Raman spectroscopy in layered hybrid organic-inorganic metal halide perovskites

The continuous progress in the synthesis and characterization of materials in the vast family of hybrid organic-inorganic metal halide perovskites (HOIPs) has been pushed by their exceptional properties mainly in optoelectronic applications. These works highlight the peculiar role of lattice vibrations, which strongly interact with electrons, resulting in coupled states affecting the optical properties. Among these materials, layered (2D) HOIPs have emerged as a promising material platform to address some issues of their three-dimensional counterparts, such as ambient stability and ion migration. Layered HOIPs consist of inorganic layers made of metal halide octahedra separated by layers composed of organic cations. They have attracted much interest not only for applications, but also for their rich phenomenology due to their crystal structure tunability. Here, we give an overview of the main experimental findings achieved via Raman spectroscopy in several configurations and set-ups, and how they contribute to shedding light on the complex structural nature of these fascinating materials. We focus on how the phonon spectrum comes from the interplay of several factors. First, the inorganic and organic parts, whose motions are coupled, contribute with their typical modes which are very different in energy. Nonetheless, the interaction between them is relevant, as it results in low-symmetry crystal structures. Then, the role of external stimuli, such as temperature and pressure, which induce phase transitions affecting the spectrum through change in symmetry of the lattice, octahedral tilting and arrangement of the molecules. Finally, the relevant role of the coupling between the charge carriers and optical phonons is highlighted.


Introduction
Hybrid organic-inorganic metal halide perovskites (HOIPs) arrived in 2009 as promising materials for photovoltaics with a power conversion efficiency of 3.8% [1], which nowadays exceeds 25% [2]. These materials with already demonstrated extraordinary optoelectronic performance in photovoltaics [3,4], LEDs [5] and photodetectors [6], surpass organic electronics in terms of their figures-of-merit and reach values close to or above Si and semiconductor technology, due to their high optical absorption coefficient, tuneable band-gap, near-unity photoluminescence (PL) quantum yield, low trap densities and excellent excitonic and charge carrier mobility, in addition to their low-cost processability and tuneable crystal structure and composition [3,4,[7][8][9][10][11][12][13][14][15]. Nevertheless, continuous efforts are being made to address several challenges originating from the composition and mixed ionic-electronic conductivity of HOIPs for their successful application in optoelectronic devices, such as the presence of Pb [16,17], low ambient stability (thermal stress, light or oxygen/moisture) [15,[18][19][20], or ion migration under operation [10,18,[21][22][23]. The development of environmentally friendly Pb-free candidates [10,[24][25][26][27][28] aiming at replacing the toxic Pb [18] led to the appearance of double HOIPs, which also present better ambient stability. These double HOIPs emerge from the three-dimensional (3D) HOIPs, with general formula A I B II X 3 (A = small organic or crystalline momentum k, energy E (or angular frequency ω) [57,60,62]. The modes are classified according to the point group associated to the value of k and each can be assigned an irreducible representation of the point group; for phonons at the zone centre (k = 0), the point group coincides with the point group of the crystal class. Since Raman scattering requires conservation of E and k, and the incoming phonons can be approximated as having zero momentum, the phonon modes observed in Raman spectroscopy at the 1st order are those at k = 0, and with an energy different from 0. The symmetry of the vibration (its irreducible representation) determines the Raman activity of the mode, and its polarization selection rules, i.e. whether a certain mode has a non-zero intensity in Raman scattering with defined polarization of incident and scattered light. The selection rules are summarized in the 'Raman tensor' . The intensity of a mode (I) is I ∝ |e i Re s | 2 , where e s , e i are the polarization vectors of the scattered and incident light, and R is the Raman tensor. The most general Raman tensor, R, has nine components. In case of non-resonant scattering (i.e. excitation far from an absorption peak), the tensor is symmetric. The number of independent components is determined by the irreducible representation associated to the mode; these Raman tensors are tabulated in the literature for each point group [60,62,63]. Polarized Raman spectroscopy is thus very effective in the assignment of the symmetry (i.e. irreducible representation) to the mode, provided that the orientation of the crystal is controlled. The information on orientation of the crystal and of the polarization vector are often reported in the Porto notation as k i (e i ,e s )k s , where the four symbols indicate the direction and of incident and scattered photons, (k i and k s ) and their respective polarization direction (e i and e s ). In this way, the notation z(yx)y indicates a scattering with light incoming from z and observed along y, and with incoming polarization along y, and observed with a polarization along x. The directions xyz usually refer to the crystal axes. For the typical backscattering geometry of figure 1(a), the direction k s is labelled asz indicating −z; in this way, a configuration may be z(yx)z. The selection of orientation is especially easy and powerful in layered materials, whose cleaving occurs in the stacking direction [64][65][66]. The experimental study of the symmetry requires the rotation of the polarization of the incident and/or the scattered light, and can be obtained in different optical configurations [67], such as rotating the sample, while keeping fixed polarizers, or rotating the excitation polarization. In figure 1(a), a set-up is shown including a rotating half-wave ( λ / 2 ) plate that rotates both incident and scattered light; the incoming polarization can be controlled with another waveplate, while the analyser at the spectrometer is fixed. In these experiments, the intensity of each Raman mode can be measured as a function  [46] a Organic cations notation: MA = methylammonium; FA = formamidinium. Techniques notation: DFT = density functional theory.
