Lead-free metal halide (halogenidometallate) semiconductors for optoelectronic applications

Metal halide semiconductors, in general, have experienced a meteoric rise in recent years due to the exceptional semiconducting properties of lead-based halide perovskites (LHPs), which offer unprecedented tunability of optoelectronic properties simply through elemental substitution and structural malleability. Contrary to prototypical elemental semiconductors such as Si and Ge, or compound semiconductors including GaAs, GaP, and GaN, heavier halide-based semiconductors are expected to take a dominant position in future, offering promise of high-performance and low-cost optoelectronic devices due to the ease of high-quality bulk crystals fabrication and thin-film growth techniques that do not require expensive equipment. These advantages have fueled their widespread adaptation in various optoelectronic devices including but not limited to photovoltaics (PV), light-emitting diodes (LEDs), transistors, memristors, and other photonic devices.

While the recent sharp rise of halide-based semiconductors is due to the emergence of Pb-based halide perovskites (LHPs), halide-based semiconductors have been well-known since the last century and played an important role in materials chemistry, especially organometallics and coordination complexes.^1–4 Later, the development flourished further in the late 1980s, driven by their rich structural diversity and phase transformations between ferroelectric, ferrielectric, and ferroelastic phases.^5–8 During this time, a plethora of organo-halides were introduced within metal halide network to establish one of its most interesting features—the polyanionic structure of metal halide tetrahedra/octahedral, which is formed via connection by corners, edges, or faces. These polyanionic structures were found to be most influential in determining final optoelectronic properties of the compounds. For example, the alkylammonium halogenantimonates and bismuthates were shown to crystallize in different stoichiometries determined by the anionic sublattice that behave as natural quantum-dots, -wires, or -wells. Unfortunately, the optoelectronic properties of these materials were mostly overshadowed by the uniqueness of their crystal structures, which comprise electrostatic, covalent, and hydrogen bonding, and most of the earlier studies were limited to the crystal structure, phase transitions, nonlinear optical properties, and spectroscopic characterizations.^9,10 Except for a few mentions of their photoluminescence properties (such as halide compounds based on mercury-like cations) in solutions, semiconducting and optoelectronic properties remained largely unnoticed.

The recent reemergence of halide-based semiconductors took place after the development of thin-film semiconductor device architectures in the early 1990s along with the massive breakthrough in LHPs in the last decade. While the performance of LHP-based optoelectronic devices has improved dramatically over the past decade,^11,12 the easy-to-fabricate LHPs also face the grandest challenge in commercialization as they easily degrade and due to the inherent toxicity associated with water soluble Pb²⁺ cations. Lead (Pb²⁺) is one of the few toxic chemicals known to have no safe threshold of exposure and it affects nearly all organs in the human body, resulting in stringent environmental regulations in most of countries.¹³ Extensive investigations have reported the calamitous effect of only a few micrograms of Pb accumulating in the human body, especially in children.¹⁴ Even in the last century, leaded gasoline was heavily advocated by the automotive industry, which resulted in widespread lead poisoning. While lead in LHPs is less dangerous as compared to tetraethyl lead (major component of leaded gasoline) due to the volatile nature of the latter, public perception of lead-based compounds remains negative. These concerns have forced researchers to search for alternative nontoxic halide compounds with similar chemical and optoelectronic properties. As the electronic structure dictates the optoelectronic properties of a semiconductor, mimicking the electronic structure of LHPs seems to be the most logical step for the development of Pb-free halide compounds. Theoretical calculations revealed that the uniqueness of the electronic structure of LHPs mainly arises from a hybridization of ns² electrons from heavy metals and np⁶ electrons from the heavier halides. Unfortunately, homovalent substitution of Pb²⁺ with the same group of elements (Sn²⁺ and Ge²⁺) resulted in a different kind of challenge as Sn-based halide perovskites (THPs) and Ge-based halide perovskites (GHPs) were found to be even more unstable when compared to LHPs.

As such, the chemical space and crystal structures were further explored with heterovalent substitution (such as Bi³⁺ and Sb³⁺) that are not strictly confined to the perovskite crystal structure. The application of these strategies has revealed the inimitable importance of corner-shared octahedral networks in tuning optoelectronic properties. For example, the electronic structures of Bi-based and Pb-based ternary halides differ widely despite having isoelectronic structures in their excited states. Consequently, the optoelectronic properties of Pb-based and Bi-based ternary halides differ massively. The role of crystal structure became increasingly important thereafter. As far as electronic properties are concerned, corner-sharing of the metal octahedra seems to be essential for producing direct bandgap semiconductors, which are the most desirable for optoelectronic applications. The corner-sharing architecture promotes destabilization of the ns² lone pair in the B²⁺ sites, leading to a very dispersive valence and conduction bands and high mobility of the charge carriers. On the other hand, the octahedral network in edge- or face-sharing configurations lead to flat electronic bands and wideband gaps, as the lone pair is lowered in energy. Unfortunately, successive investigations have shown that even corner-shared octahedral networks may not be a sufficient condition for generating direct bandgap in semiconductors. For example, one of the most famous double perovskites, Cs₂AgBiBr₆ possesses an indirect bandgap despite having nearly ideal perovskite crystal structure. Furthermore, inspired by the LHPs, a wide variety of halide compounds having different crystal structures have been (re-)discovered with some unique optoelectronic properties which were not known earlier. These halide compounds can be easily fabricated from low-cost precursor solutions, a feature that makes LHPs so popular. These halide compounds, which started their journey as lead-free photovoltaic absorber materials, currently find use in numerous other applications such as light-emitting diodes, photodetectors, sensors, and radiation detectors as well as in more emerging fields such as lasing and neuromorphic computation. Many physical/optoelectronic properties of these compounds can be further modulated by doping, alloying, and exposure to external forces such as moisture and pressure, which further widens their application area.

This review seeks to examine recent developments and new structural concepts in lead-free halide compounds or halogenidometallates. In contrast to the current literature which sometimes classifies non-related structures as perovskites, we intend to provide a universal classification for the class of compounds as octahedrally coordinated perovskite (exclusively corner-shared), perovskite-derivative (perovskite-related structure) compounds, and non-perovskite structures (discussed later). We first systematize the crystal structures of these lead-free halide compounds, covering both perovskite and non-perovskite halide compounds. We then discuss how the crystal structures of such compounds impact the optoelectronic properties. Later, we review recent advances in the emerging field of these lead-free optoelectronic devices, outlining their challenges, prospects, and strategies to further boost performance. As one overarching goal for the broader structural family, we highlight the idea of a specialized material system having greater/comparable functionality than/with LHPs for specific applications rather than one-system-for-all. We envision that many of these materials will hold promise for a variety of optoelectronic applications, including micro- and nanoelectronics, conversion of solar energy into electrical or chemical, light and radiation detection, and more. While a huge materials space exists for the lead-free system, we have only focused on ternary and quaternary compounds, containing heavier halides (Cl, Br, and I), owing to their similar chemical characteristics and ease of processability. The review is arranged by topological criteria: the introduction is followed by the classification of different compounds into perovskite, perovskite-derivative, and non-perovskite structures, which are subdivided according to the connectivity of the building blocks involved (dimensionality). Each section is devoted to a description of their crystal structure and optoelectronic properties related to the unique crystal structures.

At this point, we must set the rules to categorize perovskite, perovskite-derivative (perovskite-related), and perovskite-inspired non-perovskite compounds. Owing to polytypism of perovskite crystal structure and the discovery of many variants, we note that the definition of perovskite structure has been somewhat diluted from the original definition of aristotype SrTiO₃ (space group Pm $3 ¯$m). Consequently, a wide variety of nomenclature has been used to describe the structures such as hexagonal polytypes,¹⁵ zero-dimensional or dot perovskite, face-sharing or edge-sharing polytypes, perovskitoids,¹⁶ zigzag,¹⁷ quasi-dimensional perovskite,¹⁸ etc. In this review, we use the term “perovskite” exclusively for the compounds showing corner (vertex)-sharing octahedral networks in at least one direction. All other structures that show face-sharing, edge-sharing, or mixed octahedral networks are grouped as perovskite-derivative compounds. This is illustrated in Fig. 1. We argue that without the corner-shared octahedral network, the stacking of metal octahedral layers cannot form the idealized ABX₃ perovskite structure. On the other hand, corner-shared chains or planes preserve fragments of the perovskite structure, and with increasing numbers of layers, corner-shared octahedral networks become stepwise thicker until the end point ABX₃ structure is reached. We have also restricted isolated octahedral structures (0D) under perovskite structures as they can also be considered octahedral-deficient (defect-assisted) structures. It is a side effect of this classification as the borders are still fuzzy. Due to their close resemblance of the face-shared and edge-shared octahedral networks to the perovskite structures with composition and local coordination, we classify them as perovskite-derivative compounds. Apart from these structures, there are several interesting metal halide compounds having non-perovskite structure (either tetrahedral networks or having totally different stoichiometric compositions) which have risen in prominence recently. We group them together into non-perovskite compounds. This simple classification allows us to subdivide them into different subgroups for the analysis of the influence of various inorganic lattice conformations on their optoelectronic properties such as bandgaps. Additionally, the corner-shared octahedral network corresponds to the maximum number of degrees of freedom for various distortions and makes it possible to directly correlate with the optoelectronic properties. Next, we discuss the structural and electronic characteristics of these classes of compounds and explain the origin of their optoelectronic differences.

In addition, all of these structures can also be classified based on the dimensionality of the crystal structure, i.e., degree of connectivity across 3D space. In contrast to the “dimensionality” of nano-structured materials—such as quantum dots, which are physically confined in space—crystal structure dimensionality refers to dielectric confinement within a three-dimensional single lattice. The concept of crystal structure dimensionality was developed by Kitaigorodskii for describing packing density in organic crystals.²⁴ He defined molecular crystals as the groups of atoms in which the interatomic distance within the group is significantly shorter than the interatomic distance to an atom of a different group. While the concept is based on geometry, it can also be extended to define the dimensionality based on the bonding environment. One may refer to an excellent review by Tulsky and Long²⁵ on the crystal structure dimensionality. For halide compounds, the dimensionality can be visualized based on the degree of connectivity between metal-halide octahedral or tetrahedral network, which are predominantly covalent bonding. Other weaker interactions such as ionic or hydrogen bonding can be considered non-bonding entities. This is illustrated in Fig. 1 for describing perovskite, perovskite-derivative, and non-perovskite compounds. For example, in CsSnI₃ structure, Cs⁺ cations fit well within the voids between [SnI₆]⁴⁻ octahedral network, which are connected in all three directions. We can state accordingly that the dimensionality of CsSnI₃ extends across all three dimensions. In the case of butylammonium tin iodide ([CH₃(CH₂)₃NH₃]₂SnI₄), octahedral voids cannot accommodate large butylammonium cations, resulting in large separation of [SnI₆]⁴⁻ octahedral network along (001) direction. While butylammonium cations still fill the voids and are connected via hydrogen bonding, this results in large dielectric differences between the organic layer and the inorganic network. Accordingly, we call this structure as 2D crystal structure, extended only in the a and b crystallographic direction. Furthermore, by changing the organic cation to dimethylammonium, we can obtain 1D chain network of [SnI₆]⁴⁻ octahedra. The 1D structure can be face-shared, edge-shared, corner-shared, or a combination of both of those.²⁶ Zero-dimensional structure forms when the octahedra/tetrahedra are not connected to each other anymore, as in the case of Cs₂SnI₆. This connection mode of the inorganic octahedra heavily influences the orbital overlap between metals and halogens, thus affecting their optoelectronic properties. For example, bandgaps of halide perovskites of same composition usually follow face-sharing > edge-sharing > corner-sharing structure.

Pb-free halide compounds (ternary and above) span a broad range of compositions, crystal structures, and stoichiometries, yielding a commensurate breadth of properties. This compositional and structural diversity can be traced to the unique chemical characteristics of metal halide coordination. In Sec. III, we present the design rules and structure–property relationship of these lead-free halide compounds. We begin with perovskite structure, followed by perovskite-derived and non-perovskite halide compounds.

The crystal structure of halide perovskites, which are exclusively corner-shared in our discussion, can be further classified as 3D, 2D, 1D, and 0D structures based on the degree of octahedral connectivity (Fig. 1). When the octahedral networks are connected in all three directions, a 3D structure is formed, whereas in the 2D structure, the network of one or multiple inorganic metal halide octahedra layers propagate only in two directions, being sandwiched between the large organic molecules/inorganic cations in other direction. In 1D structures, the octahedral units are connected to each other only in one direction, thus mimicking the nanowire or nanorod structure within the crystal lattice. Similar analogies can be drawn for the perovskite-derivative and non-perovskite structures as well. Furthermore, the low-dimensional structures can be envisioned as composite materials, formed by periodic stacking of inorganic metal halide layers and large A-site cations, having contrasting properties. For example, inorganic layers are associated with excellent charge transport and generation of free carriers, whereas the organic layers reduce the charge transport across the dimension and induce Coulombically bound electron–hole pairs. However, the low-dimensional structures have fewer geometric restrictions, and consequently, a huge number of low-dimensional structures can be conceived by employing different organic cations, many of which have already been synthesized. Interested readers may refer to these excellent review articles by Mao et al.²⁷ as well as by Pitaro et al.²⁸ on low-dimensional structures for structural description.^27–29 In Secs. III A–III D, we explore the tunability of the structure–property relationships in various perovskite structures.

The formability of the 3D perovskite structure (ABX₃) with different divalent cations (B²⁺) can be empirically predicted based on the octahedral and Goldschimdt's tolerance factor. Kieslich et al.³⁰ calculated the tolerance factors for 21 divalent cations with 13 protonated amines (as A-site cation) and eight anionic species and found that only 180 compositions with heavier halides exhibit a tolerance factor between 0.8 and 1, the range that defines the formability of halide perovskites. However, the most promising candidates to replace Pb were found to be from group 14 elements (i.e., tin and germanium),³¹ which is expected considering similar electronic structures. Similar conclusions have also been reached by other independent research groups, from both theoretical calculations and experimental studies.³² Consequently, homovalent substitution of Pb²⁺ with Sn²⁺ received the most attention until, and therefore, we devote a considerable portion of this review to illustrate their unique optoelectronic properties.

Having comparable ionic radii (Pb²⁺: 1.19 Å, Sn²⁺: 1.15 Å), the structural variability in Sn-based halide perovskites (THPs) are nearly identical to LHPs. In their purest form, only FA⁺, MA⁺, and Cs⁺ cations have been experimentally demonstrated to form 3D perovskite structures, whereas the possibility of multiple A-site cations as dopant/alloy to form 3D structure remains limitless (bound by tolerance factor). The tolerance factor also predicts stable perovskite structure for RbSnX₃; however, RbSnI₃ (or RbPbI₃) is known to crystallize into face-shared 1D perovskite-derivative structure³³ [Fig. 3(a)]. THPs usually demonstrate highly symmetric cubic crystal structure at high temperatures and gradually lose their symmetry with reduced temperature to crystallize into tetragonal and orthorhombic structures [Fig. 3(b)]. These phase transition temperatures depends on the exact chemical compositions such as all inorganic compositions (CsSnX₃) usually show higher transition temperature as compared to the organic inorganic hybrid compositions.^34,35 This is illustrated in Fig. 3(b). It is worth to point out that the exact phase transition temperature of FASnI₃ remain elusive and experimental data often show conflicting results. Most notably, Schueller et al. observed an orthorhombic Pnma structure below 150 K which is not observed by other studies.^36,37 Even the room temperature (RT) phase of FASnI₃ has been reported with different symmetry, notably tetragonal (P4/mbm),³⁷ orthorhombic (Amm2),³⁸ and pseudocubic (C2mm).³⁶ These contrasting results most likely arose due to processing history as the phase stability of different polymorphs of halide perovskites is known to vary depending on the ambient environment and sample morphology (thin-film vs single crystal vs powders).³⁵ 

The wide range of crystallographic variations also leads to notable optoelectronic properties differences. Interestingly, the bandgap of FASnI₃ single crystal was found to decrease from 1.38 (280 K) to 1.12 eV (4.3 K) upon cooling which is counterintuitive.³⁶ In conventional semiconductors (such as GaAs or Si), the bandgap decreases with increasing temperature because of the thermal broadening of the bands. In Sn-based halide perovskites, this has been attributed to the dynamic off-centering of Sn²⁺ cation within the structure which reduces the overall symmetry³⁶ and carrier phonon coupling.³⁷ This role of symmetry is further illustrated in Fig. 3(c) with bonding environment. The VBM, exhibiting high covalency, is formed by antibonding contributions from Sn 5s² and X mp orbitals, whereas the CBM is characterized by an antibonding combination, but has mostly ionic character with major contributions from Sn 5p orbitals. Lowering temperatures reduces symmetry, which consequently reduces the overlap between the orbitals. However, in contrast to conventional semiconductors, a decrease in orbital overlap raises the energy of the antibonding state (VBM) in halide perovskites, resulting in a decrease in the bandgap.³⁹ 

Apart from the symmetry of the structure, the ease of tunability of optoelectronic properties via compositional alteration, especially of halides, remains one of the most interesting aspects of halide perovskites. Having corner-shared perovskite structure, 3D THPs exhibit direct bandgaps with strong absorption coefficients (>10⁴ cm⁻¹) in the visible region. The bandgaps of THPs can be modified across a wider range via halide substitution. Figure 3(d) shows the variation of bandgaps in THPs with different compositions. For instance, the bandgaps of CsSnX₃ can be tuned continuously from 1.3 to 3 eV by varying halide composition from I to Cl.⁴² However, the role of A-site cations on the bandgap is insignificant compared to that of halides. This could be explained by the electronic structure of THPs. As illustrated in Figs. 3(c) and 4(a), the band-edges are essentially formed due to hybridizations of Sn 5s, 5p and halide mp orbitals which rules out the involvement of A-site cations. The slight change in bandgap with different A-site cations is, thus, due to changes in the crystal structure. The role of halides, on the other hand, is much more predominant in determining the energy levels of VBM as the energy levels of the orbitals decrease from chlorine to iodine. As explained earlier, the decrease in orbital energies raises up the VBM due to antibonding nature, and consequently, the bandgap decreases from chloride to iodide perovskites. The bandgap values are even smaller than LHPs for same halide A-site cations, making them even superior candidates for applications that require a wider absorption range [Fig. 3(e)]. Electronic structure calculations revealed that due to low-lying Sn-based orbitals, the valence band of THPs are much higher than that of Pb-based halide perovskites, and therefore, this results in smaller bandgaps.

