Organic–inorganic hybrid perovskites represented by MAPbX₃ (MA: methylammoniun, X = Br, I) exhibit many excellent semiconducting properties that are beneficial to optoelectronic and photonic applications.^1–3 In particular, the power conversion efficiency of perovskite solar cells (PSCs) has increased from 3.8%⁴ to 22.1%⁵ within seven years. Besides impressive efficiencies, the solution processability of perovskites significantly reduces the costs of large-scale production, compared with conventional semiconductors such as Si and GaAs. A key factor for further enhancing the performance and stability of PSCs is morphology control of the MAPbX₃ thin films. Although a variety of fabrication techniques, including two-step spin-coating,⁶ hot casting,⁷ and intramolecular exchange,⁸ have been developed to achieve high device performances, relatively less is known about how different fabrication conditions affect the morphology and texture of the as-prepared MAPbX₃ films.

Theoretical calculations⁹ suggest that cuboid MAPbI₃ crystallites bearing the rectangular (110) and (001) faces are more advantageous for charge carrier diffusion and collection than other exposed faces. However, solution-grown MAPbI₃ single crystals are found in most reports^10–13 as dodecahedra featuring rhombic (100) and (112) facets, although MAPbBr₃ single crystals are usually cuboid.^12–15 This apparent discrepancy between the preferred and actual morphologies of MAPbI₃ prompted us to find factors that favor the growth of cuboid MAPbI₃ single crystals. We also wanted to identify a unified mechanism to explain why MAPbBr₃ and MAPbI₃ usually exhibit distinct crystal morphologies although the two perovskites are nearly isostructural.

For growing MAPbX₃ single crystals, we employed three methods depending on the nature of the solvent; Table 1 lists the experimental conditions in detail. Slow cooling of saturated solutions of MAPbX₃ in the corresponding aqueous hydrohalic acid¹⁶ afforded dodecahedral crystals for both X = Br and I (Figures 1A and 1D). On the other hand, oversaturation of a 1:1 mixture of MABr and PbBr₂ in N,N-dimethylformamide (DMF) (Figure 1B), regardless of whether induced by a rise in temperature or by vapor diffusion of chloroform (CF) as an antisolvent, consistently yielded cuboid MAPbBr₃ crystals (Figure 1C).

Figure 1. Photographs of MAPbX₃ single crystals of different morphologies (X = Br for left column and I for right column). (A, D) Dodecahedral MAPbX₃ from slowly-cooled aqueous HX. (B, E) Cuboid MAPbBr₃ and dodecahedral MAPbI₃ from hot organic solutions of 1:1 MAX and PbX₂. (C, F) Cuboid MAPbX₃ from antisolvent diffusion. Panels A–F correspond to Entries 1, 2, 3, 4, 5, and 8 of Table 1, respectively. Scale bar: 5 mm; rulings: 1 mm.

Table 1. Growth conditions for MAPbX3 (X = Br, I) single crystals and resulting crystal morphologies

MAPbI₃ from organic solvents, however, exhibited mixed crystal morphologies. In typical processes of inverse temperature crystallization¹² (ITC) for MAPbI₃, dodecahedral or cuboid MAPbI₃ crystals several mm in size appeared from hot γ-butyrolactone (GBL) solutions within 3–5 h (see Supporting Information, Movie 1 and Movie 2). A 1:1 solution mixture of MAI and PbI₂ at 135 °C yielded dodecahedra displaying rhombic facets obvious to the naked eye (Figure 1E). A 2:1 starting solution produced cuboid crystals with rectangular facets at 135 °C but irregular shapes at 120 °C. Antisolvent vapor-assisted crystallization^14,17 (AVC) experiments at 40 °C revealed a similar trend. Thus, a 3:1 solution mixture of MAI and PbI₂ in GBL, or a 2:1:1 mixture of TBAI (TBA: tetrabutylammonium), MAI, and PbI₂, was allowed to slowly absorb CF vapor, and cuboid MAPbI₃ crystals appeared over a period of five days (Figure 1F), but a 1:1 solution mixture of MAI and PbI₂ in GBL gave rise to irregular black crystals along with yellow PbI₂.

The powder X-ray diffraction (XRD) patterns of ground MAPbX₃ crystals (Figure 2, black curves) confirm that the MAPbBr₃ is an ideal cubic perovskite, whereas the crystal structure of MAPbI₃ belongs to the tetragonal I4cm space group, regardless of the growth method and crystal morphology. For MAPbI₃, typical lattice parameters a = 8.877(1) Å and c = 12.672(2) Å with an approximate relationship c/a = 1.428 ≈ \(\sqrt{2} \) suggest that the crystal system deviates only slightly from the cubic symmetry. By letting an X-ray beam diffract off a crystal’s top flat facet, distinct 2θ scans were obtained from the dodecahedral and cuboid MAPbX₃ single crystals. The blue curves in Figure 2 show that the rectangular facets of MAPbX₃ diffract only at ca. 14° and its multiples, which are indexed to k00 in the cubic crystal system and to kk0 (k = 1, 2, 3,…) in the tetragonal system, indicating that the rectangular facet of MAPbBr₃ is the (100)_c surface, whereas that of MAPbI₃ is the (110)_t surface. Hereafter, the subscripts c and t of the Miller indices denote the cubic and tetragonal crystal systems, respectively. Likewise, the rhombic facet of MAPbBr₃ is designated as the (110)_c surface and that of MAPbI₃ as the (100)_t surface.

