2.4.1.1 Multidimensional Perovskites

In general, the typical halide perovskite is defined by the general formula AMX₃ (where A = Cs, CH₃NH₃ ⁺ or MA⁺, HC(NH₂)₂ ⁺ or FA⁺; M = Pb²⁺, Sn²⁺, Ge²⁺, Cu²⁺; and X = I⁻, Br⁻, Cl⁻) ([1]. Goldschmidt tolerance (t, Eq. 2.4.1)) and the octahedral (μ, (Eq. 2.4.2)) factors are the tools that are commonly used to determine the structural stability of perovskites by considering the ionic radii of A⁺, M²⁺, and X⁻. The equations are defined as follows [1], respectively:

2.4.1

2.4.2

where R _A, R _M, and R _X refer to the corresponding ionic radii. The majority of stable “three‐dimensional” (3D) perovskites possess values of 0.8 < t < 0.9 and 0.442 < μ < 0.895, with significant deviations that result in the edge‐shared and face‐shared octahedral, instead of the pristine corner‐shared structure of the classic AMX₃ perovskite [1, 2]. A number of organic ammonium cations that do not accommodate within the octahedral cavities in the 3D perovskite structure, on the other hand, adopt the “two‐dimensional” (2D) perovskite slabs with corner‐shared octahedra, and conform to the Ruddlesden–Popper formulae of A _n−1A′₂M _n X_3n+1, where A′ are typically bulkier organic ammonium cations [3, 4], whereas A, M, and X retain the same definitions. Consequently, along with the development of new organic cations, numerous perovskite materials with the general formulae (RNH₃)₂(A) _n−1M _n X_3n+1 (n = integer) are now generally defined as 2D perovskites, while (RNH₃)₂(A) _m M _m X_3m+2 is categorized as a 1D perovskite, where RNH₃ is an aliphatic or aromatic alkylammonium cation [5]. Hence, these perovskites can be broadly classified as multidimensional perovskites (Figure 2.4.1a) [6], although the term 0D perovskites are strictly just molecular crystals and are not considered.

The corner‐shared PbX₆ ⁴⁻ octahedra layers accommodate larger cations and the energy difference between the ionic bonding in the inorganic layers and the van der Waals forces among the organic molecules lead to the formation of self‐assembled layered perovskites that contain alternating organic and inorganic layers [7]. This unique configuration creates internal multiple quantum wells (Figure 2.4.1b) and displays interesting photophysical properties. For instance, the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) energy gap of the organic ammonium cation is typically larger than the bandgap of the inorganic layers [8], and therefore the difference in the dielectric constants between these two layers creates periodic barriers and wells. Hence, these materials can be considered as containing a self‐organized multiple‐quantum‐well structure. The strong tendency to form layered perovskites and the solubility of both starting components in the same solvent has permitted a facile and convenient spin‐coating technique to deposit the thin films with homogeneous coverage on the substrate [9]. This controlled formation of layered structures has led to perovskites with larger cations and variable structures and sizes that alter the photophysical and electronic properties of these new semiconductors [10]. Adding to this versatility, mixed cations with different sizes can also form well‐organized layered structures where the smaller cations occupy voids created by the corner‐shared PbX₆ ⁴⁻ octahedral, while the larger cations cap the stacks of inorganic layers and interleave between the 2D nanosheets [3, 11, 12]. Some prototypical examples of mixed‐dimensional perovskites are (CH₃(CH₂)₃NH₃)₂(CH₃NH₃)₂Pb₃I₁₀ and (CH₃(CH₂)₃NH₃)₂(CH₃NH₃)₃Pb₄I₁₃, which crystallized as well‐organized layered structures [6]. The properties such as the bandgap, band energy levels, carrier binding energy, and charge transport, among others, can be easily tuned simply by varying the organic cations and the thickness of the inorganic layers [6].

2.4.1.2 Multidimensional Perovskite Photovoltaics

Tremendous effort has been placed in the conventional 3D perovskites (MAPbI₃, FAPbI₃, for example) for their solar cell applications; however, significantly less research studies were found in multidimensional perovskite PVs. Smith et al. reported the first multidimensional perovskite solar cells (PSCs) only in 2014 [13]. They presented the first single‐crystal structure of an n = 3 perovskite, (PEA)₂(MA)₂[Pb₃I₁₀] (PEA ⁺ = phenethylammonium cation), derived from dark red crystals that were obtained from slow evaporation of a saturated perovskite solution. The pure n = 3 perovskite single crystal can be grown; however, the spin‐coated thin film from the lead precursor solution actually consisted of a mixture of different orders (n = 1, 2, 3, 4, and 5) in the perovskite film due to the rapid and uncontrollable self‐assembly process. These multidimensional perovskite‐based PVs exhibit overall power conversion efficiency (PCE) of 4.73%, J _sc of 6.72 mA cm⁻², V _oc of 1.18 V, and fill factor (FF) of 0.60. Importantly, the V _oc value observed here is higher than that of MAPbI₃‐based solar cells, which is probably due to its slightly larger bandgap. Despite the lower efficiencies, this multidimensional perovskite displays high moisture resistance even after storage for 46 days under 52% relative humidity (RH), whereas the MAPbI₃ thin film had turned from black to yellow under the same conditions (Figure 2.4.2a).