Apart from smaller bandgaps, experimental studies also report excellent carrier mobility (mostly hole mobility) in THPs, ranging from 10² to 10³ cm² V⁻¹ s⁻¹ which agree well with density functional theory (DFT)-based electronic structure calculations.⁴³ Unfortunately, the high conductivity in THPs may be assisted by strong self-doping. While the exact mechanism of self-doping is still debatable, it is generally accepted that the oxidation of Sn²⁺ to Sn⁴⁺ promotes Sn-vacancies, leading to p-doping. For example, evaporated CsSnI₃ polycrystalline thin films showed an increase in conductivity by about 2–7 times when exposed to ambient as compared to the films measured under N₂, which is attributed to the oxidation-induced Sn-vacancies.⁴⁴ A comparative defect characterization study between FASnI₃ and MASnI₃ revealed that larger organic cations can increase the formation energies of Sn-vacancies by promoting weaker Sn 5s and I 5p antibonding coupling with longer Sn–I bond length [Fig. 4(a)].⁴⁵ Moreover, it was also found that conductivity of FASnI₃ can be tuned from p-type to neutral under Sn-rich growth conditions, while MASnI₃ showed high p-type behavior irrespective of growth conditions. Recently, De Angelis and co-workers utilized DFT calculations to show that Sn vacancies in bulk MASnI₃ are thermodynamically unfavorable.⁴⁶ This suggests that the origin of self-doping is the surface oxidation of Sn²⁺ to Sn⁴⁺ which later diffuses inside the bulk. They found that the formation of Sn⁴⁺ defects, i.e., the hypothesized oxidation products of MASnI₃, is not likely to form in the bulk. Moreover, Sn⁴⁺ defects, being metastable, will thermodynamically convert to Sn²⁺ by releasing two holes in the VB, which might be the reason for p-type self-doping. The corresponding defect transition levels of these species lie within the VB, making them shallow in nature, as shown in Fig. 4(b). Unfortunately, irrespective of the origin, high self-doping also leads to strong non-radiative recombination in THPs which results in short carrier lifetime (in ps and tens of ns as compared to hundreds of ns in LHPs) and poor photoluminescence quantum yield (PLQY). Earlier, Kanatzidis and co-workers showed that formation of Sn⁴⁺ centers could be prevented by introducing strong reducing agents such as H₃PO₂, which can even promote n-type mobility.⁴⁷ Several studies dedicated to the fabrication of superior Sn-based perovskite thin-films under reducing environment have shown excellent promise in improving optoelectronic properties in general.⁴⁸ Presence of excess Sn²⁺ in the precursor solution was also found to be beneficial in improving both the lifetime and radiative recombination, which are important parameters in optoelectronic applications.⁴⁹ In general, 3D THPs are expected to exhibit excellent optoelectronic properties suitable for high-performing optoelectronic devices as their electronic structure features similar characteristics as seen for LHPs. Nevertheless, the thermodynamic instability of Sn²⁺, especially in iodide perovskites, remains a major challenge for stable high-performing optoelectronic devices.

The stability of 3D Sn-based halide perovskites was improved significantly when the Kanatzidis group reported a new variant of the 3D crystal structure of the THPs family, termed as “hollow perovskite.”^50,51 This type of structure is derived from the 3D parent phase by incorporating small amounts of divalent organic cations such as ethylenediammonium (en), propylenediammonium (PN), or trimethylenediammonium (TN) without altering the 3D crystal structure [Fig. 4(c)]. A similar structure was also reported later with the incorporation of monovalent organic cations, such as 2-hydroxyethylammonium, within the FASnI₃ structure.⁵² Incorporation of these moderate-sized cations apparently violates the structural tolerance factor (t > 1) due to their large ionic radii. Nevertheless, experimental results indicate that these organic cations accommodate inside the crystal lattice, most likely by partially replacing both [SnI₆]⁴⁻ octahedra and smaller A-site cations, hence creating a hollow space within the 3D crystal structure. While it is not clear how this structure helps in preventing oxidation of Sn²⁺, experimental results indicate that the ambient stability of hollow perovskites is much higher in compared to pristine Sn-based 3D halide perovskites. Moreover, the optoelectronic properties of these hollow perovskites resemble that of 3D THPs, albeit widening of the bandgap due to a less connected octahedral network arising from Sn²⁺ and X-site vacancies. Hollow perovskites also exhibit bandgap tunability via halide exchange, thus amplifying their promise as lead-free absorber materials.

Despite having similar electronic structure and predicted promise, the Ge-based 3D analogs differ from their heavier congeners (Pb and Sn) because Ge²⁺ shows a pronounced effect of stereo-chemically active lone pair and because of their tendency to crystallize in polar space groups. Based on the tolerance factor estimation, only ammonium (NH₄⁺), Rb⁺, and Cs⁺ cations are expected to form 3D perovskite structures with [GeX₆]⁴⁻ octahedral network (t < 1).^30,53 However, cesium, methylammonium, and formamidinium have shown to crystallize in the 3D Ge-based halide perovskite (GHP) structure, albeit in trigonal crystal structure which is different from aristotype perovskite structure (Pm3m).⁵⁴ In this structure, the Ge²⁺ cation forms three short and three long bonds with the halide anions within the [GeX₆]⁴⁻ octahedron, resulting in off-centering of the metal cation [Fig. 5(a)]. The size of A-site cation heavily influences the distortion in [GeI₆]⁴⁻ octahedra, where bond distortion index increases with larger A-site cations and with smaller halides [Fig. 5(b)]. Small ionic radius and the strong stereochemical activity of the 4s² lone-pair electrons in Ge²⁺ cation is hypothesized to be the reason for this distorted structure. While the origin of the distortion is still under debate, the rotation of octahedra (octahedral tilting) is linked to many interesting phenomena, ranging from electronic and magnetic properties,⁵⁵ second harmonic generation,⁵⁴ to improper ferroelectricity.⁵⁶ First-principle electronic structure calculations revealed that this distortion leads to less overlap between metal-halide antibonding orbitals in the valence band, resulting in increase in the bandgaps of GHPs as compared to LHPs. For example, iodide-based GHPs exhibit direct bandgap ranging from 1.6 to 2.5 eV, depending upon the A-site cation, with the smallest being in CsGeI₃ [Fig. 5(c)]. This remarkable dependency of bandgaps on different A-site cation is the strongest compared to that of Pb- or Sn-based halide perovskites. From single crystal data, this remarkable modification of bandgap can be directly linked to the octahedral distortions as larger A-site cation results in larger distortions and consequently larger bandgaps.^54, Figure 5(e) further illustrates a change in optical bandgaps of GHPs with increasing distortion in metal octahedra. The structural distortion is also expected to impart anisotropy in charge transport and optical absorption.⁵⁶ The anisotropic behavior was further supported by the sub-bandgap absorption in MAGeI₃, presumably due to strong ferroelectric polarizations arising from anisotropic charge transport and absorption. This could lead to a substantial increase in incident photon conversion efficiency during photovoltaic or photodetection applications. Nevertheless, 3D Ge-based halide perovskites are also plagued by instability in ambient environment. While early theoretical calculations showed that MAGeI₃ is less likely to degrade into precursors (MAI and GeI₂) as compared to analogous MAPbI₃, experimental results indicate that Ge-based 3D halide perovskites follow similar degradation pathways like Sn-based 3D halide perovskites⁵⁷ at higher degradation rates. A detailed investigation on the intrinsic point defects in CsGeI₃ showed the presence of mid-bandgap iodine vacancies (V_I), which is remarkably different from Pb- and Sn-based 3D halide perovskites.⁵⁸ While the exact reason is not explained, we can hypothesize that distortion in octahedra and poor hybridizations are the main reasons for this anomaly. Moreover, Ge-based halide precursors (GeX₂) are also only mildly soluble in organic solvents, resulting in inadequate processability for thin-films. Therefore, experimental studies on GHPs are still scarce as compared to other perovskites and most of the studies are dedicated toward theoretical calculations.

Among other divalent cations, only Mg²⁺, Ca²⁺, Sr²⁺, and Ba²⁺ can form 3D perovskite structures according to the Goldschmidt tolerance factor estimation.³⁰ However, the absence of ns² electrons renders their optoelectronic properties vastly different from LHPs. Theoretical calculations also predict wideband gaps and unfavorable optoelectronic properties, which attracted less attention for experimental synthesis.^60,61 utilized DFT-based high-throughput screening to assess the optoelectronic properties of various divalent metal cation-based 3D perovskite crystal structures. Many of these divalent cations-based hypothetical perovskites exhibited distorted crystal structures and instability. The authors identified Mg²⁺ as a potential candidate with the calculated electronic bandgap was found to be 0.9, 1.5, and 1.7 eV for FAMgI₃, MAMgI₃, and CsMgI₃ composition, respectively, based on local-density approximations (LDA). Likewise, Krishnamoorthy et al.³¹ also carried out computational screening of 360 AMX₃ chemical compositions with A-site being Cs⁺, Rb⁺, and K⁺.³¹ While both studies agree well on the electronic bandgaps of Mg-based hypothetical halide perovskite, formation energies of Mg-based halide perovskites in the second study were found to be much larger. At present, only face-sharing low-dimensional structure of CsMgI₃ having wide bandgap (4.8 eV) has been reported,⁶² which will be discussed in perovskite-derivative section. Among others, the pseudocubic CaCaI₃ has been experimentally synthesized exhibit an optical bandgap of 2.95 eV, which makes it unsuitable for photo-absorption applications.⁶³ Theoretical calculations also predict stable perovskite structures for Sr.- and Ba-based halide perovskites, albeit they are also likely to exhibit large bandgaps due to smaller electronegativity difference and lack of d-orbitals in the valence.^64,65 However, at present, no experimental evidence can be found to prove the existence of these structures. Divalent rare-earth and lanthanide elements are also known to crystallize into perovskite structures with halides since the 1980s, as most of these studies are focused on their crystal structure and calorimetric investigations.^66–68 Early results indicate that CsEuCl₃ stabilizes into distorted tetragonal structure although degradation occurs under ambient conditions.⁶⁶ Similar results were also obtained for bromide compounds.⁶⁹ Although both the compounds exhibit large bandgaps which are undesirable for photo-absorption applications, they show strong photoluminescence, which could make them excellent candidates for light emission.

Double perovskites (or elpasolites), with a general formula of AB′B″X₆ are an extended family of 3D perovskite structure in which one monovalent (B′) and one trivalent metal cation (B″) are stacked alternatively to mimic the divalent oxidation state required for halide perovskite structures. As opposed to alloyed perovskites (such as CsPb_1−xSn_xX₃), double perovskites must contain two structurally distinguishable [Bⁿ⁺X₆]ⁿ⁻⁶ motifs. Because of the double occupancy at the B-site, these perovskites are simply called “double perovskites.”⁷¹ Halide double perovskites came into prominence when three groups independently reported synthesis and optoelectronic properties of Cs₂AgBiX₆ (X = Cl, Br) in 2016.^61,72,73 A recent review on the historical development of halide double perovskites can be found in the work by Wolf and co-workers.⁷⁴ Following the discovery of Cs₂AgBiX₆, several studies dedicated toward high throughput screening and novel synthesis protocols. Theoretical calculations predicted several double perovskites with B′ being Li⁺, Na⁺, K⁺, Rb⁺, Ag⁺, Tl⁺, Cu⁺, etc., and B″ being Al³⁺, Ga³⁺, In³⁺, Tl³⁺, Bi³⁺, Sb³⁺, and lanthanides, and subsequently, many of them have been experimentally synthesized. In a typical crystal structure, two heterovalent cations are arranged alternatively (rock salt) along three fourfold cubic axes to form corner-shared octahedral network as shown in Figs. 6(a) and 6(b). The monovalent cation still occupies the cubo-octahedral voids to hold the structure in 3D space. While the ordering for the B-site can be rock salt or random for oxide double perovskites, the former has been shown to be thermodynamically preferred for the halides.⁷⁵ Although several combinations of cation pairs can be put into octahedral positions based on oxidation state, the structural stability (aristotype) of the double perovskites still depends on both tolerance factor (t) and octahedral factor (μ). While t has same role as in conventional halide perovskite, μ [r_B/r_X, r is the radius of B-site cation (B) and halide (X)] determines whether a certain cation can form octahedral bonding with halides. Too small or too large a value of μ would result in large distortions, while an optimal value between 0.44 and 0.90 was found to promote cubic structure. A study employing ∼2000 combinations of inorganic cations in B-site along with K⁺, Rb⁺, and Cs⁺ as A-site cation, found 1149 compounds can form cubic structure [Fig. 6(d)] and 305 (not including fluorides) of them are within thermodynamic stability range [Fig. 6(e)].⁷⁰ A recent high-throughput DFT-based convex-hull calculation also predicted that only 112 of the 980 compounds are thermodynamically stable.⁷⁶ The difference between two studies is the cutoff energy used to estimate the stability. Having more than 1440 compositions that are known to have double perovskite structure, many of them are fluoride-based, which limits their solution-processed synthesizability.⁷⁷ Among heavier halides, nearly all of the synthesized double perovskites exhibit large optical bandgaps, arising from the chemical mismatch between monovalent and trivalent cations. Smaller bandgaps were predicted for In⁺ and Cu⁺ as B′ and Sb³⁺/Bi³⁺ as B″ cation combination.^61,78 Nevertheless, In⁺-based compounds suffer from poor solubility in organic solvents and spontaneous oxidation from In⁺ to In³⁺ (Ref. 79) which poses a major question on the synthesizability of In⁺-based halide double perovskites. Similarly, synthesizability of Cu⁺-based iodide double perovskite also raises questions as sixfold coordination of Cu⁺ with iodide and bromide is thermodynamically unfavorable (Fig. 2). These results indicate the need to consider accurate redox chemistry when predicting stability of new compounds, especially when less common oxidation states are involved.

The physical and optoelectronic properties of double perovskites are determined by the B-site cations in combination with halides, just like conventional halide perovskites. These promising double perovskites can be classified into nine groups based on the electronic structure of the constituent B-site cation [Fig. 7(a)] and Fig. 7(b) shows the schematic band structure of the three representative categories. For the case of the most famous halide double perovskite, Cs₂AgBiBr₆, the VBM mainly originates from the antibonding states of Ag 4d and Br 4p orbitals, while the CBM is mainly composed of Bi 6p orbitals with slight contribution from Ag 5s and Br 4p orbitals. The Bi 6s lone-pair orbitals have no significant contribution to the VBM as they lie at 10.2 eV below the VBM. This apparent mismatch of hybridization leads to indirect and large bandgap in Cs₂AgBiBr₆, which results in poor photoluminescence. Interestingly, Gao and co-workers⁸² observed that the bandgap can be reduced by 0.26 eV from 1.98 eV in pristine Cs₂AgBiBr₆ by fabricating the crystal at high temperature (150 °C). The authors claimed that temperature-induced disorder is the most likely reason for this bandgap reduction. One the other hand, alkali metals in B′-site can induce direct bandgaps, yet due to parity forbidden transition, these compounds also exhibit large bandgap and are usually transparent. A similar result also found for Cs₂AgInCl₆.⁶⁰ 

The defect chemistry of these double perovskites remains a subject under debate. The dominant defects in Cs₂AgBiBr₆, such as Ag_Bi, V_Bi, and Br_i, are found to create mid-bandgap states, despite having an antibonding VBM.⁸³ In addition, shallow defects such as V_Ag are also abundant in Cs₂AgBiBr₆. Similar findings were also obtained for Cs₂AgBiCl₆ and Cs₂AgInCl₆ compounds.⁸⁴ This is in stark contrast to conventional halide perovskites which are tolerant toward intrinsic defects. In addition, experimental studies indicate that Cs₂AgBiBr₆ possesses long carrier lifetimes (∼688 ns in crystals and ∼675 ns in powder⁷²) along with long carrier diffusion length (∼1 μm⁸⁵) and moderate defect densities (∼10⁹ cm⁻³ in crystals and 10¹⁶–10¹⁷ cm⁻³ in films^86,87). This apparent contrasting results necessitate further validation from both experimental and theoretical perspectives to quantify the defect levels and concentrations, to understand the intrinsic relationship between stoichiometry and defects and to provide guidance for reducing the deep-level defects in Cs₂AgBiBr₆.

