Anti-perovskites for photovoltaics: materials development and challenges

For the next-generation solar cells with excellent device efficiency and stability, designing advanced light absorber materials with exceptional optoelectronic properties is extremely crucial. Perovskites have attracted great attention due to their high-power conversion efficiency, and low fabrication cost. Eventhough perovskites achieved the highest efficiency of 25.7% within a decade, lead (Pb) toxicity is one of the main issues that needs to be addressed. Also, they are susceptible to degradation under ambient conditions. On the other hand, anti-perovskites, which are electronically inverted perovskites, possess structural flexibility, environmentally benign chemical composition, appropriate band gap and hence, have the capability to replace perovskites as the absorber layer for next-generation solar cells. Thus, a thorough assessment is urgently required to spark widespread concern in this family of compounds. Based on the current research progress, the potential of anti-perovskites in solar cell research is compiled in this study. The structural variety, optoelectronic characteristics, and uncharted territory of these compounds are covered in great detail. Finally, we have discussed the future research directions for the development of anti-perovskite materials for the next generation efficient and stable solar cells.


Introduction
Sunlight is the most readily available, clean, and renewable energy source for sustainable energy growth.Over the past 60 years, a great deal of research has been conducted 3 D K and P S have made equal contributions to this manuscript.* Author to whom any correspondence should be addressed.
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on the conversion of light energy by photo-electrochemical cells employing various combinations of inorganic, organicinorganic semiconductors, and organic sensitizers.The first material to be employed as a photo-absorber for solar cells is silicon.It is one of the elements that is most abundant on Earth with some of the most intriguing properties such as nontoxicity, low maintenance, and stability for 25 years [1,2].Mono-crystalline, single junction concentrator silicon solar cell has achieved a record-breaking efficiency of 27.6% [3], however, the cost is one of the main concerns.There have primarily been two advances in photovoltaic technology in recent years: first, the cost reduction in silicon photovoltaic [4][5][6] and the other one is the development of metal halide perovskite as a photovoltaic absorber material [7][8][9][10][11][12][13][14][15][16].The power conversion efficiency (PCE) of organic-inorganic hybrid perovskite has already reached up to 25.7% within only a few years, comparable to the PCE value of commercially available silicon solar cells [3].Although the use of lead (Pb) in organic-inorganic hybrid perovskite has exceptional optical and electronic properties, lead can cause serious health problems, which is why researchers all over the world are constantly looking for alternatives to lead.In order to build leadfree perovskites, many efforts have been made in which Pb 2+  was replaced with divalent (Ge 2+ and Sn 2+ ) [17,18], trivalent (Sb 3+ and Bi 3+ ) [19,20] and/or tetravalent (Ge 4+ , Sn 4+, and Ti 4+ ) [21][22][23] ions.Among these materials, Ge 2+ and Sn 2+  have stability issues [24][25][26][27], whereas, the Sb-and Bi-based trivalent replacements tend to have a band gap larger than or equivalent to 2.0 eV because of which the PCE is too low for these compounds [20,[28][29][30].Replacement of halides with chalcogenides offers a solution to toxicity associated with Pb 2+ ions, these chalcogenide perovskites are environmentally benign and have thermal and moisture stability, but have comparatively larger band gap and flat band-edges than the Pb-based halide perovskites [31,32].Synthesis of good quality chalcogenides perovskite thin films at ambient conditions is also a challenge due to the high-temperature chalcogenization [33,34].
Reversing the ion type of perovskite lattice sites is another effective strategy.In particular, a type of anti-perovskite X 3 BA with anions taking up the A and B sites and cations filling the X sites can be obtained by electronically inverting the perovskite formula ABX 3 (A and B are cations, and X is an anion).These Pb-free anti-perovskites are composed of earthabundant elements and have suitable bandgap for solar cell applications.Significant structural diversity can be achieved with these materials which can offer a library of absorber materials for photovoltaics.However, the importance of antiperovskites has been realized recently, and soon we are expecting an exploration of these unique materials as they are predicted as next-generation photo absorbers.