Almost a year later, a second demonstration of PSCs based on multidimensional perovskites was reported by Cao et al. [14]. They synthesized a series of homologous perovskites, (BA)₂(MA) _n−1PbI_3n+1 (BA = n‐butylammonium cation) by incorporating bulkier primary organic ammonium cations, thus confining the perovskites into a layered structure. Similarly, these perovskite thin films also contained multiple orders of perovskites as the films were simply prepared by the single‐step deposition method. The presence of mixed‐dimensional perovskites cannot be realistically avoided with the fast and low‐temperature self‐assembly processes currently utilized. The highest recorded efficiency for these multidimensional perovskites was only 4.02% with (BA)₂(MA)₂Pb₃I₁₀, but the perovskite film possesses high ambient stability over two months (Figure 2.4.2b). Importantly, X‐ray diffraction (XRD) analysis revealed that the lower dimensional perovskites (n = 1 and 2) tend to grow parallel to the substrate (along the (00k) and (0k0) plane), resulting in poorer charge transport in the (111) direction due to the intercalated insulating organic cation layers. Hence, stable and highly efficient multidimensional perovskites can be achieved in higher order 2D perovskites. Another key advantage of the multidimensional perovskites is their homogeneous coatings on the substrates, which were far superior to the 3D MAPbI₃ counterpart films, indicating the potential for facile processing in both laboratory‐scale and large‐scale fabrication.

The nanostructuring approach to direct the growth of multidimensional perovskites is an interesting strategy to solve the charge‐transport challenges in multidimensional perovskites to create high‐efficiency and stable PSCs [6]. The insulating organic layers present in the multidimensional perovskites tend to impede the vertical charge transport, and this challenge can be addressed by growing the perovskite perpendicular to the substrate. First, a pure 2D perovskite (n = 1) was deposited by spin coating the precursor solution containing a stoichiometric ratio of lead iodide (PbI₂) and iodoethylammonium iodide (IC₂H₄NH₃I). Subsequently, the substrate was immersed into a solution containing methylammonium iodide (CH₃NH₃I) for different dipping durations to increase the stacking order and convert it into a mixed‐dimensional perovskite. Control of the dipping duration allows to tune the optical properties, direct the crystal growth perpendicular to the substrate, and hence improve the electrical properties (Figure 2.4.2c,d). This class of multidimensional perovskites exhibited good air stability and achieved over 9% PCE with a mixed‐cation approach [6]. More importantly, the PV devices degrade at much slower rates compared to those with MAPbI₃ without any encapsulation under high RH (70–80%).

Increasing the number of stacked inorganic sheets could potentially alleviate the inferior charge transport in multidimensional PSCs. For instance, Quan et al. demonstrated the utilization of a relatively high order (n = 60) of multidimensional perovskites in PSCs, resulting in both high efficiency and stability (Figure 2.4.2e,f) [11]. The replacement of methyl ammonium iodide (MAI) with phenethylammonium iodide (PEAI) engenders higher stability owing to the latter's higher desorption energy and consequently slows down the decomposition of the perovskite film. By periodically examining the absorbance, transient photoluminescence (PL) decay, and structure (by XRD) of the perovskite films, the authors verified that the multidimensional perovskites with intercalated PEA cations possessed superior stability compared to the 3D perovskites under ambient atmospheres, likely due to the increased formation energy. The high‐efficiency MAPbI₃ PSC (16.6%) deteriorated drastically to a PCE of less than 3% over eight weeks, whereas the multidimensional PVs remained stable at 11–13% PCE.

Bulkier and hydrophobic organic cations in multidimensional perovskites could strain the surface PbI bonds and repel water molecules from reactive sites in the perovskites, thereby promoting moisture resistance and prolonging the lifetime of the PSCs under ambient conditions [15]. Therefore, polymeric organic cations are also potential candidates in preparing multidimensional perovskites with high air stability. Yao et al. demonstrated the advantages of utilizing polyethylenimine hydriodide (PEI·HI) as intercalating organic cations in forming highly stable multidimensional perovskites (Figure 2.4.3a) [16]. High‐quality pinhole‐free perovskites containing polymeric cations are readily formed after the spin‐coating process, thus minimizing the shunt paths for the leakage current and offer opportunities to manufacture scalable PSCs. The strong interaction between the polymeric organic–inorganic structures led to a lower bandgap compared to smaller molecular organic cations. The scaled‐up PSCs (active area of 2.32 cm⁻²) with polymer‐based multidimensional perovskites exhibited PCEs exceeding 8% with excellent device lifetimes (Figure 2.4.3b).

Most recently, bilayer hybrid 2D/3D perovskites were adopted in another strategy to promote the ambient stability of the existing high‐efficiency PSCs. Generally, these kinds of bilayer hybrid structures contain high‐efficiency 3D perovskites on top of mesoporous TiO₂, while lower dimensional perovskites are placed on top to enhance the moisture resistance. Docampo and coworkers deposited layered perovskites, consisting of PEA⁺ and MA⁺, on top of MAPbI₃ and obtained PSCs with PCEs up to 16.8% with increased V _oc and FF [17]. The perovskites capped with lower dimensional perovskites exhibited average PCEs of 11.4% after exposure to 19 days in 75% RH, whereas pure 3D perovskite devices only retained average PCEs of 6.1% (Figure 2.4.3c,d). In summary, it is clear that utilization of the multidimensional approach in perovskite PVs has significantly improved its ambient stability. However, more research effort was expected to enhance the PV efficiency of multidimensional perovskite devices while attaining ambient stability.

