Hybrid perovskites under pressure: Present and future directions

Over the last years, hybrid organic–inorganic perovskites (HOIPs) have emerged as outstanding light-absorbing materials for highly efficient photovoltaic cells.^1–3 From the realization of the first perovskite-based solar cells in 2009, showing a 3.8% power conversion efficiency (PCE) only,¹ a massive research effort has quickly pushed the performances of these cells, reaching PCE values beyond 29% in a perovskite-silicon tandem solar cell in 2020.^3–5 

The impressive performances of these materials are due to the unique combination of optical and electronical properties suitable for charge carrier generation and extraction, such as high absorption coefficient, long charge diffusion length, high recombination lifetimes, and small carrier effective masses although a modest carrier mobility.^6–12 These excellent properties combined with a facile and low-cost process for their fabrication, usually based on relatively simple film deposition/evaporation on a solid substrate, have pushed a huge amount of scientific production with both fundamental and applied studies. This also led to the development of various solution-syntheses and film-deposition techniques allowing controlling morphology and composition of hybrid perovskites^13–15 for optoelectronic applications including light-emitting diodes,¹⁶ lasers,¹⁷ photodetectors,¹⁸ and transistors.¹⁹ 

These applications and the underlying physical chemical properties of HOIPs arise from their hybrid nature, with many organic and inorganic constituents that can be combined to obtain a large variety of crystalline structures. Among HOIPs, three-dimensional (3D) ones are the first and probably the most studied. They have chemical formula ABX₃, where A is the organic cation [e.g., CH₃NH₃⁺ (methylammonium, MA)] or NH₂CH=NH₂⁺ (formamidinium, FA), B is the metal element (e.g., Pb and Sn), and X is the halide anion (e.g., Cl⁻, Br⁻, and I⁻). Corner-sharing BX₆ octahedra create a cubic inorganic cage surrounding the A cation as shown in Fig. 1(a). The crystal symmetry and phase stability of the 3D structure can be determined using the Goldschmidt tolerance factor, defined as t = (R_A + R_B)/√2 (R_B + R_x), which represents the ratio of the A–X and B–X distances in a rigid-body ball model, where R_A, R_B, and R_X are the ionic radii of A, B, and X ions, respectively.²⁰ Despite the intensive development and promising efficiencies of photovoltaic devices based on 3D perovskites, the presence of degradation phenomena induced by temperature,²¹ by high-intensity light,^22,23 as well as by exposure to oxygen²⁴ and/or water^25,26 poses a limitation to large-scale applications.

To try to overcome these issues, two-dimensional (2D) perovskites have emerged, demonstrating a better environmental stability and extended chemical engineering possibilities.^27,28 Their layered structure is made of 3D perovskite blocks separated by layers of organic cations. Depending on the stoichiometry and on the stacking of the inorganic blocks, they can be divided in three classes: Ruddlesden–Popper (RP), Dion–Jacobson (DJ), and alternating cation in the interlayer space (ACI), having the structures shown in Fig. 1(b). RP and DJ types have the chemical formula A′_mA_n − 1B_nX_3n + 1 (m = 1 and 2), where A′ is the molecular cation acting as an interlayer spacer, A is the smaller cation inside the voids of the inorganic layers, B is the metal, and X is the halide.^28–32 In ACI perovskites, the A cation is also found in the organic layer, following the formula A′A_nB_nX_3n + 1. These features make 2D perovskite structures more flexible and even more tunable than 3D ones. Indeed, the inorganic layer thickness can be easily adjusted by changing the stoichiometry of the A cation, and a wider range of organic cations are acceptable for the A′ site. Although this results in highly stable 2D-based solar cells, their PCE is lower than that of their 3D counterparts, owing to larger exciton binding energy, lower conductivity, and poorer carrier transport, as a consequence of mobile ions confined within the inorganic networks.³³ 

Very recently, research has been extended to lower dimensional systems, namely one-dimensional (1D) and zero-dimensional (0D) perovskites,^36,37 but they are still relatively underexplored compared to their 3D and 2D counterparts. In 1D perovskites, the metal halide octahedra are aligned in a corner-sharing, edge-sharing, or face-sharing fashion creating 1D nanowires surrounded by organic cations. Their configurations and chemical formulas depend on the connecting methods and on the selected organic cations. Finally, for 0D hybrid perovskites, individual octahedral anions or metal halide clusters are isolated and surrounded by organic cations.

