Crystal structures of perovskite halide compounds used for solar cells

: The crystal structures of various types of perovskite halide compounds were summarized and described. Atomic arrangements of these perovskite compounds can be investigated by X-ray diffraction and transmission electron microscopy. Based on the structural models of basic perovskite halides, X-ray and electron diffrac-tions were calculated and discussed to compare with the experimental data. Other halides such as elemental substituted or cation ordered double perovskite compounds were also described. In addition to the ordinary 3-dimensional perovskites, low dimensional perovskites with 2-, 1-, or 0-dimensionalities were summarized. The structural stabilities of the perovskite halides could be investigated computing the tolerance and octahedral factors, which can be useful for the guideline of elemental substitution to improve the structures and properties, and several low toxic halides were proposed. For the device conformation, highly crystalline-orientated grains and dendritic structures can be formed and affected the photovoltaic properties. The actual crystal structures of perovskite halides in the thin film configuration were studied by Rietveld analysis optimizing the atomic coordinates and occupancies with low residual factors. These results are useful for structure analysis of perovskite halide crystals, which are expected to be next-generation solar cell materials.


Introduction
One of the most serious problems in natural environment is global warming, which has been caused by generation of carbon dioxides (CO 2 ). Therefore, developments of new *Corresponding Author: Takeo Oku: Department of Materials Science, The University of Shiga Prefecture, 2500 Hassaka, Hikone, Shiga 522-8533, Japan; Email: oku@mat.usp.ac.jp clean and e cient energy resources to suppress conventional fossil fuels such as oil, coal, and natural gas have become the very important issue to achieve Sustainable Development Goals (SDGs) proposed by United Nations. Since nuclear fusion produces high energy density and forms no CO 2 , the various types of nuclear fusion reactors have been investigated and studies [1][2][3][4][5]. On the other hands, solar cells are the most promising energy device, and the merits of solar cells are as follows: 1. Use a resource that is almost in nite and free, 2. Environmentally clean, 3. No noise without moving parts, 4. Unattended operation, 5. Easy maintenance, 6. Long lifetime (~30 years), 7. Multiple use of lands [6]. However, there are several demerits such as high cost, power dependence on sunlight irradiation and small energy density. The largest barrier for spread of the solar cells is the price. Since the price for solar power generation is~4 times more expensive compared with thermal and nuclear power generation, reducing the cost of the present silicon solar cells is mandatory. Various-type new solar cells such as poly-crystalline Si, thin lm Si, CuInSe 2 , dye-sensitized TiO 2 , organic thin lms and perovskites have been developed.
Numerous researches on halogen doping such as bromine (Br) [24,27,82,83] or chlorine (Cl) [84][85][86][87] at the iodine (I) positions of the perovskite halide structures have been reported. Cl-doping lengthens the di usion length, which improves the photoconversion e ciencies [15,[84][85][86][87]. Numerous studies reported that the substitutions with atom or molecule at the MA, Pb, and/or I site of the perovskite halides in uence the device performances and microstructures of the photovoltaic devices.
Device performances are also dependent on the microstructures of thin lm con gurations, and the morphology can be controlled by additives such as poly(methyl methacrylate) [88][89][90], phthalocyanines [91][92][93][94], or polysilanes [95][96][97]. A large contact area at the TiO 2 /perovskite interface can enhance the probability of carrier separation, which improves the short circuit current density. To reduce the grain boundaries [98], homogeneous and smooth interfaces and surfaces of the perovskite layers could improve the ll factors and open circuit voltages [99]. Improvement of hole transport layers [100][101][102][103] and electron transport layers [104][105][106] are also important for the carrier transport in the actual cells. In addition, it is necessary to fabricate larger the area of the cells for the commercial use [107][108][109][110].
The photovoltaic performances of the perovskite solar cells depend on the perovskite halide structures, electron transport layers, hole transport layers, nanoporous scaffold layers, and their interfacial structures. Particularly, atomic structures of the perovskite crystals have an e ect upon energy gaps, conduction band minimum, valence band maximum, and carrier mobility, which should be analyzed in detail. In this review, the atomic structures of various types of perovskite halide crystals such as basic CH 3 NH 3 PbI 3 (MAPbI 3 ), HC(NH 2 ) 2 PbI 3 (FAPbI 3 ), elementsubstituted perovskites, low-dimensional perovskites and double perovskites, which are expected to be usable as photovoltaic device materials, are summarized and described. Because these perovskite materials often have varied nanoscopic structures for the photovoltaic devices, a summary of information on the perovskite halide crystals could be mandatory for the structural analysis and the developments of the new perovskite compounds. The nanoscopic structures of the perovskite crystals for the photovoltaic devices can be analyzed using transmission electron microscopy (TEM) and X-ray di raction (XRD) by investigating various di raction conditions. Although single crystal XRD is suitable for atomic structure determination, actual solar cells have thin lm con gurations and microcrystalline structures, and Rietveld re nements are one of the good analysis methods to determine the crystal structure of the perovskite compounds in the actual solar cell device con gurations. Electron di raction and highresolution transmission electron microscopy are also e ective instruments to analyze nanostructures of the solar cell materials [111][112][113][114] and crystal structures of the perovskite compounds [115][116][117].

X-ray di raction and transmission electron microscopy of perovskite solar cells
To fabricate the perovskite MAPbI 3 and FAPbI 3 , various methods have been developed and reported. Several representative methods to synthesize the MAPbI 3 compound have been studied and described [8,106,[118][119][120][121][122][123].  [7,124]. An energy barrier might appear at the interface between the metal and perovskite semiconductors, and the reduction of the interfacial ohmic resistances is also important [125]. Electric carriers are generated at the perovskite layer by light incidence from the transparent FTO substrate side. The TiO 2 layer collects emitted electrons from the CH 3 NH 3 PbI 3 compound, and the electrons are migrated to the FTO electrode. The holes are collected by the spiro-OMeTAD hole transport layer, and are migrated to Au electrodes. Figure 2(a) is XRD patterns of standard CH 3 NH 3 PbI 3 thin lms on the glass substrate before and after heating [123]. The di raction re ections in Figure 2 are indexed by tetragonal and cubic structures for the as-prepared and heated lms, respectively. Although only di raction T. Oku peaks due to the perovskite halide phase are observed for the as-deposited lm, a wider di raction peak owing to PbI 2 formation by heating is observed, as shown in Figure 2(a). A small amount of PbI 2 sometimes contribute to the improvement of the photovoltaic properties [126][127][128][129][130][131][132][133], which would have roles of electron-blocking and protecting the perovskite phase against the air at the surface of the perovskite layer. Figure 2(b) and Figure 2(c) are enlarged XRD pro les of Figure 2(a). Split di raction re ections of 002+110 and 004+220 for the as-prepared specimen varied to 100 and 200 re ections after heating, which shows a structure transformation from the tetragonal to cubic symmetry. The standard CH 3 NH 3 PbI 3 perovskite crystals provide structurally transition from the tetragonal to cubic structure at~330 K [134][135][136], as described in detail in the later section.