2.4.2.1 ASnX₃ Perovskites: 3D Pb‐Free Structures

Replacing Pb²⁺ with Sn²⁺ in the perovskite structure appeared to be most viable solution toward Pb‐free perovskite for optoelectronic applications. Tin(Sn)‐based halide perovskites with ASnX₃ (A = protonated cation, X = halogen element) structure is an interesting family of perovskite compounds that display temperature‐dependent phase change, bandgap tunability, ferroelectricity, and excellent optoelectronic properties, as well as composition‐dependent dimensionality [18–20]. Early studies include those by Lang et al. [21] who explored the electronic and optical properties of Sn‐ and Pb‐based perovskites using standard density functional theory (DFT) and found that all these compounds possess a similar electronic structure, expecting similar electronic behavior. However, the inherent instability of Sn²⁺ cation in the atmospheric conditions leads to poor performance as solar cell absorber materials. Theoretical investigations on Sn‐based inorganic halide perovskites had begun as early as the 1980s due to their interesting temperature‐dependent phase transitions. Sn‐based halide perovskites undergo several phase transitions from a high‐temperature cubic phase toward a lower symmetry structure with decreasing temperature. These phase changes are associated with increasing packing density through distortion and rotation of SnX₆ octahedra, rather than a complete reordering of the atoms [22, 23]. Some earlier reports also claimed that the stereochemically active lone pair electron of tin had a key role to play in the distorted low‐temperature phases [24]. Initially, the cubic CsSnBr₃ was thought to be semimetallic based on semiempirical extended Huckel theory (EHT) calculations [25]. Although this method is quite satisfactory for describing valence band structure, EHT performs poorly in describing the conduction band nature. Lefebvre et al. [26] performed band structure calculations based on the pseudopotential approach, which gives a better description of lowest conduction band along with valence electrons. Interestingly, they found CsSnBr₃ to be a zero‐bandgap compound even without considering the spin‐orbit coupling (SOC) effect. However, these results do not agree with experimental values. The bandgap problem was somewhat corrected by Bose et al. [27] when they performed a scalar‐relativistic muffin‐tin‐orbital calculation based on local density approximation (LDA) within the framework of DFT and concluded that CsSnBr₃ is a narrow bandgap semiconductor with a direct bandgap of 0.26 eV. Considering the use of LDA, it can be fairly assumed that the original bandgap should be much higher than that. Their simulation also indicated that the valence band of CsSnBr₃ is a mixture of Sn 5s and Br 4p orbitals and the role of Cs⁺ is negligible in the band edges. However, there was no change in the bandgap due to a low‐temperature structural change in the perovskite. In 2008, Borriello et al. [23] performed ab initio calculations based on DFT using the generalized gradient approximation (GGA) for exchange correlation energy on several ASnX₃ compounds (A = Cs, CH₃NH₃, NH₂CHNH₂, X = Cl, I). They have shown that in the high‐temperature cubic phase, the A site cation has little role in determining the band edges of Sn‐based halide perovskites. They concluded that the A site (organic or inorganic) cations mainly control the crystal structure of the perovskite, which has a drastic effect on the bandgap of the compound. For example, phase change in CsSnI₃ is associated with progressive tilting of SnI₆ octahedra along the ab‐plane, without any observable change in SnI bond length or the angle (Figure 2.4.4a,b). Hence, all the phases of CsSnI₃ exhibit direct bandgap, which gradually increases with progressive tilting of the SnI₆ octahedra. Even replacing Cs⁺ with MA or FO does not change the crystal symmetry at room temperature. On the other hand, the phase change in CsSnCl₃ is associated with the drastic change in the crystal structure, from a corner‐sharing octahedral network (high‐temperature cubic phase) to almost isolated edge‐sharing octahedral chain network (low‐temperature monoclinic phase), resulting in a much wider bandgap and an anisotropic valence band. Interestingly, the hybrid analogous MASnCl₃ preserves the corner‐sharing octahedra even at low temperature, which is attributed to the steric interaction between the inorganic cage and larger organic cation. The role of the A site cation thus can be generalized only as the electron donor, as neither the organic nor inorganic cations play any role in the valence band maximum (VBM) or conduction band minimum (CBM). The change in bandgap can then be explained easily by the change in lattice constant originating from different cation sizes (Figure 2.4.4c).

After the emergence of PSC, Sn‐based halide perovskites, especially CsSnI₃ and its hybrid compound MASnI₃ returned to the spotlight due to interesting optoelectronic properties such as p‐type metallic conductivity and strong luminescence. As the standard DFT calculations are not reliable in predicting the bandgap of semiconductors, Huang and Lambrecht [28] reinvestigated the electronic structure of cubic phase CsSnX₃ (X = Cl, Br, I) using quasiparticle self‐consistent GW (QSGW) method. In general, the QSGW method has been proved to be very accurate and reliable for describing the band structure and excited‐state properties for weakly correlated systems. They found that the bandgap is essentially controlled by Sn s to I p covalent antibonding interaction which is expected to be weaker with increasing lattice constant, resulting in a wider bandgap with increasing cell volume. On the other hand, the bandgap is expected to increase from Cl to I due to lower energetic anion p levels. However, the opposing SOC effect in heavier halogen atoms further compensates the increase in bandgap, and the total effect on bandgap due to the change in halogen atoms is quite small. An interesting finding from their work is that the exciton binding energy of CsSnI₃ was found to be around 0.1 meV, which is two orders smaller than the experimentally reported value of 18 meV [29]. The authors argued that the reported value of exciton binding energy can only be interpreted as exciton linewidth or the energy of bound exciton, as the free exciton binding energy should be lower than that. Based on the band structure, the effective masses of hole and electrons were found to be small and decreased from Cl to I. However, nearly equal effective hole and electron mass failed to explain the p‐type conductivity in CsSnI₃. Defect characteristics studies by Chung et al. [20] shed light on the origin of the p‐type conductivity. The role of defects in the optoelectronic properties of the solution‐processable semiconductor is crucial as the defects are in thermodynamic equilibrium with the constituents. The defect formation energy can be calculated using first‐principles calculations based on the supercell approach. An excellent review on defect formation energy calculations can be found in Freysoldt et al. [30]. Figure 2.4.5 illustrates the intrinsic defect formation energy as a function of Fermi level in three different growth conditions. The p‐type conductivity eventually arises from the Sn vacancies (V _Sn), which is the most favorable intrinsic defect in CsSnI₃. The strong luminescence at near‐band edge can also be explained by the V _Sn‐modulated defect centers. The presence of V _Sn as deep‐level defects were also confirmed by Kumar et al. [31]. In addition to PV applications, Sn‐based halide perovskite, especially formamidinium tin iodide (FASnI₃), has been shown to display excellent ferroelectric properties. Based on first‐principles calculations, polarization of FASnI₃ can be changed depending upon the spatial arrangement of FA⁺ cation [32].

