Ion migration mechanism in all-inorganic Ruddlesden–Popper lead halide perovskites by first-principles calculations

Abstract

Ion migration under light illumination or electric field could cause several complex phenomena, such as hysteresis, phase segregation, and interface passivation, in optoelectronic devices based on hybrid organic–inorganic perovskites. The high ionic conductivity of metal halide perovskites can be ascribed to the lower migration barrier of halide anions, which has been demonstrated to be inhibited by the large organic layer of two-dimensional perovskite structures. However, in all-inorganic two-dimensional perovskites, the diffusion mechanism of halide anions has not been comprehensively studied. Herein, we investigate the diffusion mechanism of halide anions in all-inorganic Ruddlesden–Popper (RP) halide perovskites by first-principles calculations. In these all-inorganic perovskites, the inorganic CsI layer can also prevent halide diffusion between the adjacent octahedral slabs via the vacancy-hopping mechanism. However, intercalation provides an additional diffusion channel for halide interstitials, which promote in-plane diffusion in RP perovskites. These results reveal the migration properties of halide vacancies and interstitials in all-inorganic RP perovskites, which would be beneficial for exploring their novel optoelectronic applications.

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1. Introduction

Organic–inorganic hybrid perovskite solar cells have experienced high-speed development in the past decade.^1,2 However, low stability is still an obstacle to their large-scale commercialization.³ The degradation of hybrid perovskites can occur via two mechanisms: one is the hydration and oxidization induced by moisture or oxygen, and the other is the lattice decomposition driven by ion migration.^4,5 The former degradation mechanism has been ascribed to unstable organic components, which can be solved by device encapsulation or replacing organic components with inorganic monovalent cations.⁶ Light-enhanced ion migration is an intrinsic phenomenon and has attracted much attention for halide perovskites. For instance, anomalous current–voltage hysteresis caused by ion migration has been observed in organic–inorganic hybrid and all-inorganic halide perovskite solar cells.⁷ Other investigations claim that ion migration could drive self-passivation in halide perovskites and is thus beneficial for improving stability.^8,9 Moreover, the resistive switching phenomenon of organic–inorganic halide perovskites has been exploited by halide migration, suggesting potential applications in resistive switching random access memory.^10–12

Ion migration has been proved to be mitigated in 2D perovskite structures owing to the unconnected octahedral slabs by incorporating large organic cations, such as butylammonium.¹³ The additional large organic layer improves the stability of 2D halide perovskite by suppressing not only the migration of intrinsic ions but also the penetration of moisture due to large hydrophobic organic cations.¹⁴ However, the quantum confinement effect resulting from the large organic layer enhances the exciton binding energy and the rate of charge recombination. To diminish the quantum confinement effect, conventional small organic cations have been developed to create organic layer in 2D halide perovskites (e.g., MA₂PbI₄), which have been demonstrated to possess reduced exciton binding energy and excellent conversion efficiency.^15,16 Previous investigations reported the relatively low migration barrier of A-site MA cation in 3D MAPbI₃ due to the protonizing effect of organic cations under illumination and electric fields.¹⁷ Inorganic cations are not facile to protonize, leading to unchanged activation energy in the dark and under illumination. Therefore, the optoelectronic properties of all-inorganic layered halide perovskites should be explored.