of the rotation angle, for configurations where the laser and the analyser polarization are parallel or perpendicular. This configuration is preferred as it does not require moving the sample, thus ensuring that the investigated spot remains the same during the polarization angle-dependent measurement. These methods have provided interesting information on 2D materials, including crystallographic orientation, strain status, and inter-and intra-layer interactions in heterostructures such as Moiré patterns [64,66]. Raman spectroscopy is also often coupled to microscopes for spatially resolved studies with resolution of hundreds of nanometres. Pressure-and temperature-dependence measurements, which are very relevant in the study of phase transitions as described in section 4, can be measured in systems with optical access, which can be easily integrated in spectroscopy setups. These include diamond anvil cells (DACs) and cryostats (figures 1(c) and (d)). Anvil cells exploit the transparency of diamond to visible light for spectroscopic access, and can apply uniaxial stress as well as isotropic stress with a pressure transmitting medium, such as silicone oil [68,69] or NaCl [70], and calibrate the pressure using ruby [68,70]. Cryostats with optical access can be He-or liquid-N 2 cooled allowing to reach temperatures in the range 4-350 K.
In tables 1 and 2, we show a summary of the reported works with 3D and layered HOIPs indicating the technique used and the aim of the study, respectively.

Inorganic and organic Raman features
From a qualitative point of view, the vibrational modes in the layered HOIPs can be divided between those related to the organic part and those related to the inorganic part. The organic cation-related vibrations typically occur at higher Raman shift (>300 cm −1 ), and several modes can be expected. These can then be qualitatively matched to the typical spectra for the molecular species, which can be found in the literature [71]. In this case, well-established spectroscopy practice identifies the modes related to chemical bonds in functional groups according to their Raman shift [71]. For the inorganic case, the modes are found at lower energy, due to the heavier atomic components [62]; typically, these modes can be directly mapped to the 3D counterparts, and their symmetry matches that of the octahedra. This simple classification assumes a   negligible interaction between the molecular cations and the inorganic octahedra, which can be justified taking into account the localized nature of the vibration of heavy atoms [72,73], but it does not describe the real scenario, which is more complex. Typically, HOIP lattices are much softer than other inorganic semiconductors, i.e. the displacement of the ions from their equilibrium positions requires little energy. As a result, the lattice dynamics occurs with large ion displacement, which results in highly anharmonic vibrations, especially at room temperature [73]; for this reason, the phonon propagation is short, and the vibrations occur as localized modes. The localized nature of the modes almost decouples the motion of the different parts in the complex unit cell, such as the inorganic cage and the organic moieties. This has been observed in lead-based [74,75] and in lead-free compounds [73]. In this sense, the study of Raman spectroscopy provides further insight into the nature of the modes, especially by identifying their symmetry with polarization selection rules and by analysing temperature (and pressure) dependence. The effect of localized modes is particularly striking in the 2D HOIPs, where the vibrations of the inorganic part retain their feature, e.g. in terms of symmetry and Raman selection rules, even in lower symmetry environment [76]. Additionally, the long organic molecules in the 2D HOIPs 'enhance' the relevance of anharmonic effects, as the inorganic layers are more decoupled by each other. This is relevant in phase transitions and in the study of electron-phonon coupling, as discussed in sections 4 and 5.
As an example of the interplay between the organic cations and the inorganic lattice, we consider the double perovskites (figure 2(a)) of the AgBi bromide HOIP family [77], which can be synthetized with n = 1 and 2, being the 3D counterpart Cs 2 AgBiBr 6 . While the organic moieties give rise to a variety of peaks, the stronger feature in the range of inorganic vibration corresponds to the A 1g mode of the 3D case, ascribed to a symmetric stretching of the octahedra in the lattice. In the layered crystals with n = 1, this Raman band is found to have similar value across samples with different organic cations, comprising the alkylammonium cations propyl-(PA), butyl-(BA) and decyl-ammonium, as well as the aromatic phenylethylammonium (PEA). Instead, in the n = 2 structures, the mode's frequency decreases with increasing alkyl chain length, while for PEA a value comparable with n = 1 case is found. A comparison with the same symmetric stretching mode of the 3D Cs 2 AgBiBr 6 indicates that in layered structures the phonon frequency (energy) is reduced, and that in the n = 1 materials the frequency (energy) is lower than in n = 2. This can be attributed to the higher stiffness of materials with a larger number of layers.