2.4.2.2 A₂SnX₆ Perovskites: Metal‐Deficient Structures

Although the electronic and optical properties of Sn‐based halide perovskites are quite tempting, poor stability of Sn²⁺ limits the extensive applications. Sn²⁺ in perovskite structure can readily be oxidized into Sn⁴⁺, which ushers in an alternate class of perovskites. The use of tetravalent Sn⁴⁺ to replace divalent Pb²⁺ results in a vacancy‐ordered perovskite structure to maintain the charge balance (Figure 2.4.6). It can also be visualized as the ordered double perovskites with the general formula A₂B′B″X₆ in which one B‐site cation is replaced with a vacancy (A₂B□X₆). However, there is some ambiguity as to whether such simple ionic model can be applied for complex salts [22, 34]. From first‐principles calculations, Sn 5s was found to be well below the Fermi level and the corresponding Bader charge analysis suggests the divalent nature of Sn [34, 35]. First‐principles calculations based on the self‐consistent, full‐potential linearized augmented plane wave (LAPW) method within DFT, using the GGA‐PBE (Perdew‐Burke‐Ernzerhof) for the exchange and correlation potential, resulted in a direct bandgap of ∼1.3 eV, which is in excellent agreement with the experimental values [36]. It should be noted that the bandgap correction was done using the modified Becke–Johnson exchange potential. Later, Saparov et al. [37] reported an experimental bandgap of 1.6 eV and calculated bandgaps of 1.27 and 1.62 eV with (Heyd‐Scuseria‐Ernzerhof) HSE06 hybrid functional with 34% and 37% exchange, respectively. However, the use of SOC was not mentioned in the calculation. Maughan et al. [33] carried out electronic band structure calculations in a similar manner, but with explicit treatment of SOC and found a direct bandgap of 0.97 eV. Their GW0 calculation, which is more sophisticated than hybrid calculations, also indicated a bandgap of 0.88 eV. Hence, the experimental bandgap of 1.6 eV may be influenced by some secondary phase formation, which is quite common in complex perovskite semiconductors. Moving on from the bandgap discrepancy, the nature of charge carriers is also different between Cs₂SnI₆ and CsSnI₃, where the former shows n‐type conductivity and the latter shows p‐type. This could be explained by the defect characteristics. The formation energies of iodine vacancies are quite small (0.14–0.39 eV depending upon the chemical potential) and the 0/1 transition states are located just 0.07 eV below the VBM, which is most likely the source of n‐type conductivities [33].

2.4.2.3 Germanium‐Based Perovskites

Like Pb‐ and Sn‐based halide perovskites, theoretical investigations on germanium (Ge)‐based halide perovskites began even before the realization of their potential applications in PVs. Unlike Pb‐ and Sn‐based halide perovskites, the smaller ionic radius of Ge²⁺ as well as the presence of stereochemically active 4s² electron pair hinders the formation of stable cubic perovskites in room temperature. Hence, the GeX₆ octahedra is distorted drastically to form a pyramidal structure symmetry, which is expected to exhibit nonlinear optical properties. However, Ge‐based perovskites also exhibit rich structural diversity depending on the temperature and protonated cation. For example, CsGeI₃ transforms from rhombohedral phase into cubic (Pmmm) symmetry above 290 °C. The band structure calculated by Li‐Chuan et al. [38] following the standard DFT approach with LDA as exchange correlational functional shows similar orbital characteristics as that of Pb‐ or Sn‐based halide perovskites. However, the bandgap seemed to be underestimated severely due to use of LDA. Follow‐up calculations also reveal the increase in bandgap from I to Cl, which is in good agreement with the experimental trends [39]. However, the potential of Ge‐based halide perovskites in solar cell absorber materials were not fully realized until Stoumpos et al. [40], and Krishnamoorthy et al. [19] synthesized organic‐cation‐based Ge iodide perovskites. Although the role of organic cation is limited to the crystal motif's formation as the interaction with inorganic network is negligible, the charge carrier properties among different hybrid Ge iodide perovskites vary significantly [41]. In comparison to Sn‐ or Pb‐based halide perovskites, the values of effective mass are much higher for similar calculations, but comparable to other thin‐film semiconductors. Sun et al. [42] studied the effect of systematic replacement of Pb²⁺ from MAPbI₃ with Ge²⁺ using DFT at different calculation levels. The incorporation of Ge²⁺ in place of Pb²⁺ displays gradual constriction in lattice constants and increase in lattice deformations. The change in bandgap is severely affected by the SOC effect for Pb²⁺, while for the lighter Ge²⁺ the effect is minimal (Figure 2.4.7a). The optical absorption coefficients of mixed Pb/Ge perovskites calculated from first‐principles calculations is projected to be higher than those of either MAGeI₃ or MAPbI₃. However, the change in orbital characteristics near the band edges is also minimal, except for a sharp increase of Ge p orbital in the CBM at the expense of Pb p orbital contribution. As for charge‐transport properties, the change in average electron and hole effective masses are shown in Figure 2.4.7b. Among the studied Ge/Pb iodide perovskites, MAGe_0.75Pb_0.25I₃ shows best transport properties with nearly balanced electron and hole effective mass.