Figure 2. X-ray diffraction (XRD) patterns of (A) MAPbBr₃ and (B) MAPbI₃. Black curves: Ground MAPbBr₃ crystals exhibit a powder pattern of the cubic Pm\(\bar{3}\)m space group, and MAPbI₃ powder belongs to the tetragonal I4cm space group. Red curves: 2θ scans off the rhombic facet of dodecahedral MAPbX₃ single crystals. Blue curves: 2θ scans off the rectangular facet of cuboid MAPbX₃ single crystals.

Figure 3 depicts atomistic models of dodecahedral and cuboid MAPbI₃ crystallites. The dodecahedral model (Figure 3A) is enclosed by four {100}_t faces that take the shape of truncated rhombus, in addition to eight rhombic {112}_t faces. All these surfaces are nearly equivalent due to the almost cubic crystal symmetry of MAPbI₃ and feature a calculated obtuse angle of ca. 109°, which agrees with the actual shape and angle (107°) of the dodecahedral single crystal in Figure 1E. The cuboid model (Figure 3B) consists of nearly equivalent {110}_t and {001}_t faces that intersect with each other at right angles, also consistent with the cuboid in Figure 1F.

Figure 3. Atomistic model of (A) dodecahedral and (B) cuboid crystallites of MAPbI₃.

MAPbBr₃ is stable in the cubic phase above −37 °C,¹⁸ but MAPbI₃ undergoes a second-order phase transition from the tetragonal to cubic phase at 54 °C,¹⁹ lower than or close to the temperatures for crystal growth in Table 1. Consequently, indexing the natural facets of MAPbI₃ to the cubic system properly reflects the surface structures during crystal growth, and also simplifies our analysis for the growth mechanism.

In the Supporting Information, we have derived the equations for conversion between tetragonal indices h_tk_tl_t and cubic indices h_ck_cl_c: h_t = h_c − k_c, k_t = h_c + k_c, and l_t = 2l_c. Therefore, the rhombic (100)_t and (112)_t planes in the tetragonal phase become (110)_c and (101)_c, which belong to the equivalent family of {110}_c planes in the cubic crystal system, whereas the rectangular planes (110)_t and (002)_t in the tetragonal phase translate to the cubic {100}_c planes. Note that the two plane families {100}_c and {110}_c do not have any member in common.

We propose a mechanism based on halide coordination to interpret the above experimental phenomena, which obey the general trend that bromide, nonaqueous solvents, and higher X⁻/PbX₂ ratios favor the growth of cuboid single crystals with rectangular {100}_c facets.

Pb²⁺ coordinates with halide X⁻ (X = Cl, Br, and I) in both water and nonaqueous solvents, and PbX₃⁻ and PbX₄²⁻ are the two complexes most intensively investigated. Table 2 shows the cumulative formation constants β₃ and β₄ in N,N-dimethylformamide (DMF) are orders of magnitudes higher than those in water. Moreover, PbBr₃⁻ and PbBr₄²⁻ are more stable than their iodo counterparts in DMF. Due to lack of experimental β values in GBL, we assume that PbX₃⁻ and PbX₄²⁻ in GBL should exhibit the same order of relative stability as in DMF, because DMF and GBL are both polar aprotic solvents with very similar dielectric constants (ε = 38.25 and 39.0, respectively²²).

Table 2. Logarithm of cumulative formation constants of PbX3− and PbX42− (X = Br, I) in water and DMF

The stability constants of PbX₃⁻ and PbX₄²⁻ reflect the affinity of X⁻ toward Pb²⁺ in solution and at the interface between crystal and mother liquor, which follows the order Br⁻ → Pb²⁺ in DMF > I⁻ → Pb²⁺ in DMF > Br⁻, I⁻ → Pb²⁺ in H₂O. This relation unifies our experimental results under various conditions, and suggests that an appropriate combination of solvent, halide, and X⁻/PbX₂ ratio that favors coordination of X⁻ to MAPbX₃ surfaces will also favor the growth of rectangular {100}_c surfaces over rhombic {110}_c surfaces. Increasing the I⁻:PbI₂ ratio without adding MA⁺ had the same effect. Quantitative study of interfacial Pb–X coordination under actual growth conditions is challenging both experimentally and computationally, because of the ion–solvent interactions and net charges on the crystal surfaces.

The morphology and natural facets of the as-grown crystals is a result of the competing growth of the {100}_c and {110}_c facets. The number density of X⁻ on the {100}_c surface equals 1/a² and that on the {110}_c surface is \(\sqrt{2} \)/a², where a is the lattice parameter in the cubic phase. Conditions that promote surface coordination of X⁻ are likely to preferentially accelerate the growth of more crowded {110}_c surface over {100}_c surface, and the latter becomes eventually visible on the macroscopic level.

To summarize, we synthesized both dodecahedral and cuboidal single crystals of MAPbX₃ (X = Br, I) using three methods under various conditions. From XRD and geometry measurements of mm-sized crystal facets, we indexed the rhombic and rectangular faces of MAPbX₃ to {110}_c and {100}_c in the cubic crystal system, respectively. Based on the known Pb(II)–X coordination chemistry and our experimental observations that bromide, nonaqueous solvents, and higher X⁻/PbX₂ ratios favor the growth of cuboid MAPbX₃ crystals, we propose an atomistic model involving stronger coordination between Pb²⁺ and X⁻ makes the more crowded {110}_c faces outgrow the {100}_c faces and eventually exposes the latter. The capability to control the crystal morphology of solution-grown MAPbX₃ will help fabricate MAPbX₃ thin films with less mismatched grain boundaries and higher interfacial stability than randomly-shaped polycrystals.