Anion diffusion in two-dimensional halide perovskites

The first utilization of halide perovskites as visible light sensitizers in solar cells was in 2009.¹ Since then, there has been a tremendous increase in research and development in the field of halide perovskite semiconductors. The hybrid organic and inorganic system of halide perovskites provides an ideal material platform for structural and compositional tunability. The high optical absorption coefficient, narrow-band bright photoluminescence (PL), low exciton binding energy, long-range carrier diffusion, and facile low temperature solution processability make halide perovskites promising for applications in solar cells, light emitting diodes (LEDs), photodetectors, transistors, and lasers. High performing optoelectronic devices have already been demonstrated using halide perovskites. For instance, fabrication of perovskite solar cells with >25% power conversion efficiency (PCE) and perovskite LEDs with >20% external quantum efficiency has been reported.^2,3 The performance of perovskite-based devices is now competitive with conventional semiconductors, and compatibility with simple solution-processing offers cost-effective manufacturing opportunities. The ultimate commercialization of halide perovskite semiconductors will require a combination of high-performance devices, low-cost manufacturing, and long operational lifetime. In addition, currently, the biggest hurdle for halide perovskite commercialization is their shorter device lifetimes compared to prevailing inorganic semiconductors.^4–6 

Continuous exposure to light, moisture, and oxygen causes chemical degradation, lattice expansion, and phase transitions in three-dimensional (3D) perovskites.^7–11 The instabilities in 3D perovskites originate from their ionic ABX₃ crystal structure, where “A” is a monovalent organic or inorganic cation, “B” is a divalent metal cation, and “X” is a monovalent anion. The surface of 3D perovskites contains dangling bonds, making them susceptible to degradation. One strategy to reduce the surface energy is utilizing two-dimensional (2D) perovskites with strong hydrogen bonding interactions at their surface. The passivation of surface with organic cations leads to fewer dangling bonds and better surface relaxation, resulting in higher stability of 2D perovskites. Additionally, first principle studies using density functional theory (DFT) calculations have shown that 2D perovskites are thermodynamically more stable due to their lower formation energies.^12,13

The simplest visualization of 2D perovskites is as slices of 3D perovskites capped with organic cations. The slicing along the 〈100〉 direction results in a high tolerance for incorporation of a variety of organic spacer cations, and thus, they are the most widely studied 2D halide perovskites. The 〈100〉 oriented 2D perovskites can be broadly divided into three categories depending on the number and charge of the organic spacer cations—Ruddlesden–Popper (RP), Dion–Jacobson (DJ), and alternating cation interlayer (ACI). The RP phase 2D perovskites can be represented by the general formula L₂A_n−1B_nX_3n+1, where “L” is a monovalent spacer organic cation and “n” is the inorganic layer thickness. DJ and ACI phase perovskites are represented by the general formula L′A_n−1B_nX_3n+1 and (A′A)_n+1B_nX_3n+1, respectively, where “L′” is a bulky organic diammonium cation and “A′” is a special organic monoammonium cation. RP phase 2D perovskites offer good control over inorganic layer thickness and, hence, have been extensively investigated.^14–18 In this Perspective, we will focus our attention to the RP phase 2D halide perovskite material system.

The improved functionality of 2D halide perovskites owing to their enhanced compositional flexibility and superior stability compared to 3D perovskites makes them viable options for applications in a wide range of solid-state electronics. Field effect transistors (FETs) with high hole mobilities of 15 cm² V⁻¹ s⁻¹ at room temperature have been fabricated with Sn-based 2D halide perovskites.¹⁹ Quasi-2D (n > 1) perovskites have been extensively used in LEDs and are considered promising materials for ultrahigh-definition displays, solid-state lighting, and optical communications.²⁰ RP phase 2D perovskites have also been employed in fabrication of solar cells with high PCE (18.04%) and high fill factor (82.4%).²¹ Additionally, optoelectronic devices with 2D perovskites used in conjunction with 3D perovskites have also been explored. The hybrid 2D/3D perovskites offer an excellent material system that combines the enhanced stability of 2D perovskites due to the presence of organic capping layers with the excellent charge transport properties of 3D perovskites. These hybrid systems are fabricated either by uniformly interspersing 2D and 3D phases, using the 2D phase as an encapsulating layer on the 3D phase, or by passivating the grain boundary of 3D phases with 2D phases. The utilization of these 2D/3D hybrid perovskites has led to overall improvement in crystallinity and reduction in defect states, resulting in superior device performance.²² 

Despite the promising results of 2D perovskites, a detailed assessment of the factors affecting its stability is required to facilitate smart material design. In this Perspective, we dive into the origins of instabilities in halide perovskites, discuss the impact of halide diffusion to material and device instability, and introduce the methodologies used in the literature to study halide diffusion and the open questions that need to be further researched to fully resolve the stability challenges in halide perovskites.

To develop a comprehensive understanding of the factors affecting halide perovskite stability, it is important to study the response of both the stand-alone materials and devices under external stimuli, including light, heat, and electric bias. Depending on the operating condition of the device, one or more of these external stimuli can play a governing role in determining the material and device stability. In turn, comparative studies of materials and devices shed light on intrinsic material susceptibilities vs extrinsic device specific susceptibilities (e.g., originating from specific material interfaces).