Nevertheless, the main challenge associated with Ge‐based perovskites is its stability in ambient atmosphere. Ge‐based perovskites readily decompose in the presence of ambient atmosphere. Sun et al. [43] investigated the effect of water (H₂O) molecule on the MAGeI₃ surface based on first‐principles calculations. They found that H₂O molecules can easily diffuse through the surface of the MAGeI₃. The most stable surface of MAGeI₃ was found to be (101) plane, which is composed of GeI dangling bonds with iodine atoms exposed on the surface. The MA⁺ cations reside inside the voids of the inorganic cage compensating the charge balance (Figure 2.4.8a). Initially, a single water molecule is adsorbed on the surface of MAGeI₃ through hydrogen bonding connected with O(H₂O) and H with nearest MA⁺ cation (region O in Figure 2.4.8a). Surprisingly, with increasing number of water molecule near the surface, the adsorption energy decreases from −0.1 eV for one H₂O molecule to a minimum of −0.27 eV for six water molecules. When the number of water molecules increases to more than six, the intermolecular hydrogen bonding becomes stronger, resulting in a decrease in the hydrogen bond strength between H₂O molecules and MA⁺ cations of the perovskite, corresponding to a greater adsorption energy. However, to degrade the perovskite completely, the water molecule needs to diffuse first through the dangling bond region (region F in Figure 2.4.8a). The energy of one water molecule inside the dangling bond region was found to be much lower than the adsorption energy with an activation barrier as little as 0.09 eV. As a consequence, water molecules are most likely to stay inside that region and the adsorption on the surface can proceed in the forward direction easily. For further penetration inside the MAGeI₃ crystal, the water molecule then needs to pass through the I–Ge–I inorganic network (region S in Figure 2.4.6). The energy barrier for that transition state was found to be 0.43 eV, which is still quite small. Based on their calculation, the authors proposed the following mechanism (Figure 2.4.8b):

1. The degradation of MAGeI₃ starts as soon as the inorganic network of GeI₂ begins to be damaged by hydration of the phase.
   

   The hydrated phase exists for N ≤ 2.

2. As soon as another water molecule is adsorbed, the perovskite surface starts degrading with release of CH₃NH₂ gas.
   
3. With increasing number of water molecules on the surface, the GeI bonds start to break due to stronger H‐binding with I⁻ anion.
4. The new hydrate generated in step 2 will continue to degrade with the release of HI
   
5. In humid atmosphere, the continuous adsorption of the water molecule will continue the release of CH₃NH₂, resulting in the degradation of the perovskite.

2.4.2.4 Bismuth/Antimony‐Based Perovskites

The excellent optoelectronic properties of lead‐based halide perovskites is often linked with the presence of 6s² lone pair electrons. Group 15 elements, especially Bi³⁺ and Sb³⁺, also possess an electronic structure similar to that of Pb²⁺ due to which similar optoelectronic properties are expected. Since these elements exist in the stable +3 oxidation state, it is difficult to accommodate Bi³⁺ or Sb³⁺ inside the conventional AMX₃ perovskite structure. Previous studies on Bi/Sb‐based ternary halide compounds had mostly focused on single‐crystal properties, ferroelectricity, phase transformations, and nonlinear optical properties [44]. Recently, the interest in these compounds has been renewed due to their potential applications in PVs. The electronic structure calculations for Bi‐ and Sb‐based ternary halides have shown remarkable similarities in band edge characteristics to that of Pb‐based halide perovskites [45]. Contrary to conventional semiconductors such as Si or GaAs, the CBM and VBM of [PbI₆]⁴⁻ cluster are antibonding in nature, contributed by the partially oxidized Pb²⁺ cation and PbI antibonding orbital, respectively [46]. For the Bi/Sb‐based ternary halide perovskite, a similar VBM nature is expected due to lone pair 6s² electrons [47]. The contribution of A⁺ cation on VBM and CBM is also negligible as the band edges are formed by the Sb/BiI bonding. Analogous observations can also be found for conventional Pb‐halide perovskites, where the influence of +1 cation is negligible on the VBM and CBM characteristics [48]. So the electronic structures of inorganic Bi/Sb‐based ternary halides can represent the family justly. The valence band of Cs₃Sb₂I₉ is mainly contributed by the p orbital of I and partly by Sb(s). These antibonding characteristics of VBM are expected to suppress the valence‐band‐derived states such as cation vacancies. The nature of the CBM, on the other hand, is quite different and is dependent on the crystal structure (dimer or layered). For example, the electronic structure of Cs₃Bi₂I₉ and Cs₃Sb₂I₉ dimer phase exhibits remarkable similarities as both possess indirect bandgap and similar conduction band features. While conduction band is mostly Pb(p)/Sb(p) characteristics in Pb‐based and Sb‐based ternary halides (layered structure), respectively, a mixture of I(p) and Bi(p)/Sb(p) orbitals dominates the CBM of dimer Cs₃Bi₂I₉/Cs₃Sb₂I₉. The p‐orbital characteristics of both valence and conduction bands lead to high joint density of states, resulting in an unusually large absorption coefficient for both Bi‐ and Sb‐based ternary halides. Although the layered structure of Cs₃Sb₂I₉ is more promising in terms of optoelectronic properties than in its dimer structure, the latter is more favorable to form under normal processing conditions. However, one possible way to solve the problem is to replace Cs with smaller cations. For example, Rb₃M₂I₉ (M = Sb³⁺, Bi³⁺) essentially forms the layered structure even under normal processing conditions and exhibits better optoelectronic properties than the homologous dimer structure [49]. The electronic structure calculations further reveals a flat band structure for both the Sb‐ and Bi‐based dimer phase, which can be attributed to the heavy effective mass of the carriers [47, 50]. In addition, Sb‐ and Bi‐based ternary halide compounds have lower crystal symmetry as compared to Pb‐based halide perovskite, which leads to anisotropic charge transfer. In addition, most of the intrinsic defects (except Cs vacancy and interstitial Cs) in Cs₃Sb₂I₉ form deep level states in the bandgap which can act as non‐radiative recombination centers in optoelectronic applications. This could be explained on the basis of the orbital characteristics of the compound. The Sb p orbital is more localized than the Pb p orbital, resulting in stronger Sb p−I p antibonding than the Pb p−I p antibonding, which in turn implies that the energy difference between the anion's p orbital and the CBM is larger for Cs₃Sb₂I₉ than for CH₃NH₃PbI₃.This results in mid‐bandgap states of the donor defects. On the other hand, weaker s–p antibonding coupling is the primary reason for deep acceptor defects. In addition to that, defect characteristics also reveal the transition from p‐type conductivity to n‐type conductivity when the crystal growth conditions can be tuned from I‐rich/Sb‐poor to Sb‐rich/I‐poor conditions.