In this review, we concentrate on the optical and electronic characteristics of anti-perovskite-type materials.The current state of research on anti-perovskites, their crystal structures, and their potential as a sizable family of solar absorber materials are outlined in this article.Also, the limitations which need to be overcome are addressed.

Structure and stability of anti-perovskites
Anti-perovskites are the electronically inverted perovskites expressed by the chemical formula X 3 BA (where X is a cation, and B and A are anions).Monovalent or divalent cations are typically placed at the X-site, while large and small anions are placed at the A-and B-site respectively.The structure of perovskite ABX 3 and anti-perovskite X 3 BA are shown in (figure 1(a)).It should be noted that some transition metals can be placed at both A and X sites, which has rarely been seen in traditional perovskites.Hence, anti-perovskites have the advantage of accommodating more varieties of elements compared to perovskites, while retaining structural similarities.This can make anti-perovskites the preferred multifunctional material compared to perovskites.The elemental constitutions of previously theoretically or experimentally formulated anti-perovskites are shown in figure 1(b).
Similar to the perovskites, the crystal structure and stability of anti-perovskites materials are defined by Goldschmidt's tolerance factor (t), which is expressed as: where r A , r B , and r X are the ionic radii of the A-, B-, and X-site ions present in the system [35].When t is between 0.85-1.0, the structure forms cubic unit cell and lower t values give tetragonal and orthorhombic structures.Mochizuki et al have investigated the structure of mixed anion anti-perovskites M 3 XN (M = Mg, Ca, Sr, Ba; X = P, As, Sb, Bi) and found that with decreasing t value, anti-perovskites favor the cubic structure over the traditional perovskites [36].Gebhart et al have investigated structures of various organic-inorganic hybrid anti-perovskites and predicted that these inverse hybrid perovskites are stable when t ⩾ 0.76 [37,38].For smaller t values, the CaIrO 3 structure is favored.The structure of a few organicinorganic hybrid anti-perovskites is shown in figure 2, in which, MA 3 BA (where, MA = methylammonium, B = O, S, Te, F and A = I, Br and Te) compounds have tolerance factors in between 0.71-0.9,makes them stable anti-perovskites.It has been found that tilting of MA units along B-X-B axis vanquish the possibilities of octahedral rotation.However, as the p-block elements present in the antiperovskites prefer to form covalent bonds and d-and f-block elements prefer to form metallic bonds, Goldschmidt's tolerance factor cannot be used to predict crystal symmetry.Beznosikov modified t as the ratio of r A and r B and predicted anti-perovskite structures for metal nitrides [39].Still, the effectiveness of this modified tolerance factor needs to be verified.
Bartel and coworkers have designed a new tolerance factor that predicts the structure of oxide and halide perovskites with 92% accuracy [40].
where τ is the new tolerance factor, r A , r B , r X are the ionic radii of elements A, B, and X; η A is the oxidation state of A. If τ < 4.18, indicate perovskite structure.The new tolerance factor also successfully predicts the structural stability of double perovskite oxide and halides.However, the accuracy for anti-perovskites is yet to be confirmed.Although ideally, anti-perovskites possess a cubic geometry, they tend to form pseudocubic or distorted lattices, and these structural distortions influence and affect their physical properties.For example, Ca 3 AsN adopts an orthorhombic unit cell.The temperature of the reaction affects the anti-pervoskites' structure as well.Reitz et al found that at lower reaction temperatures, Cr 3 GeN tends to produce an orthorhombic phase rather than the more typical tetragonal structure [41].Recently, a novel polar anti-perovskite, Cs 3 Cl(HC 3 N 3 S 3 ) with [HC 3 N 3 S 3 ] 2− rings at A-site and ClCs 6 polyhedra with a unique quasi-one-dimensional structure was recently discovered [42].Also, non-stoichiometry is common in traditional perovskites which extends the library of anti-perovskites.A series of anti-perovskite materials A 4 X 2 O (A = Ca, Sr, Ba, Eu, X = Sb, P, As, Bi) have been reported recently, which crystalize in Ruddlesden-Popper phase, provide additional structural diversity [43].
