Roadmap on organic–inorganic hybrid perovskite semiconductors and devices

Lukas Schmidt-Mende, Vladimir Dyakonov, Selina Olthof

In the last decade, research on metal halide perovskites has made tremendous progress. The certified efficiency of perovskite solar cells (PSCs) has increased drastically to over 25% (see Fig. 1) and can now compete in this respect with Si-technology. The simple fabrication, including even processing from solution, opens the possibility to integrate perovskite processing into an industrial roll-to-roll fabrication, which allows mass production at low cost. Applications are not limited to single junction solar cells anymore. The chemical tuning of the bandgap of the material makes it especially interesting for application in tandem solar cells. Additionally, also other applications, such as light emitting devices, photodetectors, and memory devices, have already been successfully demonstrated.

Researchers have significantly increased their understanding of the material class, concerning, for example, the requirements to form stable 3D perovskites or employing larger cations for 2D structure formation. Intriguingly, the success of this novel high performance semiconductor revived the search by theoreticians and material scientists to look beyond and explore further promising complex perovskite compositions.

In this Roadmap, we cover important research aspects concerning metal halide perovskite semiconductors. We address in Sec. II some fundamental properties and the specific features of this material class. In Sec. III, we cover aspects of fabrication. The processing of efficient perovskite semiconductor films has been improved drastically over the last few years. Nevertheless, the solution chemistry is still an important research field, and processing of efficient perovskites films from solution, sublimation, and chemical vapor deposition (CVD) needs further investigation. Next to thin films, the growth of single crystals has been demonstrated.

The characterization and understanding of devices (see Sec. IV) has been drastically improved since the first report of a solar cell application. However, many details of the underlying physical mechanisms are still hardly understood. Next to the perovskite film itself, the interface formation and the adjacent transport layers (TLs) play a decisive role for the device efficiency and stability.

While perovskite solar cells are the main focus of this Roadmap, we also address tandem solar cell stacks in combination with non-perovskite absorbers as well as applications beyond solar cells, such as lasing and light emitting diodes (LEDs) in Sec. V. There are still major challenges, which we address in Sec. VI. In particular, if it comes to commercialization, many additional aspects need to be taken into account. Currently, the correct and precise measurement of perovskite-based devices is still an issue as well as the reproducibility. The role of ion migration and charge carrier mobility in the device and at the interface is still only partly documented. The attempts to replace the toxic lead in these thin films with less toxic materials have only been partly successful. One major challenge remains to be solved is the stability of the devices. Even though there has been tremendous progress, the device stability is still not comparable to silicon devices. This makes data-driven prediction of novel hybrid perovskites an exciting option to find materials overcoming the current limitations. When it comes to commercialization, one also needs to consider fabrication issues related to upscaling laboratory-scale devices to larger areas.

Despite these challenges concerning understanding device physics and functionality, there has been no material class in the recent past that attracted such high interest and introduced a paradigm change concerning the efficiency of solution processed semiconductors for solar cells. In this Roadmap, we summarize various important aspects to provide an overview of the current status of perovskite semiconductor research and indicate promising directions for future research efforts.

Feray Ünlü, Khan Moritz Trong Lê, Sanjay Mathur, Selina Olthof, Andrei D. Karabanov, DoruC. Lupascu, Laura Herz, Alexander Hinderhofer,Frank Schreiber, Alexey Chernikov,David A. Egger

Feray Ünlü, Khan Moritz Trong Lê, Sanjay Mathur

Single perovskites generally adopt the crystal structure similar to CaTiO₃, which is described with the ABX₃ formula, where the B-cation is coordinated octahedrally by X-anions and the A-cation fills the cuboctahedral voids and compensates the negative charge. Single metal halide perovskites (MHPs) adopt the ABX₃ structure consisting of a three-dimensional network of corner-sharing BX₆ octahedra, where the B atom is a group 14 metal cation (typically Sn²⁺ or Pb²⁺) and X is typically Cl, Br, or I. On the A-site, Cs⁺ or organic cations, such as CH₃NH₃⁺ (MA) and NH₂CH=NH₂⁺ (FA), can be used that are chosen to balance the total charge and to stabilize the lattice. For achieving structural stability in a 3D perovskite, the ionic radii of the cation and anions should follow the empirically derived Goldschmidt tolerance factor t given by the radii of A (r_A), B (r_B), and X (r_X),² 

Tolerance factors between 0.71 and 0.9 result in tetragonal or orthorhombic structures. For halide perovskites (X = F, Cl, Br, and I), the tolerance factor follows 0.81 < t < 1.11. If t lies in the range 0.89–1.0, a cubic structure is likely to be stabilized, whereas higher t values (>1.0) result in a hexagonal structure.^3,4 Recent analysis of structural data has shown that the tolerance factor t can differentiate between perovskite and non-perovskite materials in only 74% cases and a new tolerance factor (τ) was recently introduced that derives the structural predictions from the same parameters (composition, oxidation state, and ionic radii) and higher accuracy (>90%),⁵ 

Despite these parametric guidelines, structural transformation is common for any given perovskite composition, with higher symmetry structures being prevalent at high temperatures. Based on these considerations, the large ionic radii of Pb²⁺ (188 pm) and of halides (e.g., I⁻, 220 pm) limit the ionic radius of the A site cation. As a result, only organic cations with two or three C–C/C–N bonds or inorganic cations, such as Cs⁺ (188 pm), can form stable 3D perovskites.⁶ The crystal lattice of the perovskite is associated with a certain flexibility and defect-tolerance such that constituting ions can move and migrate within the lattice.⁷ The migration of ions and their mobility in the lattice causes the drift in ionic defects already at room temperature, which is responsible for the hysteresis of energy devices.^8,9 On the other hand, the geometrical stability and allowed range of tolerance offer a broad compositional space for chemical engineering of new perovskites by systematic substitution of cationic and anionic constituents and to obtain mixed-cation or mixed-anion perovskites through isovalent substitution in the parent (AMX₃) compound. In this context, the compositional engineering is shown to be a viable strategy for tuning the optoelectronic properties and to control the phase stability and check detrimental phase transformations.^10,11 Low formation energies allow facile exchange of ions within the A- and X-sites, whereas the formation energy of B-site doping is higher.^12,13

Given the fast anion exchange kinetics in hybrid perovskites, a broad range of compositions have been synthesized by in situ processing or post-synthesis chemical transformations. Intermixing of bromides or chlorides in the iodide perovskites has shown to be effective in changing the transport behavior of charge carriers and the bandgap energies.^14,15 For instance, the lattice parameters and bandgap energy of MAPb(I_1−xBr_x)₃ were observed to linearly scale-up in relation to the Br⁻ content.¹⁶ Furthermore, the inclusion of chloride into MAPbI₃ was found to significantly enhance electron and hole diffusion lengths over 1 μm in the mixed halide MAPb(I_1−xCl_x)₃, which is ten times higher compared to diffusion lengths in MAPbI₃.^17,18 The influence of halide anions on the perovskite’s bandgap is further described in Sec. II B.