Only a few studies report the possibility to use 1D/0D HOIPs in multi-component or mixed-dimensional solar cells, claiming that more efficient and environmentally stable devices can be obtained. Indeed, introducing a layer of 1D HOIPs protect the 3D perovskite films from moisture degradation due to the hydrophobic nature of the large cations employed in low-dimension perovskite structures.^38–42 

A large amount of scientific literature is present for 3D and 2D systems, clearly demonstrating the wide range of optical and electronic properties and their dependence on the atomic structure. For instance, in 3D MAPbX₃ perovskite (X = Cl, Br, and I), the bandgap value can be modified upon halogen substitution: decreasing from 2.97 eV for Cl to 1.53 eV for I-based perovskites.¹¹ The bandgap is also affected by the organic cation⁴³ and the metallic ion (e.g., Pb and Sn).⁴⁴ The metal and the halogen elements have a direct effect on the bandgap, since the band-edge states are mainly formed by their electronic orbitals.⁴⁵ On the other hand, the electronic contribution of the organic orbitals to these states is minor. However, this does not exclude an indirect structural effect of the organic molecule on the bandgap. In the cubic $Pm 3 ¯m$ phase of 3D HOIPs, the molecule is orientationally disordered to satisfy the A-site symmetry and dynamically interacting with the surrounding inorganic cage.^46,47 Different molecular sizes, shapes, and chemical compositions modify the interactions network between the organic cation and the inorganic skeleton, thus affecting the electronic properties of the whole system. In 2D perovskites, the layered structure translates into multiple electronic quantum wells having two main consequences: a bandgap larger than in the 3D counterpart and the formation of stable excitons. It has been demonstrated that the bandgap and the excitonic binding energy decrease when increasing the number of inorganic layers through the parameter n.⁴⁸ 

The molecular orientation can also be exploited as an additional degree of freedom to tune the bandgap. Indeed, 3D HOIPs present several structural phases as a function of temperature, which are characterized by a different degree of ordering of the organic molecule. In general, when lowering the temperature, 3D HOIPs go from a cubic to a tetragonal phase, with a partial orientational order, and then enter into an orthorhombic phase where the direction of every organic cations is frozen.⁴⁹ This is accompanied by a bandgap decrease, indicating a decrease in excitonic interactions and a reduction in the lattice constants on decreasing temperature.^50,51 Changing the temperature, thus, represents a convenient way to explore the structure-properties relationship of these materials and to assess the role of thermal effects on their electronic and transport properties.

In this regard, another thermodynamic variable to consider is pressure. The application of external pressure has proven to be a powerful tool to finely tune the structural and electronic properties of materials without modifying their chemical composition. Thanks to the well-established technology of diamond anvil cells (DACs), static pressures over a range of six orders of magnitudes can be applied, whereas temperature studies usually span over a maximum of three orders of magnitude. Through pressure, the energy landscape can be explored as a function of the interatomic distances. We can, thus, verify the structural stability of a given phase against compression and discover new phases with properties of potential interest for applications.

The reduction in the atomic distances under pressures also modifies the balance between different intermolecular interactions. This is particularly interesting in HOIPs, where strong covalent bonds are present both in the inorganic framework and in organic molecule, whereas weak van der Waals interactions are established between the molecule and the framework. On one hand, the compression of the inorganic covalent bonds, which contributes to the band edges as mentioned before, can directly tune key optoelectronic properties, such as bandgap, electrical conductivity, and photoluminescence. On the other hand, the pressure-induced reduction in the inorganic cage volume and its distortion easily affect the network of weak van der Waals interactions around the organic cation, leading to a modified configuration of the molecular orientation and, possibly, to a different crystalline structure.⁵² 

The results obtained on HOIPs at high-pressure can be further exploited to understand and then master the role of strain in devices. Indeed, the efficiency and stability of perovskite-based solar cells can be drastically affected by the internal strain arising from material processing, multi-layer composition, device operation, and thermal expansion.^53–56 

In this Perspective, we first summarize the main results of high-pressure studies on HOIPs. Since the HOIPs' word is too large for a single perspective article, we will limit our discussion to completely hybrid perovskites, i.e., having an organic molecular cation, thus neglecting all inorganic perovskites and those with mixed cations. Considering very recent review and perspective papers on this topic,^52,57–62 the discussion of the state-of-the-art is limited to common features emerged in HOIPs under pressure. We then discuss what it is still missing, in the authors' opinion, about HOIPs at high-pressure and which new directions could be interesting to take in the next future. Finally, we provide an example of one of the proposed directions by presenting some preliminary results we obtained by exploring the pressure-temperature phase diagram of MAPbBr₃ by infrared spectroscopy.

Tens of studies have covered the behaviors of HOIPs under high pressure, revealing a plethora of fascinating phenomena. The main results reported in such studies on both lead and lead-free hybrid perovskites are summarized in Table I. We intentionally excluded perovskites with inorganic cations (e.g., Cs⁺), although highly relevant for photovoltaic applications, in order to focus our attention on fully hybrid systems. In Table I, we group samples based on the structural dimensionality, and for each group, we highlight the explored pressure range, the pressure transmitting media used, the experimental and computational techniques, and the identified phase transitions.