A variant of these double perovskites can also be obtained with a single metal cation having both monovalent and trivalent oxidation state. These mixed-valence double perovskites include compounds based on Tl, In, and Au (the latter shows strongly distorted octahedra). While Tl is highly toxic, pure Au-based compounds can be of interest for optoelectronic applications. All inorganic Cs₂Au⁺Au³⁺Cl₆ was first synthesized in 1922,⁸⁸ and the structure was determined later in 1938 along with Cs₂Ag⁺Au³⁺Cl₆.⁸⁹ Both compounds are black in color and crystallize in the tetragonal structure. However, early work on Au-based halide perovskites were limited to structural characterizations and pressure-induced insulator-to-metal transition.^90–92 In contrast to conventional double perovskites, Au-based halide perovskites comprises corner-connected heavily distorted haloaurate octahedra, owing to presence of linear [Au⁺X₂]⁻ and square-planar [Au³⁺X₄] complexes [Figs. 8(a) and 8(b)]. This distortion arises due to the large size difference between Au⁺ and Au³⁺.⁹³ Recently, Au-based halide perovskites gained renewed interest due to their small and direct bandgap (e.g., 1.2 eV for MA₂Au⁺Au³⁺I₆) which is highly desirable for PV applications. For instance, a theoretical study calculated power conversion efficiency (PCE) of only 50 nm thin Cs₂Au⁺Au³⁺I₆ layer can reach up to 18%, while for the same thickness, MAPbI₃ can only harvest about 8% of solar energy⁹⁴ [Fig. 8(c)]. Earlier reports indicated the origin of the small bandgap to the metal−ligand intervalence charge transfer (IVCT) between the [Au⁺X₂]⁻ and the [Au³⁺X₄]⁻ groups.⁹¹ Recent theoretical calculation indicates that the presence of intermediate bandgap, originating from an antibonding hybridization of Au³⁺ d_x²_−y² orbital and I p orbital is the most likely reason for the smaller bandgap.⁹⁴ Murasugi et al.⁹⁵ recently synthesized a series of Au-based halide perovskites and found that the crystal structure is heavily dependent on the size of A-site cation [Fig. 8(d)]. Due to heavily distorted gold halide octahedra, the perovskite structure can be formed even beyond tolerance factor limit (t > 1); however, crystal symmetry reduces at higher t values (monoclinic structure for 1.07 < t < 1.2). Figure 8(e) shows the optical absorption spectra of gold halide perovskites with different A-site cations which illustrates the continuous increase in bandgap with larger A-site cation. Additional parameter in determining the bandgap is the in-plane distance d(Au^I⋅⋅⋅I) which specifies the anisotropic optoelectronic properties.

Another family of the halide double perovskites are based on lanthanide (Ln) series where B³⁺ site is essentially occupied by lanthanide (III) cations. The development of lanthanide double perovskites began in last century as new scintillator materials for radiation detection; consequently, most of the lanthanides are used as host materials for rare-earth dopants (e.g., Ce³⁺), and their pristine physical and optoelectronic properties are often overlooked. A theoretical screening was carried out based on Embedded-Ion Method (EIM) potential⁹⁶ to characterize 640 lanthanide double perovskites, covering five alkali elements Li, Na, K, Rb, and Cs, four halogen elements F, Cl, Br, and I, and eight selected lanthanide elements La, Nd, Eu, Er, Ce, Sc, Y, and Gd. Furthermore, 13 Ln-based double perovskites were synthesized, out of which nine compounds were crystallized in cubic double perovskite structure. Nevertheless, most of the lanthanide-based halide double perovskites are expected to exhibit extremely large optical bandgap (∼6 eV or more), which makes them unsuitable for optoelectronic applications. Recently, Hu et al.⁹⁷ synthesized Cs₂NaTbCl₆ and Cs₂NaEuCl₆ crystals by hydrothermal method. Both crystals were transparent and exhibited long PL lifetime (in ms). First-principle calculations revealed that due to localized f states, large electronegativity differences between alkali cations and lanthanides, and the large distance between the trivalent cations localizes band-edges, these compounds are expected to offer poor carrier mobilities.^98,99 The discrete band structure of these compounds further suppresses thermalization of hot carriers, which is again undesirable for optoelectronic applications.

All the double perovskites described above possess a 3D corner-shared network in which two different valent cations form a rock salt structure. Nevertheless, more exotic 3D perovskite structures can be formed by introducing defects in the crystal structure. Yang's group exemplified this idea by replacing the atomic positions in conventional BaTiO₃ lattice with metal halide octahedra, thus forming an extended ionic octahedron network (ION), which is charge-balanced by the monovalent cation.¹⁰⁰ They discovered a novel perovskite structure Cs₈Au_3.5In_1.5Cl₂₃ which can be represented as [[InCl₆][AuCl₅][Au/InCl₄]₃]⁸⁻, where three different ionic octahedra [InCl₆] [AuCl₆], and [Au/InCl₆] are still connected at the vertex. While the compound exhibit process dependent properties due to spontaneous disproportionation reaction of Au⁺ and Au³⁺, this concept can provide an enormous chemical space for further exploration, and thus, it opens a new venue for the rational design of new halide perovskite materials.

Contrary to the rigid 3D perovskite structure, 2D layered perovskite structure can be rationalized as slabs or sheets of corner-shared octahedral networks sandwiched between large cations or cationic structural moieties. The structure essentially forms when the cubo-octahedral space in 3D perovskite structure cannot accommodate larger cationic moieties, resulting in separation of the octahedral sheets along certain crystallographic planes corresponding to the axis of an ideal cubic perovskite. When the two adjacent inorganic layers has an offset of (0.5, 0.5), as shown in Fig. 9(a), the large organic molecule occupies the interlayer space between the inorganic layer, and the smaller A-site cation fits within the cubo-octahedral voids generated within the inorganic layers. The larger monovalent organic cations are anchored by hydrogen bonding with halide atoms at only one side, forming an interdigitated organic layer structure. This structure is known as Ruddlesden–Popper (RP) phase. In another structure variation, the adjacent inorganic layers exhibit a coordinate displacement of (0,0), such as in butylammonium germanium iodide, which is known as the Dion-Jacobson (DJ) phase [Fig. 9(b)]. In this structure, there is only one layer of bulky organic layer between the inorganic octahedral sheets as compared to two organic layers required to form RP structure. Consequently, DJ structures usually have a shorter X−X interlayer distance as compared to RP phase. An intermediate structure is also possible when the parallel inorganic layer has a coordinate offset of (0.5, 0) and the alternating A-site cations occupy the pockets of inorganic metal octahedral layers and interlayer space between them [Fig. 9(c)]. This kind of structure is known as Alternating Cation in Interlayer space (ACI) type. The chemical formula of RP, DJ, and ACI structure can be represented as A′₂A_n−1B_nX_3n+1, A′A_n−1B_nX_3n+1, and A′A_nB_nX_3n+1, respectively, where n indicates the number of inorganic layers that are stack together [Fig. 9(d)]. In the current era, with the advent of halide perovskites, the inclusion of non-spherical and often highly anisotropic organic molecules at the inter-layer A-site opened up further variations in the layered structure, and currently “layer shift” is more often used terminology to describe low-dimensional halide perovskites, rather distinguishing between RP, DJ, and ACI phases.^101,102 Depending on the crystallographic planes, 2D layered structures can also be classified as the ⟨100⟩, ⟨110⟩, or ⟨111⟩ oriented 2D perovskites [Fig. 9(e)].

The development of organic-inorganic lead-free 2D structures also started in early 1990s when Mitzi et al.¹⁰³ reported a family of Sn-based layered halide perovskites, (C₄H₉NH₃)₂(CH₃NH₃)_n−1Sn_nI_3n+1, which showed semiconducting to metallic transition with increasing number of inorganic layers (n). These structures resemble the Ruddlesden-Popper (RP) phase. Later, the low-dimensional family was extended to Ge-based halide perovskites along with more complicated organic cations.^104–106 As there are no size restrictions for the A-site cation, a plethora of monoammonium and diammonium cations are employed to form (100)-oriented 2D structure. The optoelectronic properties of these 2D layered perovskites mostly depend on the nature of inorganic layers and the separation between them, while the organic layers play a limited role in the band edge formation. This was confirmed in early works as the electronic structure of low-dimensional tin halide perovskites, calculated using the extended Hückel tight binding method, was found to be similar to that of a single [SnI₄]²⁻ layer.^107,108 Figures 10(a) and 10(b) show the calculated band structure for an idealized undistorted 2D SnI₄²⁻ perovskite sheet and corresponding projected density of states. The band edge composition is similar to that of 3D THPs as described previously. Nevertheless, one striking difference is the strong dispersion of the band structure along in-plane as compared to that of out-of-plane direction (Γ to a point located at the edge of the Brillouin zone), rendering the valence band and conduction band to be two dimensional. Recent DFT-based calculations also agree well with the fact that A/A′-site cations do not contribute to the VBM and CBM, which are entirely formed by hybridization between metal and halide orbitals.^109–111 This is since the ammonium cations usually have larger HOMO–LUMO gaps as compared to that of inorganic layers and the organic molecules are attached by only hydrogen or van der Waals bonding with the inorganic layer. Consequently, there is negligible electronic coupling between the perovskite sheets, and flat dispersion of electronic bands are observed along the direction of the stacking axis.

The most pronounced effect of the quantum confinement and structural templating can be seen in the excitation binding energy and optical bandgap in the absorption spectrum. Excitons are Coulombically bound neutral electron–hole pairs which are prevalent in low-dimensional structures due to quantum confinement effect. Due to large dielectric difference between organic layer (∼2.6) and inorganic layers (∼6), 2D halide perovskites behave as natural quantum-well, exhibiting strong excitonic behavior. For optoelectronic applications, it is desirable that excitons either are dissociated into free carriers (e.g., for photovoltaics) or radiatively recombine (e.g., for LEDs). A critical parameter is the exciton binding energy (E_b), which is defined as the difference between the energy of the excitonic state and the electronic bandgap, determines the behavior of excitonic states in a material. In 3D halide perovskites, E_b is comparable to or smaller than kT (thermal energy) and the exciton can be dissociated easily into free carriers at room temperature. However, for efficient LEDs, a reasonably high E_b is needed to enhance electron–hole confinement. The values of bandgap and exciton binding energies in 2D perovskites depend on the number of inorganic layers (n) and the choice of organic cation. Additionally, larger differences in dielectric constants lead to higher exciton binding energies, electronic band gaps, and flat dispersion.

In the case of electronic bandgaps, quantum confinement leads to a systematic increase in the bandgap with decreasing layer thickness. Figure 10(c) illustrates the variation of computed bandgaps of a hypothetical series Cs_n+1Sn_nX_3n+1 (X = Cl, Br, I) against number of inorganic layers (n). This is a fair assumption due to negligible interaction of A-site cations on the band structure and the fact that inorganic cations usually promote a non-distorted structure. However, in-plane B−X bonds become shorter than in bulk during structure relaxation, indicating the octahedral distortion may be necessary to stabilize the low-dimensional structure. On the other hand, the bandgap gradually approaches the bulk value (n → ∞) with the increase in the layer thickness as expected. Figure 10(d) shows the computed band structures of the hypothetical Cs_n+1Sn_nX_3n+1 (X = Br, I) series. Several main features can be highlighted with increasing the number of inorganic layers (n) such as (i) nature of bandgap remain direct for any number of inorganic layers, (ii) the bandgap gradually becomes smaller, (iii) increase in sub-bands and decrease in bandwidth in both CB and VB, and (iv) substitution of I by Br lead to larger the band gaps. As previously described, the in-plane hybridization between Sn and X orbitals is valid for all the low-dimensional structure the bandgap originates which results in similar band structure, while the latter two can be explained by the reduced quantum confinement with increasing inorganic layer.

In other words, with increasing the number of inorganic layers, the optoelectronic properties of 2D layered structure draw closer to that of the 3D structure. Figure 11(a) shows the experimentally obtained optical absorption spectra of (CH₃(CH₂)₃NH₃)₂(CH₃NH₃)_n−1Sn_nI_3n+1 perovskite series. As observed in electronic band structure calculations, the optical bandgap drastically reduced from 1.83 (n = 1) to 1.37 eV (n = 5), moving close to 3D CH₃NH₃SnI₃ (1.2 eV, n = ∞).¹¹² Similar results were also obtained in analogous (BA)₂(FA)_n−1Sn_nI_3n+1 series, which shows a bandgap tunability from 1.96 (n = 1) to 1.4 eV (n = 10) only by varying number of inorganic layers [Fig. 11(b)].¹¹³ The absorption spectra of (BA)₂(FA)_n−1Sn_nI_3n+1 series were later fitted to a quantum-well model to illustrate the variation of exciton binding energies, from 287 (n = 1) to 10 meV (n = 10) [Fig. 11(c)]. Such high binding energies essentially establish the excitonic nature of the lower n (1 and 2, in this case) perovskites, while the presence of free carriers was observed in n = 5 and n =10 compounds. Similar studies were also directed toward Ge-based halide perovskites, which show surprisingly much less dependence of bandgap on the number of inorganic layers.^114,115 For example, a bandgap difference between n = 1 and n = ∞ is only 0.3 eV in (CH₃(CH₂)₃NH₃)₂(CH₃NH₃)_n−1Ge_nBr_3n+1 [Fig. 11(g)]. Through DFT-based electronic structure calculations, the weak dependence of bandgaps is attributed to the strong localized states of germanium orbitals, leading to similar band edge energies of layered structure and parent 3D perovskite.^114,116

Nevertheless, limited efforts were directed toward low-dimensional GHPs, mostly due to their large bandgap. Alloying with Sn has been shown a viable strategy to reduce the bandgap of low-dimensional GHPs.¹¹⁷ It should be noted here that in most studies, the number of inorganic layers is usually assumed based on the precursor composition (stoichiometry) as it is difficult to determine accurate crystallographic information for higher order structures. For Pb-based halide perovskites, higher n (≥ 5) compounds usually have positive formation energy,¹¹⁸ leading to unfavorable crystallization kinetics. Ma et al.¹¹⁶ computed formation enthalpies of Sn- and Ge-based RP phases with respect to two decomposition pathways: (a) oxidation to respective tetravalent state, and (b) degradation to the precursors. Both the pathways showed similar degradation trend with higher n structures having more positive enthalpy as compared to lower n structure. In addition, higher n structures are also more likely to degrade under oxidative environment, and less stable as compared to lower n structures. However, there are no calorimetric studies dedicated toward lead-free halide perovskites.

As the band-edges of halide perovskites are mostly formed by the inorganic metal halide interaction, one can presume that the A-site cations play a limited role on the optoelectronic properties. However, the final crystallographic structure and thermodynamic stability are heavily influenced by the choice of organic cation and reaction parameters, which indirectly influence the optoelectronic properties of the 2D layered structure. First, by tuning with the thickness and composition of the organic layer, one can also alter the optoelectronic properties of the layered structure. Moreover, smaller interlayer spacing, especially in eclipsed structures, lead to better electronic coupling between the perovskite layer and can promote a sizable band dispersion in the direction of reciprocal space corresponding to the stacking axis. Second, the organic spacer cation has a significant impact on the distortion of the metal halide octahedra due to the stress originating from the electrostatic and hydrogen-bonding interactions between organic and inorganic layers. In general, the octahedral distortion can be in-plane, out-of-plane, or deviated from ideal octahedra, depending on the charge density and tail group of the A-site cations [Figs. 12(a)–12(c)]. As the organic cations usually have inhomogeneous charge density (higher in head and lower in tail group), the inorganic metal-halide layer tends to distort in-plane to compensate the charge density difference. An out-of-plane distortion can occur when there is a more sterically demanding cationic headgroup, such as trimethylammonium, which is too large to accommodate. Further increases in bulkiness of the organic cation, such as in 2-BrPEA, 2-CF 3PEA, and 1-PYREA salts, can result in a combination of in-plane and out-of- plane distortions. In an early work, Mitzi and co-workers illustrated the role of distortion on the electronic structure 2D (RNH₃)₂SnI₄ (R = organic group) perovskites.^108, Figures 12(e) and 12(f) show the experimental exciton resonances and bandgap of Sn-based 2D iodide perovskites with functionalized aromatic moieties and ethylammonium against Sn–I–Sn bond angle, respectively. As expected, the impact of in-plane distortion on bandgap (excitonic energy) is found to be more severe than an idealized out-of-plane distortion due to a greater loss of overlap between Sn and I orbitals. As the valence band comprises metal s and halide p antibonding orbitals, a decrease in the level of overlap would push the valence band downwards, while the conduction band remains nearly unchanged. In another study which involves pentane-diammonium (PeDA) and iPy as the organic cations, it was revealed that the larger bandgap of (iPy)₂SnI₄ was due to the large octahedral distortion, despite a reduced out-of-plane distortion.¹²⁰ Similar results were also obtained by substituting a functional group within the organic molecule. For example, the position of the fluorine substitution on the phenyl ring in (C₆H₄FC₂H₄NH₃)₂SnI₄ leads to an increase in the in-plane distortion for the ortho, meta, and para positions, increasing the optical bandgap.¹²¹ The conformation of the organic cation was further illustrated by substituting halide group in 2-substituted phenethylammonium cations, (2-XC₆H₄C₂H₄NH₃)₂SnI₄ (X = F, Cl, Br).¹²² Smaller halides such as F and Cl substitution leads to gauche conformation, like PEA, while Br substitution resulted in anti-conformation with larger in-plane distortion. Consequently, the excitation energy shifted toward higher energies in (2-BrPEA)₂SnI₄ (2.23 eV) as compared to (2-ClPEA)₂SnI₄ (2.12 eV) and (2-FPEA)₂SnI₄ (2.11 eV).

However, a contradictory result was obtained in BA₂SnI₄, which showed larger optical bandgap at low-temperature (LT) as compared to room temperature (RT) phase, despite negligible in-plane distortion [26.4° (LT) vs 21.3° (RT)] as compared to out-of-plane distortion [22.3° (RT) vs 2.3° (LT)]. The authors concluded the cooperative effect of two distortions should be taken into consideration simultaneously, as both occur at the same time. This conclusion was quantified by evaluating the overall Sn–I–Sn bond angle.¹²³ The octahedral distortion in the inorganic layer is found to decrease with increasing the length of the organic spacer cations due to the minimization of the stress transmitted to the inorganic layer. The observation that greater structural distortion or tilting occurs in inorganic octahedra is consistent with the notion that the surface closest to the organic spacer cation layer experiences more distortion/tilting than the middle layer. In addition to the organic cation, the optical bandgap of 2D halide perovskites also increases when exchanging iodine to bromine to chlorine, much like the 3D perovskites.