A-site cation engineering includes the partial substitution of the parent organic or inorganic (e.g., MA or Cs⁺) cation by one or more co-cations, such as formamidinium (FA⁺) and/or other alkali metal cations (K⁺, Rb⁺), considering the appropriate sizes to maintain the tolerance factor. This approach was particularly successful in optimizing the stability of perovskites against undesired phase transitions, nonradiative defect sites, and was shown to be effective in enhancing carrier lifetimes and bestowing chemical stability under ambient conditions. The perspective of A-site cation engineering in tuning the functional properties and structural stability of halide perovskites were recently elaborated by Mathur and co-workers that can be found elsewhere.¹⁹ When considering the connectivity of the metal halide octahedra as the classification element, the perovskites also exist, besides the 3D configurations, in 2D layered structures, 1D chains, and 0D isolated structures.²⁰ Since there are no size rules for low dimensional networked perovskites, A-site cations of different lengths can be introduced, and therefore, low-dimensional perovskites offer tunable bandgaps and absorption/emission properties. Mitzi reported on 2D layered perovskites analogous to Ruddlesden–Popper phases with organic ammonium cations (R–NH₃⁺); here, the MX₄²⁻ anions are surrounded on both sides by organic cations stabilized by hydrogen-bonding.²¹ For 2D perovskites, the interlayer spacing between the inorganic layers is the determining factor for bandgap tuning, the longer the interlayer spacing, the wider is the bandgap. Hence, a combination of 2D and 3D perovskites is promising in terms of developing high efficiency solar cells with long-term stability. In 2D/3D systems, small organic cations are partially replaced by bulkier organic spacer cations; for instance, Grancini et al. reported one-year stable and hole transport layer (HTL)-free 2D/3D (AVA)_0.3(MA)_0.7PbI₃ [(AVA) aminovaleric acid, HOOC(CH₂)₄NH₃] PSC, without any obvious loss in power conversion efficiency (PCE 12.9%) in power conversion efficiency (PCE 12.9%) under ambient air.²² In addition, LEDs based on mixed layered perovskite materials were shown to display impressive performance and stability due to the mixed compounds acting as a photocarrier concentrator, funneling the charge carriers from high-bandgap materials to the lowest-bandgap ones to ultimately boost the external quantum efficiency (EQE).²³ More details on 2D perovskites and their properties will be discussed in Sec. II F.

B-site doping was shown to be very effective in tuning the bandgap and to influence the charge carrier dynamics of the perovskites. For example, substitution of the Pb²⁺ site in lead-based perovskite thin films or single crystals by isovalent Sn²⁺ was found to reduce the bandgap,^12,13 leading to broadening of the absorption range²⁴ and longer charge carrier lifetimes.²⁴ The Sn²⁺-doping also offers a plausible alternative to reduce the amount of Pb²⁺ content in perovskite compositions. In analogy, Ge²⁺ was recently incorporated into the double cation FA_0.83MA_0.17Ge_xPb_1−x(I_0.9Br_0.1)₃ where the solubility of GeI₂ was ameliorated by MACl additive achieving PCE over 22% and enhanced stability and photoluminescence (PL) lifetimes.²⁵ Moreover, Ge²⁺-doping in Sn based perovskites evolved to a strategic pathway to suppress the self-oxidation of Sn²⁺ to Sn⁴⁺, which in combination with A-site cation engineering and surface passivation has achieved a PCE of up to 13% so far.²⁶ Other bivalent dopants, such as earth alkali metals (Ca²⁺, Sr²⁺, or Ba²⁺), are reported to affect the bandgap and crystalline phase.^27,28 Looking at other main group elements, it was reported that Bi³⁺- or In³⁺-doping stabilizes the photoactive black perovskite phase at lower temperatures.^29,30 Transition metals, such as Mn²⁺, were investigated thoroughly in CsPbX₃ nanocrystals, leading to enhancement of long-lifetime luminescence by generating an additional exciton state associated with the Mn d–d emission.³¹ Rare-earth elements, such as lanthanoids, were used in perovskite nanocrystals achieving down- and up-conversion and quantum cutting.³¹ 

The emergence of perovskite solar cell (PSC) technology manifests the potential of chemical transformation in developing and designing new materials. In this context, the organic–inorganic hybrid perovskites have moved from phenomenological studies on compositional engineering and structure–property relations to establish themselves as drivers of an alternative photovoltaic (PV) technology as evident in their superior optoelectronic properties, summarized for a few representative compositions in Table I. While A-site cation engineering shows enhanced phase stability and durability under ambient conditions along with tunable bandgap properties through halide mixing, there are still stability issues under illumination, solar cell operation, or reverse bias conditions due to ionic migration and phase segregations in photoabsorber materials (Fig. 2). The ionic conductivity in perovskite halides was described as early as 1983³² where in MAPbI₃, the I⁻ anion was determined to be the major migrating species with four orders of magnitude higher mobility than the MA⁺ cation.³³ In particular, in mixed halide or multiple cation perovskites, the ion migration can lead to phase segregation. The phenomenon of J/V hysteresis (different voltage scanning direction with differing output current) is connected to the ion-migration (see Sec. VI C) induced poling of the perovskite,³⁴ causing reactions with adjacent (charge transport) layers and electrodes leading to overall device degradation.³⁵ Although belonging to the most efficient hybrid perovskite absorbers, mixed I/Br compositions tend to phase segregate under illumination leading to, e.g., I⁻-rich and Br⁻-rich phases.³⁶ Furthermore, organic–inorganic hybrid perovskites can suffer under thermal fluctuations, e.g., under reverse bias, which can lead to local heating and damage of the solar cell due to volatile organic components.³⁷ A possible solution against volatile components is to switch to the all-inorganic perovskites CsPbX₃; however, the wider bandgap due to mismatch of orbital energies and polymorphism are currently persisting challenges. One of the advantages of halide perovskite photovoltaics is their solution processability at low temperatures; however, the resulting polycrystalline thin films possess high defect density and pinholes that are detrimental for the functional performance. In particular, at the surface of perovskite films and grain boundaries, a large number of defects are present as the outermost ions are not saturated. The vacancies lead to trap states (energy levels in the perovskites bandgap) that reduce the overall charge transport and thereby the solar cell efficiencies, although these are shallow traps (near the band edges).³⁸ These limitations have been overcome by passivating the surface through chelation of molecular reagents.^39,40

The straightforward chemical synthesis was one of the triggers in witnessing the combinatorial explosion of compositionally engineered hybrid perovskites; however, the fundamental mechanism and insights into the formation of precursors, nature of chemical species in precursor solutions, existence of dynamic equilibria, and controlling effects of solvents (polar/non-polar) remain elusive. A better understanding of nucleation of perovskite crystals and their transformation on the substrate in a single phase perovskite composition is crucial for their application in devices and scale-up of the technology readiness level from prototypes to industrial production. Controlled synthesis of perovskite precursor ink, including precursor-intermediates that can be influenced both in situ (inks) and ex-situ (on-substrate) by coordinating ligands, is one of the deterministic factors for achieving a reproducible figure of merit for perovskite materials and devices produced in different laboratories. In particular, a better understanding of both homogeneous and heterogeneous nucleation of perovskite crystallites is inevitable to decipher the role of surface chemistry, purity of starting materials and employed solvents as well as additives in solution concentration, and precursor ratios and quality of chemicals to comprehend the various synthetic concepts that have been designated as novel and unique, albeit minimal differences in the underlying chemical interactions and nature of species. Since the interplay of above-mentioned factors is essential for homogeneous crystallization, the reproducibility of “ideal” inks continues to be difficult that aggravates with the increasing number of components, for instance, in multi-cation and anion systems. The high variability of compositions and properties makes it difficult to predict solar cell parameters, i.e., J_sc or V_oc, and associated energy losses when compared with the technological maturity of silicon photovoltaics. Current challenges of perovskite inks include a comprehensive understanding of nucleation and growth of perovskite crystals in solution and stabilization of perovskite inks to prevent uncontrolled growth and precipitation of thermodynamically preferred species from a mixture of components that is an intrinsic barrier in the scalability and shelf-life of perovskite inks that are crucial for deposition techniques, such as spin-coating, ink-jet printing, or slot die coating. In addition, relatively less attention has been devoted to fundamental studies on the chemical structure of perovskites based on mixed-cation compositions, for instance, there are no conclusive single crystal data for multi-component perovskites, which would elaborate the structural and positive influence of small amounts of dopants on the photoconversion efficiency. In addition, the homogeneity of distribution in such multiple-cation and mixed anion perovskites and its impact on the device are still an open question.