The first and most studied hybrid perovskites are undoubtedly the 3D methylammonium lead halides, MAPbX₃.^{57,61,63–68} At ambient conditions, MAPbI₃ adopts the tetragonal I4/mcm structure, whereas MAPbBr₃ and MAPbCl₃ have a cubic $Pm 3 ¯m$ one. The structure of MA-based perovskites displays a general common behavior under pressure: they first undergo a crystalline-crystalline phase transition below 1 GPa and then they enter an amorphous phase above 2.5 GPa. Transition pressures, the number of transitions, and space groups seem to depend only on the halogen atom, if hydrostatic conditions are ensured.^57,69 Indeed, it has been demonstrated that transition pressures are shifted under non-hydrostatic conditions and new intermediate phases are stabilized before amorphization. For instance, an orthorhombic Pnma has been observed in MAPbBr₃ at 1.8 GPa when no pressure transmitting media are present.^57,70–72 It is worth noting that a recent single-crystal XRD study identifies this orthorhombic phase with the Pmn2₁ space group.⁷³ From a microscopic point of view, increasing pressure reduces the B–X bond length and, thus, the inorganic octahedra shrink, and transitions are usually marked by octahedral tilting, as indicated by abrupt changes in the B–X–B angle.⁵⁹ Pressure also affects the organic counterpart, with MA molecules freely rotating at ambient pressure that become more ordered in the high-pressure phases, before being trapped in random positions when the amorphous phase is established. We stress that this behavior is intriguing from the fundamental point of view, since MA undergoes subsequent disorder–order–disorder transitions, from a dynamically disordered orientation to a statically disordered.⁴⁶ 

Formamidinium-based lead halide perovskites (FAPbX₃, with X = Br and I) have the same inorganic octahedra as MAPbX₃, with a FA cation in the A site instead of MA. At room temperature, FAPbI₃ crystallizes in a non-perovskite phase, usually named δ-phase that transforms to a cubic perovskite $Pm 3 ¯m$ phase (α-phase) above 150 °C. This phase is retained after the temperature decrease although after around ten days it converts back to the thermodynamically stable δ-phase.^74,75 FAPbBr₃ instead shows a stable perovskite cubic phase at ambient conditions.⁶⁸ Both α-FAPbI₃ and FAPbBr₃ undergo several phase transitions before reaching an amorphous phase above 4–6 GPa.^76,77 It is worth noting that under non-hydrostatic conditions, pressure-induced phase transitions in FAPbBr₃ are observed at higher pressure values compared to similar MAPbBr₃, thus meaning that replacing MA with FA makes the system less compressible.^58,76 Indeed, methylammonium and formamidinium present a different molecular symmetry, with MA dipole moment ten times higher than FA one, leading to stronger/weaker hydrogen bonds between the molecule and the inorganic cage.⁷⁸ 

3D lead-free compounds have also been synthesized and studied at high-pressure with both MA and FA as organic cation.^60,79–83 A recent review summarizes the behavior under compression of these compounds showing also their potential for applications.⁶⁰ X-ray diffraction measurements reveal pressure-induced phase transitions, as reported in Table I, but with amorphization occurring at higher pressures than in lead-based materials, with MASnBr₃ and FASnBr₃ being still crystalline at 9 and 6 GPa, respectively.^79,84 However, note that all the 3D HOIPS mentioned so far undergo reversible amorphization below 10 GPa.

Regarding the electronic properties, the bandgap behavior of 3D HOIPs under pressure is mainly determined by the competition between the shortening of the B–X bond and the changes in the B–X bond angle. Indeed, B–X bond compression enhances the coupling between the B–s and the X–p orbitals narrowing the bandgap while the octahedral tilting reduces the orbitals overlap, thus increasing the bandgap. In the case of MAPbX₃ systems, the competition between these two effects determine the pressure dependence of the bandgap with a redshift followed by a blueshift until amorphization takes place, as shown in Fig. 2.^57,58 On the contrary, FAPbI₃ bandgap decreases on compression up to 4 GPa and no blueshift is reported. However, it is worth noting that the FAPbI₃ bandgap reaches below 2 GPa 1.4 eV, i.e., the lowest value observed for 3D HOIPs, close to the ideal value for photovoltaic applications of 1.34 eV as stated by the Shockley–Queisser theory.^77,85