The XRD pro les in Figure 2 indicate the structural transformation of the CH 3 NH 3 PbI 3 compound and the partial desorption of CH 3 NH + 3 to form PbI 2 during annealing. It should be careful that the structural transformation pre-sented here could be di erent from the isolated single crystals, and the nanocrystals of perovskite halides with cubic symmetry might be "frozen" both in and on the mesoporous TiO 2 layers, as indicated in Figure 1(a). A very weak re ection corresponding to 211 of the tetragonal symmetry might appear at the left side of the cubic 111 re ection for the annealed CH 3 NH 3 PbI 3 , as observed in Figure 2(a). To be accurate, it might be better to refer to the cubic phase as a "pseudo-cubic" phase. The pseudo-cubic de ned here is a crystal structure that has nearly cubic symmetry with a/c of~1, and a weak 211 re ection of the tetragonal symmetry appears at~23.5 ∘ by violation of extinction rule of the cubic symmetry.
If amounts of the specimen are very small, it is hard to acquire the enough XRD intensity from the small specimen. Since a small amount of the sample is enough for transmission electron microscopy, the TEM analysis is one of the most powerful method to acquire the 3-dimensional atomic arrangement directly. By taking electron di raction patterns along several crystal directions, fundamental structural information such as lattice constants and crystal systems can be obtained. Many of the perovskite halide compounds have analogous atomic arrangements to the known perovskite compounds, and the atomic arrangement can be evaluated from the database on the known structures. For instance, various new crystal structures of lots of novel superconducting perovskite copper oxides have been identi ed by the TEM observation [117]. The atomic arrangements of the perovskite structures have been roughly determined from the electron di raction patterns, structural images, and elemental analysis by energy dispersive X-ray spectroscopy [115][116][117].
A TEM image of the TiO 2 /CH 3 NH 3 PbI 3 interface that is an orthodox device structure of the perovskite solar cell, is shown in Figures 3(a) [123]. In addition to many TiO 2 particles with sizes of~50 nm, the CH 3 NH 3 PbI 3 grain with dark contrast is observed in this TEM image. . Several Debye-Scherrer rings due to the anatase TiO 2 nanoparticles are observed, as indicated by white arrows. In addition to the Debye-Scherrer rings, di raction re ections due to cubic CH 3 NH 3 PbI 3 crystals are also observed as indicated by blue arrows and a rectangle. Figure 3(c) is a high-resolution structural image of the CH 3 NH 3 PbI 3 recorded parallel to the [001] direction. Dark dots indicating Pb sites are clearly recognized in the image, and iodine sites also show slight contrast between the Pb atoms along the [100] and [010] directions of the CH 3 NH 3 PbI 3 crystal. CH 3 NH 3 ions are not recognized as clear dark dots owing to the small atomic number of C, N, and H.

Estimation of structural stability by tolerance factors
The perovskite structures used for solar cell devices often have a chemical composition of ABX 3 , where A is generally a monovalent cation, B is a divalent cation, and X is a monovalent halogen anion. A basic structural model of ABX 3 perovskite is shown in Figure 4, and the B cation forms BX 6 octahedron. For the CH 3 NH 3 PbI 3 crystal, A + is CH 3 NH + 3 , B 2+ is Pb 2+ , and X − is I − . For actual application for solar cells, the basic CH 3 NH 3 PbI 3 perovskite compounds have two major problems, the toxicity of Pb and the lack of durability. The MAPbI 3 compounds are generally unstable at room temperature in air, and improvement of the stability is one of the most signi cant issue [126,[137][138][139][140]. One approach to stabilize the MAPbI 3 is to introduce several elements to the perovskite halide structures. Regarding to the toxicity of Pb, elemental substitution at the Pb sites in the MAPbI 3 compounds is one of the solutions.
To estimate the structural stability of these perovskite halide materials, an indicator called tolerance factor (t) has been computed and used [141][142][143][144]. This tolerance factor is calculated as follows: where r A , r B , and r X are the ionic radii of the A, B, and X ions, respectively, in the ABX 3 perovskite halide compounds. The ionic radii of elements constituting ABX 3 perovskites are summarized and shown in Figure 4 [8,145,146], where the coordination numbers of A, B, and X ions are 12, 6, and 6, respectively. In addition, the ionic radii of CH 3 NH + 3 (MA + ), HC(NH 2 ) + 2 (FA + ), CH 3 CH 2 NH + 3 (EA + ), and C(NH 2 ) + 3 (GA + ) are 2.17, 2.53, 2.74, and 2.78 Å, respectively [147]. When the t-value is 1, the perovskite compound has a stable crystal structure with cubic symmetry. Another approach to estimate the structural stabilities of the perovskite is to examine the octahedral factor [142,143,148]. The octahedral factor (µ) can be expressed as The t-and µ-factors are experiential guidelines that do not consider the ionic interactions in the perovskite crystal. Thus, stability ranges of the ABX 3 perovskite halides change being a ected by the elemental and ionic properties. Based on the many previous studies on halide perovskites, the perovskite structure could be experientially formed in the range of 0.813 ≤ t ≤ 1.107 and 0.442 ≤ µ ≤ 0.895 [146]. When µ increases from 0.414 to 0.592, 7coordinated octahedra would be more suitable [149], and µ values below 0.592 would be better to stabilize the BX 6 octahedra.  The t-and µ-factors of the ABX 3 perovskite halide compounds using elements and molecules in Figure 4 were calculated and summarized, as shown in Figure 5. The tfactor of MAPbI 3 is calculated to be 0.912, which indicates the MAPbI 3 may be somewhat unstable. One approach to stabilize the perovskite structure is to substitute organic ions or other elements in the MAPbI 3 crystal. The octahedral factor of MAPbI 3 is xed at 0.541, which is within the range of the perovskite formation. The t-and µ-factors of FAPbI 3 are 0.987 and 0.541, respectively, which indicates that the FAPbI 3 crystal would be more stable than MAPbI 3 . The t-and µ-values of the other compounds are summarized and listed in Table 1 and ref. [144]. Possible compositions (0.813 ≤ t ≤ 1.107, 0.442 ≤ µ ≤ 0.541) for the perovskite structures were indicated in bold fonts in Table 1, and candidates of low-toxicity perovskite compounds are indicated by green color.