Long-term stability of perovskite materials and devices represents one of the crucial requirements besides the high efficiency to achieve large-scale production and commercialization of halide perovskite PV technology. To reach structural stability the A-site cation alloying has proved to be a viable concept to achieve a tolerance fit.⁵⁰ For example, Knight and Herz reported that the triple A-site cation (Cs, FA, and MA) and quadruple cation (Cs, FA, MA, and Rb) seem to be particularly stable. Similarly, the mixing of the 25% Sn/75% Pb perovskite can lead to increased photostability; however, more research is needed to evaluate the stoichiometric balance and its interrelation to structural and electronic stability [auto-oxidation of Sn(II)].⁵¹ Additionally, suppression of ion migration leading to phase segregation is mandatory to retain long-term stability under device operation and illumination. Among the common approaches to reduce ionic drift includes the implementation of polymers or organic molecules as barriers and surface passivating agents.^52,53 Implementation of 2D perovskites is another effective strategy to suppress ion migration, although this method is not applicable to all perovskite compositions as specific ligands are necessary. Furthermore, addition of chloride is shown to be effective in reducing the halide phase segregation, which is related to improvement of grain growth, crystallinity, grain boundary passivation, reduction in halide defect densities, and increased energetic barrier for halide migration.³⁶ Hence, compositional engineering is essential for designing stable and efficient perovskite absorbers; however, in order to progress faster and facilitate the screening of suitable chemical compositions, machine learning (ML) approaches are emerging as effective and effort-saving strategies.

With more powerful computing and advances in artificial intelligence, machine learning (ML) based approaches hold the promise for faster and more efficient investigation of new materials. Instead of empirical strategies, the optimal parameters are developed by training the machine with reliable data and a working algorithm. First-principle calculations (structure–property relation by quantum mechanical methods) are computationally demanding; however, an algorithm based ML can reduce the resources and make predictions by learning from existing data.⁵⁴ For example, 333 data points collected from 2000 publications were fed into a system to predict high performance perovskite compositions for solar cells based on the prediction of underlying physical phenomena to some extent.⁵⁵ Li et al. used similar approaches with data derived from high throughput density-functional theory (DFT) calculations to demonstrate alternative and economic pathways than iterative experimental attempts. They evaluated the compositional engineering with respect to perovskite stability to suggest more effective predictions that go beyond the conclusions drawn from the empirical tolerance factor.⁵⁶ Castelli et al. demonstrated the computational screening of oxide containing perovskites using the computational materials repository. Their work showed that out of a huge number of possible perovskites (around 19 000), only 47 were interesting for water splitting applications,^57,58 manifesting the power of computational methods in order to save experimental resources and time. However, also DFT calculations need a lot of computational energy and time; therefore, machine learning models can reduce these cost factors. For instance, Li and co-workers demonstrated the application of machine learning models to predict the thermodynamic stability of oxide perovskites using a DFT database of 1900 oxide perovskite energies, ending up with four stable compositions.⁵⁹ Similar studies for the discovery of new and stable perovskite structures were made by using machine learning approaches and the field is still under development.^60–62 Furthermore, Kirman et al. used machine learning to create a high-throughput system for perovskite single crystal synthesis.⁶³ Hartono et al. investigated organic halide capping layers for MAPbI₃ surface passivation by a machine learning framework, in which 21 different organo-halide capping layers were screened in order maintain perovskite stability under ambient conditions.⁶⁴ The further development of ML processing is beneficial for investigating mechanisms, predicting device performances, and facilitating the experimental challenges to synthesize perovskite materials with adequate compositions and even proposing non-hazardous alternatives.

The high photoconversion efficiencies and possible low production and material cost (attributed to solution processability, cheap perovskite materials, alternative low-cost electrodes, and charge selective layers) have established hybrid perovskites as a potential contender to challenge silicon or other semiconductor photovoltaics. The application of perovskite materials and fabrication of devices in industrial environment has been successfully demonstrated;⁶⁵ however, what is holding back the large-scale deployment of perovskite-based solar cells is the instability and shorter lifespan of perovskite absorbers. The challenge of environmental deterioration of perovskites has been tackled by encapsulation technologies,⁶⁶ although the intrinsic instabilities of the material under applied voltage, light-soaking, thermal stress reflected in hysteresis, and performance drift continue to compromise the long-term stability. Furthermore, the use of expensive charge selective materials, e.g., spiro-OMeTAD, and gold electrode in the highly efficient PSCs increases the levelized cost of electricity (LCOE) by up to 500%–800% compared to the FTO/SnO₂/perovskite/NiO/Cu module, which was calculated to be 4.43 US cents kW h⁻¹ (in comparison, the single junction Si-module has 5.50 US cent kW h⁻¹).⁶⁷ Therefore, a lot more research and concerted efforts are necessary to address the shortcomings of charge carrier transport, ionic mobilities, and main sources of losses in bulk and at the interfaces, which is a materials challenge.

Therefore, using the big dataset from the perovskite research community as a basis, compositional engineering coupled with modern machine learning systems can enable faster transition of perovskite science and technology toward commercialization. Beside this, investigations based on solution chemistry, crystal structure, nucleation, defect engineering, and device physics are essential to ensure a steady growth in understanding of the perovskite material as the class of perovskite material offers relatively unexplored versatility in applications.

Other potential applications of perovskites include near-infrared (NIR) solid-state and wavelength tunable 390–790 nm whispering-gallery nanolasers based on CH₃NH₃PbI_3−aX_a (X = I, Br, and Cl).^68,69 Compositional engineering of perovskites is also beneficial for increasing the stability of FET devices, as shown by Cs incorporation into the MAPbI₃ lattice and employing Rb as the passivating agent.⁷⁰ Hybrid perovskites were also found to be useful for photodetection⁷¹ and as sensors for a variety of gases, such as NH₃, O₂, and NO₂, and even some volatile organic compounds.^72–74 Within the last decade, interest in the lead halide perovskite based LED has rapidly increased, as the fabrication cost is comparable to organic LEDs (see Sec. V C). The operational stability, however, is far behind, and the half-lifetime of a few hours under continuous bias is significantly short when compared to the >10 000 h of lifetime needed to compete with organic light emitting diodes (OLEDs). Nevertheless, the beneficial effects of compositional engineering efforts as demonstrated in the improvement of the PV performance also underscore the potential for further development, especially in the exploration of new application fields (see Sec. V B) for this interesting class of functional materials.

Selina Olthof

Halide perovskites, with the structure ABX₃, can be composed of a variety of different cation and anion species, as introduced in Sec. II A. Depending on this composition, the bandgap E_g can vary from ∼1.2 to 3.6 eV, as summarized in Fig. 3(a), for all primary lead and tin compounds (discussion on Ge will be omitted in this section).⁷⁵ 

This variability in E_g is highly intriguing for the field of optoelectronics as the bandgap can be tailored to meet the individual need. For example, for single absorber solar cells, a bandgap around 1.3 eV is ideal, while as a wide gap cell in tandem applications, much larger bandgaps are desired (for example, ∼1.7 eV in combination with a silicon sub-cell; see Sec. V A for further examples). In the case of light emission (see Secs. V B and V C), appropriate bandgaps for display applications range from ∼2 eV for red emission to ∼2.8 eV for blue emission.

The changes in bandgap come about due to differences in the valence band (VB) and conduction band (CB) position that are influenced by the atomistic level positions, the lattice size, and lattice distortion. Band structure calculations show⁷⁶ that the top of the VB consists of hybridized metal s (M_s) and halide p (X_p) states, as sketched in Fig. 3(b). The VB is therefore directly influenced by the energetic position of the atomic M_s and X_p orbitals that are related to the element’s electronegativity χ [with χ(Pb) < χ(Sn) and χ(I) < χ(Br) < χ(Cl)]. Hence, a change in metal or halide component will lead to a shift in the VB, as depicted in Figs. 3(b-ii) and Figs. 3(b-iii). The bottom of the CB consists of metal p (M_p) and halide s (X_s) orbitals. The orbital overlap is smaller for the conduction band, and therefore, hybridization is not as pronounced, leading to a more ionic bond in which the CB is dominated by the metal state; it was found that the atomic p states of Sn (i.e., 4p) and Pb (5p) are rather similar in energy [Fig. 3(b-ii)].⁷⁵ 

The onsets of CB and VB are furthermore affected by the lattice size, which is determined by the ionic radii of the different anions and cations. As depicted in Fig. 3(b-iv), a smaller lattice will result in confinement effects, shifting the atomic levels slightly upward affecting both VB and CB. In addition, the hybridization will increase, which mainly affects the VB and shifts it upward.