Besides 3D systems, lower dimensional HOIPs have also been studied at high pressure, especially 2D RP and DJ perovskites, revealing several structural and optical pressure-induced phenomena that are summarized in a perspective recently published.⁵⁹ In general, applying pressure on 2D perovskites results in transitions to lower symmetry phases. At ambient conditions, 2D RP perovskites usually exhibit an orthorhombic phase. The layered structure of RP systems makes them less compressible and structurally more stable compared to 3D HOIPs with amorphization usually observed above 10 GPa.^29,86 Indeed, the presence of longer cations ensures higher structural stability due to van Der Waals interactions among the monolayers.^29,87 Usually, for these perovskites. a phase transition to an orthorhombic or a monoclinic phase is observed before undergoing amorphization. On the contrary, DJ perovskites present a monoclinic space group at ambient pressure and become amorphous under compression without any other phase transition usually below 2.5 GPa. The contrasting high-pressure behavior between the two families has been attributed to the different nature of the organic cation in the spacing layer, monovalent for RP perovskites and divalent for DJ ones. The latter excludes van Der Waals π–π interactions that are instead present in RP phases.⁸⁸ 

As seen in 3D systems, structural transitions and distortion occurring under pressure in 2D perovskite cause changes in the optical properties as well.^59,90,91 In fact, high-pressure photoluminescence experiments performed on several 2D HOIPs, both in RP and in DJ phases, revealed that most of them present the characteristic blue jump already observed on 3D materials but at different pressure values depending on the specific material. After a certain pressure value, which usually correspond to phase transition, the bandgap starts to narrow again.^91–93 It is worth noting that (PMA)₂PbI₄ and (PMA)₂PbI₄ exhibit bandgap narrowing above 7 GPa but with different rates: (PMA)₂PbI₄ bandgap decreases faster than for PEA₂PbI₄ and reaches 1.26 eV at 20 GPa, i.e., a 41% reduction that is the lowest value observed in this pressure range for 2D systems. Since PMA shows less CH groups than PEA, this fast decrease could be explained by the enhancement of hydrogen bonding upon compression.⁹⁴ In 2D perovskites, pressure can also affect the quantum well electronic structure and the trapped excitons. The asymmetric PL emission of several samples, such as (GA)(MA)₂Pb₂I₇,⁹² (BA)₂(MA)Pb₂I₇,⁹⁵ and (HA)₂(GA)Pb₂I₇⁹⁶ shows, on one hand, an increase in the main peak up to around 1.5 GPa, whereas the shoulder associated to trap-state emission totally disappears when the brightest PL is observed.⁹⁶ 

Various one- and zero-dimensional hybrid perovskites have also recently been synthesized, showing interesting optical properties.^35,97,98 In a recent perspective, the high-pressure studies on low-dimensional perovskite, both hybrid and inorganic, have been summarized.⁵⁹ However, the lack of systematic investigation of 1D or 0D HOIPs under compression prevents to identify common high-pressure behavior for these systems.

Since 2015, a continuously growing number of studies about HOIPs at HP have been performed and published in scientific journals, clearly driven by the renewed scientific interest in these materials for photovoltaic applications. Rapidly after the synthesis of a new hybrid perovskite and its subsequent application, the high-pressure community often triggered its interest on the newly discovered compound. Most of the works we have discussed in Sec. II, thus, represent a first exploration of the behavior of a given HOIP at HP, where the structural changes are assessed by XRD and opto-electronic modifications mostly by PL or absorption spectroscopies. These studies, as highlighted, allowed uncovering several dramatic pressure-induced phenomena for the first time, such as phase transitions, reversible amorphization, PL emission enhancement, bandgap modulation, and metallization. These observations, undoubtedly valuable from the fundamental point of view, are also relevant for applications. This knowledge allows establishing a link between structural modifications induced by pressure and the as-obtained optoelectronic properties potentially interesting for new devices. For instance, when the bandgap is reduced under pressure to the Shockley–Queisser limit, as realized for MAPbI₃,¹²³ we know which structure could then be engineered to obtain such a bandgap in a device at ambient conditions.

We, thus, think that the present strategy of characterizing the structure-property relationship mainly through XRD, PL, and absorption spectroscopies should continue to be applied on newly synthesized HOIPs in the future. Among new samples to be considered, it would be interesting to start the investigation of nanometric HOIPs, i.e., thin films, nanocrystals, and nanowires. For thin films, it should be verified whether a deposition or growth on the diamond culet can be performed or not. Otherwise, thin substrates compatible with the available space inside the gasket hole of a DAC must be used. The behavior of a few nanocrystals at HP has been recently reported, but their study is in its infancy if compared to the number of works dedicated to bulk HOIPs. Nanowires of hybrid perovskites have been successfully synthesized and their lasing capability demonstrated. Despite this promising application, no HP investigation of HOIPs nanowires is present in the literature up to date.