The charge transport properties in this layered structure attracted much interest from the beginning when 2D tin-based iodide perovskites exhibited semiconductor to metallic transition with increasing number of inorganic layers (n).^103,124 Later, it was revealed that the self-doping of Sn²⁺ is the most likely origin of high conductivity in low-dimensional structures, much like 3D THPs.¹²⁰ In general, due to the layered structure, 2D halide perovskites exhibit highly anisotropic charge transport behavior owing to large differences in charge transport properties between organic and inorganic molecules. Thus, with increasing number of inorganic layers (n), electrical conductivity, especially charge carrier mobility was found to increase in the perpendicular direction due to Coulombic shielding offered by the inorganic layer. Nevertheless, the exact mechanism by which the carriers tunnel through the inorganic layers remains unknown. This can be directly linked to the dispersion or width of VBM and CBM which shows a decrease in carrier effective mass with increasing inorganic layer number (n) as shown for (CH₃(CH₂)₃NH₃)₂(CH₃NH₃)_n−1Sn_nI_3n+1 (n = 1, 2, and 3) series.¹²³ As compared to 3D structures in which the charge carriers are considered to move through delocalized bands, the presence of continuum organic cations in low-dimensional structures essentially acts as barriers. Thus, nature of the organic cations and their orientation heavily influence the charge transport properties in low-dimensional structure. For example, diammonium cations or molecules having π-conjugation are expected to drastically improve the charge transport properties across the inorganic sheets due to smaller interlayer distance and ease of hopping.¹²⁵ Takahasi et al.¹²⁰ studied several tin-based low-dimensional structures having monoammonium and diammonium cations in the A-site and showed wide variations in the electrical resistivity. For example, the smallest cation butylammonium, having A₂SnI₄ structure, showed the lowest resistivity which is comparable with diammonium cation (C₅di) having ASnI₄ structure. Nevertheless, structures having smaller valence bandwidths usually showed higher resistivity, indicating a decrease in carrier effective mass. Moreover, the close proximity between layers in the DJ structure coupled with the organic molecules' high dielectric constant can enhance the dielectric screening effect, thereby reducing the quantum confinement of charge carriers.

While Sn- and Ge-based low-dimensional perovskite structures receive the most attention, transition metal-based 2D halide perovskites, with a general formula of A_n+1B_nX_3n+1 with A= Cs⁺, Rb⁺, K⁺, organo-ammonium cation, etc.; B = Cd²⁺, Mn²⁺, Fe²⁺, Cu²⁺, Hg²⁺, Zn²⁺, Co²⁺, etc., X = Cl⁻, Br⁻ and n denotes the number of inorganic layers, are also well-studied for their magnetic properties.^126–129 The simplest structure is A₂BX₄ (n = 1), which adopts either K₂NiF₄ (space group I4/mmm)¹³⁰ or TlAlF₄ (space group P4/mmm)¹³¹ structure, depending on the ionic radius. These magnetic materials crystallize in a tetragonal structure, and usually have indirect band gaps with very flat bands, which usually results in poor charge transport properties. However, many of these compounds exhibit symmetry-altering phase transitions upon temperature change. The most studied compounds of this class are Cu- and Fe-based halide perovskites due to the presence of Jahn–Teller (JT) active metal cations and stereo-active lone pairs, leading to unusual physical phenomena such as piezochromism,¹³² ferro- to anti-ferromagnetic transformation,^126,133,134 and ferroelectricity under pressure and temperature.^134–136 The JT distortion, which originates from Cu 3d⁹ electronic configuration, produces in-plane distortion of the corner-sharing copper halide octahedra [Fig. 13(a)] and consequently poor overlap between copper-derived half-filled orbitals. Application of isostatic pressure has been demonstrated to reduce the orbital orthogonality (in-plane distortion) in A₂CuX₄ compounds, leading to better orbital overlap.^137, Figures 13(b) and 13(c) show the evolution of [CuCl₆]⁴⁻ octahedral under isostatic pressure in (EDBE)[CuCl₄]₄. The optical absorption spectra of (EDBE)₂[CuCl₄]₄ exhibited a red-shift with both temperature and pressure, resulting in thermochromism and piezochromism, respectively [Fig. 13(d)]. Electronic structure calculations revealed that the origin of thermochromism is the broadening of conduction band states, while piezochromism is due to reduction of JT and tilting of octahedra.¹³² Additionally, electrical conductivity was shown to increase at least by five orders of magnitude in (EA)₂CuBr₄ compounds under moderate pressure, suggesting that high pressure can dramatically improve the d-orbital overlap through octahedral tilting and Cu–Cl bond shortening.¹³⁸ One instance is (C₂H₅NH₃)₂[Fe^IICl₄], which undergoes a series of phase transition from tetragonal to orthorhombic to monoclinic (I4/mmm ↔ P4₂/ncm ↔ Pccn ↔ Pcab ↔ C2/c) as temperature is reduced from 383 to 10 K. These transitions were accompanied by both tilting and rotation of the [FeCl₆] octahedra.¹³³ The compound displayed promising multiferroicity and giant hysteresis at low temperatures, making it one of the hardest known molecular magnets.

Apart from divalent metal-based layered structure, 2D analogs of double perovskites have also received a great deal of attention recently. The recent development of low-dimensional halide double perovskites was catalyzed by a report from Connor et al.,¹³⁹ who demonstrated dimensionality reduction of the 3D Cs₂AgBiBr₆ by incorporating BA to achieve (BA)₄AgBiBr₈ (n = 1) and (BA)₂CsAgBiBr₇ (n = 2) layered structure. As there are fewer geometric constraints over A-site cation size for forming layered structures, a plethora of novel low-dimensional halide double perovskites have been synthesized, even with compositions that are known to be unstable in 3D crystal structures. For example, pure iodide-based double perovskites are rare due to unfavorable tolerance factor and higher stability of the competing phase.⁸³ However, several 2D iodide double perovskites have been synthesized, such as (AE2T)₂AgBiI₈,¹⁴⁰ (IPA)₄AgBiI₈,¹⁴¹ (AMP)₄[BiAgI₈]₂·H₂O, and (APP)₄[BiAgI₈]·H₂O (where AE2T = 5,5-diylbis(amino-ethyl)-[2,20-bithiophene], IPA = 3-iodopropylammmonium, AMP = 4-aminomethylpiperidinium, APP = 4-aminopiperidine). This increased stability window, especially in the case of iodides, is related to the higher templating capacity of the organic cation as compared to that pure inorganic compositions which are most likely to form low-dimensional ternary structures. More interestingly, fewer geometric restrictions also offers highly distorted and tilted [Bⁿ⁺X₆]ⁿ⁻⁶ octahedral units achieving a more stable configuration. For example, monovalent Cu-based 3D double perovskites is highly unlikely due to the preference of Cu⁺ for three or fourfold coordination, but several examples of Cu⁺-based 2D halide double perovskites have recently emerged where Cu⁺ adopts extremely distorted octahedral coordination.^142,143

Despite the templating effect by the organic cations, the optoelectronic properties of these low-dimensional double perovskites mostly dominated by the metal and halide composition. For example, (BA)₄AgBiBr₈ (n = 1) (BA)₂CsAgBiBr₇ (n = 2), and the 3D parent Cs₂AgBiBr₆ possess band gaps of ≈2.6, ≈2.4, and ≈2.2 eV, respectively, which is less significant modification as compared to the dimensionality engineering in divalent metal cation-based structures.¹³⁹ Even varying the organic cation has little impact on the bandgap tunability. For example, A_nAgBiBr₈ (n = 2 or 4) [A = PA, BA, octylammonium (OCA), and butyldiammonium (BDA)] exhibit similar band gaps in the range of 2.41–2.45 eV.¹⁴⁴ In a similar vein, Bi et al.¹⁴³ investigated several A_nCuBiI₈ (n = 2 or 4) compositions containing various organic cations and found that the bandgap values of these materials fall within a narrow range of 1.55–1.65 eV. A noteworthy observation from both studies is that materials with greater interlayer distances and higher octahedral distortion typically exhibit slightly larger band gaps, which is similar to the behavior of Pb- or Sn-based 2D systems.

That said, a wide range of property tunability is possible for B-site cation engineering with bandgaps spanning a remarkable range of 1.14–4.27 eV, depending on the choice of halide. As expected, the bandgaps are smallest and largest for iodide and chloride materials, respectively. Among various monovalent cations at B-site, the smallest bandgap is offered by Au-based perovskites, followed by Cu- and Ag-based compounds due to presence of intervalence charge transfer in the former and presence of d-orbitals in the Cu-based compounds. The bandgap varies with trivalent cations as Bi < Sb ≪ In with indium-containing compounds exhibit largest bandgaps due to the change in electron configuration, 4d¹⁰5s⁰ for In³⁺ vs (n − 1)d¹⁰ns²np⁰ for Sb³⁺ and Bi³⁺. The smaller bandgaps in Bi-based compounds are also expected due to larger relativistic effect as compared to that of Sb-based compounds.^139,145 A particularly interesting case of hybrid low-dimensional perovskite is the mixed valence: [NH₃(CH₂)₈NH₃]₂[(Au⁺I₂)(Au³⁺I₄)(I₃)₂] and NH₃(CH₂)₇NH₃]₂[(AuAu³⁺I₂)(Au³⁺I₄)(I₃)₂] which even exhibits smaller bandgaps than 3D analogs.¹⁴⁶ This narrowing of the bandgaps can potentially be explained by the incorporation of I₃⁻ in the low-dimensional structure. Another hybrid material that has been reported recently is (IPA)₄AgBiI₈, which has iodide as its primary component. The interlayer cation in this material is IPA, which was initially 3-bromopropylammonium but underwent an in situ reaction with hydroiodic acid to become 3-iodipropylammonium. This reaction resulted in a narrow-direct bandgap of 1.87 eV in the layered double perovskites.¹⁴¹ 

Nevertheless, the nature of bandgaps in these series of low-dimensional structure remains elusive. For example, electronic structure shows an indirect bandgap of Cs₂AgBiBr₆, whereas n = 1 (BA)₄AgBiBr₈ has a direct bandgap,¹³⁹ a trend which is markedly different in comparison with Sn-based low-dimensional perovskite structures. This change from indirect to direct bandgap is attributed to a reduction in dimensionality. Moreover, the nature of bandgap in (AE2T)₂AgBiI₈ is calculated to be indirect without spin–orbit coupling (SOC) effect, but changes to direct when SOC is considered.¹⁴⁰ In contrast, recent reports also predict a direct bandgap for (PEA)₂CsAgTlBr₇ (PEA = phenethylammonium), which is similar to the 3D double perovskite Cs₂AgTlBr₆.¹⁴⁷ The bandgap of the n = 1 compound, on the other hand, was found to be indirect, originating from Ag-to-Tl metal charge transfer. On a separate note, hybrid low-dimensional halide double perovskites generally have flatter bands which pose difficulty in accurately determining the nature of bandgap. Despite this, empirical and theoretical findings suggest that the type of bandgap is considerably influenced by factors such as the composition, layer thickness, and the degree of local structural distortion. Thus, it is crucial to conduct meticulous theoretical investigations before drawing conclusions about the trend based solely on the 3D parent material or the reduction in dimensionality.

Apart from (100) orientation, low-dimensional perovskite structures also consist of corrugated (110) and (111) oriented inorganic layers, although these are quite rare as small and highly symmetric cations are required to stabilize them.^148–150 As shown in Fig. 14(b), corrugated (110)-oriented structures can be described by the missing metal octahedra in ⟨110⟩ direction. Each layer expands through the corner-connected metal halide octahedra which can be seen as a zigzag pattern from the other direction. Both monoamine and diamine cations can be incorporated at A-site to form (110)-oriented 2D perovskite structure, adopting a general formula of AA′BX₄ (A and A′ can be same or different monoamine cation) or A²⁺BX₄ (A is a diammonium cation). An early known example of this structure is the [NH₂C(I):NH₂]₂(CH₃NH₃)_nSn_nI3_n+2 series¹²⁴ in which the open octahedral voids formed by the undulated layers contain smaller (CH₃NH₃)⁺ cations, while the large organic cation (NH₂C(I):NH₂)⁺ sits inside the interlayer spacing. Other known examples includes iodoformamidinium (IFO) tin iodide [NH₂C(I):NH₂]₃SnI₅,¹⁵¹ (Gu)_1.5(Me-ImH)_0.5SnI₄ (Gu = guanidinium, Me-ImH⁺ = 1-methylimidazolium),¹⁵² α-[NH₃(CH₂)₅NH₃]SnI₄,¹⁴⁸ and Gu₂SnI₄.¹⁴⁹ In the last example, the guanidium cation occupies both A and A′-site in the (110) oriented 2D structure.¹⁶ Perovskite layers with a (110) orientation are inherently distorted, and they are typically stabilized by secondary bonding interactions involving hydrogen or other elements. Consequently, these (110)-oriented perovskites often emit white light at room temperature due to the formation of self-trapped excitons (STEs).

On the other hand, there are no reports on divalent metal cation based (111)-oriented 2D halide perovskites. Unlike the rest of the layered perovskite configurations, (111)-oriented perovskites are essentially vacancy-ordered structures in which a metal octahedra layer is missing in each third layer (n =2) [Fig. 14(c)], which necessitates the central metal cation to be in the +3 oxidation state to maintain the charge balance with the halides. Hence, trivalent cations remain the most ideal candidates to form (111)-oriented 2D halide perovskites having the formula of A₃B⁺³₂X₉ (B = Cr³⁺, As³⁺, Sb³⁺, Bi³⁺, In³⁺).^153–156 It should be noted here that the same formula unit can also be used to describe 0D variants of those compounds which we will discuss later under perovskite-derivative structures. A smaller A-site cation and smaller halides favor the formation of (111)-oriented structures, whereas a combination of larger A-site cation along with larger halides promotes the formation of 0D structures. For example, Cs₃Sb₂I₉ prefers to crystallize into zero-dimensional dimer structure, whereas Rb-analogous are easily stabilized into (111)-oriented 2D structure.¹⁵⁷ Additionally, zero-dimensional Cs₃Sb₂I₉ can be converted to (111)-oriented 2D structure by substituting iodide with smaller halides, such as bromide or chloride.^158,159 While the electronic structures of these compounds are governed by the B-site cations and halides, the optoelectronic properties of these two polymorphs differ significantly with typically direct bandgaps in (111)-oriented 2D structures and indirect bandgaps for 0D structure owing to superior connectivity of the octahedra in the former. For the same reason, the optoelectronic properties are also nearly identical for different A-site cations for same crystallographic structure. Typically, iodide-based compounds have direct bandgaps of around 2 eV with Bi-based compounds generally having slightly smaller bandgaps (due to larger relativistic effect) compared to Sb-based compounds. The smallest bandgap that has been reported with (111)-oriented 2D (n = 2) is around 2 eV in (NH₄)₃Bi₂I₉, which is still quite larger than the optimal values required for photovoltaics.¹⁵⁶ On the other hand, bromide and chloride analogs exhibit much wider bandgaps of 2.6–3.0 eV. We should note here that CsBi₃I₁₀ is claimed to have a layered structure with a bandgap of 1.77 eV. Nevertheless, there is no single crystal data to confirm the structure as of now.¹⁶⁰ In direct comparison, 2D layered structure always offers better optoelectronic properties as compared to 0D dimer structure, at least in terms of charge transport, excitonic binding energy, and radiative recombination. Additionally, the effective mass of A₃B₂X₉ layered structures can be further reduced along certain crystallographic orientations by tuning A-site or X-site ions.

By mixing these vacancy-ordered structures, the library of perovskite-derivative compounds can be extended to many different formulas, such as A₄B³⁺B⁺⁵X₁₂ and A₄B²⁺B³⁺₂X₁₂. For example, incorporating Mn²⁺ with Cs₃Bi₂Cl₉ structure leads to heterometallic Cs₄MnBi₂Cl₁₂ (A₄BC₂◻X₁₂) vacancy-ordered triple perovskite, having 25% lower vacancies than the parent A₃B₂X₉ structure. In this arrangement, both Bi³⁺ and Mn²⁺ cations are bonded to six Cl⁻ ions to generate two distinct types of octahedral blocking units. These units are organized into a triple-layered 2D structure in which a layer of [MnCl₆]⁴⁻ octahedra is sandwiched between two layers of [BiCl₆]³⁻ octahedra. The [MnCl₆]⁴⁻ layer is held in place by sharing corners with the adjacent [BiCl⁶]³⁻ layers. Likewise, (111)-oriented (n = 3) crystal structure can be formed by intercalating Cu²⁺ (Ref. 161) and Mn²⁺ (Ref. 162) cations in 2D (n = 2) Cs₃Sb₂Cl₉.^161,162 As shown in Figs. 15(a) and 15(b), (111)-oriented 2D (n = 3) structure consists of alternating, corner sharing [M²⁺Cl₆]⁴⁻ and [SbCl₆]³⁻ octahedra with Cs⁺ occupying the voids in the framework, thus forming n = 3 layer with the chemical formula of Cs₄MSb₂Cl₁₂ (M = Cu²⁺, Mn²⁺). Interestingly, Cs₄CuSb₂Cl₁₂ exhibited an optical bandgap of 1.0 eV as compared to 3.0 eV of the parent n = 2 Cs₃Sb₂Cl₉ phase or n = 3 Cs₃MnSb₂Cl₁₂. This is a classic example of Jahn–Teller distortion originating from d⁹ configuration Cu²⁺ cations. As shown in Figs. 15(d) and 15(e), the presence of highly localized mid-bandgap states originating from Cu d orbitals is the most likely reason for low bandgap in Cu-based compounds as compared to Mn-based compounds. However, this also implies a low density of states close to the band edge, which may reduce the probability of electronic transitions drastically. (111)-oriented 2D structure can also be formed by multivalence state of Sb such as Cs₄Sb³⁺Sb⁵⁺Cl₁₂ which was reported back in 1960s, and later, Rb₄Sb³⁺Sb⁵⁺X₁₂ as an analogous structure. The [Sb³⁺Br₆]³⁻ and [Sb⁵⁺Br₆]¹⁻ octahedra are both distorted from O_h symmetry and have D_4h symmetry. Notably, these compounds exhibit an unusual dark coloration, suggesting that they possess strong visible light absorption capabilities. This light absorption is attributed to electron transfer from the [Sb³⁺X₆]³⁻ octahedra to [Sb⁵⁺X₆]¹⁻ octahedra, which is facilitated by van der Waals interactions involving the halogens and/or cations.