Finally, also the bond angles will affect the degree of hybridization. The highest orbital overlap is achieved in a cubic perovskite structure, resulting in a small bandgap. In a phase transition, e.g., to a tetragonal or orthorhombic structure due to a lowering of the temperature or introduction of an ion with large mismatch in radius, the lattice becomes distorted and the degree of hybridization will reduce. This will lead to a lowering of the VB, as sketched in Fig. 3(b-v), thereby increasing the bandgap; again, the CB is likely not affected as much due to its stronger ionic character.

Obviously, not only pure ABX₃ perovskite structures can be prepared but also different ions can be mixed on the A, B, or X site. This way, the bandgap can be gradually tuned as was already shown in the 1970s by cooling melts containing appropriate proportions of precursors, e.g., by Barrett et al. for CsSnBr_xCl_1−x⁷⁷ or by Weber for MAPbBr_xI_1−x.⁷⁸ Reports regarding recent thin film measurements will be discussed below.

A critical issue when it comes to the comparability and validity of reported perovskite bandgaps is the inconsistency with which these values are determined. Often, the transmission T through a layer of material is analyzed, and from this, the absorbance A (with A = −log T) or decadic absorption coefficient α (with α = A/layer thickness) is reported. Less often, also the reflection is included in the analysis, which nevertheless is necessary to correctly determine A and α. Strictly speaking, from such a transmission and/or reflection measurement, the absorption/reflection onset can be extracted, which is not identical to the bandgap.

For a direct bandgap, where VB and CB exhibit a square root dependency on energy, the following relationship can be derived:

Therefore, plotting (αhν)² vs the photon energy in a so-called Tauc plot results in a straight line from which the optical gap can be extracted. In the case of an indirect semiconductor, the exponent of the left-hand side term changes to 1/2; for 3D halide perovskites, theoretical calculations consistently show direct transitions at the R point, so the equation shown above should be valid. Performing this Tauc plot analysis is commonly considered to be the more accurate approach for bandgap determination; however, there are limitations: (i) Issues can arise from the presence of trap or impurity states where the distributions of CB and VB electronic states do not terminate abruptly at the band edges. Using, e.g., photothermal deflection spectroscopy, which can measure down to very low values of α, transitions between localized and tail states can be seen as widening of the so-called Urbach tails or even as distinct sub-bandgap features; only above the Urbach tail region a Tauc plot analysis is meaningful. Even though gap state formation is not very pronounced in the defect tolerant halide perovskites, they have been observed, for example, in mixed halide systems.⁸⁰ Telling apart bandgap changes and defect state formation is not trivial. In the past, bandgap narrowing of a perovskite crystal by impurity Bi-doping has been reported.⁸¹ However, follow up experiments suggest that this change was caused by a change in defect concentration.⁸² (ii) Furthermore, if an exciton feature is present, then fitting the onset using a Tauc plot is inaccurate;⁸³ rather the theory described by the Elliott formula should be applied.⁸⁴ Here, the absorption of parabolic continuum states (band-to-band transition) is combined with an additional discrete absorption by an excitonic state. From such fits, values of the excitonic binding energy and bandgap can be deduced. However, due to the large number of fitting parameters, values extracted, e.g., for MAPbI₃ at room temperature using this approach vary between 5 and 29 meV. For a review over recent results, we refer to Ref. 85. In particular, lead-based halide perovskites show a rather distinct exciton feature at the band edge (see, e.g., the supplementary material of Ref. 75), which can lead to inconsistencies in reported values.

As a final remark, it should be checked whether the intended perovskite composition is indeed given in the prepared thin film. It is well-known that when processing a MAPb(I_xCl_y)₃ precursor solution, the incorporation of Cl ions into the perovskite crystal lattice is viable only in small quantities.⁸⁶ Furthermore, solubility issues can lead to deviations from the intended film composition, especially for Cs-containing precursors. Similarly, in the case of thermal evaporation, the severe issues related to monitoring the actual evaporate rates of the small organic cations⁸⁷ can lead to deviations in the final film composition.

Even though these issues regarding consistency in data evaluation prevail, we want to give an overview over the changes that can be introduced in the bandgap when the perovskite composition is tuned. For brevity, we focus on thin film measurements, therefore leaving out research on single crystals or nanoparticles.

The first work looking at mixed halide perovskite compositions was published by Noh et al. in 2013, investigating MAPb(I_1−xBr_x)₃.¹⁶ They found a gradual reduction in lattice size with the increasing Br content accompanied by an apparent change in color from black to red and yellow. The change in bandgap from 1.58 to 2.28 eV is not linear and can be described by a bowing equation,

Here, the first two terms describe a linear change in bandgap between E₁ and E₂, and the last term introduces non-linearity with a bowing parameter b. The reasons for the non-linear behavior is still a subject of debate and could be related to changes in bond angles and the mixing of atomic states; for further reading, we refer, e.g., to Refs. 88 and 89. A similar bowing behavior was observed for MAPb(Br_1−xCl_x)₃ (E_g varying between 2.42 and 3.16 eV)⁹⁰ and CsPb(I_1−xBr_x)₃ (E_g between 1.77 and 2.38 eV).⁹¹ For FAPbI_yBr_3−y, the gap can be tuned from 1.48 to 2.23 eV, but no 3D perovskite can be formed for the intermediate compositions of y = 0.5–0.7 due to lattice instabilities.^92,93 This can be circumvented by introducing a fraction of the smaller cations MA or Cs.^94–95 Less studies on halide mixing have been published for tin based perovskites so far; here, the changes seem to be rather linear, for example, in MASn(I_1−xBr_x)₃ (E_g 1.3–2.15 eV)^96,97 and CsSn(I_1−xBr_x)₃ (E_g 1.31–1.75 eV).⁹⁸ 

The bowing effect is more pronounced in the case of mixed-metal perovskites where it can even lead to a bandgap narrowing with respect to the values of the pure materials. This can extend the absorption into the infrared region, as first reported by Stoumpos et al. for MASn_xPb_1−xI₃.⁹⁹ Absolute values reported in the literature differ somewhat due to the issues discussed above, but it seems that a reduction by 50–130 meV can be achieved in this mixed system compared to pure MASnI₃;^89,99,100 in the case of FASn_xPb_1−xI₃, the reduction is 100–200 meV.^79,88,89 For Br compounds, the reported results are less consistent, but bandgap narrowing in thin films has also been observed.^89,101,102 In an extensive study, Rajagopal et al. showed⁸⁹ that the amount of bowing in the mixed-metal perovskite scales with the macrostrain present in the pure films, which affects octahedral tilting and lattice distortion.

Mixing A-site cations has only little effect on the bandgap, introduced by minor modifications in crystal size or variations in bond angles. Such a variation of the A site cations is rather of interest for changing the phase or temperature stability of a perovskite system (see Sec. II A). Changes in E_g are mostly less than 100 meV, as, e.g., reported for FA_xMA_1−xPbI₃^103,104 and FA_xMA_1−xPbBr₃.⁹⁴ However, in mixed perovskites with significant changes in lattice distortion, the effect can be larger than 200 meV.^79,105

Overall, there is a complex interplay between variations in atomistic energy levels, lattice size, and octahedral tilting/strain that leads, in most cases, to some degree of non-linearity in the bandgap change when the composition of a perovskite film is gradually tuned, as depicted in Fig. 4. With these different effects at play, it is not trivial to predict E_g values of mixed perovskite systems, and carefully evaluated and consistent measurements are needed to provide this information.

As a further remark, the bandgap can be influenced by other parameters, such as temperature, pressure, or confinement effects in nanoparticles. For brevity, these topics have not been discussed here but present further avenues that widen the utilization of this material class and can help to understand their fundamental properties.

Andrei D. Karabanov, Doru C. Lupascu

The high efficiency of perovskite solar cells relies on high carrier mobilities, effectiveness of exciton break-up, and a long lifetime of the generated charge carriers. In this section, we show that all three are directly related to dielectric effects.

In order to understand dielectric effects, one has to realize that these can be very scale dependent. Before entering into the details of halide perovskites, we will outline a few general aspects.¹⁰⁶ 

Dielectric effects reflect the response of matter to an electric field WITHOUT DC conductivity. So essentially, one has to consider the response of a capacitor to an electric field keeping in mind that this capacitive effect can occur on very different length scales. Under AC-electric fields, conductive components will arise also in the dielectric response, which is the reason why complex impedance is introduced.