As to the samples already investigated, as more and more experiments have been performed, we notice that several inconsistencies have appeared. This clearly calls for new studies to be performed. The most apparent discrepancy is the sequence of phase transitions observed at HP depending on the PTM used. For instance, the HP orthorhombic Pnma phase is stabilized in MAPbBr₃ when Ar is used as PTM,⁷¹ whereas it is not present with He. This led to the straightforward conclusion that the lack of the Pnma phase reflects the “intrinsic” behavior of MAPbBr₃ under hydrostatic pressure, since He is usually considered as the best hydrostatic medium.¹²⁴ However, a recent work demonstrated that Ne and Ar, usually considered among the most hydrostatic PTM, can penetrate in the interstitial spaces of MAPbI₃ and alter the phase transitions sequence under pressure.⁹⁹ This demonstrates that the PTM-HOIP interaction should not be ruled out based on previous experience on other systems and that perfect hydrostatic conditions are potentially unattainable, forcing a trade-off between gaseous PTM, usually more hydrostatic but penetrating, and fluid/solid PTM, less hydrostatic but non-penetrating. This should motivate research groups to investigate HOIPs under pressure with gaseous, fluid PTM and without PTM, using XRD to evaluate the amount of deviatoric stresses on the sample in different hydrostatic conditions.^125,126 In this way, not only the role of the PTM will be fully assessed across the different perovskite classes, from 3D to 0D, but a uniform set of comparable and reproducible data will be produced.

This will represent a stable ground on which it will be possible to deepen the understanding of pressure-induced effects. Up to now, this has been achieved mainly for electronic phenomena, e.g., the HP bandgap behavior in 3D HOIPs, where the major role is played by the orbital overlap along Pb–X, and for PL emission enhancement in 2D HOIPs, where the pressure effect on the electronic trap states has been pointed out. In the future, it would be interesting to see studies focused on the role of the organic cation as well, which has been less explored besides a few works.^46,127,128 Although the molecular electronic states contribute little to the conduction and valence bands, the organic molecule play certainly a role in the structural evolution under pressure, as demonstrated by the order–disorder process found for molecular orientations in the HP phases of 3D perovskites. In 2D HOIPs, their layered nature puts the molecular component even more under the spotlight. Indeed, a couple of papers highlighted the role of the organic cation. For Liu and coworkers, a correlation between the length of the cation and the blue jump in the bandgap vs P has been shown, but the structural picture is missing.⁸⁶ For Qin et al., increasing the length of the cation decreases the compressibility and increases the amorphization pressure.⁸⁷ Although the effect on the compressibility looks clear, the amorphization pressure should be obtained in a more quantitative way. This is indeed a general problem in HP research in HOIPs since the onset of the crystal-to-amorphous transition is often obtained from a simple visual inspection of diffraction patterns, i.e., peaks broadening and disappearing. Therefore, the criterion to establish the onset is highly subjective and changes from paper to paper. It would be desirable to quantify peak widths or intensities as a function of pressure to check whether clear markers of the amorphization onset can be found or not. Coming back to the organic cation, we think that the understanding of what dictates its behavior under pressure would be of general interest for the research on other hybrid compounds, e.g., metal-organic framework, and confined molecules. To this regard, we stress again the importance of having an experimentally consistent dataset, well described, human and machine readable, to look for patterns in the HP behavior of HOIPs and identify the key parameters behind it. This could even prompt the use of machine learning techniques, as already done to find new lead-free HOIPs at ambient conditions with a suitable bandgap for photovoltaic applications.¹²⁹ 

To achieve a deeper knowledge, the set of experimental techniques used at HP on HOIPs needs to be widened. Besides the widespread XRD, PL, optical absorption, and vibrational spectroscopies, there are other techniques already successfully employed at ambient conditions or in a handful of HP studies, which would be worth to generalize. Among them, we believe that it would be important to mainly consider neutron-based techniques, such as neutron diffraction (ND), inelastic neutron scattering (INS), and quasi-elastic neutron scattering (QENS), to better probe the organic component, ultra-fast time-resolved spectroscopies, time-resolved optical Kerr effect (TR-OKE), transient absorption (TA), and optical-pump-THz-probe among others to investigate polaron formation and charge carriers' dynamics and x-ray total scattering to get information about the local structure.

Neutron diffraction on deuterated samples, being more sensitive to light atoms present in the organic cation, could complement XRD providing direct information on the molecular orientation in different HP phases, similarly to what has been done at low temperature and ambient pressure.¹³⁰ The feasibility in DACs has been demonstrated by Swainson and coworkers for MAPbr₃,¹³¹ one of the few papers about HOIPs at HP appeared before the rush of the last years but never extended to other samples. To go beyond the static picture provided by ND and XRD, INS and QENS can be used to probe the cation dynamics under pressure.^131–133 For instance, Wang and coworkers used INS to measure, at THz frequencies, the phonon DOS and lifetimes under pressure at 180 K. They demonstrated, with the aid of molecular dynamics simulations, that increasing pressure at 0.6 GPa results into an orthorhombic-like molecular configuration, thus resembling that at lower temperature and ambient pressure. This is shown in panel (a) of Fig. 3 where the phonon DOS for the orthorhombic phase at 140 K and the one at 180 and 0.6 GPa are compared. The transition is also marked by a one order of magnitude increase of optical phonon lifetimes, witnessing that the organic dynamics can be dramatically affected by pressure.