2.4.2.5 Double Perovskites: Hybrid Binary Metal Structures

Instead of a single divalent element, one monovalent and one trivalent element can replace two Pb²⁺ from the halide perovskite structure. The idea of double perovskites is not new, with the analogous oxide structures having been examined for a long time. Such atomic transmutation has been successful in even thin‐film solar cell application such as the copper zinc tin sulfide (CZTS) systems. Following a similar strategy, a Pb‐free halide perovskite family with the formula A₂M⁺M³⁺X₆ has received attention among the halide PV community. Giorgi and Yamashita [51] studied the MATl_0.5Bi_0.5I₃ and MAIn_0.5Bi_0.5I₃ based on DFT calculations and found striking similarities in electronic structure with Pb‐based halide perovskites. The bandgaps of the compounds are 1.68 and 1.03 eV, respectively, as per PBE/PAW (projector augmented wave)‐level calculations. More recently, successful synthesis of Cs₂AgBiBr₆ and Cs₂AgBiCl₆ enabled detailed theoretical understanding of these types of materials [52, 53]. The bandgap of the Bi‐based halide double perovskites are quite similar to lead‐based halide perovskites, however indirect in nature [53]. The valence band is composed primarily of the halogen p orbital and the conduction band formed by the antibonding of Ag 5s and Bi 6p states. The main problem is the admixture of Ag d orbital in the valence band, which is partially responsible for the indirect bandgap. Later, Zhao et al. [54] identified 11 potential halide double perovskites based on first‐principles calculations. For the M³⁺ cation, Bi³⁺ and Sb³⁺ cations were considered due to the similar electronic structure as that of Pb²⁺. For the M⁺ cation, they considered group IA (Na⁺, K⁺, Rb⁺)/group IB (Cu⁺, Ag⁺, Au⁺)/group IIIA (In⁺, Tl⁺) elements (Figure 2.4.9). They used four criteria to screen the perovskite compounds such as decomposition enthalpy (>0), bandgap (0.8–2 eV), effective mass (<1.0 m₀), and exciton binding energy (<100 meV). Out of all the combinations, they successfully found 11 optimal halide double perovskite compounds such as Cs₂CuSbCl₆, Cs₂CuSbBr₆, Cs₂CuBiBr₆, Cs₂AgSbBr₆, Cs₂AgSbI₆, Cs₂AgBiI₆, Cs₂AuSbCl₆, Cs₂AuBiCl₆, Cs₂AuBiBr₆, Cs₂InSbCl₆, and Cs₂InBiCl₆. Among these compounds, the first nine compounds exhibit indirect bandgap, while the bandgaps of the two In⁺ based double perovskites are direct in nature. In a similar manner, Pb²⁺ and two I⁻ can be transmuted into one M³⁺ and one Ch²⁻ (chalcogenide) anions, leading to I–III–VI–VII₂ structure. Sun et al. [55] calculated the electronic band structure of Bi‐ and Sb‐based chalcogenide‐halide perovskites and found that these compounds are promising PV materials in terms of bandgap. However, subsequent reports indicate that none of these materials are thermodynamically stable as they will be prone to decomposition into other binary or ternary phases [56].

2.4.3.1 Sn²⁺ and Ge²⁺ as Replacements for Pb²⁺ Ge$^{2+}$ replacements for Pb$^{2+}$"?>

As discussed earlier, tin with an electronic configuration [Kr] 4d¹⁰ 5s² 5p² is very similar to lead and hence was considered first as its most potential replacement. The first report on tin‐based perovskites in a solar cell was on CH₃NH₃SnI₃ with an efficiency of 6.4% [18a] formed by spin coating SnI₂ and CH₃NH₃I in dimethylformamide (DMF) in an inert atmosphere. The device exhibited a reasonable open circuit voltage of 0.88 V considering its low bandgap of 1.23 eV. However, these were very unstable in air due to oxidation of +2 Sn to +4 states, resulting in a large spread in the device efficiencies with much of the solar cells showing very low power conversion efficiencies. The presence of +4 Sn also resulted in variable self‐doping of the material, resulting in a high hole‐doping density of ∼10¹⁸ cm⁻³. The recombination with these self‐doped carriers limited the diffusion lengths to only 30 nm, significantly lower than MAPbI₃. It was suggested that reducing these background carriers could be an effective strategy to improve the performances by improving the diffusion lengths. Another interesting development in the area of Sn perovskites was the use of a mixed metal cation with lead (CH₃NH₃Pb_1−x Sn _x I₃) [57]. This resulted in anomalous behavior, with the mixed perovskite exhibiting a bandgap lower than either the pure Pb‐ or Sn‐based perovskites, thus extending the absorption range to near infrared (1050 nm). In another work, the same group investigated the possibility of a mixed halide Sn perovskite – MASnI_3−x Br _x [18b] – in order to tune the bandgap of the material. The highest power conversion efficiency realized was 5.73% for CH₃NH₃SnIBr₂.