The simplest dielectric effect is realized in the deformation of the electronic shell of an atom with respect to the position of the nucleus. Under an external field, the atom itself thus forms an electric dipole. After field removal, such an atomic dipole disappears. A similar effect can occur one scale up. In particular, in an ionic crystal, the positions of the ions are shifted under the action of an external field. Dipole formation now arises due to the shifting of the relative positions of the positive and negative ions of the lattice. After field removal, everything returns to its initial state: this is termed paraelectric behavior.

If a relative shift of ionic positions arises in a crystal lattice without the application of an external electric field, one is concerned with pyroelectric behavior because this shift is typically temperature dependent. Most systems display vanishing shifts at high temperatures and ordering when temperature is lowered. If such ordering generates permanent ordered dipoles, pyroelectric order arises. This is intrinsically related to a reduction in crystal symmetry. The most common mechanism driving the phase transition into an ordered electric state is the soft phonon effect, namely, a loss of stiffness of the crystal for one or more of its ions in the unit cell.¹⁰⁷ Crystals showing pyroelectric effects cannot have a center of symmetry in the point group of their crystal structure. This type of ordering is classified as long range because the ordered state extends over large parts of the prototype crystal, namely, a “domain” of electrical ordering.

If such an ordered state can be electrically reversed in between different stable orientations in the crystal, it is called the ferroelectric effect. Thus, a prerequisite for ferroelectricity is a non-centrosymmetric crystal symmetry and multiple stable orientations of mutually ordered dipoles within the same crystal.

Another contribution to dielectric effects arises if electric dipoles exist intrinsically, namely, if we are concerned with dipole molecules. The best known example is the water molecule. In halide perovskites, the methylammonium ion, among others, is an electric dipole molecule. Also many liquid crystals contain dipole molecules and show ordering. In certain cases, the ordering of the molecules can also be of long range character, and a ferroelectric effect is known in certain smectic liquid crystals.¹⁰⁸ 

The rotational motion of the MA ion was early on suggested to contribute to the dielectric response¹⁰⁹ as was later verified in experiment.^110,111 Chen et al.¹¹² showed in experiment that point defect interaction with MA ions highly influences photoconductivity and the Hall effect. Single crystals show much better photoconductivity than thin films. Solution grown films contain the highest number of defects.¹¹² Despite the encountered very high numbers of defects, the authors already evoked the dipolar screening by the MA ions to warrant good conduction nevertheless.¹¹² 

In a previous work, we showed that despite many theoretical assumptions in this sense, MAPbCl₃, MAPbBr₃, or MAPbI₃ are not ferroelectric. They exhibit an antiferroelectric phase transition in the range 100–150 K¹¹⁰ and show no long range ordering above this temperature. The ionic lattice shows paraelectric behavior with a very high dielectric constant of roughly ɛ_r = 30 up to very high frequencies in the gigahertz range (∼10¹⁰ Hz). In particular, we want to emphasize that these three solar cell materials are NOT ferroelectric at room temperature.

The fundamentally interesting effect in the methylammonium-containing materials is the dipole of the methylammonium ion itself. It is known that water molecules, due to their high dipole moment, strongly interact with ions and other matter. One of the effects is micellon formation, namely, the ordering of the molecules around a charged entity, typically in the radial direction and oriented to mitigate the field of the charge carrier at the center, a typical screening effect. This effect, e.g., dominates dissolution of ionic crystals. A micellon is a local state of ordering. It arises in suspensions, emulsions, ceramic slurries, biological systems, etc.

The interesting fact about the halide perovskites containing methylammonium or formamidinium is that these molecules can rotate in their lattice locations WITHOUT long range ordering. Thus, their response is very similar to a state in which they would be in a liquid state and can in a broader sense be compared to spin glass states in magnetic systems.

Now, the charged entities in a semiconductor are an electron or a hole. We proved experimentally¹¹⁰ that two mechanisms screen the electric charge of these electronic charge carriers. The first and classical mechanism is the formation of a Fröhlich polaron, namely, the relaxation of the crystal lattice of an ionic solid toward the charge. The second one arises due to the very local reorientation of the methylammonium dipole ions toward the respective charge.

We called the entity, charge carrier plus rotated dipole ion, a micellon. This micellon provides roughly 50% of the screening effect, namely, an increase in the relative dielectric constant. The remainder stems from ionic shifts in the unit cell, the classical Fröhlich polaron formation. The combination of both was termed hyperpolaron by us (Fig. 5)¹¹⁰ in order to illustrate the strong impact of this new type of charge carrier, which is solely due to dielectric screening on the properties of the methylammonium lead halides and potentially other crystals of this family that provide rotating molecules within the crystal structure.

The next question now concerns exciton breakup: How does a high local dielectric response alter the exciton binding energy? A useful analogous picture to understand the role of the dipole ions is to imagine this like a dissolution process of an ionic entity in water. The breakup of the ionic bond is much facilitated by the gain in energy due to the adherence of the surrounding water molecule dipoles. After screening, the two ions can separate. A similar process arises in the methylammonium lead halides: the two charge carriers formed during light absorption, forming the exciton, rapidly become screened. On the time scale of processes, likely the exciton forms first, then polaronic screening arises, and its time constant is slightly shorter than for molecular rotation. Then, the molecules rotate to add to the screening. Effectively, the Coulomb interaction of the electron and the hole is largely reduced, which is the same as saying that the exciton binding energy drops dramatically due to the dielectric effect.

One counter argument could be that effectively the binding energy of the charge to the lattice response is very large due to polaron formation. Thus, a small polaron should form that is localized (an electronic state deep in the bandgap). The ingenious detail is that there are two mechanisms providing the screening, each operating at other typical relaxation frequencies. Thus, the coupling arises to a much broader frequency spectrum than simple lattice relaxation. This avoids total localization of the deformation of the lattice because, effectively, a jump out of the energy well mechanism operating at another frequency helps to suppress full localization and small polaron formation. One could even imagine an energetic double well problem where the difference in intrinsic frequencies could drive a beat frequency, but theoreticians will have to deal with these details in future work.

Another important aspect of the dielectric screening is its effect on localized defects, such as dopants, ionic vacancies, interstitials, or anti-site defects. All these represent electrical charges in the lattice and thus form scattering sites for electron transport. On the time scale of lattice vibrations, these defects remain localized (even though defect jumps also arise due to collective excitation by phonons, but their constructive interference is a rare event). Hence, point defects are statically localized in the context of electron transport. Therefore, all dielectric contributions present in the crystal, even the slow components, will provide screening of the localized point defect. The charge effectively experienced by a bypassing electron or hole is smaller by a factor of 60 than in the unscreened scenario. Silicon only provides ɛ_r = 11. Dielectric defect screening in methylammonium lead halides is thus six times more effective than in silicon.

Another assumption was made that photoexcited electron and hole pairs could be separated in internal junctions between ferroelectric domains.¹¹³ After a long debate, it was concluded that tetragonal MAPbI₃ is not ferroelectric for the following reasons: most importantly, the centrosymmetry of the I4/mmm space group forbids ferroelectricity and no ferroelectric P(E) hysteresis is observed.¹¹⁰ Locally using scanning piezoforce microscopy, no dependence between the applied voltage and the resulting strain response and no polarity inversion with the change in the applied high voltage were seen, both being inherent to a ferroelectric.¹¹⁴ 

Dielectric properties of completely inorganic metal halide perovskites are also of great interest because such systems show better stability compared to hybrid halides.¹¹⁵ One of the prominent examples is CsPbX₃. This material also has a high dielectric permittivity (Fig. 6) leading to effective screening, but the contribution from dipole rotation (e.g., the MA-ion) is not available. Thus, at low frequencies, the dielectric constant amounts to merely half of the one for MAPbX₃. This reduced screening, in particular, of defects can explain the lower power conversion efficiency of CsPbX₃ perovskite solar cells, as more charge carriers are scattered at defects and the effective charge carrier mobility is reduced.¹¹⁶ 

Polarons form in any semiconductor due to the finite dielectric response, namely, its high frequency components. The higher the dielectric constant, the stronger is the polaron formation and its associated trapping energy. Due to their very high dielectric constant, the charge carrier mobilities in the lead halide perovskites are reduced in comparison to conventional semiconductors. Miyata et al.¹¹¹ used broadband dielectric spectroscopy in the frequency range 10⁶–10¹³ to see the response of polarons to the electric field in single crystals of all-inorganic CsPbBr₃ and hybrid MAPbBr₃.