Systematic studies have explored the effect of the organic cation's nature and volume on the vibrational modes of the inorganic layers, in terms of Raman shift and linewidth. For instance, Mauck et al [78] have studied lead iodide with alkylammonium cations with carbon chains of different lengths, x, (x from 4 to 9), focusing on the monolayer (n = 1) case (figures 2(b) and (c)). These compounds crystallize in the same monoclinic P2 1 /c space group, except x = 6, which belongs to the orthorhombic Pbca. It is important to note that the crystal structure may be strongly affected by the organic cation, as seen in figure 3(a), which compares the 3D lead iodide with methylammonium (MA) to its layered counterparts using BA and PEA as organic cations [79]. In [78], the Raman modes associated with octahedral vibrations are found to have a small blue or redshift for increasing chain length, with an approximately linear relation (with deviation for x = 6). However, the dependence is not the same for all modes, as some of them increase their energy for longer chains and others decrease it, highlighting that it is not a straightforward relationship, as well as the sensitivity of Raman spectroscopy to detect these changes.
On the other hand, in the case of an optical mode associated with a twisting of the octahedra in (BA) 2 MAPbI 4 (figure 2(d)), an increase in the number of octahedra in the lattice reduces the frequency (energy), with the bulk having the minimum value [90]. Here, this effect is rationalized as the interaction between octahedra directly bonded to the organic cations, and those that have only inorganic moieties around them, the latter being associated to lower energy as in the bulk.
Additionally, it is worth noting that the inorganic cage can leave enough space to allow the movement of the organic A-cation, especially at room temperature, which results in polar fluctuation and, in the spectra, in a broad zero-energy peak, which is observed in 3D and 2D cases [90,97]. In some cases, at low temperature the modes related to the motion of the whole organic cation (translation/libration, spinning) can be observed at low energy [82]. An effective way to evaluate the effect of the organic cation's nature and volume on the vibration modes of the inorganic layers for a specific lattice is to quantify the octahedral distortion in the crystal structure in terms of the M···X bond length and angle compared to the ideal octahedron, since both parts are assembled by hydrogen bonding. This can be done using the mean octahedral quadratic elongation (λ oct ) and the octahedral angle variance (σ 2 oct ) [77,86,98], following the equations: λ oct = 1 where ℓ 0 and ℓ i are the M···X bond lengths in a regular octahedron and the studied octahedron, respectively, and α i the X···M···X angles. In this way, a shift towards lower frequency (energy) values for the octahedra-related modes is generally observed when increasing the octahedral distortion [77,86]. As discussed in the previous section, the crystal symmetry of 2D HOIP is typically tetragonal, orthorhombic, triclinic, or monoclinic. When the lattice symmetry is reduced from cubic or tetragonal in the 3D cases, to orthorhombic or triclinic or monoclinic, a splitting can be expected for each degenerate mode. Indeed, the appearance of new modes at low energy in layered HOIP can be directly described in these terms. The splitting is related to the coupling with the molecular cations and can be related to a difference in the (c) Left: low-frequency Raman spectrum at room temperature (red) and 77 K (blue) for n = 2 (BA)2MAPb2I7, with Raman frequencies and activities predicted from DFT calculations (green). Right: calculated dispersion according to the Rytov model in the folded Brillouin zone (blue); in red the experimentally measured frequency. Reprinted from [90], with the permission of AIP Publishing. stiffness of the organic part. When the cations interact strongly, as in the case of aromatic cations, the stiffer organics will lead to a less symmetric structure, with the appearance of several Raman active modes. This was shown by Menahem et al [79], who compared BA, MA and PEA lead iodide with n = 1 (figure 3(a)), and Dhanabalan et al [94] have shown how PEA and BA have different effects on the spectrum of lead bromide n = 1 2D HOIP ( figure 3(b)). As PEA is stiffer, more modes are observed at low energy with respect to the softer BA. This was ascribed to a stronger coupling between octahedra due to the rigid PEA.
The symmetry assignment of the Raman modes is based on two complementary methods. The use of numerical methods such as density functional theory (DFT) allow finding the normal vibrational modes, including their expected range of frequency (energy), and intensity. Finally, the symmetry of the mode can be assessed by direct calculation of the Raman tensor as the derivative of the polarizability with respect to the normal mode [76,78,79,93,94]. DFT methods predict a large number of vibrational modes in HOIPs, as expected due to the large number of atoms in the unit cell. In these simulations, the effect of the low symmetry of the crystal is clearly visible together with the effect of the interaction between the organic and inorganic parts.
