 44 × 49 × 17 mm large MAPbBr 3 single crystal was harvested after 18 days, which displayed a carrier mobility of 81 ± 5 cm 2 V −1 s −1 , a carrier lifetime of 899 ± 127 ns, and a trap density of 6.2 ± 2.7 × 10 9 cm −3 . Its application of a photodetector had a detectivity of 6 × 10 13 Jones and response speed of 40 µs. The large area also enabled integrated projection imaging, consisting of a sensor array of 729 pixels (Figure 10a-c). Though the low heating rate minimised the massive nucleation, the thermal gradient still generated convective currents that would disturb the ordered crystal growth and induce defects. Crystallisation at room temperature is developed as a solution to the heat-induced structure distortion. One of the methods is room-temperature liquid diffused separation induced crystallisation, as reported by Yao et al. [92]. A certain amount of silicone oil was added in the precursor as a separation medium. With the diffusion of the solvent into silicone oil, the concentration of the precursor gradually decreased and reached supersaturation for crystallisation. The process is illustrated in Figure 10d. The trap density of as-grown MAPbBr 3 single crystal was lower (4.4 × 10 9 cm −3 ) than the trap density of crystals grown at 90 • C (2.2 × 10 10 cm −3 ). However, it took several days to obtain a 4-mm sized MAPbBr 3 crystal compared with several hours by the conventional high temperature ITC method. Basically, synthesis methods are developing toward a low-temperature and low-rate. It should be considered whether the enhancement on quality is worth sacrificing the growth efficiency.
Crystallisation of one crystal is usually repeated several times in fresh precursor to obtain the desired size. It inevitably causes defects and lattice mismatching when transferring into a new solution environment. The seed dissolution-regrowth (SDR) method overcomes the structural inconsistence between the nucleus and the surface of the seed crystal by keeping the precursor at a relatively low temperature after seeding and prior to heating to the target growth temperature [81]. This allows for the existing impurities on the seed surface to dissolve back and improve the structural matching. SEM images confirmed the dense and uniform structure of the SDR-crystals compared with the loose inner structure of the conventional-ITC-grown crystals, as shown in Figure 10e,f. Another strategy overcomes the mismatching between the nuclei and seed surface by removing low quality seeds. The nucleation-controlled growth method refines the precursor solution by the pre-growth of seeds to reduce nucleation sites [93]. The precursor is heated at high temperature for massive nucleation, which is then filtered and used for crystal growth with high-quality seeds. This refining step ensures the independent growth of each nuclei and removes impurities that form irregular seeds. The as-grown Cs 3 Bi 2 I 9 crystal was made into an X-ray detector that exhibited a high sensitivity of 1652.3 µC Gy air −1 cm −2 and very low detection limit of 130 nGy air s −1 .

Surface Modifications
For single crystals, the surface is critical. Due to the absence of grain boundaries in the bulk, the surfaces have a much higher concentration of defects than the bulk, which will give rise to severe recombination. Moreover, the surface recombination velocity of single crystals (2.8 × 10 3 cm s −1 ) was reported to be nearly six times that of polycrystalline thin films (0.45 × 10 3 cm s −1 ) [53]. X-ray photoelectron spectroscopy (XPS) results indicted a Pb-rich surface of single crystals, while polycrystalline thin films had a C-and N-rich surface. This is possibly due to the escape of MAI from the crystal lattice, resulted from the high crystallisation temperature [26] and partial dissolution by the residual solution on the surface [4]. Spin-coating MAI on the crystal surface for defect passivation was confirmed to be effective in enhancing the device efficiency [8]. Preserving and replenishing MAI on the surface are likely to complete surface structure and passivate vacancy defects. However, the understanding of the crystal surface is still lacking. For most of the reported trap density, the quantitative results only reflect the average trap density of the whole crystal. The low density of the interior of a single crystal drags down the overall level; the defective surface is easily overlooked. In addition to the lack of quantitative analysis, surface characterisations such as surface element distribution and surface recombination velocity are not well presented. Systematic study of the passivation effect is highly desired when designing new surface treatment strategies. For polycrystalline thin films, passivation of deep-level defects is realised through coordinate bonding, ionic bonding, and coordination of large band-gap material [94]. For example, depositing a 2D perovskite capping layer on top of the 3D perovskite thin film successfully improved VOC, FF, PCE, and the stability of 3D perovskite thin film solar cells [12,95]. Single crystals can adopt the ideas from thin films and realize overtaking. One problem is that the conventional method of spin-coating the