All-inorganic mixed-halide Ruddlesden–Popper (RP) perovskite Cs₂PbI₂Cl₂ has been synthesized by solid-state method and exhibits markedly ambient and thermal stability.^18–20 Li et al. demonstrated that this compounds shows a direct bandgap of ∼3.04 eV along the in-plane direction and the detection capacity of UV-light or α-particle.¹⁸ Pan et al. investigated the thickness dependence of the optoelectronic properties of RP Cs₂PbI₂Cl₂ by theoretical calculations and indicated that this material would be adequate for luminescent rather than photovoltaic devices.²¹ Xu et al. reported the ultrahigh electron mobility (∼9.39 × 10³ cm² V⁻¹ s⁻¹) for 2D RP Cs₂PbI₂Cl₂, which are higher than those of known halide perovskites.²² Guo et al. found that the photocurrents of all-inorganic 2D RP Cs₂PbI₂Cl₂ can be significantly enhanced over three orders of magnitude when applying 2 GPa, and the lattice compression can also facilitate the dissociation of excitons by reducing the exciton binding energy.²³ Given the good lattice matching degree, Yang et al. employed Cs₂PbI₂Cl₂ nanosheets to passivate the interfaces of CsPbI₂Br perovskite films and TiO₂ films, achieving improved efficiency and stability.²⁴ Moreover, the light-induced photochromism has been observed in 2D RP Cs₂PbI₂Cl₂, which can be used in optical encryption.²⁵ As a new type of all-inorganic perovskite, 2D RP Cs₂PbI₂Cl₂ exhibits promising potential in optoelectronic fields. However, the behavior of ion migration in all-inorganic RP halide perovskites, to the best of our knowledge, is still not available from either experiment or theoretical calculation. Therefore, a comprehensive investigation on ion migration mechanism is significant to the enhancement of long-term stability and exploration of novel optoelectronic applications for metal halide perovskite materials.

Theoretical calculations can provide atomic scale hints for understanding the ion transport properties of perovskite materials. Eames et al. computed the activation energy of various migration of MA, Pb, and I ions in MAPbI₃, revealing that the I ion is the major mobile ion with the lowest migration activation energy along the edge of the PbI₆ octahedron.²⁶ Yang et al. investigated different diffusion mechanisms of interstitialcy migration versus vacancy-mediated migration in MAPbI₃; hence, MA and I ions contribute to the ion diffusion and instability of MAPbI₃.²⁷ In this work, we investigate the ion migration properties of inorganic RP Cs₂PbI₄ and mixed-halide Cs₂PbI₂Cl₂ by first-principles calculations based on density functional theory (DFT). Our results reveal that although the migration of halide anions via vacancy-mediated mechanism is suppressed due to the layered structure, the interstitialcy migration exhibits quite low activation energy in the intercalation, which results in the fast diffusion of halide anions in RP halide perovskites.

2. Computation details

All DFT calculations have been implemented based on the plane-wave approach with the Quantum ESPRESSO package.²⁸ The ultrasoft pseudopotentials with the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional are employed to describe valence configurations.²⁹ The kinetic energy cut-off of 40 Ry and the charge density cut-off of 320 Ry are adopted for wave function expansion. The 6 × 6 × 2 Monkhorst–Pack k-mesh grid is used to integrate the Brillouin zone. The lattice parameters including lattice constants and atomic positions are fully relaxed using the Broyden–Fletcher–Goldfarb–Shanno algorithm with the force convergence threshold of 10⁻³ Ry per Bohr and the energy convergence of 10⁻⁴ Ry. For the simulation of ion migration, the 2 × 2 × 1 supercell of the RP perovskite with 3 × 3 × 2 k-mesh grid is employed. The initial and final structures are first applied to conventional geometry optimization with the force cutoff of 10⁻⁴ Ry per Bohr and then fixed during migration. The climbing image nudged elastic band (CINEB) method is used to obtain the energy profile of migration images.³⁰ The convergence force is set to 0.05 eV Å⁻¹ during minimum energy pathway optimization, and spring force is employed to ensure the finding of the lowest energy path.^31,32

3. Results and discussion

In 3D perovskite ABX₃, B-site cations and X-site anions form a corner-shared octahedron skeleton, and A-site cations occupy the octahedron interstice. The 2D RP halide perovskite exhibits a sandwich structure containing octahedral slabs and spacer cations with the general chemical formula A_n+1B_nX_3n+1, where n is the layer number of octahedral slabs. The reported RP halide perovskite must employ large organic cation to separate perovskite-like slabs. Therefore, all-inorganic RP halide perovskites are rarely reported due to instability resulting from the relatively small ionic radius of inorganic monovalent cations. The mixed-halide RP perovskite is the only reported structure of all-inorganic layered perovskites that could be synthesized by solid-state method. In this structure, small chloride anions occupy the shared octahedral corner (the 4c Wyckoff site) and the large iodide anions take the out-of-plane octahedral corner (the 4e Wyckoff site). For simplification, we employ a single-layer structure (Fig. 1) to investigate the migration properties of halide anions in 2D RP perovskites.