The t-and µ-factors can be computed by assuming that ions have rigid spheres and that the ionic radii are constant. However, the t-and µ-factors are a simple and helpful guideline to estimate the structural stability of the perovskite halides, and a new tolerance factor was also pro-posed [150]. First-principles calculations based on density functional theory also represent a powerful method to predict the stability and properties of the crystals and doped clusters [151][152][153][154].
4 Crystal structures of CH 3 NH 3 PbI 3 CH 3 NH 3 PbI 3 is the most standard and widely used compounds for perovskite solar cells. Although the crystal structure of the CH 3 NH 3 PbI 3 has been investigated in detail, there are still some vague regions, and several structural models are proposed.
The CH 3 NH 3 PbI 3 crystals have perovskite-type crystal structures and show structural transitions upon heating [155][156][157]. The transition temperatures and crystal systems are listed in Table 2. As the temperature decreases to~330 K, the cubic phase is transformed into the tetragonal phase [158] and then converted to the orthorhombic phase at~160 K [118]. This transition temperature of~330 K is nearly room temperature, which may also cause the structural instability. . .

Reference
Crystal system (structure type) Detailed crystal systems and lattice constants of CH 3 NH 3 PbI 3 are summarized and listed in Table 3. Several structural models as the α-CH 3 NH 3 PbI 3 phase have been reported, as listed in Table 3 and Figure 6. The structural models presented here are drawn with VESTA [162]. For the model in Figure 6(a), the methyl ammonium (MA) Table 3: Reported crystal systems and lattice constants of CH 3 NH 3 PbI 3 . SCND: single crystal neutron di raction, NPD: neutron powder di raction, SCXRD: single crystal X-ray di raction.

Structure type
Crystal system Space group Analysis method . NPD ion (CH 3 NH + 3 ) has polarity and C 3v point group symmetry, which could provide a pseudo-cubic structure [161]. As described in section 2, the pseudo-cubic has nearly cubic symmetry with an a/c ratio of~1. The CH 3 NH + 3 is arranged along the C 2 axis with 12 equivalent orientations in the unit cell. Hydrogen (H) atoms of the CH 3 NH + 3 provide two structural con gurations on the C 2 axis. Accordingly, the degrees of freedom of the MA + ion are 24 [157]. The entropy changes of CH 3 NH 3 PbI 3 were also measured to be 19.0 J K −1 mol −1 (161.4 K) and 9.7 J K −1 mol −1 (330.4 K), and the transition entropies indicates that the phase transitions are due to the order-disorder transition [157]. The methylammonium ions could be disordered with regard to the orientation of the C-N axis itself and around the C-N axis. Coexistence of the cubic and tetragonal phases was also observed over a range of temperature, which may indicate a predicted tricritical phase transition [136].
Along with the arrangement of the CH 3 NH + 3 , the displacement of iodine ion (I − ) perpendicular to the crystal axis is observed, as shown in Figure 6(a). Site occupancies of C, N, and I were determined to be 1/12, 1/12 and 1/4, respectively.
Although some amounts of point defects such as CH 3 NH + 3 and deviations of stoichiometry could exist at the crystal surface even for the single crystal of CH 3 NH 3 PbI 3 , the electronic charge deviation may be compensated by introducing the iodine defects or deviations of the mixed cation valences of Pb 2+ and Pb 4+ , and charge neutral conditions could be maintained electronically. This kind of tolerance for defects and nonstoichiometry would provide a wide processing window for these perovskite halide thin lm crystals with good electronic properties.
For the model in Figure 6(b), the lattice is almost pseudo-cubic, and the C-N arrangement is ordered along the [001] direction [161]. On the other hand, the N atom was assumed to be the same as the C atom for the model in Figure 6(c) [160].
Detailed structure analysis including the hydrogen atom positions of the CH 3 NH 3 PbI 3 was carried out for a single crystal using neutron di raction [159], and the detailed structural model based on the determined atomic positions (Table 4) is shown in Figure 6(d). Local structural models of CH 3 NH + 3 in the MAPbI 3 crystal aligned along three di erent main directions ( [100], [110], and [111]) were determined, as shown in Figure 7. The measured site occupancy ratios of the CH 3 NH + 3 cations for the [110], [100], and [111] directions were 0.670:0.187:0.143 [159], respectively, which indicates that the CH 3 NH + 3 cations reside primarily along the [110] direction of the cubic MAPbI 3 crystal. This result agrees well with the reported calculations of the CH 3 NH + 3 arrangement by density functional theory (DFT) [163]. Atomic displacement parameter (ADP) ellipsoids shown at 50% probability of the MAPbI 3 model in  [159].
At room temperature around 300 K, a tetragonal structure is formed, as shown in Figure 8 and Table 5 [159]. In the tetragonal CH 3 NH 3 PbI 3 crystal, I − positions are almost xed, which results in the lowered crystal symmetry compared with the cubic structure. Occupancies of C, N, and H were set as 1/8 for the MAPbI 3 with a tetragonal structure. The NH + 3 cation is disordered in 4 di erent positions and located around the adjacent I − of the PbI 6 octahedron [159]. Conversely, the CH 3 is located at 8 di erent positions around the body positions of the unit cell. For both tetragonal and cubic MAPbI 3 structures, the central points of the C-N bond are located o -center of the unit cell. This is caused by the hydrogen bond-like interactions between the NH + 3 and the I − ions of the PbI 6 octahedron in the perovskite crystal [159].

Atom
Wycko site

Atom
Wycko site : Local structural models of cubic CH 3 NH 3 PbI 3 . CH 3 NH 3 ions are set along the (a) [100], (b) [110], and (c) [111] directions.  When the temperature falls below 160 K, the tetragonal CH 3 NH 3 PbI 3 structure transforms into the orthorhombic CH 3 NH 3 PbI 3 structure, which is caused by the molecular ordering of the CH 3 NH + 3 , as observed in Figure 9. All hydrogen positions in the MAPbI 3 were determined, as indicated in the gures. Energy band gaps of the CH 3 NH 3 PbI 3 perovskite were also computed and measured [118]. The energy gap widens with lowering temperature from the rst principle calculation, and the energy gaps were measured to be~1.5 eV, which is close to the adequate energy gap value as that of solar cell materials.