As seen in Fig. 7, in CsPbBr₃, the dielectric constant is constant around ɛ_r = 20 from 1 MHz to 100 GHz and is around 60 in (CH₃NH₃)PbBr₃. The liquid-like rotational relaxation between 10¹⁰ and 10¹¹ Hz of the organic polar cations (dropping from 50 down to 20) is the same mechanism as called micellon before. The lifetimes of polarons in hybrid (CH₃NH₃)PbBr₃ are increased because their recombination is significantly hindered by this liquid-like polarization response.¹¹¹ The change in dielectric constant from 10⁶ to 10¹⁰ Hz by Δε_r = 10 can be related to a dynamic stiffening of the lattice to higher frequencies, being more pronounced in a hybrid lattice than in an all-inorganic system.

The dielectric response is also partly due to the lone-pair activity of Pb²⁺. These lone pairs can be responsible for the reduction of electron–hole recombination, leading to the increased carrier lifetimes. The polar distortions induced by lone pairs influence dielectric properties in these crystallographically centrosymmetric phases.¹¹⁷ 

The photoinduced change in the relative permittivity (Δε_r) gives information about the polarization in the perovskite systems. Conventional perovskites, such as MAPbI₃ and FAPbI₃ exhibit no measurable photoinduced changes in the real component of relative permittivity (Δε_r). Double and triple-cation perovskites show high values of Δε_r, meaning that more complex mechanisms lead to the polarization response of double and triple-cation perovskites.¹¹⁸ 

FA_0.83Cs_0.17Pb(I_0.9Br_0.1)₃ (FACs) and (FA_0.83MA_0.17)_0.95Cs_0.05Pb(I_0.9Br_0.1)₃ (FAMACs) enable high power conversion efficiencies. Hong et al.¹¹⁸ examined the frequency-dependent time-resolved microwave conductivity (TRMC) at frequencies of 10 GHz helping to reveal molecular motions of A-site cations. Δε_r of the above-mentioned compounds was measured as a function of time before, during, and after illumination by a nanosecond pulsed laser.

It was found that there is a proportionality of change in relative permittivity to the photogenerated carrier density (Fig. 8).¹¹⁸ ε_r decays with a shorter time constant than conductance, meaning that the photoinduced free charge carriers induce an immediate additional “dielectric” response that rapidly decreases while the lifetime of free carriers is significantly longer. The mechanisms explaining this effect locally are not yet determined. The photoinduced polarizability in FACs is larger in comparison with FAMACs.¹¹⁸ The local mechanisms behind this difference remain to be determined. The local polarizability could, e.g., be related to exciton lifetimes on the different organic cations.

Apart from conventional 3D perovskites, 2D and 1D crystal structures are studied nowadays. Claims on ferroelectricity in these systems could be justified due to the lower symmetries of crystals, but experimental verification does not typically meet the full requirements in the “ferroelectrics”-society. As we do not want to exclude the validity of these data, a brief summary of this work follows.

Several 2D perovskite ferroelectric structures were presented recently.^120–121 The change in the dimensionality is reached by the substitution of the A-cation by organic molecules, such as benzylamine(C₇H₉N),¹²⁰ hexahydroazepine (C₆H₁₃N),¹¹⁹ and others. Ferroelectricity can be obtained by fluorination of these structures. In this process, the substitution of one hydrogen atom (monofluorined substitution) or several hydrogen atoms (perfluorined substitution) with fluorine atoms is done. This leads to the structural change and enhancement of ferroelectric performance. One of the examples is (PFBA)₂PbBr₄ (PFBA = perfluorobenzylammonium)—multiaxial ferroelectric with the Aizu notation of 4/mmmFmm2(s), which shows a large piezoelectric response, a spontaneous polarization of 4.2 C cm⁻², a high Curie temperature of 440 K, and it is a semiconductor with a direct bandgap of 3.06 eV.¹²⁰ 

Another method is the substitution of A-cations by organic molecules containing organic functional groups R or S. This leads to the possibilities of changing the photofunctionality and conductivity properties of the perovskites. Moreover, the environmental stability of these materials could help in engineering the robust and highly efficient solar cell.

Yang et al.¹²² proposed [R-1-(4-chlorophenyl)ethylammonium]₂PbI₄ (R-LIPF) and [S-1-(4-chlorophenyl)ethylammonium]₂PbI₄ (S-LIPF) 2D lead iodide perovskites, R and S denoting the enantiomers (Fig. 9). Ferroelectricity of these materials was derived from piezoresponse force microscopy (PFM)-based hysteresis loop measurements. The spontaneous polarization was calculated using the point charge model. The bandgap from a Tauc plot is 2.34 eV, which is favorable for the application in photovoltaics.¹²² At present, it cannot be said whether we are concerned about real ferroelectricity or a PFM-tip induced effect.

Polarization can be increased when additional small A-site cations are introduced in the spaces of octahedral sheets, forming a quasi-2D metal halide perovskite (MHP; formula of R₂A_n−1B_nX_3n+1). The higher complexity of the temperature-dependent structural phase transition in these materials in comparison to the 2D MHPs is dictated by the distortion of the octahedra due to smaller A-cations, which lead to lattice displacement, providing an additional contribution to polarization.

The multi-layered (n = 3) quasi-2D MHP (BA)₂(MA)₂Pb₃Br₁₀ (BA = n-butylammonium, C₄H₉NH₃; MA = methylammonium, CH₃NH₃) was synthesized by Li et al.¹²³ by alloying the 3D MHP MAPbBr₃ perovskite with n-butylammonium. The organic components, namely, MA and BA, lead to the order-disorder transition, inducing electric polarization, which can be seen in Fig. 10, allowing for ferroelectricity. X-ray diffraction (XRD) analysis at room temperature showed that this material can be ferroelectric with a polar space group of Cmc2₁.¹²⁴ 

A decrease in dimensionality is also possible with systems containing other organic groups as A-cations, such as (R)-(–)-1-cyclohexylethylamine (R-CYHEA, C₈H₁₅NH₂) or (S)-(+)-1-cyclohexylethylamine (S-CYHEA, C₈H₁₅NH₂), which leads to the formation of 1D R-CYHEAPbI₃ and S-CYHEAPbI₃ perovskites. These organic groups remove the inversion symmetry of the material, making it a potential ferroelectric, while the PbI₆ octahedra are responsible for the semiconducting properties. The absence of the inversion symmetry was also proven by several methods, such as density functional theory and structural and spectroscopy analysis. Ferroelectricity was confirmed with dependent synchrotron XRD, differential scanning calorimetric, temperature-dependent dielectric constant, and temperature-dependent pyroelectric current. Such materials could open new possibilities, for example, in spin-orbitronics.¹²⁵ 

Dielectric studies play an important role in the understanding of materials for the use in the optoelectronics and photonics. The examination of different dielectric responses in a broad range of frequencies can reveal screening effects, the influence of the organic and inorganic cations on the polarizability, charge-carrier lifetime, effects stemming from the defect states, and charge carrier mobilities.

The examination of perovskite systems with different techniques, such as impedance spectroscopy, microwave or THz-time-domain spectroscopy and piezoforce microscopy, can help to reveal carrier mobilities, effectiveness of exciton breakup, and lifetime of charge carriers, as well as the presence of electric polarization and ferroelectricity or the absence of these.

The challenge of revealing ferroelectricity is due to several artifacts that can arise during PFM measurements, erroneous assignment of the space group, leakage current in the ferroelectric P(E) hysteresis, and many others. Irrespective of all these techniques, a thorough understanding of the symmetry group of the crystal is the basis of assigning pyroelectric, piezoelectric, or ferroelectric effects.