The Cs₄BB′₂X₁₂ family has been the subject of both experimental and theoretical investigations regarding their optoelectronic properties. For instance, one recent study on Cs_n+3B_n+2Sb₂I_3n+9 (B = Sn, Ge) compositions¹⁶³ found that presence of [SnI₆] or [GeI₆] octahedral layers between [Sb₂I₉] bilayers promote better optoelectronic properties including smaller band gaps and effective mass, larger dielectric constants, lower exciton binding energies, and higher optical absorption when compared to the pristine compound (Cs₃Sb₂I₉). The thickness of the inserted octahedral layers ([BX₆]) can be further tuned to optimize the band gaps and effective mass across a wide range. The larger optical bandgaps of these series of compositions prompted another theoretical study for the new transparent conductors. Among 54 potential compositions (B²⁺ = Mg²⁺, Ca²⁺, Sr²⁺, Zn²⁺, Cd²⁺, Sn²⁺; B³⁺ = Sb³⁺, In³⁺, Bi³⁺; X = Cl⁻, Br⁻, I⁻), seven compounds were predicted to have ideal properties for p-type transparent conductors, with Cs₄CdSb₂Cl₁₂ showing particular promise.¹⁶⁴ A subsequent study by Hu et al.¹⁶⁵ suggests that these optically transparent compounds are probably electrically insulating, which contradicts the earlier findings. While computational research in this field persists,¹⁶⁶ it is evident that further advances are needed on the experimental front.

In contrast to 2D halide perovskites in which the octahedral network propagates in a 2D plane, the metal halide octahedron ([Bⁿ⁺X₆]ⁿ⁻⁶) can also be connected to each other via terminal halogen bridging to form an infinite array of 1D octahedral chains, separated by single or multiple A-site cations. The metal halide octahedron can be connected to each other either via trans- or cis-vertices, forming linear or zigzag chain of (BX₅)_∞ respectively [Fig. 16(a)]. A classic example of the linear 1D structure is the end member of the (110)-oriented [NH₂C(I)NH₂]₂A_mSn_mI_3m+2 2D series.¹⁶⁷ When m = 1, the 1D perovskite system can be expressed as [NH₂C(I)NH₂]₂ASnI₅ [A = NH₂C(I)NH₂⁺ or NH₂CHNH₂⁺] in which each [SnI₆]⁴⁻ octahedron share opposite corners to form nearly linear 1D chains of [SnI₅]_n³ⁿ⁻ extending down the crystallographic a-axis. The A-site cations lie between the chains while iodoformamidinium (IFO) cations separate the chains horizontally. While there are fewer constraints for the size of the interlayer organic cations for forming 1D structures, trans-connected 1D perovskite chains are known for only one case of each Sn²⁺ and Cu²⁺ cation (excluding lead and fluoride compounds). A Cambridge Structural Database survey, carried out on the CSD version 5.43, indicates only fewer than 10 entries containing [BX₅]ⁿ⁻_∞ chains where B is the divalent cation (4 Mn-based, 1 Fe-based, 1 Cu-based, 2 Sn-based).

1D perovskite structures, on the other hand, are more common for trivalent metal cations such as Bi³⁺- and Sb³⁺-based halide perovskites, adopting a general formula of A₂BX₅ (A is monoamine) or ABX₅ (A is diamine).^168–173 As these ions are weakly bonded to outer s electrons and easily polarizable, a great degree of distortion and aggregation of the [B³⁺X₅]_n²⁻ chain can be observed. Moreover, the covalency of Bi and Sb halide bonds exhibit low-directional-correlations, which promote a much higher tendency to form novel metalate halide structures such as these 1D chains. Both cis- and trans-connected structural motifs are observed in these trivalent metal cation-based halide perovskites. In the most common case, especially for iodides, [BX₆]³⁺ are connected via cis-halogen bridging, thus forming zigzag octahedral chains. In the ideal structure, the B−X−B bridges lay in the plane of B atoms (180°), however, often the structure is distorted (140°–150°) depending on the interaction with the organic cations. Additionally, a special case can arise when the zigzag segments can also be built from three octahedra instead of two, a unique feature similar to 2D halide perovskites.¹⁷⁴ The [BX₆]³⁺ units can also form a straight octahedral chain (trans-connected) which is most common in chloride and bromides.

Intriguingly, the 1D structures often feature inorganic motifs that create a van der Waals gap or galley, presenting an opportunity for excess organic cations or foreign molecules to intercalate. Zaleski and Pietraszko¹⁷⁵ explored intercalated structures in Gu₂SbCl₅·GuCl, in which the anionic sublattice comprises of a 1D chain of [SbCl₅²⁻]_n and isolated chlorine atoms. The chains consist of distorted [SbCl₆]³⁻ octahedra connected at corners which align along the crystallographic c-direction to form elongated cavities where the isolated chlorine ions reside. The guanidinium cations are linked to chlorine atoms through hydrogen bonds in the cavities created by polyanionic chains [Fig. 16(c)].

Currently, there are no strict guidelines for selecting suitable bulky cations for the formation of 1D perovskite chains, although several trends can be observed from the reported literature. First, 1D chains with heavier halides are all hybrid structures (all inorganic 1D chains exclusively form with fluorides) owing to easily deformable perovskite chains and higher degrees of freedom. Another structural requirement is the shape and size of the organic cations as these molecules not only accommodate themselves within the inorganic framework, but they should also provide adequate structure rigidity for 1D octahedral chains. Additionally, primary (H⋅⋅⋅X) hydrogen bonding, which is an important parameter for 2D perovskite structure formation, cannot determine the 1D structure alone as the close-packing of the metal halide complex is also apparently important and the optimal structures are believed to arise when there is a harmonious interplay between these two factors.¹⁷⁶ Cariati et al. investigated the crystal structure of [bzpipn]₂[BX₅] and [bzpipzn][BX₅] (bzpipn = 4-benzylpiperidinium cation, bzpipzn = N-benzylpiperazinium dication; B = Sb or Bi; X = Cl or Br) to observe the effect of hydrogen bonding as 4-benzylpiperidinium and N-benzylpiperazinium cations have similar dimensions.¹⁷² Based on the vibrational spectra of these compounds, the molecular structures of the complexes were found to depend more on the halogen atoms rather than on the counter-cation dimensions and hydrogen-bonding abilities. Furthermore, the lattice energy of crystal structures can be dominated by electrostatic interactions, which can outweigh the effects of local hydrogen bonding. This results in molecular packing that appears to be primarily influenced by shape complementarity and Coulombic forces.

While the earlier studies were focused on the crystal structure of these polymeric chains, recent successes of halide perovskites have led to reasonable attention on these 1D structure for optoelectronic applications. Earlier, Mitzi and co-workers discovered that 1D structures, [NH₂C(I)NH₂]₂ASnI₅ [A = NH₂C(I)NH₂⁺ or NH₂CHNH₂⁺], possess higher bandgaps and are electrically insulating when compared to semiconducting 2D (m ≥ 2) and conducting 3D perovskite structures (m→∞).¹⁶⁷ This outcome is anticipated due to stronger dielectric confinement within 1D structure. However, the dielectric confinement can be reduced by implementing organic cations with higher electron affinity. A case in point is the zigzag chain structure of (naphthalimide ethylammonium)₂BiI₅ (NBI), where the high electron affinity of naphthalimide creates a type-IIa band alignment at the organic–inorganic heterojunction, overcoming the charge transfer bottleneck.¹⁷⁷ This heterojunction structure leads to the efficient separation of electron–hole pairs and longer excited state carrier lifetimes. Unfortunately, anisotropic electrical properties also observed in NBI single crystals of NBI along the directional growth of [BiI₅²⁻]_n inorganic chains. Another approach to reducing dielectric confinement is to use a diammonium cation that can also participate in charge transport and optoelectronic properties. (TMP)[BiX₅] (TMP = N,N,N′,N′-tetramethylpiperazine) is a noteworthy example of this type. The compound features alternating layers of inorganic [BiI₅]_n²ⁿ⁻ chains and (TMP)²⁺ cations along the b axis. The inorganic layers consist of a 1D array of [BiI₅]_n²ⁿ⁻ chains that extend along the [011] direction of the structure.¹⁶⁸ The twist in the zigzag structure was found to increase monotonically from iodide to chloride structure, resulting in significant structural changes. The optical band gaps, as calculated from reflectance spectra, were determined as 2.02, 2.67, 3.21 eV for iodide, bromide, and chloride, respectively. Additionally, octahedral distortion is also found to control the optoelectronic properties significantly. For example, [NH₂C(I)NH₂]₂ASnI₅ [A = NH₂C(I)NH₂⁺ or NH₂CHNH₂⁺] exhibit similar building blocks for both A-site cations, However, the large iododformamidinium cation [A = NH₂C(I)NH₂⁺] induces larger distortions as compared to formamidinium cation, which reflects in their corresponding color (orange yellow for A = iodoformamidinium and dark red for A = formamidinium).

In general, the 1D structures can be an excellent model for self-trapped excitons as they are easily deformable under photoexcitation due to greater vibrational degrees of freedom, which enhances the self-trapping of excitons.¹⁷⁸ 1D quantum wire perovskites have already shown excellent potential in various applications including ferroelectrics, LEDs, superlattice heterojunction devices, lasers, and light harvesting; in particular, 1D nanowire structures show directional propagation of hole, electron, or photon that could enable improved device performances in certain directions.^179,180 However, in-depth investigations of optoelectronic properties in 1D perovskite crystal structures are still scarce.

Another vacancy-ordered low-dimensional structure is formed by tetravalent metal cations with the general formula of A₂B⁴⁺X₆, popularly known as K₂PtCl₆-type (antifluorite) structure, or 0D perovskites. These structures are crystallographically identical to double perovskites, having one of the B-site cations is partially replaced by a vacancy (at a ratio of 1:1), resulting in isolated metal halide octahedra. Nevertheless, the close-packed anionic lattice structure is still retained [Figs. 17(a)–17(c)]. This type of structure has been well-known for a long time, along with their symmetry-lowering phase transition at low temperatures.¹⁸¹ Earlier studies focused on their applications as diamagnetic hosts for paramagnetic ions (Ir⁴⁺, Re⁴⁺, Os⁴⁺),¹⁸² scintillation and gamma-ray spectroscopy.¹⁸³ According to Brown,¹⁸⁴ the structure type of A₂BX₆ compounds mainly depends on the ratio of the ionic radius of the A cation and that of the hole (gap) inside the BX₆ lattice. As the size of the A cation decreases, the crystal structure of A₂BX₆ compounds distorts from cubic to tetragonal or lower symmetry. If the ratio is greater than 0.98 (as in Panichiite), a cubic structure is observed at any temperature. However, for ratios between 0.89 and 0.98 (such as in K₂SnCl₆), the structure is cubic at room temperature but transforms to a lower symmetry at lower temperatures. Over 30 different metal cations have been incorporated as B-site cations in A₂BX₆ structures, and hundreds of compositions have been synthesized and characterized so far.^182,185 A number of these compounds exhibit symmetry-lowering octahedral rotations and tilting as a result of over- or undersized A-site cations¹⁸⁴ and stereo-chemical activity of B-site cations.¹⁸⁶ While the earlier studies were mostly focused on rare-earth and third-row transition metals as B-site cations, their recent revival of interest originates from unusual optoelectronic properties exhibited by Cs₂SnI₆ which is an undesired degradation product of CsSnI₃. Despite having isolated octahedra, initial reports indicated strong absorption in the visible range (direct bandgap of 1.3 eV), extremely high charge carrier mobility (310 cm² V⁻¹ S⁻¹), and superior air-stability of Cs₂SnI₆ as compared to parent CsSnI₃, making it an extremely promising material for photovoltaic applications.^35,187,188 While subsequent investigations reported many contrasting results regarding the optical bandgap (1.3–1.6 eV) and mobilities (1–310 cm² V⁻¹ S⁻¹), which were found to be highly dependent on the process history and characterization techniques employed,^153,189,190 the reasonably smaller bandgap and unusually high carrier mobility still sparked much interest. DFT-based electronic structure calculations revealed heavy effective mass of electrons and holes which is expected due to the low-dimensional crystal structure. However, the close-packed halide lattice can still offer reasonable charge transport across the lattice. Additionally, the presence of defects such as iodine/tin vacancies can also be abundant depending on the process history and the defects can have huge role in charge transport as previously observed for low-dimensional Sn²⁺-based compounds. Hence, several hypotheses for high mobility have been suggested such as surface-mediated charge states,¹⁹¹ presence of defects such as iodine vacancies,¹⁹² and impurity phases such as CsSnI₃.

The optical bandgap, on the other hand, could be influenced by the measurement techniques employed; for example, diffuse reflectance spectroscopy is more sensitive toward sub-bandgap states which would most likely indicate a smaller bandgap.¹⁹⁰ Similar to other halide perovskites, optoelectronic properties of vacancy-ordered A₂BX₆ are mostly determined by the electronic states of B- and X-site ions. Thus, tuning of bandgap is also possible by alloying with bromine and chlorides which widens the bandgap, following a linear relationship. Figure 17(d) shows the computed bandgap of the A₂BX₆ structure. Experimental studies agree well with the trends in the bandgap variation such as in Cs₂SnI_6−xBr_x and Cs₂SnI_6−xCl_x series. Similar results are also predicted with Ge-based analogous Cs₂GeCl₂I₄, Cs₂GeBr₂I₄, and Cs₂GeI₂Br₄.¹⁹³ The magnitude and nature of bandgap (direct vs indirect) is often determined by the B-site and halide ions. For example, Cs₂SnI₆ possesses a direct bandgap, whereas replacing Sn with Te at the B-site yields comparatively larger indirect bandgap. Several other A₂B⁴⁺X₆ structures with B = Pd, Pt, and Ti show promising optoelectronic properties with optical bandgap in the visible range, long photoluminescence lifetime, and dispersive electronic bands. For example, the bandgap of Cs₂TiX₆ (X = Br, I) can be continuously varied from 1.02 to 1.78 eV by partially replacing iodine with bromine.¹⁹⁴ However, their application on optoelectronic devices remains questionable due to issues on both their stability and their ability to efficiently harvest light.

The nature of defects or impurities is yet to be fully understood, as DFT-based calculations often produced contrasting results. Moreover, there is still a debate regarding the true valence of Sn in the compound, as some computational works suggest that it is +2.¹⁹⁵ Nevertheless, electronic structure calculations are in agreement that the I 5p non-bonding states form the VBM in Cs₂SnI₆, while the CBM arises from the anti-bonding state resulting from the hybridization of Sn 5s and I 5p orbitals. Tin vacancies are predicted to form at energies similar to those related to the Sn–I antibonding orbitals, akin to CsSnI₃, and therefore, at a transition level within the bandgap but in proximity to the CBM. Additionally, due to the smaller bandgap, iodine vacancies are predicted to be shallow in nature. Interestingly, when Sn is replaced by homovalent Te or Ti, the defect tolerance is lost.¹⁹⁶ The larger bandgap in Cs₂TeI₆ arises from the covalent interaction of Te 5p states with I 5p states, which pushes the conduction band to higher energies. As a result, the I vacancy becomes a deep-level state [Fig. 17(e)]. On the other hand, the defect intolerance of Cs₂TiI₆ is attributed to the large number of possible oxidation states and relatively localized d-electronic states.

A unique feature of this class of compounds is their isolated octahedra, resulting in quantum confinement, which is potentially beneficial for light emission applications. The photoluminescence of these compounds can be further enhanced by doping, which has been demonstrated to be an effective strategy to control the luminescence and even to induce new functions. However, the rules for selecting the impurity dopant ions still unclear at present. Therefore, further investigations toward structural engineering, pure-phase formation, and theoretical calculations are necessary to assess the optoelectronic properties of this series.

While there is still dissent on the exact boundaries in the broad perovskite family, we classify the compounds in which metal halide octahedra are connected by edge or face to form octahedral network as perovskite-derivative compounds. Ionic compounds usually adopt a corner-shared network to decrease the Coulombic repulsion as compared to face- or edge-shared network in which intermetal distances are shorter. Hence, ABX₃ compounds, being ionic in nature, usually adopts corner-shared perovskite structure assuming stable structures can be formed, i.e., within tolerance factor limit. However, if the size of A-site cation is too large as compared to that of B-site cations, the corner-shared octahedral network often collapses and face-shared or edge-shared octahedral network dominates. Additionally, if the binding forces become more covalent in nature (as observed in [BiI₆]³⁻ complex), the Madelung term in the stabilization energy decreases significantly. This leads to greater orbital overlap and often deters the preference for corner-sharing structures, instead favoring higher modes of connectivity such as face-shared octahedral networks. Like perovskites, these compounds can also be classified as 3D, 2D, 1D, and 0D structure based on the degree of connectivity (Fig. 1).