Both microstructures and crystal structures of the perovskite halide compounds can be investigated using XRD. The measured XRD results indicate whether the specimen is single phase or mixed phases with other compounds. If the specimen is composed of nanoscale grains, the crystallite size parallel to the substrate can be calculated from the full width at half maximum (FWHM) of the di raction angle. Using the XRD information, analyses of electron di raction patterns and high-resolution TEM structural images will be easier. If the specimen has a known and reported structure, Miller indices and the plane distances (d) Figure 10: Calculated X-ray di raction patterns of CH 3 NH 3 PbI 3 with cubic, tetragonal and orthorhombic structures.
can be estimated from the XRD re ections. If the specimen is a completely unknown material, the d values can be calculated using XRD data, which can facilitate the structural analysis.
Calculated XRD pro les of the cubic, tetragonal, and orthorhombic CH 3 NH 3 PbI 3 are shown in Figure 10, and the Miller indices, di raction angles, d-spacings, and relative intensities of the CH 3 NH 3 PbI 3 with cubic and tetragonal structures are summarized and listed in Tables 6 and 7, respectively. Asterisks in the tetragonal phase indicate the 211 and 213 di raction re ections, which are inconsistent with cubic symmetry and helpful in distinguishing between the cubic and tetragonal symmetry of the CH 3 NH 3 PbI 3 crystal.
Calculated XRD patterns of tetragonal CH 3 NH 3 PbI 3 with four FWHM values are shown in Figure 11. As the crystallite size becomes smaller, the FWHM value increases, and the re ection intensities change as shown in Figure 11(a). Figure 11(b) displays enlarged XRD pro les for the tetragonal CH 3 NH 3 PbI 3 . As the FWHM values increase, the 004 and 220 re ections for a tetragonal symmetry appear to be combined into the one 220 peak, which corresponds to the 200 peak of a cubic symmetry. This com-T. Oku Table 6: Calculated X-ray di raction parameters of cubic CH 3 NH 3 PbI 3 . Equivalent indices were combined. For space group
bined peak due to the small crystallite size could mislead the results from the XRD structural analysis, and one should be very careful of that. Computed crystal parameters of the CH 3 NH 3 PbI 3 with cubic, tetragonal, and orthorhombic structures, which were calculated by rst principle DFT calculation, are summarized in Table 8. Although these parameters indicate similar values to the experimental data, listed in Table 3, there seems some structural distortion for the cubic and tetragonal structures after structural optimization, which would be due to the anisotropy of the CH 3 NH + 3 .

Electron di raction of cubic and tetragonal CH 3 NH 3 PbI 3
As described in section 2, the electron di raction patterns of perovskite crystals in nanoscale regions can be obtained, and the di raction re ections should be indexed for the structure analysis. To analyze the crystal structures by electron di raction, several important crystaldirections with low indices should be chosen and calculated. Figure 12 is structural models of cubic CH 3 NH 3 PbI 3 T. Oku Figure 13: Calculated electron di raction patterns of cubic CH 3 NH 3 PbI 3 along (a) [100], (b) [110], (c) [111], and (d) [210]. observed along the [100], [110], [111], and [210] directions. It should be noted that the mean positions of CH 3 NH 3 sites are shown in the projected structural models. The resultant electron di raction patterns of the cubic CH 3 NH 3 PbI 3 computed along these four di erent directions are shown in Figure 13. Clear re ections with 6-fold symmetry are observed along [111], as shown in Figure 13(c). Figure 14 is structural models of the tetragonal  directions, which correspond to [100], [110], [111], and [210], respectively, of the cubic CH 3 NH 3 PbI 3 in Figure 12. For the tetragonal phase, deviations of the iodine site are decreased, and the mean positions of CH 3 NH 3 are shown in the projected model. The resultant electron di raction patterns of the tetragonal CH 3 NH 3 PbI 3 computed along the 4 di erent crystal directions are shown in Figure 15. As indicated by arrows in Figure 15(c), the symmetry of di raction re ections for the tetragonal perovskite is not perfect 6-fold symmetry, and is lowered than that of the cubic perovskite. Several re ections in Figure 15 have dissimilar re ection intensities compared with those in Figure 13, which is due to the reduction of the crystal symmetries of the CH 3 NH 3 PbI 3 crystal.
Di raction re ections of the perovskite crystals are observed in the experimental di raction pattern in Figure 3(b), which is indicated by cubic indices with P. Both computed electron di raction patterns of the cubic CH 3 NH 3 PbI 3 projected along the [210] (Figure 13(d)) and the tetragonal CH 3 NH 3 PbI 3 projected along the [221] direction (Figure 15(d)) agree well with the observed di raction pattern in Figure 3(b), as indicated by the rectangles with blue lines. Intensity ratios of the re ections in the experimental di raction pattern may resemble those of the tetragonal phase in Figure 15(d).
TEM is a very useful tool for structural analysis of nanostructured materials such as perovskite compounds. Since the CH 3 NH 3 PbI 3 and related halide compounds are unstable under the vacuum or at raised temperatures, specimen damage by electron beam bombardment must be avoided. Several TEM analysis studies on the perovskite halide compounds for solar cells have been reported, and the crystal structures and nanostructures were investigated by the structural images and electron di raction patterns [118,165,166].
6 Crystal structures of HC(NH 2 ) 2 PbI 3 In addition to the most standard CH 3 NH 3 PbI 3 perovskite compound, HC(NH 2 ) 2 PbI 3 and mixed MAPbI 3 /FAPbI 3 perovskite compounds are also widely used and studied. The structural models of the HC(NH 2 ) 2 PbI 3 crystals are summarized and shown in Figure 16. High photoconversion e ciencies were reported for α-HC(NH 2 ) 2 PbI 3 with a cubic structure [167,168], which is a stable black phase at room temperature, as shown in Figure 16(a). When the α-HC(NH 2 ) 2 PbI 3 crystal is cooled below~200 K, the α-phase is transformed to β-HC(NH 2 ) 2 PbI 3 with a trigonal structure, as shown in Figure 16(b) and 16(c). On the other hand, the α-HC(NH 2 ) 2 PbI 3 phase is converted to the δ-HC(NH 2 ) 2 PbI 3 phase with a hexagonal structure in the presence of a liquid interface (e.g., during spin-coating) below 360 K [167], as shown in Figure 16(d). This cubic-tohexagonal structural phase transition could be attributed to the Gibbs free energy because of the isotropic rotations of the HC(NH 2 ) + 2 cations. Local arrangements of the trigonal planar HC(NH 2 ) + 2 cations in the unit cell were determined by neutron di raction [167], as shown in Figure 17. The HC(NH 2 ) + 2 cation exists at the central mirror plane of the cube, and the HC(NH 2 ) + 2 is aligned along twelve di erent directions (Figure 17(a)). Then, the C-H bonding is aligned to face-center of the unit cell, as observed in Figure 17(b). On the other hand, hydrogen atoms of the NH 2 group interact with the iodide ions of PbI − 3 [167]. ADP ellipsoids shown at 50% probability of the model in Figure 16(a) are shown in Figure 17(c). Although displacements of iodine ions are observed, the displacements are smaller compared with those of MAPbI 3 observed in Figure 6(e).