To motivate this Perspective, we present a comparison of the typical photodegradation behavior of 2D and 3D perovskites (Fig. 1). The Br:I mixed halide 3D perovskite, MAPb(Br_0.6I_0.4)₃ (MA = methylammonium) thin film initially exhibits a high energy emission corresponding to bromide-rich species [Fig. 1(a)]. After light soaking for two minutes, a new low energy emission associated with iodine-rich species dominates the PL spectra. This change in PL emission was observed under sequential light soaking and dark relaxation cycles. The reversible change in emission response of halide perovskite under photoexcitation shows the instability of the material under illumination and alludes to halide movement in the thin film.²³ Compared to 3D perovskites, 2D perovskites offer better stability due to their higher formation energies and encapsulation by organic spacer cations.¹³ However, even for 2D perovskites, ionic diffusion and stability issues are not completely resolved. Figure 1(b) shows the absorption spectra of pristine (PEA)₂PbX₄ (X = Br, I, PEA = phenylethylammonium) thin films coated on glass slides. The pristine absorption spectra exhibit a 405 nm peak from (PEA)₂PbBr₄ and a 515 nm peak from (PEA)₂PbI₄. The bromide and iodide perovskite glass slides are then clamped together and annealed at 140 °C. The external heat stimulus induces Br/I halide migration, leading to change in composition and thereby absorption spectra of the pristine films. After thermal annealing, both bromide and iodide thin films show a single absorption peak at 435 nm, indicating the homogenization of halide composition across the two films.²⁴ 

The intrinsic material instabilities in halide perovskites also lead to reliability issues in devices. In Fig. 1(c), the PCEs of three perovskite-based solar cells are tracked over a period of ∼8 days. Over this period, the solar cells were tested for their heat stability by placing them on a 85 °C hot plate in an open atmosphere with a relative humidity (RH) of 40%–70%. The 3D MAPbI₃ based solar cell showed a 50% reduction in PCE within 1 h of operation. In contrast, the 2D propylamine (PA) perovskite solar cells maintained 95% of their initial PCE for several hours, followed by PCE degradation to <30% after 168 h. The 2D 1,3-propanediamine (PDA) based perovskite devices demonstrated the best stability and maintained 95% of their initial PCE after continuous heating in air for 168 h.²⁵ The better stability of 2D perovskites under damp heat stress can be attributed to the stabilizing effect of the organic layers on the overall crystal structure. The thermal stability of 2D perovskites although comparatively superior to 3D perovskites is still not on par with commercial semiconductors.

In addition to light and heat activation, halide migration in perovskite-based devices also leads to detrimental device hysteresis when subjected to electrical bias. Figure 1(d) depicts the current–voltage (I–V) characteristics of a MAPbI₃ based solar cell. The forward and reverse voltage scans do not follow the same curve showing hysteresis behavior. Hysteresis can be linked to halide diffusion in the absorbing layer and subsequent interaction with the other contact layers.²⁶ Another example of halide diffusion under external bias is the observation of electrical poling. Figure 1(e) shows the schematic of a lateral perovskite device with Au metal contacts. Photocurrent response of the device is shown in Fig. 1(f). The non-poled device sustains no photovoltaic effect and exhibits zero open circuit voltage (V_OC) because of the symmetric structure of the device. The poled device depicts a reversal in photovoltaic response upon changing the direction of the bias. This effect can be ascribed to the ionic movement in the perovskite layer. Positive poling leads to accumulation of cations at the Au electrode, forming a p–i–n homojunction structure, whereas negative poling leads to formation of a n–i–p homojunction.²⁷ 

Investigation into the diffusion channels and diffusing species in halide perovskites is crucial to understand and resolve the material stability challenges. The crystal lattice of halide perovskites is considered “soft” and tolerant to defects.²⁸ Though this defect tolerance enables facile synthesis, it also facilitates ionic diffusion. Local lattice distortions caused by charge accumulation, impurities, and strain also act as ion transport channels. Point defects tend to accumulate more at interfaces and grain boundaries than within the bulk crystal; therefore, polycrystalline films exhibit faster ionic diffusion compared to single crystals. In the bulk crystal, the predominant diffusion pathway is mediated by vacancies as depicted in Fig. 2(a).²⁹ Schottky defects produce an equal number of cationic and anionic vacancies, whereas Frenkel defects produce a cationic (anionic) vacancy and interstitial defect pair. To deconvolute the impact of different mobile species on overall diffusion, many computational modeling studies have been performed. Using DFT, researchers have estimated the activation energies required for formation of cationic and anionic vacancies. Figure 2(b) provides a summary of activation energy calculations for I⁻, MA⁺, and Pb²⁺ vacancies. Based on the sample data points collected from various diffusion studies, average energy barriers for I⁻, MA⁺, and Pb²⁺ migration are 0.29, 0.62, and 1.56 eV, respectively. The lowest activation energy for iodide ion vacancies indicates that halide migrations predominate the diffusion in the perovskite lattice.^30–35 Similar activation energy calculations were performed for MAPbBr₃ and CsPbCl₃ perovskites, resulting in energy barrier estimation of 0.09–0.41 eV for Br⁻ vacancies and 0.29 eV for Cl⁻ vacancies.^33,36–38 It should be noted that although anionic vacancies offer the lowest energy barrier for diffusion in halide perovskites, the absolute values of activation energy barriers for both cationic and anionic species are dictated by the crystal lattice and therefore need to be independently evaluated for each perovskite system.

To experimentally validate the governing role played by anionic vacancies, Senocrate et al. measured ionic conductivity of a MAPbI₃ pellet under different iodine partial pressures. The ionic conductivity decreased with increasing iodine partial pressure, which can be explained by the reduction in mobile iodide vacancies due to incorporation of I₂ from the gas phase. To further demonstrate the dominant role of I⁻ rather than MA⁺ species in ionic migration, the authors performed a tracer exchange experiment. The experiment involved placing two samples of MAPbI₃ in contact with each other in which one of the samples was enriched with ¹³C- and ¹⁵N- isotopes, as schematically represented in Fig. 2(c). After annealing the two samples, a depth profile across the MAPbI₃ sample was obtained using time-of-flight secondary ion mass spectroscopy (ToF-SIMS). From the depth profile in Fig. 2(d), it is evident that there is negligible diffusion of ¹³C- or cationic species into the MAPbI₃ sample.³⁹ 