The first report on fully inorganic Sn‐based perovskite was on CsSnI₃ [31] with a power conversion efficiency of 2.02%. It was found that the pristine CsSnI₃ exhibited very poor PV performance due to the presence of Sn vacancies. These tin vacancies were passivated by addition of 20% SnF₂ to attain good PV performance. This was also reflected in the reduction of carrier density of 10¹⁹ cm⁻³ in pristine sample to 10¹⁷ cm⁻³ with 20% SnF₂ addition. The excess SnF₂ increases the Sn chemical potential, leading to increase in formation energy of Sn vacancies and a decreased concentration of these defects. The background carrier density of 10¹⁷ cm⁻³ is still very high compared to CH₃NH₃PbI₃ (with carrier densities of 10⁹–10¹¹ cm⁻³), which could be the reason for the limited V _oc of 240 mV in the champion device. Higher open circuit voltages were obtained by opening up the bandgap through halide substitution, although power conversion efficiencies were still limited [58]. The bandgap of CsSnI_1−x Br _x was tuned between 1.27 and 1.75 eV (Figure 2.4.10a) with a reduction in charge carrier densities to 6.3 × 10¹⁵ cm⁻³ for CsSnIBr₂. Another strategy to tune the bandgap of the Sn perovskite is to change the A cation. Formamidinium‐based Sn perovskites crystallize in an orthorhombic (Amm2) crystal structure and exhibit a slightly higher bandgap of 1.41 eV, which is close to the optimum value for single‐junction solar cells. FASnI₃‐based solar cells were fabricated with an efficiency of 2.1% [60] by again utilizing the SnF₂ addition to reduce tin vacancies. However, the low solubility of SnF₂ in DMF resulting in phase separation is a limiting factor to achieve higher voltage. Another report on the same material suggests that the solubility of SnF₂ in DMF can be improved by addition of pyrazine [61], which can form a complex with SnF₂. This avoids phase separation and yielded perovskite films with full coverage on TiO₂, improving the efficiency to 4.8%.There are also reports on Cs‐ and FA‐based Sn perovskites on inverted architectures, albeit with lower efficiencies [62]. In addition to the challenges rendered by tin oxidation, morphology control of these tin halide perovskites is challenging. The rapid crystallization of the Sn perovskite with DMF as solvent limits the ability to form pinhole‐free film by spin coating and limiting the open circuit voltage. A systematic study of various solvents (DMF, dimethyl sulfoxide (DMSO), N‐methylpyrollidone (NMP)) suggested that DMSO could be a better alternative to the commonly used DMF [63] in obtaining higher quality films. The reason is the ability to coordinate strongly to the SnI₂, forming an adduct of formula SnI₂·3DMSO. This adduct allows the MAI ions to react with SnI₂ in a controlled manner limited by the rate of DMSO removal to obtain controlled crystallization and uniform coverage.

Moving even further up in the group of the periodic table, the smaller Germanium was also investigated as a potential candidate to form perovskites with PV properties. CsGeI₃, MAGeI₃, and FAGeI₃ exhibit a bandgap of 1.63, 2.0, and 2.35 eV, respectively [64]. All of them crystallize in rhombohedral symmetry at room temperature. However, solar cells of CsGeI₃ and MAGeI₃ suffered from a very low V _oc of 74 and 150 mV, respectively, restricting the efficiencies to 0.11% and 0.2% only. Germanium is even more unstable compared to Sn and gets easily oxidized to the +4 state, which is the reason for the poor performance. The problem is aggravated by its poor solubility in polar solvents, which restricts good film formation.

Most of the research on lead replacement was focused on Sn or Ge in the same group. However, it is known that the inert pair effect responsible for the stability of the +2 state of lead reduces as we move up in the group. Thus, Sn²⁺ and Ge²⁺ are very unstable and gets oxidized to +4 ions. These +4 ions can act as traps leading to recombination and hence limit the performances. Furthermore, reports show that Sn perovskites can be even more toxic compared to lead due to its potential oxidation to the +4 oxidation state releasing HI into the environment [65]. This necessitated expanding the search to other group elements and other perovskite derivatives as well.

2.4.3.2 A₂SnX₆ as a Stable Alternative to ASnX₃ alternative to ASnX$_{3}$"?>

The use of tetravalent Sn is a strategy to enhance the stability of the Sn perovskite. However, a +4 Sn can only form compounds of structure A₂SnX₆, which is considered a 0D perovskite structure with isolated (SnI₆)²⁻ octahedra (Figure 2.4.10b) [59]. There are several reports utilizing Cs₂SnI₆ as a hole‐transporting material in dye‐sensitized solar cells due to its exceptional p‐type conductivity [36, 66]. However, the reports on the bandgap, carrier densities, mobility, and type of charge carriers are still inconclusive, as shown in Table 2.4.1. It is claimed that the pristine material is n‐type and the reported p‐type behavior is caused by doping with Sn²⁺. Nevertheless, the optimum bandgap of 1.3–1.6 eV of the material makes it interesting as an absorber for solar cells. The only report (so far) of Cs₂SnI₆ as a solar cell absorber material is by utilizing ZnO nanorods as electron‐transporting layer and poly(3‐hexylthiophene‐2,5‐diyl) (P3HT) as hole transporting material (HTM) reaching an efficiency ∼1% [67].