From the experimental side, polarization-resolved Raman spectroscopy measurements allow to identify the symmetry of each mode, which can be matched with an analysis of the symmetry of the crystal. An example of the experimental polarization-dependent results is shown in figure 4(a), for BA 2 PbI 4 (layered HOIP with n = 1) and MAPbI 3 (3D). The colour maps highlight the 4-fold symmetry for the vibrational modes of the inorganic cage, associated with the symmetry of orthorhombic lattices. Interestingly, similar symmetry is found in crystals without 4-fold axes, such as the monoclinic (UDA) 2 PbBr 4 [76]. There, the pattern results from the symmetry of the octahedra, due to the localized nature of the modes. Additionally, the organic cation can affect the polarization dependence. In [94], a band assigned to Pb-Br scissoring has a distinct anisotropy with PEA but not with BA, suggesting an effect of the relative orientation of the phenyl ring and the inorganic octahedral lattice. This anisotropy appears as a band found in depolarized spectrum of PEA crystal, but not in the corresponding polarized spectrum.
The anisotropic response is even more striking in cases where the plane of inorganic octahedra is very relevant. This occurs in materials that present the so-called 'post-perovskite' structure, which is strikingly different from Ruddlesden-Popper (RP) and Dion-Jacobson (DJ). Here, the octahedra share a corner in one direction (y) and share an edge in the orthogonal direction (x). As shown in Selivanov et al [96], Raman spectra with parallel polarization xx and yy will be different, being stronger in the direction of the corner sharing octahedra since the vibration amplitude is larger.
The low energy range is particularly interesting as it can host modes associated to a variety of phenomena, as has been demonstrated for other materials [99]. Global vibrations of nanoparticles, such as breathing of carbon nanotubes [62] or breathing of 2D CdSe nanomaterials [100][101][102][103], can be found here. In the case of layered structures, such as semiconductor superlattices [104] and 2D HOIPs, vibrations with long wavelength can be associated to the periodicity of the stack of the layers, in analogy with multi quantum wells [90]. They arise from the longitudinal acoustic waves of the individual layers, which are folded in the 'mini Brillouin zone' of the superlattice, yielding 'phononic minibranches' . In 2D HOIPs, different elastic properties of the inorganic and organic parts would give rise to well-separated minibranches. Dahod et al [90] have analysed the low energy spectrum of (BA) 2 MAPb 2 I 7 with n = 2 following this model, as shown in figure 4(c). In particular, they assumed that the velocity of sound in the organic and inorganic parts is the same as in the bulk and used a continuum approximated model (the Rytov model [104]) to calculate the zone-folded longitudinal acoustic modes (zf-LA) expected in a superlattice. This result is used to explain the appearance of a peak at ∼25 cm −1 , whose experimental high intensity was not predictable by DFT. This assignment, although not conclusive, is supported by the dependence of this mode on the choice of the organic moieties and of the number of octahedral layers (n) of the inorganic lattice. Nonetheless, it is interesting to note that this interpretation of the low-frequency mode is in stark contrast to a motion of the heavy ion, the latter being typically local, while the former is long-ranged by definition. The difference can be quite important in the interaction with electrons, as discussed in section 5, because of the relevance of the lattice distortion generated in the two cases, that can lead to different optical properties. This further highlights the need for a proper identification of vibrational modes in these materials. Table 3 contains a summary of the vibrational modes described in the literature for layered HOIPs.
Another important case of modes at low energy is related to soft modes in phase transitions, discussed in the following section.