Diffusion studies in halide perovskites have focused on utilizing numerous electrical characterizations to probe the density of defects in the material. Halide perovskites contain both electronic and ionic defects; therefore, it is important to understand the impact of these defects on the observable signals in the measurement techniques. A key difference between ionic and electronic defects is the time scale of the underlying conduction processes [Fig. 3(a)]. For electronic defects, the electrons and holes are captured at the defects and are subsequently emitted. The emission time depends on the activation energy and temperature. Typically, the emission time is much longer compared to the capture time. For ionic defects, the migration of the ions is dependent on the concentration gradient (diffusion) or electric field (drift). Both drift and diffusion processes are dependent on temperature. The diffusion time scales are typically slightly longer or equal to the drift time scale. Therefore, measuring the time scales of both processes can help in differentiating the electronic and ionic defects.⁴⁰ 

Impedance spectroscopy (IS) and deep-level transient spectroscopy (DLTS) are two of the most commonly used techniques to probe the ionic defect landscape in halide perovskites. Figure 3(b) shows the capacitance (C) and voltage (V) curve obtained using IS for an MAPbI₃ perovskite solar cell measured at different temperatures. The difference in C–V characteristics in the low frequency high temperature and high frequency low temperature regimes depicts two distinct defect states in the perovskite. Similar capacitance measurements can be performed using DLTS. The transients in DLTS are measured during and after the filling pulse, which leads to movement of mobile ions from the interfaces to the bulk and then back to the interfaces. Depending on the measurement temperature and precursor ratio, the DLTS data also reveal two or three defect states.⁴¹ In addition to IS and DLTS, which mostly capture the response to voltage perturbations, a range of electrical techniques have been developed to measure the response to light perturbations. A light stimulus has been used to measure the current in intensity modulated photocurrent spectroscopy (IMPS) and measure the voltage in intensity modulated photovoltage spectroscopy (IMVS). A simplified equivalent electrical circuit of the connections used for IS, IMPS, and IMVS measurements in perovskite solar cells is shown in Fig. 3(c).^42,43 A summary of the temperature-dependent ionic migration rates extracted using IS, DLTS, IMVS, and IMPS characterizations is shown in Fig. 3(d). It is evident that the various perturbations (voltage or light) and observables (capacitance, current, or voltage) in both the frequency and time domain yield comparable migration rates.^44,45

For all the electrical characterizations highlighted in this section, it is challenging to deconvolute the impact of device architecture, interlayers, and cationic and anionic migrations. Therefore, characterization techniques are required that isolate these factors. A major development in this regard is the use of perovskite heterostructure platforms to probe intrinsic anionic diffusion. Contrary to the indirect electrical methods discussed in this section, heterostructures offer versatile, simple, and direct characterization of halide diffusion in perovskites. In Secs. IV and V, we will discuss the various synthesis techniques for perovskite heterostructures and their utilization in qualitative and quantitative diffusion studies.

While the fabrication of semiconductor heterostructures is crucial to both fundamental studies and device applications, the soft lattice and rapid anion diffusion of halide perovskites has greatly hindered the development of perovskite heterostructures, in general, and perovskite–perovskite heterostructures, in particular. So far, limited success in fabricating sharp heterostructures has been found in 3D perovskites. For example, a single crystal MAPbI₃/MAPbBr₃ heterojunction was synthesized by the anion exchange method that resulted in tens of micrometers of diffusion length.⁴⁶ Photo-induced spinodal decomposition was utilized to synthesize an epitaxial MAPbI₃/MAPbBr₃ double heterojunction.⁴⁷ In contrast, the reduced dimensionality and rigidness of 2D perovskites result in low ion diffusivity and high thermal stability, which enable several heterostructure synthesis strategies. In this section, we will review some pioneering investigations focused on the synthesis of perovskite heterostructures, cataloged by the orientation of the heterostructures relative to the 2D structure.

Early investigations focused on bulk scale perovskite nanosheets and utilized two-step syntheses, including chemical intercalation and anion exchange reactions, to obtain heterostructure patterns on pre-synthesized 2D perovskite crystals. For example, the gas–solid intercalation of MA⁺ cations was utilized to obtain both lateral and vertical (BA)₂PbI₄–(BA)₂(MA)Pb₂I₇ (BA = butylammonium) heterostructures.^48,49 In a typical reaction setup, an MA⁺ source, such as MAI or MACl, is introduced to pre-synthesize n = 1 perovskite plates at an elevated temperature, and the orientation of the heterostructure is controlled by masking the substrate. Unmasked substrate prefers vertical growth, possibly due to the lattice mismatch. (BA)₂PbI₄ substrate masked in the vertical direction, on the other hand, forms lateral heterostructures. This two-step strategy is applied to (BA)₂PbBr₄–(BA)₂(MA)Pb₂Br₇ and (PEA)₂PbI₄–(PEA)₂(MA)Pb₂I₇ perovskites, showing high stability with no significant change in optical properties over 60 days.⁴⁸ A similar solution-based method has been developed based on this intercalation method to form vertical heterostructures, which will be discussed later in this section.⁵⁰ Prototypical photodetectors have been fabricated based on patterned 2D perovskite heterostructures, showing enhanced on/off ratio and high photocurrent. Therefore, the intercalation technique leads to the formation of unique 2D/quasi-2D heterostructures; however, PL images reveal that the heterostructures obtained by these intercalation methods still lack a sharp interface between the two phases. If the 2D/quasi-2D heterostructures could be further optimized to provide a clear interface, it could serve as an exciting platform for studying diffusivity across materials with different dimensionalities.