Laura Herz

The performance of solar cells critically depends on efficient photocurrent extraction, which, in turn, relies on sufficient mobilities of charge carriers. As a rough guide, charge-carrier diffusion lengths, which depend on the mobility-lifetime product of charge carriers, ought to exceed the thickness of the perovskite film required to absorb a substantial fraction of the incident sunlight. Much attention has therefore been devoted toward optimizing charge-carrier mobilities in metal halide perovskites and developing a fundamental understanding of the underpinning factors.^126,127 Here, a distinction has been made between intrinsic factors, such as charge–lattice interactions that cannot fundamentally be avoided, and extrinsic issues, such as grain boundaries, defects, energetic disorder, or background doping.¹²⁶ Specifically, for the class of metal halide perovskites, the intrinsic mechanisms limiting charge-carrier mobilities are now fairly well understood.^127–130 As a first approximation, intrinsic limits are well-described within the Fröhlich model of large polarons,¹³¹ which derives from the coupling of charge carriers to the electric polarization field generated by the collective longitudinal optical (LO) vibrational modes of the metal halide sub-lattice. Absolute charge-carrier mobility values derived from this model form reasonable upper limits when compared to the spread of available experimental data and seem to agree well with mobility trends with compositional variations.¹²⁶ For example, the Fröhlich model correctly predicts the experimentally observed¹³² decreasing trend in charge-carrier mobility along the iodide–bromide–chloride substitution line, which derives from the increasing ionicity of the lead-halide bond and the associated changes in the dielectric response of the metal halide sub-lattice.^129–130 Similarly, increases in charge-carrier mobilities with substitution of tin for lead^126,133,134 may result from the resulting increase in LO phonon frequencies,¹³⁵ given that the Fröhlich model depends on the dimensionless ratio of LO-phonon to thermal energies. A-cation substitution (e.g., MA, FA, or Cs) has, on the other hand, been found to have insufficient influence on charge-carrier mobilities because the electric field to which charges couple arises primarily from the LO phonon mode of the lead-halide sub-lattice.¹²⁷ Such models limit the maximum charge-carrier mobilities attainable for the prototypical MAPbI₃ at room temperature to 100–200 cm² V⁻¹ s⁻¹, which is substantially lower than the equivalent value for GaAs,¹²⁷ because of MAPbI₃’s lower LO phonon frequency (lead is a heavy atom), higher ionicity of the polar lattice, and, in the case of conduction-band electrons, significantly higher effective mass.

Aside from these intrinsic limits posed by electron–phonon coupling, charge-carrier mobilities in metal halide perovskites may also be subject to extrinsic effects arising from material imperfections, which have formed a persistent challenge for a range of specific materials.^{126,133–134} Charge-carrier mobilities in prototypical metal halide perovskites implemented in high-performance solar cells, e.g., APbI₃, where A is typically a combination of MA, FA, and Cs, are already likely to be close to what can be achieved in terms of optimized mobilities. However, lingering challenges persistently remain for specific cases, including mixed bromide–iodide lead perovskites with intermediate bromide fractions between 20% and 90%, for which poor crystallinity and charge-carrier mobility¹³² combined with light-induced halide segregation⁵¹ pose a barrier to the optimization of high-bandgap metal halide perovskites. Similarly, at the low-bandgap end, mixed lead–tin iodide perovskites have seen charge-carrier mobilities significantly suppressed by the formation of tin vacancies, which result in unintentional background hole doping that enhances the scattering of charge-carriers.^134–135 Such effects form a current hurdle to bandgap-tunability of metal halide perovskites that is particularly detrimental to the development of silicon-perovskite and all-perovskite tandem solar cells. Further challenges also remain to the development of fully accurate theoretical models of charge-carrier mobilities in metal halide perovskites that take account of the special characteristics of these materials. While the Frohlich model presents a good first approximation of electron–phonon coupling in metal halide perovskites, some difficulties arise from the inherent softness of these materials^136,137 and the presence of many atoms per unit cell, which leads to multiple LO phonon modes needing to be considered.¹³⁰ In this context, there has been much debate around the experimentally observed^138,139 T^−1.5 temperature-dependence of the charge-carrier mobility in MAPbI₃, which at first¹⁴⁰ appeared to be incompatible with a simple application of Frohlich theory. However, subsequent investigations have revealed that careful consideration of electronic couplings across the full range of low- and higher-energy LO phonon modes present in MAPbI₃ can replicate the experimentally observed temperature dependence suitably well.¹³⁰ In addition, anharmonicity of the lattice potential has been raised as a concern, given that metal halide perovskites tend to be fairly soft, meaning that the harmonic approximation employed by Frohlich theory could be particularly inaccurate for these materials.^51,137 Recent theoretical models¹³⁷ based on full nuclear dynamics combined with first-principles calculations avoided such implicit harmonic approximations, approximating the steep temperature-dependence of the carrier mobility in MAPbI₃ fairly well.¹³⁷ The extent to which such special characteristics of metal halide perovskites directly affect their optoelectronic properties will therefore form another challenge to be resolved over the coming years.

With regard to bandgap-tunable metal halide perovskites comprising mixed iodide–bromide or tin–lead perovskites, further advances in charge-carrier mobilities and stable performance will no doubt be made based on the ever-improving feedback loop between material synthesis and passivation protocols and advanced characterization techniques. A myriad of improvements in material morphology and reduction in defects are being made, while advanced non-contact probes of charge-carrier mobilities^126,141 have obviated the need for device fabrication to assess such parameters. However, while optimism in the field remains high with regard to raising these specific iodide–bromide and lead–tin compositions to the same optoelectronic and stability standards as their high-performing APbI₃ counterparts, an alternative strand has developed that focuses on the vast category of non-perovskite metal halide semiconductors.¹⁴² Such approaches acknowledge the substantial materials space available outside the much narrower ABX₃ space,¹⁴³ including Ruddlesden–Popper two-dimensional layered perovskites, new double perovskites with mixed metals (A₂BB’X₆), vacancy ordered materials, networks of corner- or edge-sharing [Metal-Halide₆]⁴⁻ octahedra, and general materials with metals in different oxidation states (e.g., 3+ and 4+). While opening a vast new materials space will offer many potential advantages not only restricted to improvements in charge-carrier mobilities but also, for example, to the pursuit of lead-free materials (see Sec. VI F), it also offers fresh challenges. Here, computational screening based on high-throughput first-principles calculations^141,143 will help to narrow down the huge parameter space, identifying promising candidates to explore for synthesis (see Sec. VI H). Continuous development of first-principles computational methods and increasing power of supercomputing infrastructures now allow for rapid materials screening, transforming the discovery of new semiconductors from the current slow, trial-and-error, “needle-in-a-haystack” search into a rapid, targeted, and systematic exploration of a vast group of potential candidate materials.¹⁴¹ Further improvements in this area may also ultimately derive from the increased use of machine learning or “artificial intelligence” in such screening attempts. While such fast-screening approaches already succeed in evaluating relatively straight-forward parameters, such as chemical stability, band structure, and the resulting charge-carrier masses, more complex calculations still pose difficulties. In particular, full evaluation of charge-carrier mobilities relies on the accurate calculation of electron–phonon couplings, which still needs to be brought within reach of genuine fast-screening approaches. Such calculations may be further complicated if an enhanced presence of surfaces and increased structural flexibility potentially enhance polaronic effects in certain new metal halide semiconductors,¹⁴² requiring a level of computational resource even higher than those currently employed for metal halide perovskites.

While much progress has been made over the past five years with regard to an understanding of charge-carrier mobilities in metal halide perovskites, significant work remains to be done within the wider class of metal halide semiconductors. While prototypical metal halide perovskites are now widely accepted to fall within the Frohlich picture of large polarons, some theoretical work is still required to clarify the specific couplings to existing phonon modes and the relative importance of anharmonic contributions of the lattice. Certain extrinsic material challenges also remain, in particular, for large-bandgap bromide–iodide lead perovskites and narrow-gap lead–tin perovskites. In contrast, the factors governing charge-carrier mobilities for the much wider space of non-perovskite metal halide semiconductors are still relatively unexplored. Such materials bear some resemblance to ABX₃ perovskites in that they often comprise similar octahedral building blocks. However, they may differ substantially in terms of lattice flexibility and polarizability, surfaces, and interfaces, thus opening up a vast new area of research.