Phase transitions
The hybrid nature of these materials plays a key role in the phase transition, which results from the coupling between the structural modulation of the inorganic octahedra layer and the conformational flexibility of the organic cations, both connected by hydrogen-bonding interactions at the R-NH 3 + moiety. The phase transitions can occur as related to the order state of the organic moieties [77]; in this case, the discontinuous nature is clearly evident in the Raman spectrum of the inorganic part as a 'jump' in peak position and linewidth, while in the organic part a transition from 'solid-like' (narrow peaks) to 'liquid-like' (broad peaks) is observed. This leads to strong distortion (tilting) of the inorganic octahedra [77,79], affecting the optoelectronic properties. This mechanism is slightly different from the case of 3D HOIPs; in that case, it has been pointed out that octahedral tilting is responsible for the phase transition as well as for the strong anharmonicity [105]. In this way, the inorganic composition (metal and halide) and the organic cation nature (R = alkyl chains, aromatic, or more complex molecules) determine the phase transition temperature of the resulting compound. Therefore, it is possible to establish some general rules. Fixing the metal halide (e.g. PbI 4 − , AgBiBr 8 4− ) and varying the organic spacer, it has been observed that the phase transition temperature progressively increases with the number of carbon atoms, x, in alkyl ammonium cations, C x H 2x+1 NH 3 + , and when using aromatic molecules such as PEA. To cite some examples, in the case of the most studied lead halide HOIPs, different reports have shown this trend in the transition temperature: (PA) 2 PbI 4 ∼200-250 K [106] <(BA) 2 PbI 4 ∼ 250-270 K [107,108]; for x > 4 there is more than one phase transition [78,108], whereas (PEA) 2 PbI 4 [87] shows none. Another example is the AgBiBr 8 4− double HOIP: (PA) 4 Table 3.      the phenyl rings results in a π-π stacking in the organic layer, providing more rigidity and larger volume, minimizing the possibility of an interlayer deformation [12,77,94,109]. In a similar way, the halide anion plays a key role. The size of the perovskite lattice increases in accordance with the anionic radius series as Cl − < Br − < I − . This translates into differences in the phase transition temperatures, as shown by Takahashi et al for Pb-based 2D HOIPs [110]. In this scenario, temperature-dependent Raman spectroscopy allows monitoring the dynamic order-disorder structural changes happening at the phase transition by studying the modes involving the R-NH 3 + bonds and the inorganic octahedra vibrational modes. In this way, Moral et al [89] studied the phase transition of (BA) 2 PbI 4 prepared as powder and thin film. Their results demonstrated that R-NH 3 + bonds behave as soft modes, i.e. modes whose energy goes to zero as the transition temperature is approached. The authors find that the temperature dependence of these soft modes is given by: 1/3 , where T 0 is the transition temperature. The 1 / 3 in the exponent corroborates that it is a second order transition with short-range correlations. Most interestingly, Moral et al highlight that the preparation method has an influence on the phase transition temperature, finding values of 230-242 K for powder and 260-278 K for thin films. Dragomir et al [87] also performed temperature-dependent Raman studies in (BA) 2 PbI 4 together with (PEA) 2 PbI 4 , showing that the nature of the dynamic order-disorder transition is different. Using PEA, no first order phase transition exists in the range studied, while with BA there is a transition at 220-260 K. The relevance of the crystal structure is also highlighted. For example, the appearance of multiple modes in BA vs PEA can be due to the stiffening of the lattice due to octahedral distortion (<200 cm −1 ). Moreover, some modes are more sensitive than others to the phase transition. In the case of the (BA) 2 PbI 4 , due to the greater tilting of octahedra in the inorganic lattice, there is a high sensitivity of the Pb-I equatorial stretching vs Pb-I apical stretching mode to the phase transition. In (PEA) 2 PbI 4 an order-disorder transition at 100 K is evidenced by the broadening of organic-related vibrations and the suppression of others related to the π−π stacking among molecules. Going a step further in the Raman analysis of these materials, Menahem et al [79] used polarized-orientation Raman spectroscopy and compared the structural dynamics of MAPbI 3 with its layered counterparts, (BA) 2 PbI 4 and (PEA) 2 PbI 4 ( figure 3(a)). In this way, they show that the structural dynamics of the layered counterparts has certain features in common with the 3D one. They exhibit similar Raman mode frequencies and atomic motions related to the inorganic lattice, which are split by the incorporation of the organic cations in the structure due to intermolecular interactions. Moreover, the authors gain insight into the order-disorder phase transition of (BA) 2 PbI 4 at ∼274 K demonstrating that it involves the relaxation of octahedral tilting coupled to anharmonic thermal fluctuations, which affect the optoelectronic properties. Apart from the temperature, another external stimulus than can promote structural changes and therefore, property modulation due the hybrid nature of the HOIPs, is pressure. Indeed, pressure up to 50 GPa has been applied to modulate the optoelectronic properties of these HOIPs. Recent studies have shown that the achievement of an effective bandgap tunability while keeping an efficient PL quantum yield is a matter of materials design, specifically, of