Fig. 1 Schematic diagrams for (a) cubic CsPbI₃, (b) RP Cs₂PbI₄, and (c) mixed-halide RP Cs₂PbI₂Cl₂.

We firstly optimize the lattice parameters of all-inorganic 3D CsPbI₃, 2D RP Cs₂PbX₄ (X = Cl, Br, I), and mixed-halide RP Cs₂PbI₂Cl₂, which are presented in Table S1 (ESI†). The Pb–I bonds are elongated in the c-direction and simultaneously shortened in the ab-plane due to the existence of intercalation. In mixed-halide RP Cs₂PbI₂Cl₂, the lattice constant further decreases to 5.75 Å in the ab-plane due to the smaller ionic radius of Cl, while the lattice constant and Pb–I bond in the c-direction are still close to that of RP Cs₂PbI₄. Given that the halide anion at the 4c site plays a role in connecting two adjacent octahedra, the hybridization of Pb with halide anion at the 4c site would be stronger than that of Pb with halide anion at the 4e site. Fig. 2 shows the calculated partial density of states for 3D CsPbI₃, RP Cs₂PbI₄, and mixed-halide RP Cs₂PbI₂Cl₂. In 3D CsPbI₃, upper valence bands exhibit the antibonding characteristic between Pb 6s and I 5p orbitals, and all iodide anions contribute equally to the ionic interaction of PbI₆ octahedron. In RP perovskites, the energy level of I_4e 5p orbital is higher than that of I_4c 5p orbital. Therefore, the antibonding characteristic of Pb–I_4e would be stronger than that of Pb–I_4c, leading to the weaker covalence bond between Pb and I_4e ions. Moreover, the outer-shell electrons of A-site Cs cations do not contribute to electronic structures near the band edges. Therefore, the bond properties of the octahedron would be significant to the migration of halide anions in RP perovskites.

Fig. 2 Calculated density of states for cubic CsPbI₃, RP Cs₂PbI₄, and mixed-halide RP Cs₂PbI₂Cl₂. The Fermi energy is set to 0.

3D perovskite CsPbI₃, halide anions mainly diffuse along the octahedral cage, and therefore all diffusion routes are isotropic. In RP perovskites, the removal of one halide ion could respectively create two different vacancies, i.e., V₁-type vacancy at the 4c site or V₂-type vacancy at the 4e site, which would show different diffusion features (Fig. 3). Moreover, the 4d Wyckoff site (0, 1/2, 1/4) in the intercalation could accommodate one halide ion to form isolated I₁-type interstitial. During interstitial defect migration, the halide interstitial could temporarily form a dumbbell-like pair with one original halide ion at the 4c or 4e site. The interstitial correlated to the 4c site is respectively I₂-type or I₃-type defect in terms of axial direction, and the interstitial correlated to the 4e site forms I₄-type defect. All defective structures are fully optimized (Fig. S1, ESI†) and employed as the initial or final states of halide migration.

Fig. 3 Different defects and migrations in RP perovskites Cs₂PbX₄ (X = Cl, Br, I).