The comprehensive discussion on the theoretical and experimental studies of electronic and optical properties of antiperovskite type materials which can be explored as absorber materials in the solar cell is mooted in this review article.This work possesses very deep insight into the properties of antiperovskite-type materials and we believe that this review will help the researchers in the respective field.

Materials properties
While designing materials for photovoltaic applications, it is important to consider the optoelectronic properties.According to Shockley-Queisser's (SQ) theory for single-junction photovoltaic absorbers, solar photons whose energy falls below the band gap have no effect on the electrical current.The difference between a photon's energy and an output energy that is slightly below the band gap energy is lost as heat for a photon with energy above the band gap.Because of this, the theoretical maximum efficiency of an ideal single junction cell kept at a temperature of 300 K cannot go higher than 41% when exposed to sun irradiation and at maximum concentration.This limit is 31% in the absence of concentration.For a range of band gaps between 1.1 and 1.6 eV, this maximum efficiency is attained or almost attained [44][45][46].Not only band gap energy but also the type of band gap affect solar cell efficiency.Direct band gap semiconductors are better for thin film solar cells because of their efficient light absorption.However excited electrons and holes need to be extracted immediately to inhibit their recombination.
The dielectric constant or relative permittivity gives an idea about the optical response of the material at all photon energy.The dielectric function is a complex number and is described as: where ε 1 (ω) and ε 2 (ω) are the real and imaginary parts respectively.At zero frequency (ω = 0), the real part of the dielectric function ε 1 (ω), called static dielectric function ε 1 (0), describes the ability of a material to get polarized due to incident electromagnetic transitions.The value of it for CH 3 NH 3 PbI 3 is ∼13 [47].Usually, the real part ε 1 (ω) describes the charge storage ability while the imaginary part ε 2 (ω) is the energy loss.It also illustrates the absorption behaviors, directly related to the electronic band structure of the material.The refractive index n(ω) describes the electromagnetic radiation propagation through the material.That means when photons are propagating through the material, due to the interaction with the electrons they decelerate.The refractive index will be higher if more photons decelerate.That means a high refractive index implies high electron density.The static refractive index n(0) value for CH 3 NH 3 PbI 3 is approximately 2 and the maximum value reaches ∼2.5 at 800 nm (∼1.55 eV) [48], which is lower compared to Si and GaAs [49,50].At 600 nm (∼2 eV), the refractive indices for Si and GaAs are approximately 3.9 and for CH 3 NH 3 PbI 3 the value is ∼2.2.Due to this, CH 3 NH 3 PbI 3 is a promising candidate for tandem solar cells.As well as the extinction coefficient k(ω) indicates the attenuations of the incident electromagnetic radiations, which means the higher the extinction coefficient the more radiation the material will absorb.During the event of absorption, the photon energy excites an electron from the ground state to a higher electronic state which makes it mobile and able to provide electric current.Therefore, higher photon absorber material is preferable to photovoltaic absorber materials for higher efficiency.At 600 nm (∼2 eV), extinction coefficients for Si and CH 3 NH 3 PbI 3 are 0.03 and 0.37 respectively [48].
The reflectivity R(ω) of a material indicates that the ratio of reflected to the incident power is equal at the surface.Photocurrents, which are influenced by reflectivity and the absorption coefficient of the absorber material, are lost in part by reflection losses and transmission losses.