properly selecting the organic cation in terms of molecule size and configuration. In 3D HOIPs PL tunability has been demonstrated for MAPbX 3 <80 meV and for FAPbX 3 ∼120 meV before PL quenching due to lattice distortion and bond bending. Instead, this tunability can be further increased using 2D HOIPs, reaching up to 520 meV, due to their layered nature and large A-site organic cations [69,70]. Considering the sensibility of the vibrational properties to changes in the crystal structure and environment, Raman spectroscopy is a powerful tool to monitor these materials under pressure. In this way, Liu et al [69] determined an enhancement of the interlayer interaction of PEA cations as a systematic blueshift of the benzene ring mode during the hydrostatic compression applied to PEA 2 PbI 4 microplates in a DAC. Furthermore, the Raman modes disappear at the same pressure as the PL quenching. This indicates that, when placed under pressure, the organic part is the first to be compressed (as it is softer). As pressure continues to increase, the inorganic lattice (harder part) begins to undergo changes as well, such as distortion and tilting. The process is irreversible and does not originate a phase transition. This is in contrast to the behaviour observed for [(BA) 2 (MA) n−1 Pb n I 3n+1 , n = 1, 2, 3, 4], which undergo phase transitions under compression, indicating the key role of the organic cation [111][112][113]. Indeed, a detailed recent in-situ Raman study in a DAC with single crystals by Yin et al [92] demonstrates that first the BA cation accommodates the compression by rotating along the C-C/C-N chain, leading to different consequences depending on the dimensionality of the HOIP. For n = 1, molecular tilting drives the adjacent inorganic layer to shift in the same direction, promoting a pressure-induced phase transition not observed for n > 1. Additionally, the n = 1 system presents an elastically reversible compressibility in terms of tilting and bond lengths, absent in the n = 2 case. All these changes were observed following the evolution of peak position and intensity of BA bending and rocking Raman modes under pressure (<3.2 GPa) evidencing the rotation of the BA molecules during the compression. In detail, for n = 2, the bending (CCC) and (CCN) modes merge into one band accompanied by a decrease of the rocking modes' intensity and an enhancement of the Raman active modes related to the new BA conformers generated by the applied pressure. A further increase of the compression (>5.5 GPa) all the BA-related Raman peaks become weak and disappear due to the structure amorphization [92]. For the n = 1 structure, the phase transitions (Pbca → P2 1 /a) were detected as a narrowing of the octahedral in-phase and out-of-phase bending modes in the low-frequency region of the Raman spectra with an additional octahedral out-of-phase rotation mode appearing in the P2 1 /a high-pressure phase. Moreover, the reorientation of the BA molecules is highlighted by the sharpening of the BA rocking mode in Pbca and the appearance of BA breathing and C-N stretching modes in the P2 1 /a phase. All these Raman shifts are reversible upon decompression [88]. In terms of pressure-induced PL modulation, n = 1 reaches ∼300 meV, while n = 2 ∼ 190 meV [88,92]. Similarly, Guo et al [95] studied (HA) 2 (GA)Pb 2 I 7 crystals (HA = hexylammonium; GA = guanidinium) under pressure, observing a redshifted two-fold enhanced PL emission, with respect to the pristine material, which corresponds to a new phase, presenting even different colour. The monitoring of the Raman modes related to the Pb-I vibrations (∼40 and ∼110 cm −1 ) allowed them to identify the lattice compression while increasing the pressure. Indeed, these modes systematically blueshift and sharpen in the new phase, but increasing the pressure leads to peaks broadening and weakening, revealing a higher structural disorder as result of the interlayer-distance reduction and lattice contraction. Most importantly, the changes introduced in the structure are irreversible, since the initial Raman spectrum and, therefore, the pristine crystal structure, are not recovered. Changing the halide, Li et al [70] studied the pressure effect on the PL emission of [(BA) 2 (MA) n−1 Pb n Br 3n+1 , n = 1, 2] crystals leading to redshifts of 520 meV for n = 1 and 230 meV for n = 2. Most importantly, the (BA) 2 (MA)PbBr 7 (n = 2) crystal undergoes two different phase transitions, related to (PbBr 6 ) 4− octahedra, BA, and MA molecule tilting motion, detected by the appearance of new octahedral motion-related Raman modes ( figure 5(b)). In contrast, the BA 2 PbBr 4 (n = 1) shows one phase transition, related to (PbBr 6 ) 4− octahedra tilting and BA rearrangement, as indicated by the appearance of a Raman mode at ∼30 cm −1 in the new phase, while inside the phase increasing the pressure systematically blueshifts and broadens the mode.

Electron-phonon interaction
Several important and interesting optical properties of 3D and 2D HOIPs arise from the strong and peculiar interaction of the charge carriers with the lattice vibrations, which are quite different from standard inorganic semiconductors [72]. Raman spectroscopy, as discussed above, is a valuable tool to obtain information about the typical energy and symmetry of the vibrational modes, and about the nature of lattice dynamics, such as anharmonicity and phonon lifetime, which are relevant in electron-phonon coupling.
As discussed in section 3, a peculiarity of vibrations in HOIPs is the large ion displacement due to the softness of the lattice, which results in anharmonic properties and localization of the phonon mode.