2.4.3.3 Cu²⁺: an Alternative Divalent Metal Cation

If one excludes group 14 elements, the next alternatives are the transition metals due to their ability to form +2 oxidation states essential for AMX₃ halide perovskite structures. However, the small size of the transition metal cations limits their ability to form corner‐sharing structures. Instead, most of them form linear chains of face‐sharing octahedra which might seriously affect the charge transport in these class of compounds. In addition, most of the transition metal halides are moisture sensitive as well. However, one alternative is to form 2D perovskites of the structure A₂MX₄ exhibited by metal ions such as Cu²⁺, Ni²⁺, Co²⁺, Fe²⁺, etc. Some research groups have investigated 2D perovskites of Cu for application in solar cells due to their stable +2 oxidation state in aerobic environment and good absorption in visible region. A detailed analysis of the copper perovskites of the structure (CH₃NH₃)₂CuCl _x Br_4−x revealed that the presence of Cl is essential to stabilize the system against copper reduction and enhance crystallization [1a]. In addition, changing the Br/Cl ratio helped tune the absorption within the visible to near‐infrared range. However, the solar cells fabricated were limited by low V _oc and short circuit current densities. The low absorption coefficient and the heavy mass of the holes arising from the layered nature of the material were found to be the reasons for this poor performance. In addition, the paper also discussed the probability of Cu⁺ formation, which could act as potential traps. Copper‐based 2D perovskites of the structure: (p‐F‐C₆H₅C₂H₄‐NH₃)₂CuBr₄, and (CH₃(CH₂)₃NH₃)₂CuBr₄ [68] were also demonstrated as solar cell absorbers albeit with very low efficiencies.

The poor performance of copper perovskites may also be due to the absence of the outer ns² electrons, which provide the defect tolerance and the dispersive valence band in case of lead. Thus, a more logical strategy is to search for compounds with outer ns² electrons. This necessitates looking for elements with other oxidation states as well rather than confining to +2.

2.4.3.4 Bi³⁺ and Sb³⁺: Toward Trivalent Metal Cations Sb$^{3+}$, trivalent metal cations"?>

As discussed earlier, Bi³⁺ and Sb³⁺ which have electronic configuration similar to that of Pb²⁺ are other viable alternatives. The presence of ns² electrons must also equip them with the defect‐tolerant property of lead. However, the +3 state constrains their ability to form a 3D corner‐sharing perovskite structure. Instead, they form A₃Sb₂X₉ compounds with a dimer structure (with fused bi‐octahedron) or a layered structure (with corner‐sharing octahedron).The first report on bismuth‐based perovskite was on Cs₃Bi₂I₉ with an efficiency of ∼1% [69]. The material consisted of fused bi‐octahedral (Bi₂I₉)³⁻ clusters surrounded by Cs atoms. It is claimed to be nontoxic and was reported to be stable over a month, with no noticeable reduction in efficiency when stored at humidity less than 10%. The PL and PV performance of MA₃Bi₂I₉ was found to be very low compared to Cs₃Bi₂I₉ consistent with the other reports on MA₃Bi₂I₉ solar cells with a low efficiency of 0.19% [70]. MA₃Bi₂I₉ exhibited p‐type conductivity with a carrier density of 10¹⁶ cm⁻³ and mobility of 1 cm² V⁻¹ s⁻¹. This high background carrier density was suspected to have contributed to bulk recombination, leading to a low V _oc of 0.35 V. Other reports attribute the lower performance to poor morphology of the MA₃Bi₂I₉ layer, with the efficiency influenced by the underlying mesoporous TiO₂ layer [71]. The devices made on anatase TiO₂ mesoporous layer showed better performance than those on a mesoporous brookite TiO₂ layer or a planar architecture. A detailed material study on MA₃Bi₂I₉ [72] suggested that post treatment with pyridine can improve the PL lifetime of the material possibly by passivation of under‐coordinated bismuth ions on the surface. A maximum PL lifetime of 0.76 ns was achieved, depending on the processing technique adopted. This is encouraging because materials with <1 ns lifetimes have been reported to achieve efficiencies close to 10% [73]. Interestingly, double perovskites of the formula Cs₂AgBiBr₆ exhibited extraordinary PL lifetimes of 660 ns, which are on par with MAPbI₃, substantiating the defect‐tolerant property of bismuth. In addition, the compound was found to exhibit extraordinary stability in moisture and light exposure even after one month. However, the presence of Ag seriously inhibits the solution processability of the material. The potential of bismuth halides as potential replacement is also corroborated by the AgBi₂I₇ solar cells with efficiency of 1.22% [74] and BiI₃‐based solar cells with efficiency of 0.3% [75, 76].

There are also reports of A₃M₂X₉ structures based on Sb as viable PV materials. However, the highest efficiency reported till date is only 0.5% with MA₃Sb₂I₉ as absorber [77]. It is claimed that the layered structure of A₃Sb₂I₉ should exhibit better optoelectronic properties compared to the dimer form from first‐principles calculations [47]. However, the lack of solution processability of the structure is a bottleneck to its formation. In addition, the material is also susceptible to various defects which can induce deep traps, limiting the PV performance. A smaller cation like Rb was found to template the formation of the layered phase even via a solution process [49] (Figure 2.4.10c). However, the presence of deep defects possibly limited the device performance. Thus, a strict control over the stoichiometry using optimum fabrication conditions will be necessary to obtain good performance with these classes of compounds (Table 2.4.2).