In 2D RP perovskites, three paths are considered for vacancy-mediated migration: (1) P₁ is the migration of the halide ion from the 4c site to the adjacent V₁ site; (2) P₂ denotes the migration from the 4c site to the adjacent V₂ site; (3) P₃ represents the migration from the 4e site to the adjacent V₂ site. The migration paths are also schematically shown in Fig. 3. For the isolated I₁ interstitial, three migration motions exist: (1) direct migration between two adjacent 4d sites (denoted as P₄) in the intercalation; (2) the correlated interstitialcy migration between two adjacent 4d sites in the intercalation mediated by the original halide ion at the 4e site;^33,34 and (3) correlated migration between two 4d sites separated by the octahedral slab mediated by the original halide ion at the 4c site. The correlated interstitialcy migration denotes that the isolated I₁ interstitial migrates onto the neighboring 4e site and kicks the correlated halide ion onto the equilibrium 4d site. The I₄ interstitial could serve as the intermediate state of the correlated interstitialcy migration; thus, we simply simulate the symmetrical half path (I₁ → I₄) of interstitialcy migration, which is denoted as P₅. The symmetrical half path from the 4d site toward the 4c site is calculated as P₆ migration. In addition, halide interstitials probably diffuse along the edge of octahedron via dumbbell-like motion.³⁵ Thus, we simulated two dumbbell-like migrations between in-plane 4c sites denoted as P₇ and from the 4c to the adjacent 4e site denoted as P₈. Given that two species of halide interstitials are correlated to the 4c site, we also simulate the rotation mechanism P₉ for the transformation between I₂ and I₃ interstitials.³⁶ Halide vacancies can diffuse long-distance through any of these three migration paths but via P₂ and P₃ together for diffusion in the c-direction. Halide interstitials can migrate in parallel to the octahedral slab through any of P₄, P₅, P₇, or P₈. For long-range diffusion in the c-direction, halide interstitials have two transport channels. One is along the P₆ individually, and the other is through the correlated interstitialcy migration P₅ and dumbbell-like migration P₇ sequentially.

The diffusion rate D of a defect within the bulk of a crystal material can be described by the Arrhenius equation: D ∼ exp(−ΔE_a/k_B·T), where k_B and T are the Boltzmann constant and absolute temperature; ΔE_a is the required activation energy for defect migration from one equilibrium site to the neighboring one and can be obtained by comparing the energy of the transition states optimized by the CINEB method. Fig. 4 shows the calculated energy profiles of halide migration in RP Cs₂PbI₄. The P₁ migration in RP perovskites is similar to that of the 3D counterpart, while the energy barrier of P₁ migration in Cs₂PbI₄ is predicted to be higher than that of the 3D analogs, e.g., 0.46 eV of the tetragonal MAPbI₃.³⁷ This finding reveals that the layered structure has a crucial effect on the migration of vacancies in halide perovskites. The P₂ migration shows the lowest energy barrier of 0.33 eV among three migrations of halide vacancies. As the energy of V₁-type defect structure is slightly lower than that of V₂-type vacancy, the inversive direction of P₂ migration has lower barrier of 0.3 eV. The P₃ migration shows a high-energy barrier, suggesting that the inorganic CsI layer can suppress the migration of halide vacancies between octahedral slabs. These results indicate the intense diffusion of halide vacancies in RP Cs₂PbI₄ due to the low barrier of P₂ migration, though this diffusion is evidently anisotropic. For halide interstitials, the migration barrier of the direct P₄ is twice higher than that of the correlated P₅. As mentioned above, the simulated P₅ motion is the symmetrical half of correlated interstitialcy migration. The energy barrier of P₅ is predicted to be equal to the difference in the energy of I₁ and I₄ interstitials. Therefore, the remaining half of the correlated interstitialcy migration would be a spontaneous motion. The I₄ interstitial could migrate from the 4e site to the adjacent 4c site through the P₈ direction. As the P₈ migration has an energy barrier of 0.18 eV, the I₄ interstitial probability migrates via the correlated interstitialcy motion rather than the dumbbell-like P₈ migration. In addition to the combination of P₅ and P₈, P₆ is another transport channel for halide interstitials to realize long-range diffusion in the c-direction. The energy barrier of P₆ migration is predicted to be slightly higher than the sum of P₅ and P₈. Another in-plane mechanism of halide interstitials is P₇ migration. The energy of I₂ interstitial is higher than that of other interstitials, and I₃ is difficult to become the I₂ site via P₉ rotation motion. Thus, the P₇ migration is probably not a frequent motion even though it has a quite low migration barrier. Overall, we can see that the migration of isolated halide interstitial would be confined in the intercalation and shows the anisotropic diffusion feature.

Fig. 4 Calculated energy profiles of different migrations for halide vacancies and interstitials in RP Cs₂PbI₄ by using CINEB method.