Recently, Jin and co-workers developed a gas–solid anion exchange strategy by exposing 2D perovskite microplates (loaded on the polymer substrate) to HBr vapor in a gas flow reactor, forming a 2D perovskite heterostructure with different halide compositions.⁵¹ The kinetics of the anion exchange can be modulated by the organic ligand, for instance, the most rigid PEA ligand results in better stability of the junction, whereas the less rigid BA and hexylammonium (HA) ligand allows for more free structural rearrangement and therefore faster diffusion of the halide anion. Additionally, the dimensionality (n) of the 2D perovskite microplates also heavily impacts the sharpness of the junction. Only the 2D n = 1 perovskites and quasi-2D n = 2 perovskite heterostructure showed a sharp interface and high thermal stability, whereas the n > 2 junction possesses a halide gradient across multiple micrometers [Figs. 4(a)–4(d)]. The sharpness of the halide sublattice for n = 1 and n = 2 heterostructure was confirmed by ToF-SIMS and scanning electron microscopy (SEM)/energy dispersive x-ray spectroscopy (EDS) mapping, showing that the Br sublattice envelops the I junction in both the lateral and vertical directions with micrometer level sharpness [Figs. 4(e)–4(i)]. The anion exchange strategy could be further expanded to incorporate the versatile tunability in spacers (BA, HA, PEA), A cations (MA, FA = formamidinium, GA = guanidinium), and dimensionality (n = 1–4).

The above-mentioned two-step intercalation and anion exchange strategies utilize structural flexibility to fabricate patterns on bulk perovskite crystals. However, post-synthesis modifications inevitably introduce defects, and the precision of the heterostructure is limited by the resolution of the lithography method. Ideally, epitaxial growth will result in a lower defect density and more relaxed strain, thus serving as a better platform for diffusion studies. Recently, Shi et al., developed an epitaxial synthesis method for n = 1 2D perovskite nanocrystal heterostructures by fine-tuning the nucleation and growth kinetics of solution evaporation.⁵² A wide range of 2D perovskite heterostructures were synthesized with alternating spacers (PEA, BA, 2T = bithiophenylethylammonium, BTm = 7-(thiophen-2-yl)benzothiadiazol-4-yl)-[2,2′-bithiophen]-5-yl) ethylammonium, and 4Tm = quaterthiophenylethylammonium), metals (Pb and Sn), or halide ions (Br and I) [Figs. 4(j)–4(o)]. The versatility of the synthesis method allowed for fabrication of varying electronic structures with different band alignments (type I and type II alignment) between ligands and the inorganic [PbX₆]^4– framework or across the heterostructure junction, providing a diverse platform for diffusion studies. Furthermore, the mild solvent evaporation process can be generalized to the formation of multi-heterostructure superlattices, where several alternating layers of 2D perovskites were grown to produce onion-like super lattice structures [Figs. 4(l) and 4(o)]. The large size and rigidity of the conjugated ligands suppressed halide diffusion and produced a sharp junction interface with nanometer-level precision, as characterized by transmission electron microscopy (TEM) elemental mapping [Figs. 4(p)–4(s)]. This solution-based synthesis technique paves a clear pathway to produce a library of lateral heterostructures with high compositional tunability and atomic-level sharpness, serving as an excellent platform to study the transport properties of 2D perovskite materials.

Construction of well-defined vertical heterostructures is crucial for investigation of anion diffusion along the vertical axis. To realize such high quality vertical heterostructures, each nanosheet must be single-crystalline and possess a uniform surface with minimum defect density. These nanosheets must also be transferred onto each other to form a good contact that can facilitate anion diffusion across the interface. This process presents two challenges related to the growth of the nanosheets and fabrication of a junction with a well-established contact. Here, we review some of the most recent methods that attempt to tackle these challenges and construct vertical heterojunctions in a controlled manner.

Early approaches to create vertical heterojunctions were done through the gas–solid phase intercalation method discussed earlier. In this method, a 2D perovskite single crystal with a single inorganic layer (n = 1) is first grown, then quasi-2D perovskites with two inorganic layers (n = 2) are formed on top of the original crystal using the chemical vapor deposition (CVD) system using methylammonium iodide (MAI) vapor.⁴⁸ Solution-based methods of synthesis have also been developed based on the different solubilities of 2D/quasi-2D perovskite phases with different n numbers. One protocol reports a BAI solution injected into a PbI₂ solution at 80 °C followed by addition of MAI precursors. Due to their solubility difference, (BA)₂PbI₄ (n = 1) preferentially forms first as the temperature is lowered, followed by (BA)₂(MA)Pb₂I₇ (n = 2) precipitation. When these phases grow as crystals, they preferentially grow vertically on one another instead of laterally due to lattice mismatch across the lateral direction.⁵⁰ However, both methods mentioned above lack well-defined, sharp junctions as the fabrication of the junctions relies on the diffusion of MA⁺ ions into the original n = 1 crystals. In addition, these heterostructures lack tunability since both layers must consist of the same species of halide anions.

To create a sharp junction with more control over quality and tunability, many recent approaches have been focused on making separate nanosheets and then transferring one onto another to form vertical heterostructures. Two conventional synthesis methods that have been widely used are solution-phase growth and mechanical exfoliation [Figs. 5(a) and 5(b)].⁵³ The solution-phase method employs a ternary solvent–antisolvent system consisting of dimethylformamide, chlorobenzene, and acetonitrile where the ratio effectively modulates the solubility of the 2D perovskite crystals. This solution is drop-cast on a substrate, which is then heated to induce fast solvent evaporation yielding square shaped ultra-thin 2D perovskite nanosheets.⁵⁴ The downside of this method is that it lacks control of the size, orientation, and location of the nanosheets. Furthermore, application of the solution-phase growth method has been limited to 2D perovskites with a single inorganic layer (n = 1).