Combined with the small effective mass of the electrons, the localization strongly affects the electron-phonon interaction, since it results in strong electric fields due to the ionic nature of the material. Because of this, the coupling of electrons and phonons cannot be neglected even in simpler descriptions of the material [72,118]. This strong coupling is usually described in terms of polarons (i.e. a coupled state of excited electrons and ionic lattice deformation), but HOIPs have proved to need more detailed modelling. The polaron picture does not fully apply to HOIPs, and a better description considers the charges dynamically localized because of the slowly moving lattice, due to the anharmonic vibrations (dynamic disorder); this enables the prediction of properties such as the mobility and optical band gap [72,119,120].
Electron-phonon interaction is a critical mechanism in metal halide perovskite-based devices, as it intervenes in limiting the carrier mobility and the efficiency and broadening of the emission [121,122]. Studies of PL dynamics have shown that polarons can form and interact with longitudinal optical phonons and that their large binding energy greatly affects the emission properties [123]. Furthermore, the photoexcited charges, while being mostly localized in the inorganic layers of the hybrid perovskite, can interact with vibrational modes of the inorganic part [124]. All these effects lead to broadband, white-light emission of interest for LEDs. Indeed, the polaronic effects are found to be very relevant for the fate of excited states in 2D HOIP, and several questions are open. For example, in 2D, free and self-trapped states could not coexist, as there is no energy barrier between the states. By contrast, in PEA 2 PbCl 4 with n = 1, both emissions have been observed in PL, suggesting an interaction between the 2D layers [125].
The experimental techniques for assessing the electron-phonon coupling typically combine measurements of phonon spectra, such as Raman spectroscopy, with optical spectroscopy for the electronic transitions, such as PL and absorption. Time-resolved methods are especially useful, as they can identify the dynamics of the electronic transitions. Using PL, the effect of phonon modes stemming from the organic moieties has been found to affect the emission in more complex ways with respect to self-trapping or polaron confinement. In (BA) 2 PbI 4 , Moral et al [89] found a double emission peak resulting from the splitting of the exciton by interaction with specific modes of the BA. Their picture of interaction is summarized in figure 6(a), as a subsequent relaxation of photoexcited hot electrons into free and then bound excitons, that are coupled by phonon emission. Here, Raman spectroscopy provides the necessary support to evaluate the energy of phonon modes (figure 6(b)), together with IR absorption. By comparing these results with the analysis of the PL linewidth, the authors identified the vibrational modes of the polar heads of BA as directly coupled with the exciton. A strong coupling between the vibrational modes of the inorganic cage and those of the organic part has also been reported [126]. This coupling can be mechanical, or can originate from electron-phonon interactions. Both cases would affect the dynamics of charges in the material.
Mauck et al [78] have used ultrafast time-resolved methods on thin films of n = 1 lead iodide with long alkyl chains C x H 2x+1 NH 3 + with x > 4. Using femtosecond transient absorption, they photoexcited the material with a short resonant light pulse and probed the absorption as a function of time with a broadband light pulse. Since the pump pulse is shorter than the period of vibrations, the absorption is modulated by the motion of the atoms, and this is observed in the time domain as oscillations in the absorption, whose frequency corresponds to the energy of the vibrational modes coupled to the excited states. The Fourier transform of the oscillation ( figure 2(b)), called the Resonant Impulsive-Stimulated Raman Spectra (RISRS), can then be compared directly to standard, continuous-wave Raman spectra. Mauck et al find that the energy of phonons coupled with the photoexcited states is in the range of the vibrations of the inorganic part, and varies little with the choice of organic moiety, in agreement with their study of PL linewidth. This is in contrast to the observations in short chain (BA) 2 PbI 4 (x = 4) [89], where the exciton dissociation was ascribed to interaction with organic modes.
Electron-phonon coupling is inherent to the Raman effect [57], yet in the typical measurement, when the excitation energy is far away from electronic resonances, the spectra are usually interpreted in a picture of independence of phonons and electrons. Instead, in resonant Raman the two systems are strongly coupled and their interaction is easily observed. Using this method, Gong et al [12] found differences in lead bromide with n = 1 for different type of cation, in particular BA and PEA. The resonant-excitation spectrum of the alkyl is much stronger than the one of the phenyl, indicating stronger electron-phonon coupling in the former system. This is associated with the lower rigidity of the alkyl chain. The effect of the stronger interaction in the alkyl sample is a larger non-radiative decay of photoexcited carriers, and thus a less efficient luminescence.
Another relevant peculiarity is the anharmonicity in the vibrational modes [46,107,[127][128][129][130]; its effect on the electronic states must be taken into account, since thermal fluctuations, which are usually treated as a perturbation, can instead give rise to large deviations when the vibrations are not described by harmonic normal modes.