Types of anti-perovskites for photovoltaic applications
We have divided the anti-perovskite materials into three different categories: oxide-based anti-perovskites, nitride-based anti-perovskites, and halogen-based anti-perovskites

Oxide-based anti-perovskites
The ferroelectric behavior of metal oxide perovskites facilitates the separation of electrons and holes.However, the large band gap of these perovskites prevents their use as absorber material.Few perovskites such as LuMnO 3 having a band gap of 1.48 eV which falls under the SQ theory limit, yield only 0.11% PCE due to a very low photocurrent density of 0.52 mA cm −2 [51].This is partly explained by the fact that charge carriers in ferroelectric materials are localized in nature.Recently, Kang and Han have shown the potential of Ba 4 As 2 O and Ba 4 Sb 2 O oxide 2D Ruddlesden-Popper anti-perovskites for photovoltaic applications, using density functional theory (DFT) and many-body quantum-mechanical applications [52].The direct nature and optimal band gap (1.1 and 1.3 eV for Ba 4 As 2 O and Ba 4 Sb 2 O respectively) of oxide anti-perovskite can make them the preferred choice for photovoltaics.These anti-perovskite oxides, in contrast to other ferroelectric oxides that have been described, exhibit low effective masses of charge carriers, suggesting easy extraction of photo carriers.Markov et al have also explored a series of Ruddlesden-Popper anti-perovskites, A 4 X 2 O (A = Sr, Ba; X = Sb, P, As, Bi), in which Ba 4 Sb 2 O shows the highest direct band gap of 1.22 eV, which is in agreement with the findings of Kang and the coworkers [43].All of the remaining compounds also exhibit direct band gap, with band gaps ranging from 0.57 eV to 1.00 eV, except Sr 4 Sb 2 O, which shows an indirect band gap.It has been observed that Sr-based compounds have a higher band gap than Ba-based compounds computed with PBE exchange-correlation functional.
Hassan and coworkers have also investigated the electronic and optical properties of A 3 SnO (A = Ca, Sr, Ba) using DFT calculations [53].Contrary to their perovskite counterpart, these anti-perovskites have a direct band gap.Band gap energy for Ca 3 OSn, Sr 3 OSn, and Ba 3 OSn are 0.51 eV, 0.48 eV, and 0.10 eV respectively.Direct band gap nature provides hope for the use of these anti-perovskites in photovoltaics in the near future by required tuning in band gap energy.The band gap type and band gap energy of different oxy-anti-perovskites are tabulated in table 1. Haque and Hossain have investigated the influence of Ca doping on the band gap, the effective mass of electrons and holes (figure 3) [54].They have shown a maximum band gap of 0.62 eV and the highest effective electron mass is obtained for x = 0.5 whereas, the maximum hole effective mass was obtained for x = 0.37.It can be seen from figure 3 that with Ca substitution, Fermi energy shifts to a lower value, and the parabolic character of the conduction band increases, indicating the semiconducting nature of the materials.Though the optimum band gap with anti-perovskites is yet to be realized, the substitution of ions can be used as an effective tool to tune the band gap.Maximum refractive indices of these materials occur nearly at 2 eV similar to Si and CH 3 NH 3 PbI 3 .The reflectivity of these compounds also lies in the UV region making them a potential candidate for tandem solar cells [54].

Nitride-based anti-perovskites
Nitride-based anti-perovskites are the most studied class of anti-perovskites.In 1992, the synthesis of a series of nitridebased anti-perovskites having the chemical formula Ca 3 NM (M = P, As, Sb, Bi, Ge, Sn, Pb) was reported [90].In the series, Ca 3 BiN and Ca 3 SbN have shown semiconducting behavior, providing hope for their use in photovoltaic applications.Later on, other groups also investigated the properties of Ca 3 NBi and Ca 3 NSb.Moakafi et al have evaluated the band gap of Ca 3 NSb and Ca 3 NBi using generalized gradient approximation developed by Engel and Vosko (GGA-EV) and found that both the compounds are direct band gaps having band gap energy of 0.65 eV and 0.36 eV for SbNCa 3 and BiNCa 3 respectively [61].Later, Bilal et al also investigated the band profiles and optical properties of the same materials using DFT [56].However, their investigated band profiles do not agree with the results of Moakafi et al.They found both of the compounds have direct band gaps and the gap energies are 1.1 eV and 1.09 eV for SbNCa 3 and BiNCa 3 respectively.Ullah et al have investigated structural and optoelectronic properties of a series of anti-perovskites having chemical formula X 3 NZ (X = Ca, Sr, Ba; Z = As, Sb, Bi) [57].They found that all these nine compounds have direct