Mechanical exfoliation is an alternative approach where bulk crystals are grown by slow-cooling crystallization from a solution-phase and then mechanically exfoliated. The exfoliation process is similar to the method used for isolating other van der Waals 2D materials into thin layers, such as graphene and transition metal dichalcogenide (TMD).⁵⁵ While the solution-phase method directly deposits relatively small nanosheets onto the substrate through fast crystallization, mechanical exfoliation affords 2D perovskite nanosheets with higher crystallinity since they are obtained from large crystals that are grown over longer periods of time. Furthermore, mechanical exfoliation can create nanosheets with more than a single inorganic layer (n > 1). Unlike the uniform crystals obtained from solution-phase growth, mechanical exfoliation typically results in random shaped crystals that are broken in pieces.

Utilizing both the solution growth and mechanical exfoliation methods, we have demonstrated a method to successfully fabricate high quality vertical heterostructures of 2D perovskites.⁵⁶ The method consists of first depositing the nanosheets onto the substrate through solution growth and then transferring exfoliated nanosheets onto the solution grown nanosheets. The AFM image shows that this method can produce an ultrathin vertical heterostructure where both layers are few nanometers thick. The SEM/EDS elemental mapping in Figs. 5(c)–5(f) and confocal PL mapping in Figs. 5(g)–5(j) show that the vertical junction is well defined with clear boundaries.

Although the two-step method utilizing mechanical exfoliation and solution-phase growth produces sharp junctions, limitations still exist as one layer must always be n = 1 and the exfoliated layer is random in shape. In addition, the fabrication procedure is subject to the imprecision of the transfer process. Another recent approach utilizing solution floating growth reported by Pan et al. aims to achieve deterministic fabrication of vertical heterostructures.⁵⁷ This method uses the crystallization at the solution–air interface while heated 2D perovskite precursor solutions cool down. Then, a polydimethylsiloxane (PDMS) film is gently pressed on to the solution surface to retrieve the nanosheets. The schematic of the process is demonstrated in Fig. 6(a). Using a transfer stage equipped with an optical microscope, the nanosheets on the PDMS film can be transferred onto a substrate and precisely manipulated to be deposited on each other. It can be seen from Figs. 6(b)–6(d) that this fabrication method produces high quality vertical heterostructures with sharp junctions. Moreover, because precise control of transfer is possible, this method also allows for the fabrication of well-defined triple junction vertical heterostructures [Figs. 6(e)–6(g)].

Recent methods have allowed the fabrication of arbitrary vertical heterostructures with high degrees of compositional freedom and controllability in terms of shape, phase, and orientation of the crystal nanosheets. This versatile platform also enables studies to further understand anion diffusion mechanisms in distinct 2D perovskite materials. There is a continuous addition to the library of vertical heterostructures as a variety of building blocks for 2D perovskites are being investigated. Fabrication of vertical heterostructures with bulky conjugated ligands with greater hydrophobicity is yet to be broadly realized, and future works are expected to further expand and diversify the current library of 2D perovskite vertical heterostructures.

The recent advances documented above in fabricating perovskite-based heterostructures have created opportunities to study halide diffusion in 2D perovskites. Characterization of compositional variation across a heterostructure before and after a diffusion experiment is critical to analyze diffusion dynamics. In the field of perovskite heterostructures, a variety of techniques such as ToF-SIMS, SEM, energy dispersive x ray (EDX), and TEM have been employed to study the elemental and atomic distribution. For instance, Shewmon et al. used EDX mapping to obtain bromide and iodide concentration profiles across the MAPbI₃–MAPbBr₃ heterostructures fabricated using ion exchange.⁴⁶ Similarly, Kennard et al. determined the interface profiles across the perovskite lateral heterostructures using EDX characterizations.⁵⁸ Although the ToF-SIMS, SEM/EDX, and TEM measurements provide direct information about the composition across a heterostructure, these techniques have only been used with limited success, owing to the degradation of halide perovskites either during sample preparation or measurement. PL tracking of the heterostructure resolves this issue since it provides a simple and non-destructive technique to observe halide diffusion. Several studies have leveraged the composition-dependence of halide perovskite PL to track diffusion across heterostructures.^58–61 Pan et al. employed PL line mapping to compare the diffusion behavior across CsPbBr₃–CsPbCl₃ and MAPbBr₃–CsPbBr₃ single-crystal nanowire heterostructures.⁵⁹ Zhang et al. employed confocal PL microscopy to understand halide exchange kinetics in CsPbBr₃–CsPbI₃ heterostructures.⁶¹ These PL tracking studies have mainly focused on 3D perovskite heterostructures fabricated using ion exchange reactions.

The two-step fabrication of 2D perovskite vertical heterostructures, developed by our group in 2021, provides sharp heterojunction interfaces that can be used for analyzing halide diffusion. Figure 7(a) shows the optical and PL image of (BA)₂PbBr₄–(BA)₂(MA)₂Pb₃I₁₀ vertical heterostructures at room temperature and after heating at 100 °C for different time durations. The pristine vertical heterostructure shows a blue emission from the bottom bromide perovskite and red emission from the top iodide perovskite. It is evident from the PL images after annealing that Br–I inter-diffusion across the vertical heterostructure led to a change in emission color at the junction. This change in the emission profile upon heating is also captured using the PL spectrum in Fig. 7(b).⁵⁶ 

Since the 2D RP perovskites are anisotropic materials, it is important to characterize their diffusion behavior in both in-plane and out-of-plane directions. The epitaxial heterostructure synthesis developed by Shi et al. offers a platform for studying lateral halide diffusion across atomically sharp interfaces.⁵² Since the domain size for lateral heterostructures synthesized using this method falls in the μm scale compared to the nm domain in vertical heterostructures, it is possible to use a point-by-point laser mapping using confocal imaging to obtain the PL profile across the heterostructure. Figure 7(c) shows the confocal mapping of a (PEA)₂PbI₄ – (PEA)₂PbBr₄ lateral heterostructure at room temperature (RT) and after heating for 30 min at 100 °C. To spatially resolve the PL emissions across the lateral heterostructure, four discrete emission channels (411–446, 446–482, 482–517, and 517–553 nm) were monitored. The dimensions of the emitting regions have also been added in each PL image to highlight their change upon heating the samples. The merged image depicts the combined PL emission channels from 411–553 nm. Upon heating the lateral heterostructure at 100 °C for 30 min, the evolution of the PL spectrum evidences the movement of halide ions [Fig. 7(d)].⁶² 