Calculated XRD patterns of α-, β-, and δ-HC(NH 2 ) 2 PbI 3 crystals with cubic, trigonal, and hexagonal structures [161] are shown in Figure 18, and computed XRD parameters of the cubic and hexagonal FAPbI 3 are summarized and listed in Tables 9 and 10, respectively. In the cubic α-FAPbI 3 phase, site occupancies of C-H and N-H are 1/6 and 1/12, respectively. For the δ-FAPbI 3 , the occupancies were set at 2/3 for N and 1 for C. The 100 reection position at lower 2θ angles is characteristic of the δ-FAPbI 3 phase [161], and can be applied for distinction between the α-and δ-phases. Several small re ections appear in the di raction pattern for the β-FAPbI 3 , which

Elemental substituted perovskites and double perovskites
In previous sections, two most standard crystal structures of CH 3 NH 3 PbI 3 and HC(NH 2 ) 2 PbI 3 were described.
In addition to these standard MAPbI 3 and FAPbI 3 halide perovskites, elemental substitution is possible for ABX 3 type perovskite crystals as described in section 3, which provide various compositions, structures and electronic properties. Numerous kinds of elemental substituted perovskite halides have been reported, which are summarized and listed in Table 11. Partial elemental substitutions are often introduced for these MAPbI 3 and FAPbI 3 perovskite crystals to control the optoelectronic properties. For example, iodine atoms (X site) can be replaced by Br and Cl Figure 19: Calculated X-ray di raction patterns of CH 3 NH 3 PbBr 3 , CH 3 NH 3 PbCl 3 and CH 3 NH 3 SnCl 3 with cubic structures.  Figure 19, indicating the e ect of halogen substitution. When the Br − ions are substituted by Cl − ions, the di raction peaks of CH 3 NH 3 PbCl 3 are shifted to higher angles compared with those of CH 3 NH 3 PbBr 3 . Furthermore, when Pb 2+ ions are substituted by Sn 2+ ions, the di raction intensities of CH 3 NH 3 SnCl 3 fairly change compared with those of CH 3 NH 3 PbCl 3 . CH 3 NH + 3 ions can also be substituted by Cs + ions, as shown in the structural models of CsSnI 3 and CsPbBr 3 in Figure 20(a) and 20(b), respectively.
Calculated XRD patterns of HC(NH 2 ) 2 SnI 3 , CH 3 NH 3 SnI 3 , and CsSnI 3 are shown in Figure 21, which indicate the A site substitutions in the ABX 3 perovskite. The di raction pattern of MASnI 3 is similar to that of FASnI 3 , whereas the di raction peak intensities of CsSnI 3 are fairly di erent from those of the MASnI 3 and FASnI 3 , despite almost the same di raction angles. Although large crystals of the Cs-based perovskites have not been synthesized and grown easily, nanoparticles can be produced, and quantum dots of the Cs-based perovskite halides have been investigated [180,181].  Table 11: Crystal systems of various perovskite halide compounds.

Compound
Crystal system

Space group
Lattice parameters (Å) and degrees Z Temperature Lattice constants of several perovskite halide compounds with the ABX 3 structure are plotted in Figure 22. Changes in the lattice constants are strongly dependent on the halogen X site substitutions compared with the A or B site substitutions for the ABX 3 structure.
In addition to the ordinary elemental substitution, atomic orderings of the substituted elements have also been achieved and reported, which is called double perovskite or elpasolite. The general formula is A 2 BB'X 6 , and the ionic valence of B/B' is 1 + /3 + or 2 + /2 + . One of the examples of the double perovskite structure is Cs 2 AgBiBr 6 , and the structural models observed along the [100], [110], and [111] crystal directions are shown in Figure 23(a), (b), and (c), respectively. AgBr 6 and BiBr 6 octahedra are alternately ordered in the perovskite crystal, as shown in Figure 23(b) and 23(d).
T. Oku  MA + ions can be substituted at the Cs site, and structural models of MA 2 KBiCl 6 double perovskite structures observed along [001] and [100] are shown in Figure 25(a) and 25(b), respectively, in which hydrogen atoms are omitted. Calculated X-ray di raction patterns of Cs 2 NaBiCl 6 , (CH 3 NH 3 ) 2 KBiCl 6 , and (CH 3 NH 3 ) 2 AgBiBr 6 are shown in Figure 26. If the Cs + ions are substituted by the MA + ions,  the di raction peaks of MA 2 AgBiBr 6 are shifted to lower angles compared with those of Cs 2 NaBiCl 6 , and the di raction intensities fairly change. Since the MA 2 KBiCl 6 has a rhombohedral symmetry, the di raction patterns are completely di erent from other double perovskite halides with cubic symmetry.
Some of these double perovskite elpasolite compounds are expected to apply to Pb-free solar cells [199][200][201], and the energy gaps have been reported [187,199]. Application of the double perovskite elpasolites are also be expected for thermal neutron scintillator materials [202][203][204]. Other types of double perovskite compounds such as vacancy-ordered double perovskites and 2-dimensional double perovskites have also been reported, which will be described as low-dimensional perovskites in the next section.
For the 0-dimensional (0D) perovskite, all BX 6 octahedra are isolated in the perovskite crystal, as shown in   [110], and (c) [111]. perovskites. Despite the isolated octahedral BX 6 units, the close-packed iodide lattice provides electronic dispersion, and Cs 2 SnI 6 and other perovskites were applied to solar cells [237,238]. Pb free solar cells such as FA 4 GeSbCl 12 have been reported [239], in which the double elements were selected to replace Pb. Cs 2 TiIxBr 6−x vacancy-ordered double perovskite compounds were also reported to have stability and bandgaps between 1.0 and 1.8 eV [240].