band gaps with Ca-based antiperovskite nitrides having the larger band gap values.Iqbal and his team studied a series of cubic anti-perovskites Ca 3 MN (M = Ge, Sn, Pb, P, As, Sb, and Bi) [58].The band structures of the materials are calculated by Tran-Blaha modified Becke-Johnson and their finding shows that valence bands and the conduction bands of Ca 3 GeN, Ca 3 SnN, and Ca 3 PbN overlap with each other and there is no band gap across fermi level; suggesting metallic behavior.On the other hand, the conduction band minima (CBM) and valence band maxima (VBM) for the compounds Ca 3 PN, Ca 3 AsN, Ca 3 SbN, and Ca 3 BiN lie at the same symmetry point, indicating they have direct band gaps.The band gaps of Ca 3 PN, Ca 3 AsN, Ca 3 SbN, and Ca 3 BiN are 1.497 eV, 1.448 eV, 1.006 eV, and 0.957 eV respectively.Dai et al have also investigated optical properties using first principle calculations and the calculated band gap energies are 0.65 and 1.14 eV for Ca 3 BiN and Ca 3 SbN respectively [59].The absorption coefficient of these two anti-perovskites was comparable with commonly used CsPbI 3 and CH 3 NH 3 PbI 3 (figure 4(a)).Considering the smaller band gap compared to CH 3 NH 3 PbI 3 ; Ca 3 BiN and Ca 3 SbN exhibit good infrared absorption.This indicates that they can be good alternative materials in tandem solar cells.Thermodynamical stability and good tolerance also add to their advantages.Other than Ca 3 BiN and Ca 3 SbN, non-toxic Ca 3 PN having a band gap of 1.63 eV can be a potential alternative to halide perovskites as solar cell absorber material [64].The highest value of the imaginary part of the dielectric function ε 2 (ω), the extinction coefficient k(ω) as well as the absorption coefficient α(ω) present around 6 eV.The reflectivity shows less than 25% around the energy 2 eV.The calculated hole effective mass and electron effective mass for this material are 0.460 and 0.419 respectively.Cheng et al have conducted a theoretical analysis of pressure-dependent structural and electro-mechanical properties of Ca 3 PN [65].Their report suggests that Ca 3 PN can be a good solar cell material with a ternary direct band gap of 1.4 eV.
In addition to Ca-based nitride anti-perovskites, Mg-based anti-perovskites have shown promising results as solar cell absorber materials.Chi et al are the first to report Mg-rich anti-perovskites, Mg 3 AsN, and Mg 3 SbN [91].These polycrystalline cubic materials have much larger resistivity than good metals, e.g.Mg 3 SbN has a resistivity of 10 −6 Ω cm.Hence, according to the Mott criterion, these materials can be considered as semiconductors.However, the high band gap of Mg 3 AsN (∼9.0 eV) makes it an insulator.Shein and Ivanovskii, Okoye, and Bouhemadou and Khenata have also theoretically predicted electronic band structure, chemical bonding, and optical properties of Mg-based nitride antiperovskites with the help of various DFT tools [75][76][77]81].Shein and Ivanovskii have investigated band structure with The electrical resistivity of the film was determined by I-V measurement and it is found a suitable candidate for optoelectronic applications.The dielectric constant of Mg 3 SbN is higher than the halide perovskite and it also has relatively low hole effective masses (0.9 m 0 ) and electron effective mass (0.7 m 0 ), which makes it a suitable absorber material for solar cells.
The band gap energy of these Mg-rich nitride antiperovskites indicates that they can be utilized as absorber materials for solar cells.Though Mg 3 PN has a comparatively higher band gap than the optimal band gap range, other Mg-rich anti-perovskites such that Mg 3 AsN, Mg 3 SbN, and Mg 3 BiN have values near or in the optimal band gap range.Also, A-site compositional engineering can be used to further tune the band gap of these materials.However, experimental band gap results are waiting for their use in the solar cell.Heinselman and his co-workers' experimental work showed hope in these Mg-rich anti-perovskites.The static dielectric constant value of Mg 3 SbN is comparable to the value of MAPbI 3 and for Mg 3 AsN, it is less.This indicates that these materials also possess approximately the same ability to get polarized as CH 3 NH 3 PbI 3 .The static refractive indices of Mg 3 PN, Mg 3 AsN, Mg 3 SbN, and Mg 3 BiN also show prominent results.The maximum refractive indices for Mg 3 AsN and Mg 3 SbN are higher than the value of CH 3 NH 3 PbI 3 .This indicates the electron density is higher in these compounds compared to CH 3 NH 3 PbI 3 .The reflectivity for these materials also lies in the ultraviolet and near visible regions.This means they transmit or absorb the IR or visible light making them more suitable for tandem solar cells as well.