Focusing on the cation dynamics is also motivated by the fact that polaron formation in HOIPs is favored by molecular dynamical reorientations’ screening of charge carriers.¹³⁵ Polarons are important since they explain some of the peculiar charge carriers' properties that make HOIPs suitable light absorbers. Their existence has been demonstrated through TR-OKE and TA at ambient conditions.^135,136 An example of the TA spectrum of MAPbI₃ recorded at ambient conditions in the 830–940 nm spectral range is shown in Fig. 3(b) (Ref. 134) while Fig. 3(c) reports the TR-OKE response from MAPbBr₃.¹³⁵ In particular, TR-OKE transients recorded with a tunable pump pulse below and above the gap allow revealing the signal related to the polaron formed by photoexcited carriers and optical phonons. TR-OKE has been very recently used to study the water dynamics at HP in a DAC¹³⁷ and could, thus, been used to investigate how polarons are affected by lattice compression, which modify the structural dynamics taking part in polaron formation itself. The potential of combining time-resolved and HP has been also demonstrated by a recent work where femtosecond transient absorption spectroscopy applied to MAPbBr₃ revealed that the photogenerated carriers' dynamics is modified across pressure-induced phase transitions.¹⁰¹ Electrodynamics could be also probed by optical-pump-THz-probe spectroscopy, where the electrical conductivity is measured at THz frequency after a short optical pulse, then providing the charge carrier mobility as done at ambient conditions.¹³⁸ Finally, there is a widespread agreement on the presence of local distortions in the HOIP structures, but experimental studies based on techniques able to probe the short-range order are scarce and mainly focus on the MAPbX₃ family. Low-temperature neutron and x-ray pair distribution function (PDF) analysis proved to be valuable techniques to investigate octahedral tilting and hydrogen bonds arising between the organic cation and the inorganic skeleton.^139,140 Performing the PDF analysis on HOIPs at high pressure would give the opportunity to probe local structural evolution under compression and shed light on complex and reversible pressure-induced amorphization observed for the vast majority of HOIPs.¹⁴¹ The large set of data produced by these new experimental investigations will undoubtedly need the aid of theoretical studies as well.

The new and old experimental tools we described should be also applied in a larger pressure range than a few tens of GPa to search new electronic and structural phases. For instance, reaching pressure close to the Mbar would allow to investigate insulator-to-metal transitions in HOIPs, as done only on MAPbI₃ so far.^100,105 The search for new phases will also benefit from combining pressure with temperature, thus starting an exploration of the PT diagram of these materials that could reveal new structures, with unknown properties. Different phenomena could be investigated at temperatures above or below room temperature such as the possibility to recover quenched metastable phases of HOIPs observed at high pressure and temperature, as recently done in the inorganic counterpart CsPbI₃.¹⁴² HP high-temperature (HT) studies would also be interesting to investigate the solid-to-liquid transitions and glass phases quenched after melting, as recently discovered only at HT.^143,144 At low-temperature (LT), as discussed in Secs. I and II, MAPbX₃ undergo a cubic-tetragonal-orthorhombic sequence of transitions, which is characterized by an increased ordering of the organic molecules. When increasing pressure at room temperature, a similar ordering has been observed before amorphization takes place at higher pressure, with the consequent loss of long-range ordering.⁴⁶ Therefore, from the fundamental point of view, the HP and low-temperature (LT) combination allows investigating the interplay between cation ordering at low temperature and pressure-induced disordering.

To the best of our knowledge, only two experimental studies have been published a long time ago on the pressure-temperature phase diagram of MA lead halide perovskites.^145,146 The first paper has been published in 1992 by Onoda-Yamamuro et al. that investigate MAPbX₃ (X = I, Br, and Cl) using a high pressure differential thermal analysis (DTA) apparatus between 0.1 Pa and 200 MPa and from 90 to 400 K.¹⁴⁵ In another study, Gesi describes the dielectric properties of MAPbX₃ single crystals up to 700 MPa and in the 100–360 K temperature range.¹⁴⁶ These two studies, although pioneering, explore a very limited PT range and have never been confirmed or extended using more powerful and widespread techniques as vibrational spectroscopy and XRD. About theoretical studies, there is only one recent publication where the emergence of new MAPbI₃ structures at low temperature and high pressure has been discussed. The authors employed the minima hopping method to explore the potential energy surface of MAPbI3 and found two new thermodynamically stable phases that could emerge by compressing the orthorhombic low-temperature phase. These phases present a 1D structure consisting of face sharing octahedra stacked on top of each other's forming pillars surrounded by the organic cations.¹⁴⁷ However, this study is still waiting for experimental verification. Since we consider HPLT studies particularly worth of attention in future research on HOIPs at extreme conditions, in Sec. IV, we will present a preliminary study on MAPbBr₃ performed by our group as an example.