On the other hand, excess Cs and insu cient Pb in the Cs 4 PbBr 6 crystal yield the 0D structure, as shown in Figure 28. Another type of 0D perovskite halide structure is shown in Figure 29. Because of the ionic valence of antimony ion (Sb 3+ ), the suitable composition of the com-   Lattice parameters (Å) and degrees Z Reference pound is Cs 3 Sb 2 I 9 , which satis es the charge neutral condition. The faces of two SbI 6 octahedra are connected to each other, and the SbI 6 dimers or bioctahedra are isolated in the crystal.  Calculated XRD patterns of Cs 4 PbBr 6 , Rb 2 SnCl 6 , and Cs 3 Sb 2 I 9 , with trigonal, cubic, and hexagonal symmetries, respectively, are shown in Figure 30. For the Rb 2 SnCl 6 compound, Miller indices of the di raction patterns are similar to those of ordinary double perovskite structures (Figure 24) since the crystal system belongs to the same space group of Fm3m. However, the re ection intensities are different from those of common double perovskite, which is due to the vacant B' site for the A 2 BB'X 6 double perovskite structure. Di raction patterns of Cs 4 PbBr 6 and Cs 3 Sb 2 I 9 are fairly di erent from that of Rb 2 SnCl 6 , and a 002 re ection appears at a 2θ of 8.4 ∘ (not shown in Figure 30) for the Cs 3 Sb 2 I 9 crystal.
In addition to the perovskite compounds having a dimer octahedron, 1-dimensional continuously connected octahedra exist in CsTiCl 3 , as shown in Figure 31. Out of the eight faces of one TiCl 6 octahedron, two opposite faces are directly connected to the two neighboring octahedra along the [001] direction, and the connected chain is innitely continuous.  MA 2 CuClxBr 4−x were also synthesized as Pb-free light harvesters [241,242], as shown in Figure 33(b).
XRD patterns of the 2D α-Cs 3 Sb 2 Cl 9 , 1D β-Cs 3 Sb 2 Cl 9 , and 1D CsTiCl 3 perovskite compounds were calculated, as shown in Figure 34. Various re ections are observed, which re ects their unit cells. Although the CsTiCl 3 is called vacancy-ordered double perovskites, the XRD pattern is dissimilar to those of double perovskites in Figure 24, which is due to the lack of B' site atoms.
Other types of 2D layered perovskites were also reported, which is called the Dion-Jacobson (DJ) structure [208]. The lead iodides with DJ perovskite structures have the standard formula of A(MA) n−1 PbnI 3n+1 . C 6 N 2 H 16 PbI 4 , (C 6 N 2 H 16 )(CH 3 NH 3 )Pb 2 I 7 , and (C 6 N 2 H 16 ) (CH 3 NH 3 ) 3 Pb 4 I 13 with the 2D DJ perovskite structures are shown in Figure 35. The organic molecules isolate the PbI 6 octahedra, and the 2D layered structure is formed. XRD patterns for C 6 N 2 H 16 PbI 4 , (C 6 N 2 H 16 )(CH 3 NH 3 )Pb 2 I 7 , and (C 6 N 2 H 16 )(CH 3 NH 3 ) 3 Pb 4 I 13 were calculated as shown in Figure 36, and several di raction re ections are observed at 2θ angles lower than 10 ∘ . This indicates that 2D DJ perovskite compounds have larger lattice constants with long periodicity compared with the standard perovskite halides, as observed in the structural models in Figure 35.  Other 2D perovskites with the Ruddlesden-Popper structure were also reported [209]. These perovskite compounds consist of inorganic perovskite layers inserted with butylammonium cations, and they have the general formula (CH 3 (CH 2 ) 3 NH 3 ) 2 (CH 3 NH 3 ) n−1 PbnI 3n+1 (n = 1, 2, 3, 4, ∞). The perovskite iodides of (CH 3 Figure 37(a), (b), and 37(c), respectively. Comparing the structural models of the 2D DJ perovskite structures in Figure 35, PbI 6 octahedra in the Ruddlesden-Popper 2D structure are observed to have an anti-phase arrangement at the sides of the inserted spacer.

Actual microstructures of highly (100)-oriented thin lms and dendrites
In the previous sections, crystal structures of various perovskite halide compounds were described, which directly T. Oku Figure 37: Structural models of (a) (   in uence the semiconductor and photovoltaic properties.
On the other hand, the morphology of perovskite thin lms also strongly a ects the photovoltaic properties [83,84,243]. Wide interfacial areas between n-type TiO 2 electron transport layers and the perovskite layers can promote charge separation, which contributes to the increase of the short circuit current density. Homogeneous and smooth surface/interface structures of the perovskite layers would improve the ll factors and open circuit voltages [99]. Crystal growth and crystallization of the perovskite compounds during annealing are also important and have been investigated [244][245][246].
E ects of adding ammonium chloride (NH 4 Cl) to perovskite CH 3 NH 3 PbI 3 (Cl) solar cells fabricated by an air blowing method are described here [246]. NH 4 Cl has a role of surfactant, which would facilitate forming homogeneous perovskite surface structures [83,243,247]. In addition, the carrier di usion length in the perovskite halides would be improved by doping Cl [15,85]. The Cl-added perovskite halide compound is designated as CH 3 NH 3 PbI 3 (Cl) here.
For the perovskite layer, a mixture solution containing CH 3 NH 3 I (190.7 mg), PbCl 2 (111.2 mg) and NH 4 Cl (0~5 mg) was arranged [248][249][250][251], and the solution containing CH 3 NH 3 PbI 3 (Cl) was spin-coated on the mesoporous TiO 2 layer. An air-blow method was introduced during the spincoating, and then, the devices were heated at 140 ∘ C to form perovskite halides [246]. When decaphenylcyclopentasilane is used over the perovskite layer, the annealing temperature can be raised to~200 ∘ C, and the devices show excellent stability [97].