In the 3D case, especially in lead-iodides, these effects are very relevant, and are typically related to the small size of the cation that allows a tilting of the octahedra [131][132][133] away from high-symmetry configurations; in double perovskites such as Cs 2 AgBiBr 6 , which has been theoretically investigated by Klarbring et al [73], a soft and anharmonic lattice affects phase transitions and thermal conductivity. Recent results [46] have shown that in CsPbBr 3 and Cs 2 AgBiBr 6 the anharmonicity has quite different effects, and these can be revealed by Raman spectroscopy. In the double perovskite, at high temperature, well-defined modes are observed, whose Raman activity and polarization dependence follow the prediction of group theory. In the single perovskite, the modes at high temperature are damped, and they break the predicted selection rules, indicating that the distortions associated with octahedral tilting (thus with the anharmonicity of the modes) is so strong that the equilibrium position of the ions is not described by the (average) cubic structures.
The case of layered perovskites in this respect needs to be investigated in more detail; it is expected that the movements of the octahedra can be large enough to bring the vibration beyond the harmonic approximation, due to the presence of large organic cation. Menahem et al [79] compared the case of 3D MAPbI 3 with 2D BA 2 PbI 4 . At low temperature, the 2D HOIP has modes similar to the 3D, but they split because of the interaction with the organic moieties (or, correspondingly, because the crystal symmetry is reduced with respect to the 3D case, as discussed in the previous section). At high temperature, both crystals undergo a phase transition. From orthorhombic phase, MAPbI 3 becomes tetragonal at ∼162 K. BA 2 PbI 4 changes in another orthorhombic structure at ∼274 K. In the high temperature phase, their Raman spectra exhibit broad features due to the strong anharmonic tilting. Similar to 3D MAPbI 3 , this is related to the phase transition via relaxational octahedral tilting, i.e. octahedral corrugation angles change, and there is an additional tilting due to the bonding between the iodides and the amine group.
As mentioned, electron-phonon coupling can be obtained by combining the Raman data and the optical properties of the crystals [12,31,134,135]. Understanding a materials' electron-phonon coupling is essential for device design, as the coupling strength between the charge carriers and optical phonons plays a key role in determining the non-radiative recombination processes occurring in HOIP-based optoelectronic devices.The evaluation of the electron-phonon coupling from a quantitative point of view often relies on the Huang-Rhys factor (S) [136]. This factor can be calculated from the Stokes shift energy (∆E Stokes ) [137] and the LO phonon energy (ℏω LO ) of the strongest overtone as ∆E Stokes = 2Sℏω LO [85,134]. Another way to determine the Huang-Rhys factor is from the temperature dependent full width half maximum of the PL , where ℏω phonon is the phonon energy [31]. Although the absolute S values obtained from both methods do not always match, the order of magnitude is similar, allowing to distinguish between strong (S ≫ 1) and weak (S ∼ 1) electron-phonon interaction. Estimations of the Huang-Rhys factor found in the literature usually show strong coupling for the 3D HOIPs, e.g. MAPbI 3 [138], Cs 2 AgInCl 6 [31], Cs 2 AgBiBr 6 [85,134], or Cs 2 Ag 1-x Na x BiCl 6 (0 < x < 1) [139], while scarce values are reported for layered HOIPs [76,77]. Thus, more efforts are needed in this direction to better exploit the 2D HOIPs for device integration.

Summary and perspective
We have presented the potential of Raman spectroscopy for the study of 2D HOIPs. The insight into the phonon modes provided by this technique is of great value to understand the optical and electronic properties of these hybrid materials. Methods such as polarization-dependent and resonant Raman spectroscopy can provide important information about the symmetry of the modes and their coupling with electrons and excitons. Temperature and pressure dependent measurements reveal an interesting landscape of phase transitions determining not only the temperature onset, but also their origin from a structural point of view. Additionally, this review highlights that the main focus has been done to date on Ruddlesden-Popper structures and Pb-based 2D HOIPs. These results will be important in the study of new compounds and crystal structures accessible when working with and designing 2D HOIPs, in combination with XRD measurements, by studying the coupling between organic cations-and inorganic lattice-related Raman modes. The effect of the localization of vibrations in the interaction with electrons and excitons can be explored, to assist in the challenge of incorporating layered HOIPs in devices such as solar cells with 2D/3D heterostructures. Here, Raman spectroscopy can be very useful to assess and monitor the quality of optoelectronic devices and their ambient stability. Finally, we mention that Raman spectroscopy has demonstrated to be a powerful tool to explore, locate and map the strain in layered materials and 3D HOIPs. However, until now this potential has only been investigated in early reports on 2D HOIPs. Furthermore, we envision that the versatility of Raman spectroscopy, with the possibility to couple with different set-ups, will play an important role in establishing the structure-properties relationship in layered HOIPs. This may be considered an essential first step towards the design and optimization of these hybrid materials for their use in high-performance optoelectronic devices.

Data availability statement
No new data were created or analysed in this study.