In the mixed-halide RP perovskite Cs₂PbI₂Cl₂, P₁ denotes the in-plane migration of Cl, and P₃ represents the migration of I between two adjacent octahedral slabs. The P₂ motion is not available for the long-range diffusion of halide vacancies due to different species of halide ions at the 4c and 4e sites. For Cl interstitials, the correlated interstitialcy migration P₅ and the dumbbell-like migration P₈ only allow the long-range axial diffusion and no longer be able to realize equatorial diffusion. For iodine interstitials, the I₃-type interstitial is unstable due to the great disparity of the ionic radii of Cl and I. During the relaxation of I₃-type structure, the I interstitial moves into the intercalation to form an I₁-like structure (Fig. S3, ESI†). Therefore, migrations related to the I₃-type interstitial are not included in this work, e.g., P₆, P₈, and P₉. Moreover, the P₇ migration is not considered for I interstitials because the I₂-type interstitial cannot migrate over long distance via this dumbbell-like mechanism. Therefore, we simulate all six migrations for Cl interstitials and two migrations P₄ and P₅ for I interstitials in the mixed-halide RP Cs₂PbI₂Cl₂, and their energy profiles are presented in Fig. 5. In the mixed-halide RP Cs₂PbI₂Cl₂, the Pb–Cl bond is longer than that of RP Cs₂PbCl₄ and shorter than the Pb–I bond of RP Cs₂PbI₄. Thus, the migration bottleneck of P₁ will be larger than that of Cs₂PbCl₄, and the bottleneck of P₃ is smaller than that of Cs₂PbI₄, leading to lower barrier of P₁ and higher barrier of P₃ in the mixed-halide Cs₂PbI₂Cl₂. In RP Cs₂PbI₄, the P₂ migration provides the fast transport channel for halide ions vis the vacancy-hopping mechanism; while in the mixed-halide RP, this fast transport channel is not available. Therefore, the migration of halide vacancy is also suppressed in the mixed-halide RP perovskite.

Fig. 5 Calculated energy profiles of different migrations for (a) halide vacancies, (b) iodide interstitials, (c) and (d) chloride interstitials in mixed-halide RP Cs₂PbI₂Cl₂ by using CINEB method.

The lattice expansion of Cs₂PbI₂Cl₂ compared with Cs₂PbCl₄, leading to the decrease in the energy difference between Cl interstitials related to the 4c site (e.g., I₂ or I₃) with the 4d site. In consideration of the low migration barrier of P₇, the probability of in-plane dumbbell-like migration would be higher than that of Cs₂PbI₄. However, the mixed-halide RP Cs₂PbI₂Cl₂ still has a high barrier for the rotation motion between I₂ and I₃. Moreover, the mixed-halide RP Cs₂PbI₂Cl₂ shows similar properties of halide migration with RP Cs₂PbI₄. The migration of halide interstitials has lower barrier than that of halide vacancies along the same direction. For instance, the barrier of P₇ for Cl interstitial is lower than that of P₁, and the barrier of P₅ for I interstitial is lower than that of P₃. The correlated interstitialcy migration of isolated I₁ interstitials possesses lower barrier than the direct interstitial migration. Due to the contracted lattice compared with RP Cs₂PbI₄, the migration distance in the ab-plane decreases as well in the mixed-halide RP Cs₂PbI₂Cl₂. Therefore, P₄ and P₅ exhibit reduced barrier, suggesting the increased diffusion rate of halide interstitials in the intercalation. Only the I ion could adopt the correlated interstitialcy migration mechanism to realize long-range diffusion in the intercalation. At the end of the P₅ migration, the Cl ion would migrate toward the 4c site along the P₈ to form the I₃-type interstitial. Consequently, the higher barrier of the P₇ migration further decreases the diffusion rate of Cl interstitials along the c-direction, so the low migration barrier of P₅ to some extent could not considerably facilitate the diffusion of Cl interstitials in Cs₂PbI₂Cl₂. We should emphasize that Cl and I ions in Cs₂PbI₂Cl₂ exhibit the lower barrier of interstitialcy migration than that of Cs₂PbI₄, suggesting the higher migration frequency of halide interstitials in the mixed-halide RP Cs₂PbI₂Cl₂.