Optical microscope (OM) images of the CH 3 NH 3 PbI 3 (Cl) cells are shown in Figure 40 [246]. As shown in Figure 40(a), particle sizes are in the range of 5-10 µm for the perovskite grains without NH 4 Cl. The particle sizes of the perovskite grains were decreased by addition of NH 4 Cl to the perovskite, and network-like microstructures are observed, as shown in Figure 40(b), which would possibly increase the conversion e ciency. A scanning electron microscope (SEM) image is also shown in Figure 40(a), and the inclined crystal surface is observed. Elemental mapping images by energy dispersive spectroscopy indicate that the particles observed in Figure 40 correspond to the CH 3 NH 3 PbI 3 perovskite compound. Atomic compositions were estimated by the energy dispersive spectroscopy analysis [246], which indicates that the Cl would be doped into the CH 3 NH 3 PbI 3 compounds, as listed in Table 14. Figures 41(a) and 41(b) show XRD patterns of the FTO/TiO 2 /CH 3 NH 3 PbI 3 (Cl)/spiro-OMeTAD/Au devices without or with NH 4 Cl, respectively [246]. The di raction re ections are indexed by the cubic perovskite halide. An XRD pattern of a CH 3 NH 3 PbI 3 (Cl) device fabricated without PbCl 2 or air blowing is also shown in Figure 41(c). All di raction intensities due to the perovskite compound are very weaker compared with those of Figure 41(a) and 41(b), and di raction peaks corresponding to TiO 2 and FTO are observed.
As seen in Figure 41, di raction intensities of 100 and 200 re ections were enormously enhanced to more than 100 times by introducing NH 4 Cl and air blow. The di raction intensity ratio I 100 /I 210 were measured and summarized, as listed in Table 14. If the CH 3 NH 3 PbI 3 perovskite grains are randomly oriented, the I 100 /I 210 value should be 2.1, as shown in Table 14. The orientation index I 100 /I 210 is 61 for the cell fabricated using air blow and without NH 4 Cl, which indicates that the perovskite grains are preferentially (100)-aligned against the cell substrate. The orientation index I 100 /I 210 was further enhanced to 3600 by the addition of NH 4 Cl, which is 1700 times higher than that of randomly aligned perovskite grains. The cell fabricated with NH 4 Cl and without PbCl 2 or air blow provided an orientation index I 100 /I 210 of 2.8, which indicates the most of the perovskite grains are randomly aligned in the thin lm con guration. The orientation indices of T. Oku  I 100 /I FTO are also listed in Table 14, and the I 100 /I FTO also increased by using the NH 4 Cl and air blow. Two formation mechanisms were proposed for the highly (100)-aligned perovskite thin lms on the mesoporous TiO 2 . The rst mechanism is air blow-driven crystal growth of the perovskite grains. When the precursor solution crystalizes into the perovskite grains, rapid heating using air blowing promotes oriented-crystallization of the perovskite grains on the mesoporous TiO 2 . The (100) of the cubic perovskite structure has low surface energy, which facilitates the crystal growth of (100)-aligned grains. The highly aligned grains reduce the area of highangle grain boundaries, which induces decrease of the series resistance and increase of the open-circuit voltage. Another formation mechanism is a surfactant e ect of NH 4 Cl, which enhanced the construction of homogeneous crystal-aligned microstructures during heating. Networklike microstructures that connect perovskite grains with nanowire-like crystals are also constructed in the perovskite layer, as observed in the optical microscope image of Figure 40(b). Then, the surface covering ratio and carrier transport e ciency were improved, which resulted in the increase of the ll factor and short-circuit current density. Improvement of the photoconversion e ciencies could be understood by these formation models. Cl substitution at iodine sites also improves the carrier di usion in the perovskite halide compounds. Excess CH 3 NH 3 Cl is vaporized from the initial stoichiometry of 3(CH 3 NH 3 I) + PbCl 2 [248][249][250][251], and a little remained Cl is substituted at the I site of the CH 3 NH 3 PbI 3 structure. The doped-Cl lengthens the exciton di usion length [15,85], which improves the short-circuit current density. As a result, the constructed (100)-aligned perovskite grains improved the photovoltaic properties. The present airblowing method combined with NH 4 Cl addition is an e ective method to form highly crystal-aligned perovskite thin lms in the device con guration. For the formation of the perovskite compounds in thin lm con gurations, grain growth due to di usion limitation by solute elements could be the main factor. Figure 42(a) is an optical transmission microscope image of HC(NH 2 ) 2 PbI 3 on the mesoporous TiO 2 and F-doped SnO 2 substrate, and the perovskite grains with dark contrast are distributed keeping their distances of~10 µm [252]. Figures 42(b), 42(c) and 42(d) are also optical microscope images of HC(NH 2 ) 2 PbI 2.85 Br 0.15 , HC(NH 2 ) 2 PbIBr 2 , and HC(NH 2 ) 2 Pb 0.95 Sb 0.05 I 3 , respectively [48,253]. They are FAPbI 3 doped with Br and Sb at the I and Pb sites, respectively. By adding a small amount of Br and Sb, perovskite crystals with dendritic structures grew densely, and the surface coverage of the perovskite grains on the cell substrate increased. Due to these dendritic structures, short circuit current densities and photo conversion efciencies increased. Gibbs-Thomson coe cients and liquidus line gradients were estimated, and the dendrites would be formed by satisfying neutral stable conditions on the grain growth rate by increasing the kinds of solute elements. Fractal dimensions of the dendrite structures in Figures 42(b)-42(d) were calculated to be~2.8 by using a box-counting method. These dendrite structures would contribute increase of the surface coverage and interfacial area at the interpenetrating pn junction, which provided the higher current densities and conversion e ciencies.