Having the stoichiometry of ABX₃, the most common 3D perovskite-derivative structures are commonly known as hexagonal-type perovskites. However, unlike conventional perovskite structure the structural framework is formed by face-sharing [BX₆] octahedra or A or B-centered trigonal prisms. This structural arrangement results in dimers, trimers, tetramers, or longer fragments of chains and shorter metal–metal distances and smaller metal–halide–metal bond angles as compared to conventional perovskites. These structural variations occur when the ionic radius of the A-site cation is much larger than the B-site cations, such as the compounds containing monovalent alkali metals in A-site and d-transition metals at B-site, so as to release the strain caused by the mismatch in the size of the cations. The transformation from conventional cubic perovskite to these hexagonal type perovskites can be visualized by the stacking sequence of [AX₃] layers. If the stacking is entirely cubic in nature (ABA), the structure resembles conventional perovskite structure, whereas hexagonal stacking (ABC) with respect to adjacent layers results in 1D face-shared halo-metalate chains. In between these two extremes, the ratio of cubic to hexagonal stacking determines the length of the one-dimensional chains. Figure 18 illustrates representative structural evolution of [MnCl₆]⁴⁻ octahedral networks between conventional corner-shared perovskite structure (KMnCl₃) and pristine face-shared 1D chloro-manganese chain (dimethylammonium manganese chloride). Moving from the smallest A-site cation (K) toward largest A-site cation (dimethylammonium), the ratio between cubic to hexagonal connectivity decreases and the compounds develop more face-shared network. These structures are often represented by Ramsdell notation in which the structure is described by a number which indicates the number of layers, followed by symmetry of unit cell, denoted as R for rhombohedral, H for hexagonal, and C for cubic. For example, CsMnCl₃ structure can be noted as 9H, which consists of face-shared [Mn₃Cl₁₂] trimers, stacked octahedrally (corner-shared) to form 3D network [Fig. 18(c)]. A two-dimensional close-packed structure with the chlorine atoms is formed by fitting the cesium cations into holes between the [Mn₃Cl₁₂] trimers. A full structural description of these hexagonal types of oxide perovskites can be found in the article by Tilley.¹⁹⁷ 

To date, hexagonal type halide perovskites have received much less attention as compared to the perovskite structures, and the reports on their structural and optoelectronic properties are fairly limited. Except for Cu²⁺, nearly all the first-row transition metals in their divalent state are known to form hexagonal type perovskite structure with chloride and bromides. However, most of these compounds are moisture sensitive and easily degrade in ambient conditions.^149,198 Due to presence of magnetic transition metal cations, most of the earlier studies were focused on their magnetic properties.¹⁹⁹ Recently, Daub et al. synthesized ANiX₃ (A = Gu, FA, MA; X = Cl, Br) and MAMnBr₃ via solution processing routes.²⁰⁰  Figures 18(e) and 18(f) illustrate that the optical spectra are not influenced by the A-site cation, while a noticeable red shift in the charge transfer (CT) and “d–d” transitions for the bromide compounds is observed when compared to the chloride compounds. In addition, the typical d–d transitions of Ni²⁺ (d⁸ system) surrounded by octahedral geometry are also present. Furthermore, due to the face-shared octahedral network, the bands near the band edges tend to be relatively flat, resulting in larger bandgaps and inferior charge transport properties. Although the hybridization between metal and halides states enables adequate band dispersion along the face-shared chain, the separation of chains in other directions typically leads to flat bands in the corresponding directions and imparts anisotropic properties.

Apart from typical ABX₃ stoichiometry, many different stoichiometric compounds are possible by reacting monovalent alkali halides and transition metal halides, and many of them form 3D octahedral network. For example, the multivalent state of In can provide a unique 3D structural network in Cs_1.17In_0.81Cl₃ where both corner- and edge-sharing InCl₆ octahedra and InCl₇ pentagonal bipyramids are present²⁰¹ [Fig. 18(g)]. Nevertheless, the predicted large indirect bandgap of ∼2.27 eV suggests poor photo-absorption properties, and further characterizations are still needed to rule out this unique structure. A similar crystal structure was also reported in CsMn₄Cl₉.

Like low-dimensional perovskites, perovskite-derivative compounds that do not offer 3D octahedral network are grouped here. The first member of this group is the face- or edge-shared chains, which propagate in one of the crystallographic directions [Figs. 19(a) and 19(b)]. The optoelectronic properties of these 1D structures are highly anisotropic and exhibit high exciton binding energies and large bandgaps. Nevertheless, as the geometric constraints are further reduced, a much wider range of organic cations, including large organic molecules, chromophores, solvated ion cluster, and even transition metal complexes can be incorporated into the 1D perovskite-derivative structure. This unique opportunity further extends the excellent tunability of the optoelectronic properties for a wider range of applications such as luminescence,²⁰² photochromism,²⁰³ ferroelectricity,²⁰⁴ magnetism.²⁰⁵ Low-bandgap organic molecules can enhance the optical properties of a compound by acting as strong light absorbers through electron or energy transfer processes. One example is (C₇H₇)BX₄ (B = Sb, Bi, X = Cl, Br, I), which contains edge-sharing [BX]₆ chains separated by π-stacked tropylium (C₇H₇⁺) cations and photoinduced electrons transfer occurs between inorganic and organic layers.²⁰⁶ Utilization of polarizable organic cation with inorganic lattice further opens up new avenues to tune the excitonic binding energies of these low-dimensional structure. However, achieving highly ordered and efficient π–π stacked organic semiconductors within the structure can be challenging. Nonetheless, using smaller organic cations could lead to shorter X•••X or X•••C distances between the 1D chains, resulting in larger intermolecular interactions and reduced dielectric confinement.^207,208

The 1D perovskite-derivative structure also offers the advantage of facilitating ferroelectric transitions, which is another crucial aspect. This can be achieved by incorporating transition metals and organic cations with potential order-to-disorder (OTD) characteristics at the B-site, thereby leading to the formation of various functional 1D perovskite-derivative compounds. The flexible alkyl amines, saturated naphthene-based amines, saturated heterocycle-based amines, rigid DABCO (DABCO = 1,4-diazabicyclo[2.2.2]octonium) and their derivatives are typically used as potential OTD cations.^209–211 For instance, (pyrrolidinium)MnCl₃ exhibits excellent ferroelectric properties and a high photoluminescence quantum yield.²¹² The pyrrolidinium cation is disordered at room temperature, and it undergoes an ordered transition when cooled down to 273 K. This OTD transition of the organic cation enables the crystal structure to undergo a nonpolar to polar phase transition, which is an indication of ferroelectricity. Since the functional groups are A-site cations, ferroelectric properties can be modified by appropriate A-site cations. For instance, replacing pyrrolidinium with 3-pyrrolidinium resulted in the formation of a new ferroelectric compound with improved spontaneous electronic polarization, high Curie temperature, high fatigue resistance, and superb luminescence efficiency.²¹³ Substituting Mn²⁺ with Cd²⁺ at the B-site also leads to similar ferroelectric features as they have similar ionic radii and coordination types.²⁰⁴ These examples demonstrate that lead-free perovskite-derivative compounds can be excellent alternatives for designing multifunctional devices such as ferroelectric photovoltaics, ferroelectric LEDs, and multiferroics.

Additionally, 1D perovskite derivatives often provide much needed stability due to the shielding effect of the large organic cations. For instance, 1D (DAO)Sn₂I₆ (DAO, 1,8-octyldiammonium), which forms 1D edge-shared chains, was found to be stable in water for more than 15 h.²¹⁴ The 1D face-shared or edge-shared infinite chain can be transformed into 0D bi-octahedral structure by introducing metal cation defects. These 0D structures are common in trivalent metal-based ternary halides. For example, a direct substitution of Pb²⁺ with trivalent metal cations (B³⁺) leads to a general formula of A₃B₂X₉ which can be considered as a defect-variant structure of perovskite derivatives. Keeping the metal octahedra ([B³⁺X₆]³⁻ or [B⁴⁺X₆]²⁻) as the core, different organic or inorganic monovalent cations can be incorporated within these structures. For example, if only 2/3 of the B-sites are occupied and 1/3 of the B-sites remain vacant (at a ratio of 2:1), that can be represented as A₃B₂◻X₉, where ◻ denotes a vacancy. These A₃B₂X₉ structures form two polymorphs depending on the size of the A-site cations. For larger A-site cations and halides, the structure consists of isolated bi-octahedra [B³⁺₂X₉]³⁻, leading to a 0D structure. Furthermore, these isolated bi-octahedra can form via two types of coordination such as face-sharing²¹⁵ and edge-sharing octahedron units, with the latter being the most common. Current research efforts are mostly focused on the Sb³⁺- and Bi³⁺-related halide compounds which are phase-stable in ambient environment and their stable valence ns² electrons hybridize with halides to form a similar electronic structure as that of Pb-based halide perovskites. Nevertheless, their 0D electronic structure results in flat bands, high effective mass, and large optical bandgaps. For example, polycrystalline films of A₃Bi₂I₉ (A = MA, Cs) show carrier mobilities less than 1 cm² V⁻¹ s⁻¹ at room temperature which is at least an order of magnitude smaller than the mobility of Sn- and Pb-based 3D halide perovskites.^216–219 Similarly, Sb-based 0D compounds also have heavy carrier effective masses and low mobilities at room temperature.^157,220

Despite the popularity of perovskite and perovskite-derivative halide structures, several non-perovskite structures also show interesting optoelectronic properties with excellent promise in optoelectronic devices. The stoichiometry of these compounds typically differs from perovskite compositions and may offer tetrahedral metal halide coordination as opposed to purely octahedral coordination in perovskite structures. Nevertheless, due to presence of halides, the chemical nature of these compounds is strikingly similar to that of halide perovskite and perovskite-inspired compounds and can offer rich structural diversity as well. With the heavier halides (Cl, Br, I), these non-perovskite compounds show excellent solution processability and have the prospects for implementation in device architectures like that of perovskite-based compounds. Among these non-perovskite structures, they can be further classified as 3D structure and low-dimensional structure based on the propagation of metal halide network.

One of the major challenges for trivalent metal cation-based perovskite and perovskite-derivative compounds is their charge transport bottleneck arising from electrostatically bonded A-site cations which results in low-dimensional crystal structures. To mitigate that, A-site cations can be replaced by transition metal cations that are also capable of hybridization with the halogen orbitals. As opposed to 12-coordinated A-site cations, these transition metals offer octahedral coordination with halides and active participation in the band edge formation in the final structure. This replacement strategy resulted in a plethora of compounds in which a 3D metal halide network could be preserved via face-shared, or edge-shared, or even corner-shared octahedra. One of the most notable examples from this series is the solid solution of silver iodide and bismuth iodide with the chemical formula of Ag_aBi_bI_a+3b. These structures closely resemble to O₃-type transition metal oxide (e.g., Na_xFeO₂, x <= 1) structures in which an alternate layer structure with alkali cation sheets is sandwiched between transition-metal slabs, resulting in a close packing ABCABC pattern [Fig. 20(a)].²²¹ However, in contrast to typical O₃-type transition metal oxide structure, the cation layers in silver bismuth iodides also comprise vacancies determined by the charge neutrality rule originating from partial occupancy of metal cation sites. Consequently, the determination of the exact crystal structure of silver bismuth iodide series remains difficult and is often ambiguous. For example, the smallest composition of these series, AgBiI₄ can be structurally resolved to both CdCl₂-type (R $3 ¯$m) or cubic defect-spinel (Fd $3 ¯$m) within a similar percentage of error.²²² Nevertheless, the CdCl₂-type rhombohedral structure is predominant in silver-rich compositions having Ag/Bi > 1, while the bismuth-rich fraction (Ag/Bi < 1) adopts a cubic defect spinel structure.²²³ In the rhombohedral structure, disordered Ag⁺ and Bi³⁺ cations occupy every other ⟨111⟩ layer of the space and the halides form a cubic close-packed sub-lattice as a base matrix. The cubic spinel structure, in contrast, contains more vacant sites in the edge-shared cation octahedral sublattice as compared to the rhombohedral structure. Figure 20 illustrates these crystal structures. It should be noted here that hexagonal rhombohedral structure is sometimes called as ruddorfite, following Turkevych and co-workers' suggestion,²²⁴ although a mineral with similar structure was earlier termed as caswellsilverite by Okada and Keil in honor of geologist Dr. Caswell Silver.²²⁵ On the other hand, the O₃-type structure is well-known in the field of cathode materials and is also heavily used in scientific literature.

The substitution of silver with copper leads to analogous compositions of Cu_aBi_bX_a+3b, although the crystal structure and stability of these series are still under debate. Like silver bismuth iodides, copper bismuth iodides were also reported to crystallize in two compositions, a defect spinel CuBiI₄ and a rhombohedral Cu₂BiI₅ with ambiguous structural information.^227,228 However, as copper has a much smaller ionic radius (0.6 Å) as compared to silver (1.15 Å for Ag⁺) and is known to form tetrahedral coordination with halides, it is highly likely that Cu⁺ occupies the tetrahedral sites in these structures, thus differing from silver bismuth iodide structures. Recently, Sansom et al.²²⁶ carried out detailed investigations to resolve the crystal structure of CuBiI₄, which also faces similar issues as that of AgBiI₄ (possible crystal structure can be both CdCl₂-tupe rhombohedral and defect spinel). They also commented that CuBiI₄ is most likely a metastable phase as the composition converts to CuI and BiI₃ at room temperature.²²⁹ Recently, a theoretical study predicted 15 possible crystal structures of CuBiI₄ with low formation energy, relying on their mechanical and dynamic stability. However, there is currently no experimental evidence to validate these findings.²³⁰ 

Replacing bismuth with antimony has proven to be an interesting strategy in lead-free halide perovskites. However, very few reports exist of silver antimony halides or copper antimony halide compositions. Recent studies indicate that AgSbI₄ and AgSb₂I₇ exhibit similar structural features to those of bismuth-based analogs with AgSb₂I₇ forming the Ag-deficient Fd3m cubic crystal structure²³¹ and AgSbI₄ crystallizes into CdCl₂-type rhombohedral structure.²³² On the other hand, there is only one report on the possibility of Cu₃SbI₃ compound formation which unfortunately lacks any structural information.²³³ 

The optoelectronic properties of these compounds depend heavily on stoichiometry and vary significantly due to cationic disorder and non-stoichiometric composition. The optical bandgaps of rhombohedral and cubic Ag_aBi_bI_a+3b composition series are reported in the range of 1.55–1.82 eV (indirect) and 1.6–1.93 eV (direct) with cubic structures (Bi-rich) usually exhibiting smaller bandgaps [Figs. 21(a) and 21(b).^{223,224,234–236} However, all of the compositions of Ag-Bi-I ternary systems, in general, exhibit absorption coefficients in the range of 10⁵–10⁶ cm⁻¹, which is advantageous for realizing photovoltaic devices. While the photoluminescence from these compounds is poor, the carrier mobility is decent enough to offer good optoelectronic properties [Fig. 21(c)]. Both the crystal structures exhibit indirect band gaps from DFT calculations. In comparison to the cubic structure, the computed bandstructures demonstrate larger indirect band gaps and shallower valence band maxima in rhombohedral structure. Defects such as the presence of excess Ag in the rhombohedral phase and the deficiency of the octahedral sites in the cubic phase contribute significantly to optoelectronic properties. There are currently several challenges associated with this series in achieving high-performance optoelectronic devices such as stability in ambient environment, presence of impurity phases, and cationic disorder in the crystal structure. Further improvement in optoelectronic properties was observed by alloying with Cu, which reduces cationic disorder and improves PLQY and carrier lifetime as shown in Figs. 21(d)–21(f).

Low-dimensional non-perovskite halide compounds are characterized by tetrahedral metal halide coordination as opposed to the octahedral coordination found in perovskite and perovskite-inspired structures. Most of these compounds can be considered as large bandgap semiconductors with the bandgap ranging from 2 to 5 eV depending on the tetrahedral network and stoichiometry. Most interestingly, the emission profiles of these compounds are mostly in the visible range.

As mentioned earlier, when the size difference between metal cations and halides is smaller than 0.414, tetrahedral coordination is preferred. The most notable example is the monovalent Cu-based ternary halide compounds. Monovalent Cu usually possesses coordination numbers of two, three, and four, resulting in coordination geometries of linear, trigonal, and tetrahedral, respectively. These compounds can be characterized by low-dimensional crystal structures using the general formula of A_aCu_bX_a+b. They usually crystallize into two different polymorphs: 0D structures having isolated copper halide tetrahedra, and 1D structures where copper halide tetrahedra are connected via either face- or edge-sharing networks. These structures should not be confused with Cu⁺-based organic polymeric complexes or coordination complexes, which are denoted with the general formula of Cu_xX_yL_z (X= halides, L = N, S or P based organic ligand). While the building blocks in both cases are based on copper halide complexes, there is no charge transfer between organic and inorganic motifs in the former case, while organic ligands actively take part in optoelectronic properties in organic polymeric complexes in the latter. Interested readers can look at an excellent review by Peng and co-workers on Cu-based coordination polymers.²³⁷ Our discussion here is limited to low-dimensional ternary Cu-based halides in which A-site cation has no direct role in determining the optoelectronic properties of the compounds but rather provides rich structural diversity which indirectly affects the optoelectronic properties. The zero-dimensional Cs₃Cu₂I₅ was initially reported by Hosono et al. in 2018, showcasing bright blue emission with a peak at 445 nm, large Stokes shift of about 155 nm, and high PLQYs of 90% and 60% for single crystals and thin films, respectively.²³⁸ Subsequently, several ternary Cu-based non-perovskite structures were discovered with 0D and 1D Cu-X tetrahedral network. Figure 22(a) illustrates the different coordination environments of Cu halide and two polymorphs of A_aCu_bI_a+b exhibiting 0D structure and 1D Cu halide network. The emission peaks are illustrated in Fig. 22(b). The structural reorganization of excited states caused by the Jahn–Teller distortion can account for the emission mechanism of these compounds.

Apart from monovalent Cu compounds, several transition metals exhibit tetrahedral coordination with halides such as Zn²⁺, Mn²⁺, Ni²⁺, and Co²⁺, adopting a general formula of A₂MX₄. Tetrahedral coordination is common for iodide compounds, while chloride and bromides usually form octahedral coordination. Despite their existence for several decades, these compounds have recently gained renewed interest due to their PLQY, narrow spectral emissions, and remarkable stability under ambient conditions. For instance, Mn²⁺ in tetrahedral coordination exhibits green emission, making it a suitable candidate for phosphors. The high PLQY observed in these 0D structures with tetrahedral coordination can be attributed to the confinement within isolated tetrahedra.