The low ion conductivity in 2D perovskites has been demonstrated by experiments and theoretical calculations, which can inhibit the J–V hysteresis of perovskite solar cells. Chen et al. reported that the migration barrier of I ions in organic–inorganic hybrid 2D RP perovskite PEA₂PbI₄via the vacancy-hopping mechanism is obviously higher than that of MAPbI₃.³⁸ In this hybrid RP perovskite, migration barriers are predicted to be about 0.7 eV in both P₁ and P₂ directions. For P₁ migration, the higher barrier is derived from the smaller migration bottleneck as a result of the lattice contraction in the ab-plane; while for the P₂ migration, the barrier is mainly due to the energy difference between V₁ and V₂ structures. In all-inorganic RP Cs₂PbI₄, however, this energy difference between V₁ and V₂ structures is quite small (about 0.03 eV). Therefore, the Cs₂PbI₄ shows a smaller barrier of P₂ migration compared with P₁ migration, which provides fast transport channel for halide ions.

The ion migration barrier is generally sensitive to the lattice parameter and the ionic interaction. In lead halide perovskites, the unique antibonding characteristic of Pb 6s with I 5p orbitals at upper valence bands weakens the Pb–I bond of the octahedron, resulting in the low barrier of halide migration.³⁷ For RP perovskites, the edge of octahedron is also an important transport channel for halide vacancies. As mentioned previously, the peak of p orbital from the 4e site is higher than that of the 4c site. As a result, the out-of-plane I anion has weaker interaction with Pb cations than the in-plane I anions. The ion migration along the octahedral edge involves breakage and reconstruction of chemical bonds. This process is often accompanied by the charge transfer between B-site cations.³⁹ In this study, we calculate the Bader charge of the adjacent Pb cations for the P₁ migration in Cs₂PbI₄ (Fig. S4, ESI†). At the initial state, electrons reorganize onto Pb_A and Pb_C which are adjacent to the vacancy due to the existence of iodine vacancy, thus resulting in the lower Bader charges on Pb_A and Pb_C than that on Pb_B. With the movement of the I ion, the Bader charge on Pb_B decreases and the charge on Pb_C increases, indicating that electrons on Pb_C move to Pb_B. This reveals that the electronic configuration of B-site cation plays a significant role in the halide migration of perovskites. The toxicity of Pb has raised serious concerns, and much effort has been devoted to explore Pb-less or even Pb-free alternatives.^40–42 It should be noted that apart from electronic properties the influence of non-Pb element on the ionic conductivity is also worthy of further considerations.

The migration bottleneck has been proposed to investigate the effect of various B-site cations on the barrier of X-site oxygen migration in ABO₃-type ion-conducting perovskites.^43,44 The bottleneck radius of X-site ion migration is proportional to the size of the triangle formed by the B-site cation with two adjacent A-site cations in regular perovskites, and determined by the lattice constant and the ionic radii of A-site and B-site cations. Given that the lattice constant is correlated to the ionic radius and bond properties, the ionic interaction can also influence the radius of migration bottleneck. Accordingly, the migration bottleneck is an intuitive method used to understand the tendency of migration barriers. We investigate five different bottlenecks for halide migration in RP halide perovskites (Fig. 6). The first migration bottleneck is determined by the triangle formed by the Pb cation with two adjacent Cs cations in the c-direction, which is responsible for halide migrations between two 4c sites along the octahedral edge, e.g., P₁ and P₇. Similarly, the second bottleneck is composed of one Pb cation with two adjacent Cs cation in the a-axis, which will affect migrations between 4c and 4e sites, e.g., P₂ and P₈. The third is composed of adjacent Cs cations with halide anions in the intercalation. In this case, the radius of bottleneck is determined by the diagonal length of the parallelogram. This bottleneck would influence the vacancy migration P₃ and the direct interstitial migration P₄. The fourth bottleneck is also a triangle composed of three adjacent Cs cations in the intercalation, which controls the P₅ migration. The final one is a square formed by Cs cations with halide anions in the ab-plane, which is related to the P₆ migration. In consideration of different species of halide anions in the mixed-halide RP perovskite, the ratio of the ionic radius to the bottleneck radius would be more adequate than the pure bottleneck radius to explicate the migration barrier. Consequently, we calculate the radius ratio for various migration bottlenecks based on the Shannon ionic radii and optimized lattice parameters. Apparently, the larger the bottleneck is, the lower the diffusion barrier will be; by contrast, the larger ratio implies higher barrier. For the majority of halide migrations, the radius ratio is greater than 1, which can be ascribed to the covalent bond of Pb cations with halide anions. For migrations along the octahedral edge, the second bottleneck has a smaller radius ratio than the first one, which is in accordance with the lower barriers of P₂ and P₇ compared with P₁ and P₆. The third bottleneck has the highest value of the radius ratio, which corresponds to the highest barrier of P₃ migration. For the migration of isolated interstitials, the fourth bottleneck has smaller ratio than the third type, which explains the lower energy barrier of P₅ than that of P₄. For the P₈ migration, the barrier is mainly due to the energy difference between the I₁ and I₃-type defects, so that the barrier is predicted to be higher than that of P₅ and even the fifth bottleneck shows the smallest radius ratio.