Comparing the PL spectrum evolution in Figs. 7(b) and 7(d) highlights the distinct halide diffusion behavior across the lateral and vertical planes of 2D perovskites. For the vertical heterostructures, the thermal stimulus leads to the formation of a distinct alloy phase with green PL emission. Only one alloy phase is detected throughout the heating experiment, indicating the presence of a thermodynamically favorable Br–I composition after diffusion. During continuous heating of the vertical heterostructures, conversion to the preferred alloy phase occurs layer-by-layer as indicated by the increase in the intensity of the green PL emission. A steady-state composition is achieved when there is no further intensity enhancement in the alloy PL. The mechanism of halide diffusion across the vertical heterostructure is quite unique, and this layer-by-layer quantized diffusive behavior is schematically represented in Fig. 8(a). In contrast, the thermal stimulus to the lateral heterostructures leads to a gradual red shift in the intrinsic bromide perovskite PL emission and blue shift in the intrinsic iodide perovskite PL emission [Fig. 8(b)].⁵⁶ This is akin to the classical concentration-gradient mediated diffusion observed for 3D perovskites.

Tracking the PL emissions across the heterostructures provides a qualitative analysis of halide diffusion. To use the PL measurements for quantitative assessment, we need to understand the correlation between PL emission and perovskite composition. Vegard proposed that for binary systems with same crystal structures, such as the bromide and iodide perovskites forming the heterostructures, the bandgap of the alloy follows a linear scaling with the bandgap of the constituents as shown in the equation in the following:⁶³ 

where “b” is the bowing parameter. The linear approximation in Eq. (1) does not accurately represent the bandgap variation in all alloy perovskites. Interplay between the crystal lattice of the alloy perovskite and thermodynamic factors can lead to quadratic or cubic deviations from the linear approximation as shown in Fig. 8(c). Perovskite systems with linear and quadratic correlation between bandgap (PL emission energy) and concentration (halide mole fraction) have already been reported.^56,62 Therefore, it is imperative to establish this correlation either experimentally or through DFT calculations for diffusion analysis in every perovskite system.

Once the PL vs composition relationship is established, the PL profiles in Figs. 7(b) and 7(d) can be utilized to obtain the concentration profiles. The quantized halide diffusion in vertical heterostructures leads to a layer-by-layer change in the composition as depicted in Fig. 8(d). The blue curve at the initial time step (t₀) shows the heterojunction between the pristine bromide and iodide phases, and the pink curve at final time step (t_f) shows the thermodynamically stable compositions in the top and bottom perovskites at the steady state. The classical concentration-gradient driven halide diffusion that is observed across the lateral heterostructures is shown in Fig. 8(e). Similar to Fig. 8(d), the blue curve shows the initial composition across the heterostructure, and the pink curve shows the almost uniform composition across the heterostructure at the final time step (t_f).⁵⁶ 

Using the heterostructure platform and concentration profiles, we can estimate the inter-diffusion coefficients. The inter-diffusion coefficients determined through the heterostructure experiments represent the rate of halide movement in a binary Br/I system per unit area. The concentration dependent diffusion coefficient, D(x), describing a one-dimensional transient diffusion problem can be mathematically represented as follows:⁶⁴ 

where “x” is the concentration of bromide, “t” is the heating time, “y” is the diffusion length, and “D” is the halide inter-diffusion coefficient. Notably, this diffusivity is composition dependent since it reflects the combined diffusion of two species. The concentration profiles at the final time steps for both vertical and lateral heterostructures can be fitted with Gaussian distribution, and the Br–I inter-diffusion coefficient is then calculated by the Boltzmann–Matano (BM) method,⁶⁵ 

where “x^*” is the bromide mole fraction in the alloy, “x_l” is the bromide mole fraction at the steady state, and “x_M” is the Matano interface (a mathematical parameter that divides the concentration profile into two equal area plots).

The Br–I inter-diffusion coefficients calculated using the BM method for various vertical and lateral heterostructures are listed in Table I.^56,62

Theoretical or numerical estimations of halide diffusion rates provide powerful tools for corroboration of experimental trends. Numerical methods can be used to estimate self-diffusion coefficients, which represent the rate of halide movement per unit area in a pure species. The self-diffusion coefficient, D, for vacancy-mediated diffusion can be expressed as⁶⁶ 

where “f” is jump correlation factor, “a” is the lattice parameter, “C_v” is the vacancy concentration, and “k” is the atom jump frequency, or in the Arrhenius form

where “D_o” is the diffusion prefactor, “k_B” is the Boltzmann constant, “T” is the temperature, and “E_a” is the activation energy for ion migration.