Lead-free halide compounds have long lived in the shadow of LHPs in the field of optoelectronic devices, due to the lack of an exciting mix between bandgap energy, carrier mobility, and the electron-velocity field, which is highly tunable in LHPs, especially in 3D structures. However, there has been a recent surge in the prominence of lead-free halide semiconductors, as they are now being developed to meet the specific needs of different applications, rather than attempting to optimize a single compound for every application. In Sec. VI A–VI F, we will briefly review their exciting prospects in optoelectronic applications, highlighting current challenges and potential remedies for future development. By exploring the unique properties of these materials, we may unlock new possibilities for optoelectronic devices that can meet the specific demands of various applications.

According to Shockley–Queisser limit, a semiconductor with a bandgap of about 1.3 eV is ideal for single junction solar cells and a bandgap of about 1.7 eV is ideal for being a top cell with Silicon tandem architecture. While very few lead-free halide compounds satisfy the single junction solar cell requirement, there is a vast compositional space suitable for the top cell in tandem architecture. Aside from the bandgap, charge transport properties and carrier lifetime are other major requirements for high-performing photovoltaic devices. In general, low-dimensional structures (2D, 1D, and 0D) offer large excitonic binding energy, and poor charge transport properties which favors charge recombination over charge separation. Consequently, 3D structures remain the most appropriate solution for photovoltaic applications. Since the first report on MASnI₃-based lead-free perovskite solar cell,²⁴¹ significant efforts have been devoted to various lead-free halide semiconductors for photovoltaic applications. The topic remains one of the most active areas of research within the perovskite community. Nevertheless, the great success of LHPs has not yet been replicated in lead-free halide compounds. In general, an excellent photovoltaic absorber usually possesses broad and strong light absorption (small and direct bandgap), efficient charge carrier generation (small exciton binding energy), long carrier diffusion length (long career lifetime), and tolerance toward native defects. While LHPs offer all of those properties, lead-free compounds usually lack one or two key properties. For example, low-dimensional halide compounds (0D and 1D) usually have inefficient charge carrier generation due to large exciton binding energy and poor hot carrier extraction due to molecular crystal structure. On the other hand, 3D double perovskites which offer better charge transport properties, usually exhibit large and indirect optical bandgaps, making them transparent toward most of the visible solar spectrum.

Among the lead-free halide compounds, THPs have been the most investigated semiconductors for PV applications and are currently the most efficient absorber materials. Unfortunately, Sn-based halide perovskites are prone to self-doping due to easy oxidation of Sn²⁺ to Sn⁴⁺, even in mild oxidizing conditions, which results in poor device performance and stability.²⁴² Approaches to increase stability by preventing Sn²⁺ oxidation, such as optimizing the precursor composition and purity, controlling the synthesis environment, and alloying with reducing agents have had encouraging successes. However, nearly all of these techniques require stringent control over the environment and fabrication procedures. Alarmingly, it has been shown that Sn²⁺ can oxidize even in organic solutions such as DMSO, which warrants better control of the fabrication procedures.²⁴³ Moreover, crystallization kinetics in THPs are extremely rapid; this makes it challenging to control film morphology within a short period of time during spincoating. Hence, it is still a grand challenge to formulate a universal method such that the crystallization dynamics can be controlled and the oxidation of Sn²⁺ can be greatly reduced. A recent study probed into the strong coupling between oxidation rates of Sn²⁺ and solvent chemistry, shedding light on future directions to achieve high performance.²⁴⁴ 

Alternatively, the stability of THPs can also be improved by incorporating large organic molecules to transform the 3D structure into a 2D structure. Additionally, the large organic molecules act as a protective layer on top of the inorganic [SnI₆]⁴⁻ network from oxidizing environment.^47,245 Consequently, shelf life and operational stability of Sn-based halide perovskites have improved significantly in the past decade.²⁴⁶ Further improvement is warranted in the development of low-dimensional compounds as the inorganic octahedral networks tend to crystallize in parallel directions to the substrates, which greatly impede the charge transport properties in vertical solar cell architecture. In addition, low-dimensional structures also suffer from larger bandgaps and larger exciton binding energies which are detrimental for high-performance solar cells. These challenges can be alleviated by employing mixed 2D/3D crystal structures. A small amount of large organic molecule can promote the formation of low-dimensional structures in a controlled manner, whereas the optoelectronic properties of the compounds are mostly controlled by the 3D structure.²⁴⁷ Another major breakthrough was achieved by the development of hollow perovskites in which 3D Sn-based halide perovskites was converted into mixed-dimensional structure by incorporating diammonium cations.^50,51,248 In these structures, the divalent organic cations partially replace both A-site and Sn²⁺ cations, resulting in better morphology, higher stability, and fewer defects in the thin-films.²⁴⁹ 

Unlike THPs, Ge-based halide perovskites usually have larger bandgaps, and poor solution-processability, resulting in abysmal performance as PV absorber materials^31,250 Additionally, Ge-based halide perovskites also suffer a similar fate to that of THPs due to rapid oxidation of Ge²⁺ to Ge⁴⁺ even in mild oxidizing environments. Surprisingly, this undesirable property was found suitable for the development of mixed Ge/Sn-based halide perovskite systems,³¹ which was found to be coated with GeO₂ that prevents further degradation. A CsGe_0.5Sn_0.5I₃-based solar cells showed >10% PCE with excellent stability in ambient environment.²⁵¹ Mixed Ge/Sn alloys exhibit significant advantages over pure Ge-based perovskites, including narrower bandgaps and enhanced stability, positioning them as superior alternatives to lead-free perovskite solar cells compared to pristine Sn- or Ge-based halide perovskites. With further advancement in germanium and Sn–Ge alloyed materials, they have the potential to outperform the best-performing lead-based halide perovskite devices currently available.

In the past few years, explorations of trivalent Bi³⁺- and Sb³⁺-based ternary iodides have been reinvigorated as nontoxic and stable alternatives to LHPs for PV applications. Compared to Sn-/Ge-based halide perovskites, these trivalent metal halides are highly stable under ambient conditions and require less control over solution chemistry to achieve pure phase formation. Unfortunately, the optical bandgaps of these trivalent metal ternary iodides are quite large (∼1.9 eV which is smallest among different halides) and the single-junction solar cells will be limited by small short-circuit current density. Considering the rapid rise of tandem architecture in PV, an efficiency of ∼10% could be a gamechanger in the PV industry and these trivalent metal halides could be an excellent prospect for tandem applications as the top cell along with Si as the bottom cell due to their excellent ambient stability. Early studies on Bi-based ternary iodides showed exciting results with PCE reaching over 1% in mesoporous solar cell architecture.²⁵² However, optical characterization revealed extremely short carrier lifetimes of below tens of nanoseconds and low PLQY, signifying the adverse role of defects.²⁵³ The prevalent defects in Cs₃Bi₂I₉ arise due to iodine vacancies, which can be passivated by synthesizing in excess BiI₃ environment.^254,255 Currently, the best performing Bi-based ternary halide is Cs₃Bi₂I₉ which recorded an efficiency of 3.2% by employing a very thin absorber layer that enhances the carrier extraction efficiency.²⁵⁶ Still, the devices showed large open-circuit voltage loss, which can be attributed to the poor film morphology and splitting of the band edge.

However, the major bottleneck arises from the molecular crystal structure of these trivalent ternary halide compounds which limits efficient charge extraction. Utilizing smaller A-site cations could improve the dimensionality of these structures from 0D to 2D as seen for Sb³⁺-based ternary iodides. For example, replacing Cs⁺ with NH₄⁺ or Rb⁺ or I⁻ with Cl⁻ can improve the dimensionality of Sb-based ternary iodide from 0D to 2D structure, which subsequently enhances the optoelectronic properties, and eventually PV performance.^157,257 The best performing ternary Sb-based halide compounds solar cell with 3.3% efficiency was recorded with 2D MA₃Sb₂(I/Cl)₉ as absorber layer.²⁵⁸ Interestingly, a recent report demonstrated that despite low-dimensional crystal structure, more than 80% external quantum efficiency (EQE) was recorded from (N-EtPy)[SbBr₆]-based solar cells.²⁵⁹ The authors suggested that the short Br···Br distance between neighboring [SbBr₆]⁻ octahedra is the most likely reason for assisting the charge transport between the inorganic metal octahedral, resulting in better performance compared to Sb³⁺-based ternary halides.

The limitations of charge transport properties due to molecular structure can be eliminated in double perovskite structures that possess the corner-shared octahedral network while exhibiting excellent ambient stability. Several small bandgap halide double perovskites are also predicted theoretically.^60,61 As of today, only Cs₂AgBiBr₆ showed the promise as a PV absorber material with a large carrier lifetime of ∼700 ns. However, Cs₂AgBiBr₆ has an indirect optical bandgap of 1.95 eV (Ref. 72) which is a major limitation in achieving higher efficiency in single junction solar cells. In addition, theoretical calculations also revealed its poor tolerance toward intrinsic defects.⁸⁴ Hence, most of the focus on the Cs₂AgBiBr₆-based solar cells has been devoted toward fabrication of high-quality thin-films to minimize the non-radiative recombination. Currently, the highest efficiency for Cs₂AgBiBr₆-based solar cell devices have reached to 1.5% and 2.84% PCE in planar and mesoscopic architecture, respectively.^260,261 This is a significant advancement for lead-free perovskite solar cells considering the low toxicity and excellent stability of over months under ambient conditions.

Among non-perovskite structures, Ag_aBiI_3+b system has shown suitable bandgap and decent charge transport properties for PV applications. They have 3D edge-shared octahedral network along with excellent ambient stability. The optical bandgap of the Ag₃BiI_3+b system was found to be in the range of 1.75–1.9 eV depending upon the ratio of Ag and Bi. Moreover, Ag₃BiI_3+b system is highly stable and can be processed in ambient atmosphere, which is an added advantage over LHPs. At present, the highest PCE of 4.3% was recorded based on Ag₃BiI₆ composition in a mesoscopic architecture.²²⁴ Nevertheless, reducing bandgap by doping could be a viable option as experimental results indicate that partial replacement of I⁻ with S²⁻ could induce notable contractions of the band gaps. Subsequently, 4 wt. % S-doped Ag₃BiI₆ solar cells recorded an efficiency of 5.4%, which is the highest among lead-free non-perovskite structures.²⁶² 

In summary, the tremendous progress of LHPs made in the field of PV through novel film fabrication techniques and cation transmutation has failed to translate into the progress of lead-free halide compound-based solar cells. Sn-based halide perovskites still have the edge over other lead-free halide perovskites and perovskite-inspired materials, at least in terms of optoelectronic properties and solar cell performance. Hence, despite the poor stability in ambient conditions, THP performances saw a gradual increase over time along with improved stability, although it is still quite far away from that of LHPs. There are at least four fronts which need further investigations and optimizations to fully exploit the optoelectronic properties of THPs such as (1) passivating and reducing agents that can prevent self-doping, (2) better understanding of film formation dynamics, (3) improved device architecture with efficient charge collection and extractions, and (4) modification of crystal structure to stabilize the divalent oxidation state of Sn. On the other hand, other lead-free halide systems, especially low-dimensional structures, are quite far away from the desired PV properties due to large optical bandgap, positions of band edges, and poor charge transport properties. Nevertheless, they also offer new possibilities for obtaining stable structures with improved efficiency. Low-dimensional materials are particularly advantageous because they allow for the tunability of multifunctional organic molecules, improving their charge transport characteristics. In addition, several proof-of-concept devices based on novel lead-free halide systems have been proposed. An alternative approach would be modifying the device architecture for lead-free halide systems which remain unexplored. For example, bulk heterojunction devices could overcome the challenge in charge transport properties in low-dimensional structures. In material systems, doping and alloying remain a largely unexplored space to exploit the full potential of lead-free systems. One example is Tl doping, which reduces the bandgap of Cs₂AgBiBr₆ from 1.9 to 1.6 eV. While Tl is highly toxic, even more so than Pb²⁺, this indicates that there may be several possibilities for selective alloying. Overall, active research on lead-free systems is still limited, and compared to LHPs, there are few investigations into the mechanisms of film formation, doping, and device architecture. Negative results could further aid in efficiently screening lead-free system for PV in an accelerated motion.

Beyond photovoltaics, the use of lead-free halide compounds in photodetection has gained significant attention in recent times. While traditional semiconductors like silicon and the III–V s have been effective, the quest for higher efficiencies and lower costs fuels ongoing exploration. The convenient and low-cost solution preparation methods of lead-free metal halide compounds, coupled with their nontoxic nature, make them essential for commercial applications. As a result, the utilization of lead-free metal halide compounds in photodetection is becoming increasingly promising for next-generation technologies.

Many of the lead-free halide compounds exhibit direct bandgaps, high absorption coefficients, and low dark currents, which are some of the important parameters for high photoconductivity gain. In addition, the bandgaps of these halide compounds, especially THPs, can be tuned such that a wide range of photon energies such as NIR to UV can be sensed efficiently. At present, 3D Sn-based iodide perovskites exhibit one of the lowest bandgaps among lead-free halide perovskites and subsequently, NIR photodetectors based on these compounds have already been demonstrated. For example, FASnI₃-based NIR photodetector, demonstrated by Yan's group²⁶³ delivered a responsivity of 1.1 × 10⁵ A W⁻¹ under a driving bias voltage of 0.5 V along with a decent detectivity of 1.9 × 10¹² Jones. As the stability of Sn-based 3D halide perovskites remains a challenge, Fan's group²⁶⁴ grew CH₃NH₃SnI₃ nanowire arrays inside the porous alumina, which resulted in excellent stability with decent NIR detection performance. Stability can also be improved by employing zero-dimensional perovskite-derivative compounds such as Cs₂SnCl_6−xBr_x.²⁶⁵ As a broadband photodetector for visible light detection, 2D (PEA)₂SnI₄-based single crystal devices recorded excellent specific detectivity of 1.92 × 10¹¹ Jones (calculated). Moreover, these low-dimensional compounds exhibit much better stability and lower dark current than their 3D counterparts.

Unfortunately, these layered compounds exhibit anisotropic charge transport that demands vertical growth of crystallites during the fabrication process. The stability of the photodetectors can be further enhanced by employing trivalent metal ternary halides such as Bi³⁺- or Sb³⁺-based compounds. While single crystals showed low performance due to anisotropy, the microcrystalline structure greatly enhances the photon detectivity due to efficient charge collection. One of the highest detectivities among lead-free compounds was obtained with CsBi₃I₁₀ thin-film for red light detection.²⁶⁶ The devices also showed excellent stability over 3 months. The stability and charge transport properties can be simultaneously improved by employing double perovskite structures. Cs₂AgBiBr₆-based photodetector demonstrated excellent photo response (∼17 ns) along with ultralow detection limit.⁸⁷ One major shortcoming remains the large bandgap which results in responses only in the range of below 500 nm.

Nevertheless, a large bandgap semiconductor could be useful for UV detection. Recently, Cu⁺-based non-perovskites have shown excellent promise as alternatives to the traditional UV detectors based on oxides, such as zinc oxide (ZnO) and tin oxide (SnO₂), which usually suffer from a slow response time and high temperature processing costs. The first report on a Cs₃Cu₂I₅-based device showed poor performance, owing to difficulties in uniform thin-film fabrication.²⁶⁷ Overall, the emerging field of lead-free perovskites and perovskite-inspired halide compounds has demonstrated significant promise, with impressive strides made in the area of photodetector applications. These materials enable broad-spectrum photodetection spanning from near-infrared to ultraviolet light, thereby providing numerous opportunities for practical implementation. However, substantial work remains to enhance their figure-of-merit, and innovative approaches that differ significantly from those developed for LHPs are crucial for improving material quality. Advancements in this area have the potential to transform the field of optoelectronics, enabling a broad range of applications and accelerating progress toward next-generation technologies.

At present, the direct detection of high-energy radiation, such as gamma and x-rays, is utilized in various fields, including but not limited to nondestructive material characterization, space exploration, security screening, medical diagnostics, computed tomography (CT), positron emission tomography (PET), and nuclear reactions. In direct detection, high energy radiation is absorbed by the detector, which converts radiation into electrical signal, just like photodetection. While the basic requirements remain the same as with photodetection, the semiconductors also need to be stable under high energy radiation and should possess high attenuation coefficients. Perovskite-inspired halide compounds have many desirable properties for low-cost radiation detectors, including high attenuation coefficients, low dark current, excellent stability, and ease of synthesizability. Elements having higher Z-number provide higher interaction volume for the high energy radiation, thus higher attenuation coefficients or better stopping power. This interaction also generates electron–hole pairs which are directly proportional to the sensitivity of the detector. Hence, to increase the sensitivity and energy resolution, a low-bandgap semiconductor is preferred. However, smaller bandgaps also lead to higher dark currents that reduce the signal-to-noise ratio, thus degrading the detector performance. Bandgap values between 1.5 and 3.0 eV were found to be the ideal range to balance these two effects.²⁶⁸ 

Furthermore, a radiation detector should also possess a large μτ product to efficiently extract all the charges from the millimeter-scale thick layer, an important device parameter to fully absorb radiation. At present, Bi- and I-based compounds are front-runners in achieving high-performance radiation detector devices due to their high atomic mass. The first report on lead-free x-ray detector was reported with Cs₂AgBiBr₆ single crystals.²⁶⁹ Due to the long penetration depth of X-rays, single crystals are usually preferred for high energy detectors. The thick single crystals (mm to cm scale) also have a low defect density which increases μτ product, a large value of which is beneficial for high signal-to-noise ratio. The sensitivity of Cs₂AgBiBr₆ single crystal detectors for X-rays was found to be comparable to those made from MAPbBr₃. Apart from the single crystal detector, flexible x-ray detectors can also be fabricated using a polymer-Cs₂AgBiBr₆ composite with similar performance as those of the single crystals.²⁷⁰ 

Low-dimensional structures that offer higher resistance against ionic migration and higher resistivity are expected to perform better than 3D structures and can offer long-term stability. For example, a low detection limit of 55 nGy_air s⁻¹ (in perpendicular direction) is realized in 2D layered (NH₄)₃Bi₂I₉ single crystal devices. Moreover, low-dimensional structures exhibit anisotropic charge transport, which is beneficial for anisotropic detection required for medical applications.^271,272 Rb₃Bi₂I₉, another analogous structure also showed a record low detection limit of 8.32 nGy_air s⁻¹ along with high resistance to ionic mobility.²⁷³ Ionic mobility can be further reduced by adopting zero-dimensional crystal structures such as A₃Bi₂I₉ which also exhibited descent x-ray detection performances.^274,275

The advancements made in lead-free halide compounds for high energy detection are remarkable, offering a plethora of benefits such as low-cost fabrication, scalability of large area systems, and earth-abundant precursors. However, for these compounds to be practically useful, their figure-of-merit must be improved. The large dark currents exhibited by these halide-based detectors can obscure electronic signals, reduce sensitivity, and increase the lowest limit of detection. The inherent defect and impurity self-doping of Sn-based halide perovskites and the weak ionic bonding in halide compounds lead to increased dark currents and ionic conductivity, making it necessary for more research and effort to fully expand their potential. Reducing dark current and addressing radiation hardness are essential for enhancing the lowest detectable dose and evaluating reliability, long-term use, and disposability. With further investigation and innovation, these lead-free halide compounds can provide unparalleled benefits and revolutionize the field of high energy detection.