Surface Modifications
For single crystals, the surface is critical. Due to the absence of grain boundaries in the bulk, the surfaces have a much higher concentration of defects than the bulk, which will give rise to severe recombination. Moreover, the surface recombination velocity of single crystals (2.8 × 10 3 cm s −1 ) was reported to be nearly six times that of polycrystalline thin films (0.45 × 10 3 cm s −1 ) [53]. X-ray photoelectron spectroscopy (XPS) results indicted a Pb-rich surface of single crystals, while polycrystalline thin films had a C-and N-rich surface. This is possibly due to the escape of MAI from the crystal lattice, resulted from the high crystallisation temperature [26] and partial dissolution by the residual solution on the surface [4]. Spin-coating MAI on the crystal surface for defect passivation was confirmed to be effective in enhancing the device efficiency [8]. Preserving and replenishing MAI on the surface are likely to complete surface structure and passivate vacancy defects. However, the understanding of the crystal surface is still lacking. For most of the reported trap density, the quantitative results only reflect the average trap density of the whole crystal. The low density of the interior of a single crystal drags down the overall level; the defective surface is easily overlooked. In addition to the lack of quantitative analysis, surface characterisations such as surface element distribution and surface recombination velocity are not well presented. Systematic study of the passivation effect is highly desired when designing new surface treatment strategies. For polycrystalline thin films, passivation of deep-level defects is realised through coordinate bonding, ionic bonding, and coordination of large band-gap material [94]. For example, depositing a 2D perovskite capping layer on top of the 3D perovskite thin film successfully improved V OC , FF, PCE, and the stability of 3D perovskite thin film solar cells [12,95]. Single crystals can adopt the ideas from thin films and realize overtaking. One problem is that the conventional method of spin-coating the passivation layer may lead to dissolution of the crystal surface, consequently inducing more defects. Caution should be paid when choosing the solvent.
Degradation is one of the serious weaknesses of perovskite. Single crystals are much more stable than polycrystalline thin films. Even so, single crystals experience fast decomposition and degradation of the surface. After a long period of exposure in oxygen and moisture, the crystal surfaces of MAPbBr 3 are prone to form a hydrate and polycrystalline surface [96], as shown in Figure 11a-c. Aged surfaces showed differences in band gap, PL position, light absorbance, and carrier lifetime with a pristine fresh surface, which were similar to those of polycrystalline thin films. This study lays stress that the preservation of the single-crystalline surface from degradation is as vital as the treatment afterward.
Energies 2020, 13, x FOR PEER REVIEW 20 of 27 passivation layer may lead to dissolution of the crystal surface, consequently inducing more defects. Caution should be paid when choosing the solvent. Degradation is one of the serious weaknesses of perovskite. Single crystals are much more stable than polycrystalline thin films. Even so, single crystals experience fast decomposition and degradation of the surface. After a long period of exposure in oxygen and moisture, the crystal surfaces of MAPbBr3 are prone to form a hydrate and polycrystalline surface [96], as shown in Figure  11a-c. Aged surfaces showed differences in band gap, PL position, light absorbance, and carrier lifetime with a pristine fresh surface, which were similar to those of polycrystalline thin films. This study lays stress that the preservation of the single-crystalline surface from degradation is as vital as the treatment afterward.