The driving force of grain growth is grain boundary energy, which might be caused by the defects at the grain boundary. Since Pb and Sb could be more stable in the perovskite structure, it is believed that the grain boundary energy would be induced by the di usion of HC(NH 2 ) 2 , I, and Br on the surface of the perovskite grain, as illustrated in Figure 42(e). The grain boundary energy (E b ) with a scalar form has a same dimension as the interfacial tension (σ) with a vector form, and can be calculated from the following equation: where ∆G V , E b , D, and Vm are the Gibbs free energy, grain boundary energy, grain size, and molar volume, respectively. When the CH 3 NH 3 PbI 3 decomposes into PbI 2 and CH 3 NH 3 I, the ∆rG ∘ was calculated to be 10.2 (kJ mol −1 ) [254]. Grain sizes of perovskite crystals observed perpendicular to the substrates are measured to be~5 µm in Figures 40 and 42, and the grain boundary energies were estimated to be~170 J m −2 . On the other hand, crystallite sizes of these thin lms measured parallel to the substrates by XRD were~50 nm, and the grain boundary energies were estimated to be~1.7 J m −2 . Practically, only the surface of the perovskite grains might decompose, and the actual E b would be smaller than that. A transition temperature of single crystal of MAPbI 3 is~330 K as described in section 4, which is nearly room temperature. Therefore, the crystal structures of hightemperature phase with cubic symmetry might be frozen in the thin lm con guration, which could be restricted by grain boundary energy. In the next section, Rietveld structural re nement of perovskite crystals in actual thin lm con gurations will be described. 10 Rietveld re nement of crystal structures for solar cell con guration As described in sections 4 and 6, single-crystal XRD and neutron di raction would be the best methods to reveal the accurate crystal structures of perovskite compounds. Although large single crystals such as 5~10 mm have been obtained for the perovskite structure analysis [159,255], the actual microstructures of the perovskite compounds in the solar cell device con guration must be di erent from those of the single crystals; this is because of the various parameters including formation of microcrystals during rapid annealing, coexistence with TiO 2 layers and hole transport layers and other fabrication conditions. To understand the actual microstructures of the perovskite compounds in the device con guration, the actual cells should be measured and analyzed. The Rietveld analysis method has been often utilized to examine the crystal structures of microcrystalline materials [256]. Nevertheless, this method has rarely been applied for crystal structures in actual perovskite solar cell devices [257]. The Rietveld re nement technique can be applied to investigate the crystal structure of the perovskite halides, and to determine the accurate atomic position and site occupancy of each atom constituting CH 3 NH 3 PbI 3 in the solar cell con guration [258].
Crystal structures of CH 3 NH 3 PbI 3 and CH 3 NH 3 Pb 0.85 Sb 0.15 I 3 perovskite lms for the solar cell conformation were investigated and analyzed by the Rietveld analysis. This method could be also useful for the Pb-de cient perovskite compounds [259]. Using the Rietveld program RIETAN-2000 [260], a computed XRD pattern was re ned to match the measured XRD pattern of the perovskite crystal in the solar cell con guration, as shown in Figure 43 [258]. Extra peaks from PbI 2 , TiO 2 , Au, and F-dope SnO 2 in the measured XRD patterns were excluded for the optimization process, and the charge-neutral conditions were considered and applied for the re nement.
First, the positions of MA and I ions in CH 3 NH 3 PbI 3 were investigated and determined. The reported basic crystal structure [134] was used to calculate the site occupancies for CH 3 NH 3 PbI 3 , and the residual factor (R-factor, Rwp) was determined to be 3.38%. XRD pro les agreed well with the computed data by optimization of the atomic coordinates and site occupancies in the unit cell, as listed in Table 15. The re ned ratio of the composition elements of the perovskite was Pb : MA : I = 1 : 1 : 3. For the Sb-added perovskite crystal, elemental concentrations of MA : Pb : Sb : I were determined to be 0.85 : 0.81 : 0.19 : 3. The reduction of MA occupancy would be due to the compensation e ect by substituting Pb 2+ with Sb 3+ , which compensates the de ciency of the CH 3 NH 3 groups during the formation of a CH 3 NH 3 PbI 3 lm [46].
Conversion e ciencies of the photovoltaic devices were improved by adding a small amount of Sb [46,47], and these values monotonically decreased for the excess Sb concentration (z > 0.03). The improvement of conversion e ciencies would be due to the suppression of PbI 2 formation by the Sb addition, which would improve the short-circuit current density and ll factor by the electron blocking e ect. Addition of Sb would also reduce the lattice constant of CH 3 NH 3 Pb 1−z SbzI 3 because of the smaller cationic radius of Sb 3+ compared to the Pb cation. The reduction of the lattice constant of the perovskite would increase the energy gap, which results in the increase of the open-circuit voltage. On the contrary, the decrease in conversion e ciencies was observed for the devices with high Sb content. From the Rietveld analysis, CH 3 NH 3 vacan-cies were found to be introduced in the CH 3 NH 3 Pb 1−z SbzI 3 , and the MA vacancies could promote the recombination of an electron and a hole. Such Rietveld re nement could be an e ective method to determine the actual crystal structures for actual device con gurations.

Conclusion
Crystal structures of various types of perovskite halide compounds possibly used for solar cells were reviewed and summarized. Structural models, XRD patterns, and electron di raction patterns were calculated and presented to compare these structures, which could be useful for structural analysis of these types of perovskite halides by X-ray di raction and transmission electron mi- croscopy. The stabilities of the perovskite structure could be examined by calculting the t-and µ-factors, and several candidates of low-toxicity perovskite compounds can be proposed from this kind of survey. Crystal structures of the most standard CH 3 NH 3 PbI 3 and HC(NH 2 ) 2 PbI 3 compounds were described in detail, especially on the arrangements of CH 3 NH 3 and HC(NH 2 ) 2 in the crystals. In addition to the standard crystals, various types of elementsubstituted perovskite and double perovskite halides were described, and their XRD patterns were calculated and compared. Cation-or vacancy-ordered double perovskite compounds could be the one of the candidates for Pb-free perovskite solar cells. Low dimensional perovskite compounds with 2-, 1-, or 0-dimensionality and 2-dimensional double perovskites were also summarized and described, which will provide the further diversity of these perovskite halides. The structural transition from tetragonal to cubic structures in the actual CH 3 NH 3 PbI 3 thin lms was described, and the nanocrystals with cubic symmetry might be restricted and frozen both in and on the mesoporous TiO 2 layers. A very weak re ection corresponding to the tetragonal symmetry may appear, and it might be better to refer to the cubic phase as a "pseudo-cubic" phase. The perovskite layer containing dense grains with high (100)orientation could be obtained by NH 4 Cl addition and air blowing method. Dendritic perovskite crystals were also obtained by Br and Sb doping for FAPbI 3 , which would be e ective to control the morphology. Crystal structures of perovskite CH 3 NH 3 Pb 1−x SbxI 3 lms in the actual de-vice con guration were examined using Rietveld analysis. XRD pro les agreed well with the computed data by optimization of the atomic positions and site occupancies in the unit cell. Even for the single crystal of MAPbI 3 , some amounts of defects such as CH 3 NH 3 could exist, and the electronically neutral conditions may be maintained by the iodine defects or mixed cation valences of Pb 2+ and Pb 4+ . This kind of tolerance for defects and nonstoichiometry would provide a wide processing window for these perovskite thin lms. These perovskite halide crystals not only could be used for solar cells, but also could be applied for light-emitting diodes [261], laser diodes [262], catalysts [263], scintillator [264][265][266] and others, and the future developments of the new perovskite halide crystals are expected.