E_a can be calculated by DFT calculations or molecular dynamics (MD) simulations.^{31–33,67,68} Alternatively, E_a can be estimated via experiments.^{31,39,69–73} Several studies have calculated the activation energy for both anion and cation diffusion in single and mixed cation 3D perovskites, e.g., tetragonal MAPbI₃, FAPbI₃, CsPbI₃, MAPbBr₃, and MA_0.75Cs_0.25PbI₃, via DFT [Figs. 9(a) and 9(b)]. For 2D/quasi-2D perovskites, we recently used MD simulations to calculate the free energy profiles for various ion migration pathways with different organic cations on the surface and inorganic layer thicknesses.⁶² The prefactor D_o in Eq. (5) is comparatively more difficult to obtain from simulations since it is a function of the vacancy concentration (C_v). This dependence of the prefactor on the vacancy concentration is also explicitly represented in Eq. (4). Calculating the vacancy concentration is complicated by the fact that the vacancy distribution is non-equilibrium in real materials, as evidenced by both the hysteresis behavior mentioned earlier as well as the large range of ionic mobilities observed in nominally the same material but synthesized by distinct fabrication protocols. For this reason, this factor is either ignored or approximated by assuming a typical attempt frequency.^31,32 Performing comparisons across materials and ignoring this factor is equivalent to assuming identical vacancy concentrations and attempt frequencies. Alternatively, Lai et al. have used the equilibrium vacancy distribution to calculate the diffusion rate for halides in CsPbBr₃–CsPbI₃ nanowires via MD simulations and Eq. (4).⁶⁰ At equilibrium, C_v can be calculated as

where “ΔF_f” is the free energy of vacancy formation. The Bennet–Chandler method was used to calculate k,^74,75

where “κ” is the transmission coefficient and k_TST is the rate given by the transition state theory,

where “q” is the reaction coordinate, which is the migration distance in such problems, “β” is the inverse thermal energy –$kBT−1$⁠, “ΔF(q)” is the free energy profile for ion migration [Fig. 9(c)], and “q*” denotes the position of the maximum free energy barrier.

In the Bennet–Chandler method, the transmission coefficient, κ, is given by the long-time limit of the time dependent transmission coefficient, κ_t [Fig. 9(d)],

where “$Hqt$” is the indicator function,

Equation (4) now becomes

where “f” is the jump correlation factor, which is dependent on the lattice type. The diffusion rate D can thus be extracted by MD-calculated $a,ΔFf,ΔFq$⁠, κ, and f.

An alternative approach is to treat the vacancy concentration as a fit parameter for a diffusion simulation. We have recently adopted this approach using Kinetic Monte Carlo (KMC) to perform lattice-based diffusion simulations with MD-calculated hopping rates as the input.^76,77 These calculations are inexpensive enough that many vacancy concentrations can be simulated. They also have the advantage of accounting for spatial correlations in the vacancy distribution that cannot be captured analytically (e.g., vacancy–vacancy repulsion or attraction). In the KMC algorithm, a list of all possible hopping events that are consistent with the system state is assembled at each step. Out of this list, one event is stochastically selected to occur that satisfies

where the index “i” runs over all possible events, “j” is the selected event, the overall rate constant “k_tot” represents the sum of rate constants of all possible hopping events at the current configuration, and “γ₁” is a uniformly distributed pseudo-random number between zero and one. After the system configuration is adjusted according to the selected event, the time is also advanced stochastically to t → t + Δt where Δt is given as

where “γ₂” is a second uniformly distributed random number. From the updated configuration, a new list of possible events is regenerated, and the procedure repeats. Following this scheme, the simulation system can be propagated step by step until the desired time/configuration is achieved. Based on ensembles of simulated trajectories, the diffusivity can be extracted from the mean squared displacement of the particles,⁷⁷ 

where the vector “$r⇀it−r⇀it0$” indicates the change in the position of a particle after time t–t₀ has elapsed, the angle brackets indicate the ensemble average over all trajectories and starting times, “t₀,” and “N” is the number of ions in the system.

We investigated the halide diffusion in 2D perovskite vertical and lateral heterostructures using analysis from experiments and simulations.^56,62 For 2D halide perovskite vertical heterostructures, in contrast to classical solid-state inter-diffusion models, which feature a continuous concentration profile evolution, a quantized layer-by-layer diffusion governed by a concentration threshold and ion-blocking effects of the organic cations was discovered experimentally [Fig. 8(d)]. A 2D KMC lattice model was built based on the proposed layer-by-layer diffusion where a concentration threshold criterion for the interlayer diffusion was introduced. The KMC-calculated inter-diffusion coefficient’s good fit to the Arrhenius prediction of exponential temperature dependence provides additional credibility to the proposed layer-by-layer diffusion mechanism.

Through experimental BM calculations and theoretical KMC estimations for vertical heterostructures, we found that bulkier π-conjugated organic cations show better inhibition to halide diffusion compared to short aliphatic chains. This trend was also observed through analytical BM calculations and numerical MD simulations for lateral heterostructures. To develop further insights into the observed diffusion trend, the various available diffusion pathways—equatorial-to-equatorial (layer 1 ↔ 1) and equatorial-to-axial (layer 1 ↔ 0)—were investigated (Fig. 10). Among all the sampled organic cations, the short aliphatic cation BA⁺ shows the softest lattice requiring strongest constraints on neighboring halides to inhibit off-target diffusion. Therefore, the interaction of bulkier π-conjugated organic cations with the halides in the inorganic layers helps in stabilizing the perovskite lattice and slows down the halide diffusion process.

In addition to the dependence on organic cations, we also observed that halide diffusion increases with increase in the n number, i.e., the inorganic layer thickness in L₂A_n−1B_nX_3n+1 perovskites. Furthermore, MD calculations revealed that the surface layer diffusion has the highest activation energy barrier irrespective of the n number [Fig. 10(b)], which can be attributed to the proximity of the surface layer to the stabilizing organic cations. The activation barriers between the inner layers of quasi-2D perovskites (layer 2 and 3) quickly converge to the same low energy barrier of 3D perovskites [Fig. 10(b)], suggesting diffusion in higher n number perovskites is facilitated by the availability of additional pathways.