Interface Engineering
Layer-structure optoelectronic devices require intimate contact between each layer, in order to confirm efficient carrier transport and reduce ohmic loss as well as facilitating fabrication. Attaching freestanding perovskite single crystals on functional substrates is challenging due to the weak interactions of hydrogen bonds and van der Waals forces between them. Commonly, the spaceconfined solution-process method is viable for the direct growth of crystals on substrates, but Newton's rings and voids exist between the thin crystal and the substrate, even for the champion device [26,78]. Phase transition is likely to be the origin. Huang's group seeded perovskite on modified Si wafer, which was treated by brominated (3-aminopropyl) triethoxysilane (APTES) [97]. The interlayer with functional groups strengthens the interaction. The hydrolysis of Si-O-C2H5 groups form strong covalent Si-O-Si bonds with the -OH on the Si, and the [-Si(CH2)3NH3] + binds to the [PbBr3] − octahedra of MAPbBr3 perovskite, as illustrated in Figure 12a. The interaction overcame a pulling force of 10 g. Their X-ray detection device with the Au/BCP/C60/MAPbBr3/Si structure had a sensitivity of 2.1 × 10 4 μC Gyair −1 cm −2 under 8 keV X-ray radiation. Still, the interlayer induced extra defects at the interfaces. Recently, without the interlay, MAPbBr3 was directly grown on the Si wafer with an improved interface, the interaction of which overcame a pulling force of 50 g [98]. Rather than grown by the ITC method, AVC was chosen for better control of the crystallisation rate. Si wafer was put in the precursor as demonstrated in Figure 12b. The similar lattice constants of Si and MAPbBr3 are beneficial for epitaxial growth. The resultant Si/perovskite/Au photodetector had a broad detection range from 405 nm to 1064 nm, a detectivity of 5.9 × 10 10 Jones, and ultrafast response time of τr 520 ns, ascribing to intimate contact. Adding the interlayer and finding suitable substrates with similar lattice constants are two directions to optimize the contact between single crystals and conductive substrates, which should work together with thin film fabrication. However, one of the challenges is how to attain good contact while maintaining sufficient ion diffusion for singlecrystalline thin film growth in the narrow gap between two substrates.

Interface Engineering
Layer-structure optoelectronic devices require intimate contact between each layer, in order to confirm efficient carrier transport and reduce ohmic loss as well as facilitating fabrication. Attaching freestanding perovskite single crystals on functional substrates is challenging due to the weak interactions of hydrogen bonds and van der Waals forces between them. Commonly, the space-confined solution-process method is viable for the direct growth of crystals on substrates, but Newton's rings and voids exist between the thin crystal and the substrate, even for the champion device [26,78]. Phase transition is likely to be the origin. Huang's group seeded perovskite on modified Si wafer, which was treated by brominated (3-aminopropyl) triethoxysilane (APTES) [97]. The interlayer with functional groups strengthens the interaction. The hydrolysis of Si-O-C 2 H 5 groups form strong covalent Si-O-Si bonds with the -OH on the Si, and the [-Si(CH 2 ) 3 NH 3 ] + binds to the [PbBr 3 ] − octahedra of MAPbBr 3 perovskite, as illustrated in Figure 12a. The interaction overcame a pulling force of 10 g. Their X-ray detection device with the Au/BCP/C 60 /MAPbBr 3 /Si structure had a sensitivity of 2.1 × 10 4 µC Gy air −1 cm −2 under 8 keV X-ray radiation. Still, the interlayer induced extra defects at the interfaces. Recently, without the interlay, MAPbBr 3 was directly grown on the Si wafer with an improved interface, the interaction of which overcame a pulling force of 50 g [98]. Rather than grown by the ITC method, AVC was chosen for better control of the crystallisation rate. Si wafer was put in the precursor as demonstrated in Figure 12b. The similar lattice constants of Si and MAPbBr 3 are beneficial for epitaxial growth. The resultant Si/perovskite/Au photodetector had a broad detection range from 405 nm to 1064 nm, a detectivity of 5.9 × 10 10 Jones, and ultrafast response time of τ r 520 ns, ascribing to intimate contact. Adding the interlayer and finding suitable substrates with similar lattice constants are two directions to optimize the contact between single crystals and conductive substrates, which should work together with thin film fabrication. However, one of the challenges is how to attain good contact while maintaining sufficient ion diffusion for single-crystalline thin film growth in the narrow gap between two substrates. Energies 2020, 13, x FOR PEER REVIEW 21 of 27