Fig. 6 Various migration bottlenecks in RP perovskites viewed along the (a) a-axis and (b) c-axis. (c) Calculated radius ratio of halide anions with migration bottlenecks in RP Cs₂PbI₄ and mixed-halide RP Cs₂PbI₂Cl₂.

In organic–inorganic hybrid perovskites, the organic MA cation has shown redistribution phenomenon under a small electrical field. Yuan et al. studied the MA migrations by employing the photothermal induced resonance microscopy and obtained a migration barrier of 0.36 eV for MA cations in MAPbI₃.¹⁷ In these RP perovskites, the A-site cation is no longer confined by the octahedral framework, thereby the A-site cation probably participates in ion diffusion via intercalation. We simulate six different migration motions (Fig. S5, ESI†) for Cs cations in these RP perovskites, and the calculated energy profiles are presented in Fig. S6 (ESI†). In contrast to the halide migrations, the interstitial-defect migration of the Cs cation has higher barrier than the vacancy-mediated diffusion. This is also distinguished from the MA diffusion in MAPbI₃ that the interstitialcy migration has a smaller barrier than the vacancy-mediated mechanism.²⁷ The in-plane P₁ migration has the lowest barrier for Cs cations among various migrations, and the barrier decreases in the order of Cl, Br, and I as a result of the expansion of the crystal lattice. In the mixed-halide Cs₂PbI₂Cl₂, the barriers of P₁ and P₂ are higher than that of Cs₂PbX₄, probably due to the incongruous halide anions at 4c and 4e sites, leading to the smaller migration bottleneck for P₁ and P₂ and larger bottleneck for P₃. Similarly, the migration of Cs cations in the c-direction needs P₂ and P₃ together. Therefore, P₁ is still the most likely diffusion mechanism for Cs cations in Cs₂PbI₂Cl₂.

4. Conclusions

We investigate the ion diffusion mechanism of halide vacancies and interstitials in the RP perovskite Cs₂PbI₄ and mixed-halide RP perovskite Cs₂PbI₂Cl₂ by first-principles calculations. The interstitial migration has a lower barrier than vacancy-mediated migration along the same direction. The migration between adjacent octahedral slabs has the highest barrier among various vacancy-mediated migrations, revealing that the halide vacancy is confined within the octahedral slab in the layered RP perovskites. The halide interstitial is likely to adopt the correlated interstitialcy migration to realize long-range diffusion in the intercalation. Moreover, the migration barrier of halide interstitial penetrating the octahedral slab is about twice higher than that of the interstitialcy migration in the intercalation, indicating the anisotropic feature of interstitial diffusion. In consideration of the relatively large bandgap and high ionic conductivity, these RP halide perovskites would not be a promising visible-light absorber of solar cells, but worth exploring for other optoelectronic applications, such as resistive switching memories, artificial synapses, and photonic memory devices.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This work was supported by National Natural Science Foundation of China (11947068) and Chongqing Municipal Education Commission (KJQN201801123, KJQN202001109).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1cp03631a

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