The limited results and the lack of recent experimental studies at HP and LT prompted us to perform a preliminary investigation of the phase diagram of methylammonium lead halides by means of IR spectroscopy. Although an unambiguous structural characterization can come only from diffraction studies, as done for the majority of high-pressure studies on hybrid perovskites, IR spectroscopy represents a powerful and sensitive technique to probe the organic dynamics, providing valuable insights into its motion and local interactions as hydrogen bonding.^46,148 In particular, we focused on MAPbBr₃ since previous studies have clearly established that MAPbBr₃ adopts the cubic Pm-3m phase at room temperature, differently from MAPbI₃ that is tetragonal at 300 K, and undergoes several phase transitions when lowering the temperature. Two tetragonal phases I4/mcm and P4/mmm are stabilized below at 237 and 155 K, respectively. An orthorhombic Pna2₁ phase appears below 149 K.¹⁴⁹ Infrared spectra of low temperature phases have been reported and well discussed in a paper by Schuck and collaborators.¹⁵⁰ On the other hand, MAPbBr₃ at HP and room temperature has been explored with several techniques (XRD, Raman, IR, photoluminescence, among others) as already discussed in Sec. II. When a fluid or solid PTM is used, three phase transitions are reported: from cubic Pm-3m to Im-3 around 1 GPa followed by an orthorhombic Pnma (or Pmn2₁)⁷³ at 1.8 GPa and finally to an amorphous phase above 4 GPa.^46,70,71 In the two aforementioned papers, the presence of a triple point of coexistence among Pna2₁, P4/mmm, and I4/mcm phases at 43 MPa and 153 K was observed for MAPbBr₃. Moreover, Gesi found a new phase, labeled phase V, above 500 MPa between 260 and 140 K.¹⁴⁶ 

We performed synchrotron-based infrared spectroscopy measurements on MAPbBr₃ at high pressure and low temperature using membrane DACs with 400–600 μm culets, stainless steel gaskets, a He flow cryostat, and a custom IR microscope at the SMIS beamline of the synchrotron SOLEIL. NaCl has been used as a pressure-transmitting medium.¹⁵¹ Measurements at ambient pressure and 100–300 K were performed using a Linkam cell working with liquid N₂. MAPbBr₃ powder samples were synthesized by the group of Professor Lorenzo Malavasi according to the procedure described in Ref. 152. We collected several IR spectra along a total of six P–T paths: one isobar at constant ambient pressure down to 100 K, a quasi-isobar from room-temperature and 0.6 GPa to 50 K and 1.2 GPa, and four isotherms at 300, 190, 120, and 50 K. This allowed us to explore the evolution under compression of the three structural phases reported at ambient pressure and low temperatures. Infrared spectra collected during cooling at ambient pressure are in good agreement with previous results.^150,153,154 In order to track phase transitions, we focus on the fundamental frequencies of the MA cation detected in the 800–1750 cm⁻¹ frequency range; in particular, on the CH(NH) rocking modes at 917 (1252 cm⁻¹), the C–N stretching mode at 969 cm⁻¹, and CH(NH) symmetric and asymmetric bending modes at 1427 (1455 cm⁻¹) and 1477 (1585 cm⁻¹).¹⁵³ In Fig. 4, four selected spectra of MAPbBr₃ up to 6.1 GPa at 50 K (bottom panel) and 190 K (upper panel) are compared in the frequency ranges of interest. Note that in the bottom panel, the spectrum at ambient pressure is collected at 120 K and it is shown as a reference spectrum of the orthorhombic phase stabilized below.¹⁵⁰ In general, increasing the pressure at 50 and 190 K, clear peak shifting, splitting, and intensity changes are observed in the three frequency ranges, witnessing some pressure-induced structural modifications affecting the MA vibrational dynamics.

At 190 K, the spectra at 1.8, 3.4, and 6.1 GPa resemble, respectively, those of Im-3, Pnma, and amorphous phases observed during compression at room temperature. This suggests that the same sequence of transitions occurs at 190 K but starting from the I4/mcm phase, at variance with the the Pm-3m phase at ambient conditions. To verify this hypothesis, we performed synchrotron x-ray powder diffraction measurements at the CRISTAL beamline of the synchrotron SOLEIL at 190 K up to 5.9 GPa. Diffraction patterns at selected pressures are shown in Fig. 5. It can be noticed that at 1.3 GPa, two new Bragg reflections appear between 7.5° and 10°, while at 3.4 GPa, an additional reflection is observed slightly above 10°. These new patterns can be nicely fitted through the Le Bail method using the Im-3 and the Pnma phases previously mentioned. At 5.9 GPa, a few main diffraction peaks can be still observed but broadened and with a diffuse scattering background developing around 11°, witnessing the formation of the amorphous phase. These findings confirm that the high-pressure phases occurring at 190 K are the same reported for room temperature compression.