Alexander Hinderhofer, Frank Schreiber

Scattering methods (e.g., x-ray scattering and neutron scattering) are versatile tools for investigating the structure and morphology of hybrid perovskite materials. With the various scattering methods, many different characteristics of a given sample can be retrieved, including crystal structure, domain sizes, defect densities, roughness, electron densities, unit cell orientation, and phase composition.

X-ray and neutron scattering on single crystals and powder samples or thin-film samples with various degrees of texturing were used to determine the crystal structure and phase behavior of different hybrid perovskite formulations. The continuously tunable element composition of hybrid perovskites leads often to correspondingly shifting unit cell sizes and corresponding characteristics.¹⁴⁴ 

In particular, the application of neutron scattering also allows for the determination of the position of hydrogen atoms within the unit cell and has shown that the central organic cation, often methylammonium or formamidinium, can be present in several different orientations.¹⁴⁵ This is related to the extremely important question of structural dynamics in these systems.¹⁴⁶ 

More challenging is the structure determination for perovskite thin films, which are relevant for device applications. Such thin films are typically polycrystalline with a varying degree of texture (preferred unit cell orientation).

As a standard method for thin film characterization, often x-ray diffraction (XRD) in the classical 2θ Bragg Brentano geometry is applied or, alternatively, x-ray reflectivity (XRR) with parallel beam optics to determine the position of out-of-plane Bragg reflections. In particular, XRR from surfaces and interfaces has developed into a versatile tool, now being frequently used for the characterization of the surface/interface morphology. In the simplest version, the method measures the specular reflection, i.e., the flux of the specularly reflected radiation as a function of the angle of incidence. Specular XRR contains important information, in particular, the thicknesses and electron densities of individual layers in a layered sample as well as root-mean square roughnesses of the interfaces. For more complex structures, the interference between the layers can provide information about the overall coherence of the structure, such as the formation of superlattices.

Two additional experimental configurations are used for complete reciprocal space mapping. Using grazing-incidence small-angle x-ray scattering (GISAXS), island size distributions (small Q) can be probed and analyzed. For large values of the in-plane scattering vector Q_||, lateral structures with very small sizes (down to few nm, including in-plane lattice spacings) can be probed using grazing-incidence wide angle x-ray diffraction (GIWAXS). Since, in a standard experimental configuration, the coherence width of the partially coherent primary x-ray beam is much smaller than the irradiated footprint on the sample surface, the measured signal is averaged over a statistical ensemble of all microscopic configurations of the interface.¹⁴⁷ 

The demanding properties for stable highly efficient solar cell materials present several structural challenges. Even slight changes in the preparation conditions of thin perovskite thin films can lead to significant changes in the structure, texture, and morphology, which in return impact the device characteristics. This makes it essentially compulsory to include structural characterization as a matter of common practice.

Another challenge is the phase behavior of highly efficient formamidinium based perovskites. FAPbI₃ is unstable at room temperature and decays into a hexagonal structure. To avoid the decay, several stabilization methods can be used, for example, changing the perovskite composition or and/or solvent and temperature treatment or capping layers.¹⁴⁸ However, the specific phase composition of a given perovskite structure poses still a problem.

There are several challenges in the area of perovskite structure formation or conversion: for example, in high performance multiple cation perovskite materials, the cation distribution is often unknown. If a respective cation is included in the lattice, how the cations distribute (e.g., statistically vs phase-separation tendency) is sometimes unclear. This poses an interesting challenge to the structural characterization.

Another big challenge for hybrid perovskites is the fast degradation in the presence of water or oxygen. To meet this challenge, 2D-perovskites or a combination of 2D on 3D perovskite structures are applied.¹⁵⁰ Such structures have additional peculiarities from a structural viewpoint. The pure 2D structures include additional spacer molecules (see Sec. II F on 2D perovskites). The formation of an alternating 2D/3D structure is not possible for all kind of spacer molecules, and the domain orientation is of great importance for charge transport properties. Finally, in 2D or 3D perovskites, the 2D layer functions as a passivation against degradation. For the structural characterization, the challenge is here to obtain information on the interface between two layers. This can be achieved by applying GIWAXS and by the variation of the angle of incidence. With such a setup, depth dependent information on the crystal quality, lattice parameters, domain orientation, and the coherence length of a 2D superstructure can be obtained.¹⁴⁹ Some of the above issues can be addressed using scattering methods with time resolution.

Real-time in situ scattering measurements during sample preparation or modification can be used to follow the structural evolution with a temporal resolution of down to 10 ms. The solvent layer during sample preparation can be penetrated by applying high photon energies. This allows for a detailed tracking of intermediate phases and conversion time scales, which improves the understanding of perovskite formation. Figure 11 shows, for example, the perovskite conversion of MAPbI₃ into MAPbCl₃ by the application of MACl solution on MAPbI₃. Figures 11(b)–11(d) shows the corresponding GIWAXS data obtained in situ.¹⁵¹ 

One method to determine the element and ion distribution in mixed perovskite lattices could be anomalous x-ray scattering. Anomalous x-ray scattering (i.e., scattering employing energies near core level of specific elements) can be used to probe the distribution of the lattice site occupation of these specific elements in alloys and doped crystals. In mixed perovskites, e.g., in a mixed iodine–bromine perovskite, the correlation between iodine-occupied lattice sites and bromine-occupied lattice sites can be determined. So far, this method was mainly applied to study well-ordered inorganic perovskite structures.¹⁵² We expect hybrid perovskite layers to be highly ordered and that anomalous dispersion x-ray scattering can be successfully applied.

We believe that in view of the sensitivity of the performance of perovskites to structural details, employing scattering methods is and will remain indispensable for routine characterization. Furthermore, some of the challenges to the understanding of these materials will require the application of advanced tools, such as anomalous scattering, time-resolved methods, or depth-dependent detection schemes. These require typically support from neutron or synchrotron facilities.

Alexey Chernikov, David A. Egger

In addition to three-dimensional systems, the family of metal halide perovskites hosts a rich variety of nanostructures, such as two-dimensional (2D) Ruddlesden–Popper compounds. These materials have been studied and explored for many decades¹⁵³ but have recently re-emerged with renewed interest in their potential for high-efficiency photovoltaic and light-emitting applications¹⁵⁴ as well as in view of their intriguing fundamental properties. This is strongly motivated by the design flexibility associated with their structural characteristics that presents opportunities from the perspectives of technology and fundamental solid state science. As schematically illustrated in Fig. 12, 2D perovskites exhibit a layered structure common for the broader family of van der Waals materials. They adopt the generic structural formula (RNH₃)₂(A)_n−1BX_3n+1, where RNH₃ is usually an aliphatic or aromatic cation that constitutes the spacer between perovskite layers formed by the A, B, and X ions with the number of sublayers denoted by the integer n. The release of the structural constraints that are otherwise implied for the formation of the 3D lattice offers excellent tunability of 2D metal halide perovskites, which further involve multiple types of subclasses, depending on the stacking directions in the crystal. Conceptually, these systems can be understood as natural quantum wells where the electronic excitations are confined in the inorganic layers surrounded by the organic barriers.

This structure leads to a central distinction in the optoelectronic properties of the 2D metal halide perovskites from their 3D counterparts that originates in the strongly enhanced Coulomb interaction due to both quantum confinement and, most importantly, weak dielectric screening from the organic spacer layers. It leads to the formation of highly robust exciton states with binding energies on the order of several hundreds of meV¹⁵⁵ that dominate the optoelectronic response of these materials. Consequently, a rather small spatial proximity of the electron and hole constituents in an exciton also results in a very strong light–matter coupling that is beneficial for efficient absorption and emission. In contrast to more traditional quantum wells or inorganic 2D semiconductors, however, the lattice of the 2D perovskites is unusually soft with characteristic features of anharmonic effects around room temperature,