Regulation of Dimensions
Practical applications of single crystals desire a large area of more than several tens of square millimetres and thickness below tens of micrometres. How to obtain the desired dimensions, while still keeping high crystallinity is one of the biggest challenges for single crystals. For state-of-art single-crystal solar cells, the thickness of the perovskite layer is hardly below 10 μm. It is speculated that inefficient ion diffusion into the narrow space between substrates during the crystallisation would be the main reason for the formation of the cracks and the low crystallinity. Though theoretical calculation revealed high PCE can be obtained when the crystal thickness is around 200 μm [8], thin crystals from space-confined crystallisation are not comparable with freestanding crystals with regard to optoelectrical properties, especially for carrier diffusion length. The key point is to balance the growth rate and nucleation rate. The former determines the growth efficiency. The later should be minimised to ensure fewer nuclei sites and avoid lattice distortion caused by the combination of other nuclei. On the other hand, high-quality thin crystals from the top-down method have damaged crystal surfaces, which triggers new challenges of surface treatment and substrate incompatibility. Systematic surface characterisation gives support to designing rational slicing strategies and surface modifications.

Summary
In summary, perovskite single crystals stand out as one of the most promising semiconductor materials to be applied in optoelectronic applications. Various synthesis methods have been developed, aiming at harvesting high-quality and large-size single crystals. The as-obtained single crystals showed excellent performance in the fields of photodetectors and X-ray detectors, even better than commercialised semiconductor counterparts such as α-Se. As required by the device fabrication,

Regulation of Dimensions
Practical applications of single crystals desire a large area of more than several tens of square millimetres and thickness below tens of micrometres. How to obtain the desired dimensions, while still keeping high crystallinity is one of the biggest challenges for single crystals. For state-of-art single-crystal solar cells, the thickness of the perovskite layer is hardly below 10 µm. It is speculated that inefficient ion diffusion into the narrow space between substrates during the crystallisation would be the main reason for the formation of the cracks and the low crystallinity. Though theoretical calculation revealed high PCE can be obtained when the crystal thickness is around 200 µm [8], thin crystals from space-confined crystallisation are not comparable with freestanding crystals with regard to optoelectrical properties, especially for carrier diffusion length. The key point is to balance the growth rate and nucleation rate. The former determines the growth efficiency. The later should be minimised to ensure fewer nuclei sites and avoid lattice distortion caused by the combination of other nuclei. On the other hand, high-quality thin crystals from the top-down method have damaged crystal surfaces, which triggers new challenges of surface treatment and substrate incompatibility. Systematic surface characterisation gives support to designing rational slicing strategies and surface modifications.

Summary
In summary, perovskite single crystals stand out as one of the most promising semiconductor materials to be applied in optoelectronic applications. Various synthesis methods have been developed, aiming at harvesting high-quality and large-size single crystals. The as-obtained single crystals showed excellent performance in the fields of photodetectors and X-ray detectors, even better than commercialised semiconductor counterparts such as α-Se. As required by the device fabrication, controlling the thickness of single crystals down to at least the µm-scale is one of the prerequisites for high-performance applications, especially for solar cells. Device performance can be further boosted with smaller crystal thickness. Adapted from conventional crystallisation methods, advanced fabrication strategies have successfully realised confinement on the thickness of single crystal thin film from hundreds of nm to tens of µm. The champion single-crystal solar cell has a PCE of 21.93%, but still there is a huge gap between the single-crystal device and polycrystalline perovskite thin film counterpart (25.2%). Major obstacles for the development of perovskite single crystal applications are the surface defects and compatibility with functional layers. Fundamental study and quantitative analysis for the exploration of single crystal surface defect type and properties are lacking. In addition, single crystal thin films experience different surface states with bulk single crystals, arising from the influence of substrates and the slicing process. Therefore, systematic characterisation of surface defects is needed to point out the direction for surface treatment. Effective solutions could be learned from the experience of surface passivation strategies for polycrystalline thin films. On the other hand, the contact between the single crystal and the functional layer is not perfect. The voids could hinder carrier transportation and thus affect the device performance. Adding interlayers is viable to strengthen interactions, but the additional defects at the interfaces should be seriously considered. Efforts need to be focused on modifying the crystallisation process toward low-temperature and steady processing in order to minimise structure disorder. For practical applications, large area and controlled thickness are essential. The study on the crystallisation mechanism and defect engineering should run in parallel. It is expected that perovskite single crystals will soon surpass their polycrystalline counterpart and become an excellent alternative for optoelectronic applications.