On the contrary, increasing the pressure at 50 K (Fig. 4, bottom panel) reveals the presence of new spectral shapes never observed before, which could witness the presence of unknown structures. To have some insight into these IR spectra, it is important to underline that the NH symmetric and asymmetric bending vibrations at 1455 and 1585 cm⁻¹ are doubly degenerate E modes, while the C–N stretching around 970 cm⁻¹ and the two symmetric CH bending modes around 1427 cm⁻¹ are non-degenerate A₁ modes.¹⁵⁵ Splitting of degenerate bands can be explained by degeneracy lifting due to the lowering of crystal symmetry as we observed, for example, for the mode at 1455 cm⁻¹ when entering the orthorhombic low-temperature phase at ambient pressure.^150,155 Surprisingly, pressure also causes the splitting of non-degenerate modes at about 970 and 1427 cm⁻¹ when MAPbBr₃ is pressurized at 1.2 GPa at 50 K, although less apparent. This effect may be explained by a doubling of the unit cell with molecules with non-equivalent C–N orientations. Moreover, the rocking mode at 917 cm⁻¹ shows a very complex shape at 1.2 GPa, with several components, while one main component can be appreciated in the starting Pna2₁. This mode is considered a good marker for orientational ordering of MA cations as it becomes narrow decreasing the temperature, coherently with the growth of the correlation time τ_c linked to the cations’ motion.^154,156

Finally, we want to stress that applying pressure along very different isotherms (50, 120, and 190 K), the spectra collected above 5 GPa are actually identical to the spectra ascribed to the amorphous phase above 4 GPa at room temperature.⁴⁶ This leads to the conclusion that a common amorphous phase exists above this pressure value over the whole temperature range explored.

In conclusion, the analysis of all the collected spectra allowed us to plot a tentative pressure-temperature phase diagram for MAPbBr₃, as shown in Fig. 6. Each point corresponds to a measured IR spectrum at corresponding P and T values. The slopes of the phase boundary lines where no data are available have been established following a general rule that applies for oxide perovskites: passing from a high symmetry form to a low symmetry form implies octahedral tilting consistent with a phase boundary having dT/dP > 0.¹⁵⁷ It is clear that although further spectroscopical and diffraction measurements are required to draw a definitive phase diagram, our results provide a first evidence of a complex scenario of structural transformations over an extended thermodynamic region.

In this Perspective, after a general introduction about HOIPs’ structure and properties, we briefly reviewed the general findings of previous research about hybrid perovskites at high pressure, summarizing the main results in table to make them available to the reader approaching this field. In particular, we tried to highlight common behavior in both 3D and low-dimensional perovskites under compression. Afterward, we have proposed future research directions for high-pressure research on HOIPs along these axes:

1. Continue to characterize the HP behavior of newly synthesized HOIPs of interest for applications.

2. Complete and uniform the studies on HOIPs already investigated using the best hydrostatic conditions possible, paying attention to the possible insertion of gaseous media in the structure and avoiding sample exposure to air.

3. Deepen the knowledge on pressure-induced phenomena, focusing on the role of the organic cation that has been less explored, finding key structural parameters behind common behavior in different samples.

4. Enlarge the experimental techniques park, for instance, time-resolved spectroscopies or different techniques with sources other than photons, such as neutrons.

5. Extend the investigations to a wider range of extreme conditions, i.e., higher pressures to explore insulator-to-metal transitions and combining HP and low-temperature to explore the phase diagram of HOIPs in search of new unknown phases.

Finally, we provided as example a preliminary infrared spectroscopic study we performed on MAPbBr₃ at high-pressure and low-temperature, which suggests that new structural phases exist and are characterized by an ordering of organic cations, although deeper and final conclusion needs an extensive x-ray diffraction study.

The authors acknowledge Paolo Postorino for help in designing the research at high pressure and low temperature of MAPbBr₃. Lorenzo Malavasi and members of his research group are acknowledged for providing the MAPbBr₃ powder samples. We also thank Francesca Ripanti for help during the early stage of this perspective. The authors gratefully acknowledge synchrotron SOLEIL (Proposal No. 20181853 and in-house projects) for provision of beamtime on the SMIS and CRISTAL beamlines. Pierre Fertey is acknowledged for support at the CRISTAL beamline.

The authors have no conflicts to disclose.

Anna Celeste: Data curation (lead); Formal analysis (equal); Investigation (equal); Software (equal); Visualization (lead); Writing – original draft (equal); Writing – review & editing (supporting). Francesco Capitani: Conceptualization (lead); Funding acquisition (lead); Investigation (lead); Methodology (lead); Supervision (lead); Writing – original draft (equal); Writing – review & editing (lead).

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