As an indirect detection technique for high energy radiation, scintillation detection requires only the scintillator crystal which absorbs the radiation (usually high frequencies) and emits light in another part of the spectrum (usually longer wavelength). The scintillators can then be easily integrated with commercial light detection hardware like charge-coupled devices or complementary metal-oxide-semiconductors. Current commercial scintillators are usually bulk crystals and their synthesis usually requires high temperatures (621 °C for CsI:Tl, more than 2000 °C for Lu₂SiO₅:Ce³⁺) which increases the production cost. Therefore, there is a great demand for scintillating materials which can be synthesized easily.

Low-dimensional lead-free halide compounds, which exhibit high photoluminescence quantum yields, but suffer from poor charge transport properties, have huge potential as scintillators.²⁷⁶ Luminescence in these compounds usually originates from self-trapped excitons which also eliminates the self-absorption. Furthermore, these compounds can be easily embedded in a flexible matrix to fabricate a functional composite film. Hence, much of the focus remains on the development of low-dimensional structures by incorporating large organic molecules. A prime example is Mn-based 0D structures with extremely high PLQY in the solid-state. By varying the A-site cations, a wide variety of scintillators has been demonstrated with Mn-based low-dimensional perovskites,^277–279 with the most notable being ethylenebis-triphenylphosphonium manganese bromide [(C₃₈H₃₄P₂)MnBr₄] a zero-dimensional Mn-based hybrid exhibiting 95% PLQY, recorded a light yield of ∼80 000 photons MeV⁻¹, along with a low detection limit of 72.8 nGy s^−1.280

While perovskite structures have dominated the research, non-perovskite structures such as Cu-based ternary halides have emerged as strong contenders due to their strong PLQY and stability. Moreover, their emissions can be easily tuned, enabling the development of scintillators for specific applications. Notably Rb₂CuBr₃ has demonstrated remarkable performance with near-unity photoluminescence quantum yield (98.6%) and a record-breaking light yield of ≈91 056 photons per MeV, thanks to its strong carrier confinement and x-ray absorption capability.²⁸¹ Even zero-dimensional structures such as Cs₃Cu₂I₅ and β-Cs₃Cu₂Cl₅ have near-unity PLQY, excellent x-ray absorption, and low detection limits. These compounds also demonstrate remarkable operational stability and radiation hardness, making them suitable for long-term use.^279–281 Moreover, the emissions of these compounds can also be tuned by doping suitable elements such as Mn²⁺ or rare-earth elements. Large-scale scintillator devices have also been successfully realized using close-space sublimation and nanoscale seed screening strategies, achieving high spatial resolution in x-ray imaging.²⁸² One of the current challenges is the afterglow (long lifetime) of the luminescence in these compounds which limits their detection limitations. Recent advancements in Ag-based ternary halides and 0D Cs₄EuX₆ have shown promising results in this regard, which bodes well for the future of lead-free halide scintillators. Low-dimensional Rb₂AgCl₃ has recently been reported to have fast scintillation decay time (in ns) which is a key parameter in dynamic x-ray imaging.²⁸³ For gamma ray scintillation, 0D Cs₄EuX₆ showed excellent promise with high scintillation yield, which is even better than that of the commercial scintillator NaI:TI.²⁸⁴ However, the challenge of afterglow still persists, limiting their detection sensitivity. Overall, these compounds offer a safer and more efficient alternative to traditional lead-based scintillators and have the potential to revolutionize the field of x-ray imaging.

Double perovskites with lanthanide ions are also promising scintillator compounds considering they exhibit extremely high PLQY and are stable at high temperatures. Cs₂NaLnCl₆ (Ln = Tb³⁺ or Eu³⁺) is an excellent example, showing a light yield even higher than that of commercially available scintillators and lead-based halide perovskites.⁹⁷ By utilizing doping and compositional engineering techniques, the optical and electronic properties of double perovskites can be effectively modulated. For instance, Cs₂AgInCl₆ doped with Na⁺ and Bi³⁺ has been identified as an outstanding scintillator for real-time x-ray imaging.²⁸⁵ 

An outstanding scintillator should possess several essential properties such as high PLQY, low self-absorption, fast decay time, and high light extraction efficiency. Unfortunately, many lead-free halide systems that exhibit exceptional figure-of-merit often ignore one critical factor: afterglow. Long afterglow times can cause imaging artifacts, superimposing the signal on the previous exposure. Additionally, defects within the scintillator can lead to non-radiative recombination, reducing the yield. Currently, scintillators-based on 3D structures are limited by their small Stokes shift, but low-dimensional structures with self-trapped excitons show great promise in increasing this parameter. To overcome this bottleneck, excitonic emission or down-converters with perovskite emitters can be used to simultaneously achieve large Stokes shift and fast response times. Systematic studies on the stability against temperature, humidity, and radiation are also crucial parameters to meet the international standard IEC 60749 requirements.

The potential of optically pumped LEDs as transformative technology is immense, offering efficient and cost-effective solutions for white-light LEDs and down-converted displays. Their working principle is based on the efficient downconversion of high-energy photons, which requires materials with high PLQY and negligible self-absorbance. Optically pumped LEDs have opened up exciting opportunities for advanced display technologies as well as for applications in solid-state lighting and biomedical imaging. The key advantage of these LEDs lies in their simplicity of structure, spectral design flexibility, and high luminous efficiency. Given their immense potential, the development of high-performance down-converter materials remains a crucial area of research in materials science and engineering.

A huge number of down-converter luminescent materials based on lead-free halide compounds have been reported till date, thanks to their high PLQY and broad, large Stokes-shifted emission. These compounds cover nearly the entire visible light spectrum and even extend to near-infrared wavelengths, making them versatile components for efficient downconversion phosphors. Their excellent stability and color rendering properties make them a perfect candidate for indoor lighting.^286–288 Doping strategies such as Bi and Sb-doping have also been found to increase the PLQY of these compounds, resulting in mixed yellow phosphors that achieve a high CIE coordinate and color rendering index (CRI).^289,290

Apart from perovskite structures, halide compounds with non-perovskite structures have also become a focus of intense research as high-performance downconversion luminescent materials. Among them, Cu-based ternary halides are particularly noteworthy for their intense and broad photoluminescence spectra, making them desirable for white light-emitting diode (WLED) applications. These compounds exhibit high thermal and chemical stability, which makes them practical for a range of applications. For example, Cs₃Cu₂I₅ and CsCu₂I₃ mixtures were used to fabricate a high-performance WLED with a CRI of 88.4.²⁹¹ These tetrahedrally bonded compounds offer high chemical and thermal stability and have emerged as a promising nontoxic substitute for inorganic pigments. In another study, (18-crown-6)₂Na₂(H₂O)₃Cu₄I₆ was used to create a WLED with a high luminous efficiency of 156 lm/W and a color rendering index of 89.6.²⁹² Additionally, indium-antimony (In/Sb) alloyed halide single crystals also have demonstrated near-unity photoluminescence quantum yield and potential for use in high-performance WLEDs.^293,294

LEDs based on solution-processed semiconductors have great application potential in energy-efficient lighting and displays. While lead-based halide perovskites are the front-runners in electroluminescence devices, lead-free perovskites and derivative compounds have the potential as nontoxic alternatives for wearable displays and are currently gaining momentum. The first lead-free perovskite LED based on MASn(I/Br)₃ thin-films was demonstrated by Tan and co-workers.²⁹⁵ In the same year, all-inorganic CsSnI₃ was also utilized as an emitting layer to demonstrate near-infrared LED²⁹⁶ with the maximum EQE of 3.8%. Nevertheless, both devices exhibited poor stability during operating conditions, which led to the development of low-dimensional Sn-based perovskites offering better stability against ionic migration and better confinement of excited carriers. A quasi-2D multiple quantum-well structure based on the composition of (PEAI)_3.5(CsI)₅(SnI₂)_4.5 shows much better stability than 3D counterpart, with LED devices exhibiting EQE up to 3% at 940 nm luminescent peak.²⁹⁷ Several other low-dimensional Sn-based halide perovskite-based LED devices have also been demonstrated, such as orange emission from (C₁₈H₃₅NH₃)₂SnBr₄,²⁹⁸ red emission from (PEA)₂SnI_xBr_4−x,²⁹⁹ 2-thiopheneethyllamine iodide (TEAI)SnI₄³⁰⁰ to name a few. However, charge transport properties of 2D perovskites is restricted to inorganic layers by insulating organic long chains, resulting in inferior device performance compared to their 3D structures.³⁰¹ This drawback prompted researchers to adopt a vertical crystal arrangement in optoelectronic devices, with inorganic layers oriented perpendicular to the substrate. This strategy promotes efficient transport of charge carriers, circumventing the limitations imposed by organic chains and boosting device performance.

While several Sb- or Bi-based perovskite-derivative compounds exhibit reasonable PLQY, working devices are scarce at present. Chu's group³⁰² was the first to demonstrate a functional device based on Sb-based perovskite derivative. However, the performance of these devices fell short due to the relatively low PLQY of the active layer and non-optimal device structure design. Tang's group attempted to improve the situation by using Cs₂Ag_0.6Na_0.4InCl₆:Bi³⁺ films to fabricate electrically driven WLEDs, but the obtained EQEs were very low, indicating the need for further optimization of the device structure and materials.³⁰³ 

In recent years, the remarkable photoluminescence and ambient stability of Cu-based low-dimensional structures have garnered significant attention for electrically pumped LEDs. In 2019, Hosono's group achieved a major milestone by successfully demonstrating the first-ever deep-blue LED that utilized Cs₃Cu₂I₅ films as the emitter. This LED emitted at a wavelength of 445 nm and exhibited CIE coordinates at (0.16, 0.07), meeting the stringent blue NTSC standard. The devices also displayed descent operation stability, with a half-lifetime (T₅₀) of 108 h.²³⁸ However, poor thin-film morphology of Cu-based compounds posed a major challenge in reducing the leakage current and improving device performance. Subsequently, the CsCu₂I₃-composition with yellow emission was also investigated for its potential use in functional LEDs.³⁰⁴ Poor thin-film morphology of these Cu-based compounds remained a major challenge in reducing the leakage current, and subsequently improving the device performance. Recently, antisolvent treated uniform thin-films of CsCu₂I₃-based LEDs demonstrated an EQE of 0.17% and a luminance of 47.5 cd m⁻², representing a significant improvement.³⁰⁵ Another breakthrough was achieved when Liu et al. reported mixed phases of Cs₃Cu₂I₅ and CsCu₂I₃ through antisolvent treatment, resulting in a WLED with a small onset voltage of 2.9 V and tunable CIE coordinates of (0.327, 0.348).³⁰⁶ The two-component strategy is further explored by Shi's group with CsCu₂I₃@Cs₃Cu₂I₅, as active layer that exhibited tunable white light emission by adjusting the ratio of CuI/CsI. The tunable WLEDs also exhibited an excellent operation stability with a long T₅₀ of ∼238.5 min.³⁰⁷ 

Nearly a decade ago, the first solid-state solar cell comprising lead-based halide perovskites was demonstrated. Since then, research efforts on halide perovskites have picked up considerably and the performance level of lead-based perovskite devices have rapidly improved. Nevertheless, heavy metal toxicity associated with lead remains one of the major environmental concerns for their wide-spread applications. While the research efforts are driven by the search for LHP replacement, lead-free halide compounds itself present a unique opportunity for high-performing and solution-processable materials platform, which is well-suited for a range of optoelectronic applications. The recent results also showcased decent progress in terms of performance metrics. Nevertheless, a deeper understanding of the crystal structures, optoelectronic properties, and passivation strategies are currently missing, and more efforts are still required to unlock their full potential such that lead-free halide compounds can rival existing semiconductors, including LHPs in terms of optoelectronic device performances.

In this comprehensive review, we have highlighted the vast chemical space of lead-free halide compounds and made a compelling argument for the previously overlooked diversity of structures and properties. These structural tunability and compositional adjustment remains one of the major strengths in lead-free compounds which are neither limited by perovskite structure nor Goldschmidt's tolerance factor. For example, perovskite-derivative compound Cs₃Bi₂I₉ can be easily converted into Ag_xBiI_3+x only by replacing Cs⁺ with Ag⁺ which leads to smaller bandgap, and better charge transport properties, and subsequently superior photovoltaic performances. Similarly, the discovery of hollow Sn-based halide perovskites exhibited much better ambient stability as compared to 3D analogs, which can be considered a significant leap toward lead-free perovskite solar cells. These results unequivocally indicate that the crystal structure and composition can be readily manipulated to achieve desired electronic, optical, and chemical properties. It showcases the immense potential in tuning the semiconducting properties, which basically depend on the crystal structure and the chemical composition for targeted optoelectronic devices. However, it remains a challenge to achieve a perfect combination of semiconducting properties. While the exploratory discovery of novel functional materials often carried out by traditional laboratory-scale experimentation, recent progress on high-throughput computational methodologies accelerated the prediction of materials properties from chemical composition and structure manifold. Furthermore, recent advances in accelerated materials development such as in automated robot-assisted chemical space exploration has recently found momentum for lead-free research.³⁰⁸ 

However, significant strides must be made in device fabrication to ensure the desired chemical and optoelectronic properties are reliably reproducible. Considering the bottleneck of charge transport properties, the low-dimensional structures could be employed for ultrathin device architecture in which transport bottleneck can be physically overcome. A notable example is the ultrathin Cs₃Bi₂I₉ nanosheets that exhibited remarkable photovoltaic properties.²⁵⁶ It should also be noted that high-quality solution-processed synthesis routes, which have been extremely successful for lead-based halide perovskites, may not be directly translatable for different chemical spaces. Currently, several non-solution phase solid-state synthesis routes have gained interest such as mechano-synthesis, or ball-milling. While these techniques may not be suitable for thin-film device fabrication, they can offer a high-throughput synthesis environment to explore the lead-free halide chemical space. Apart from solid-state synthesis, high vacuum evaporation techniques or close-space sublimation, which hold the key to industrial scale perovskite-based solar scale fabrication, have proved to be equally suitable for lead-free halide compounds.^282,309

Another important characteristic is the defects in these halide compounds that play a crucial role in their macroscopic behavior, and understanding their dynamics is vital for future device development. The concentration, nature, and interactions of defects give rise to complex phenomena that cannot be captured by traditional density functional theory calculations or simple averages. Therefore, a comprehensive understanding of these materials requires a holistic approach that combines optical and electrical characterizations supported by theoretical calculations. At present, there is no evidence that these compounds cannot be defect tolerant for normal synthesis environment and it is interesting of theoretical research that there is a consensus regarding the defect tolerance of halide perovskites. Experimental studies already indicated that the formation of defects can also be manipulated by the synthesis conditions, which warrants further study in terms of synthesis strategies.

Expanding our understanding of highly confined electrons in low-dimensional structures presents exciting opportunities for advanced optoelectronic applications. However, harnessing these unique electronic and optical properties in high-performing devices remains a significant challenge that must be addressed to achieve optimal performance. Recent advancements in 3D non-perovskite structures highlight the vast untapped potential for new material discoveries. By applying external stimuli or replacing constitutive elements, one can finely tune optoelectronic properties, ultimately yielding new and functional materials such as in piezochromism³¹⁰ or nanogenerator.³¹¹ 

Overall, halide compounds offer a vast array of structures and properties that can be tailored for specific optoelectronic applications. One of the major advantages of lead-free halide compounds is the near-infinite chemical space with rich structural diversity that can accommodate a wide range of optoelectronic applications. We expect more lead-free halide compounds will be developed/discovered and promising functional properties can be achieved. There is no doubt that a successful realization of lead-free halide compounds which effectively combine the great photophysical properties of the LHPs with the fascinating solution-processability, ambient stability, and nontoxicity will be a major breakthrough in the field of optoelectronic devices.

This research is supported by the National Research Foundation (NRF), Singapore, under its Competitive Research Program (CRP) (Grant No. NRF-CRP25–2020-0002). B.G. would like to thank KU Leuven for PDM Scholarship (Grant No. PDMT1/22/011). M.B.J.R. acknowledge financial support from the KU Leuven Research Fund (Grant Nos. C14/19/079 and iBOF-21–085 PERSIST) and the Research Foundation—Flanders (Grant Nos. G098319N and G0A5923N).

The authors have no conflicts to disclose.

Biplab Ghosh: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Writing – original draft (equal); Writing – review & editing (equal). Darrell Jun Jie Tay: Data curation (supporting); Resources (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Maarten Roeffaers: Funding acquisition (supporting); Supervision (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Nripan Mathews: Conceptualization (equal); Funding acquisition (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

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