In this Perspective, we have discussed the various synthesis techniques for 2D halide perovskite heterostructure assembly and utilization of these heterostructures for analyzing diffusion behavior. The PL tracking of heterostructures provides a simple and non-destructive method for studying the emission and concentration profile evolution. Diffusion coefficient calculations revealed the impact of different structural components on halide diffusion. The halide diffusion in perovskites was found to increase with an increase in the inorganic layer thickness or “n” number. The choice of capping organic cations was found to play a dominant role in governing the diffusion behavior compared to the inorganic layer thickness. Incorporation of bulkier and π -conjugated organic cations plays an inhibitory role and stabilizes the perovskite structure. Additionally, halide diffusion in 2D perovskites was found to be anisotropic with the in-plane diffusion following a classical behavior and the out-of-plane diffusion depicting a quantized layer-by-layer mechanism. These experimental estimations were corroborated with numerical calculations. The numerical calculations emphasized the role of transport channels within the perovskite crystal and differences in surface vs bulk diffusion behaviors. The insights gained from these investigations provide a guideline for the design of stable 2D perovskites. However, to develop a comprehensive understanding of the halide diffusion behavior in 2D perovskites, further studies need to be conducted.

Majority of the fundamental studies on understanding perovskite stability have focused on thermally activated halide diffusion. This provides a good indication of the stability performance of perovskite when subjected to normal device operating conditions. However, it is important to test the perovskite system under external stimulus of light and bias to improve the stability predictions. Photo-activated diffusion rates can be extracted by exposing the heterostructures to illumination from different light sources—lamps, lasers, and solar simulators—at varying light intensities. Electrically driven ion migration can be activated by subjecting the heterostructures to an external bias via a metal contact. In addition to studying the halide diffusion, it is important to compare the response of the material under various external stimuli, for instance, answering questions whether π-conjugated organic cations also play a stabilizing role in light and bias induced diffusions. Comparing and contrasting the stability of various perovskite systems under different external stimuli can also assist in developing a correlation between the responses. This correlation can be used to predict the behavior of a new system under different external stimuli based on their response to one of the stimuli.

Deepening fundamental understanding regarding halide diffusions in 2D perovskite heterostructures is ultimately expected to contribute to preventing ionic diffusion in the future device applications. However, due to the complex architecture of devices, this process leading from fundamental analysis to device stability and reliability enhancement requires us to answer multiple intermediary questions to achieve the final goal. One of the first questions that need to be answered is the prediction of the stability of layered devices based on halide diffusion studies conducted on relatively simple junction structures. Predicting halide diffusion in devices, unlike diffusion in single crystals, requires considerations from a myriad of contributing factors such as grain boundaries, surface defects, film thickness, and overall junction quality. With multiple factors in play, it is important to emphasize that device stability does not solely rely on halide diffusion. Therefore, all other contributing factors need to be carefully controlled and fixed to truly extract the relationship between halide diffusion and device stability. Finally, it is anticipated that in situ studies of halide migration in thin film devices must be conducted to validate and improve the our mechanistic understanding of halide diffusion in 2D perovskites.

As we have discussed above, the effect of the ligand framework and the dimensionality of the 2D perovskite on the diffusivity has been well-characterized. However, a complete picture of the stability issues in 2D perovskites requires investigations into other structural components as well. Preliminary studies have shown that some “A” cations for quasi-2D perovskites, such as FA, lead to suppressed halide diffusivity.⁵¹ The structural source of the stability should be analyzed. Another interesting area could be exploring other 〈100〉 oriented 2D perovskites. For instance, the eclipsed interlayer halide alignment and enhanced interaction of organic cations with inorganic layers in DJ perovskite may lead to suppression of the halide diffusion, thus leading to stable device applications. Furthermore, the characterization of anion diffusivity is mostly based on 2D perovskite nanocrystals, which possess large specific surface area. Whether the large surface area assists in halide diffusion is another interesting topic worth investigating.

The vacancy concentration plays an important role in diffusion but is difficult to directly estimate both experimentally and through simulations. Experimental characterization of charge carrier transport properties such as intrinsic charge carrier density, PL lifetime, and mobility can provide an indication of the vacancy concentration. It is important to deconvolute the impact of various structural components on charge carrier transport and consequently on defects and vacancies. The choice of synthesis technique can also impact the vacancy concentration in the perovskite system. An indirect estimation can be made based on the free energy of vacancy formation. An alternative is to fit the vacancy concentration in KMC simulations so that the resulting diffusion coefficient aligns with the experiments. The former depends on the accuracy of the method/system used to calculate the free energy, and the latter depends on the accuracy of the MD- or DFT-calculated input rate k for KMC. Most studies assume similar defect concentrations as the qualitative analysis of the free energy alone agrees with the experimental trend. However, the direct estimation of vacancy concentration is needed to unveil a more detailed impact on ionic diffusion. An accurate estimation of vacancy concentration can also shed light on the impact of dimensionality modulation (3D vs 2D) on intrinsic material defects and consequently on the observed diffusion characteristics. Finally, it is crucial to analyze the correlation between vacancy concentration and device performance.

DFT simulations are most widely used for calculating the free energy barrier of migration in perovskite systems. In addition to the expensive computational cost, the DFT simulations are based on nudged elastic band calculations, which neglect entropic contributions. MD simulations, compared to DFT simulations, are computationally cheaper. Furthermore, more molecular details can be probed by the MD’s high flexibility in alternating properties of the system, e.g., the concentration of different anions. However, accuracy of MD simulations highly depends on the atomic potential, i.e., force fields, used to describe the atomic interactions. To date, there are very few available validated force fields for perovskite systems, but none have considered the dynamics of electrostatics. Better atomic potential description of perovskite systems is needed to improve the accuracy of MD simulations so that more detailed quantitative analysis can be made to deduce the effect of other factors, such as vacancy concentration, involved in the diffusion process.

The work by Akriti and H. Yang was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0022082. The work by Z.-Y. Lin and B. M. Savoie was supported by the U.S. Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy (EERE), under Solar Energy Technologies Office Award No. DE-EE0009519. The work by J. Y. Park and L. Dou was supported by the National Science Foundation (NSF), Division of Materials Research (DMR), under Award No. 2143568.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.