Strontium (Sr) and barium (Ba) based nitride antiperovskites were also shown potential as solar light absorbers.Sr-based nitrides anti-perovskites were first reported by Beznosikov [39].Later, Gäbler et al also synthesized singlephase Sr 3 SbN, Sr 3 BiN, Ba 3 SbN, and Ba 3 BiN in powder form from the reaction of melt beads [70].The former two crystallize in cubic phase with Pm-3m space group while the remaining two crystallize in the hexagonal phase with P6 3 /mmc space group.The band gaps of Sr 3 SbN and Sr 3 BiN were determined by the diffuse reflectivity technique and the obtained gap energies are 1.15 eV and 0.89 eV respectively.Based on first principles total energy calculations, Haddadi et al have also predicted the electronic properties of Sr 3 AsN, Sr 3 SbN, and Sr 3 BiN using GGA and found that all the materials are direct band gap semiconductors with energy gaps 0.49 eV, 0.31 eV, and 0.26 eV respectively [68].Hichour et al calculated the structural, electronic, and optical properties of these materials using GGA-EV and reported that all the materials are direct band gap materials with band gaps of 0.84 eV, 0.55 eV, and 0.36 eV respectively [67].In the optical properties, the main peak of the imaginary part of dielectric constant ε 2 (ω) for Sr 3 AsN, Sr 3 SbN, and Sr 3 BiN are located at 4.18 eV, 3.95 eV, and 3.65 eV respectively and the static dielectric constants ε 1 (0) are found at 7.50, 8.0 and 10.07 respectively.The refractive index reaches a maximum value of 3.21, 3.26, and 3.35 at 1.91 eV respectively.Whereas the maximum reflectivity of these materials occurs in the energy range of 3.5 eV to 5.4 eV, which is in the ultraviolet region.
Rached et al have also calculated the band gap of Ba 3 BiN by using LDA approximation [74].Their approximation predicted that Ba 3 BiN is a direct band gap semiconductor with a gap energy of 0.5 eV.Haque et al have also investigated the optoelectronic properties of Ba 3 SbN and Ba 3 BiN with the help of DFT calculations [73].Both materials have direct band gaps with gap energies of 1.35 eV and 1.33 eV respectively, which falls under the SQ limits.These materials also possess high absorption coefficients and high electrical conductivity, needed for photovoltaic applications.Kang has also suggested Sr 3 MN and Ba 3 MN anti-perovskites (M = Sb or Bi) as potential lead-free absorber materials for thin-film solar cells [72].The GW approximation calculations confirmed the direct bandgap characteristic which is suitable for solar cell applications.Furthermore, significantly high absorption coefficients for visible light exceed 10 5 cm −1 .They have shown that film thicknesses of ∼500 nanometers are sufficient for Sr 3 MN and Ba 3 MN to generate significant PCEs by examining spectroscopic limited maximum efficiency (SLME) based on calculated absorption coefficients as shown in figure 4(b).Sr 3 SbN is predicted to be an absorber material as efficient as GaAs in terms of SLME; both Sr 3 SbN and GaAs have SLMEs greater than 20% with a film thickness of only 200 nm.The SLME of Sr 3 BiN is relatively low, remaining below 20% even at higher thickness.This is attributed to a smaller bandgap of Sr 3 BiN, which limits V OC to lower values.Nonetheless, Sr 3 BiN has the potential to be used as an infrared absorber in tandem solar cells.Within the given thickness range, however, Ba 3 MN has higher SLMEs than Sr 3 MN.This is due to the adequate bandgap of Ba 3 MN, which can produce high J SC and V OC at the same time.Particularly Ba 3 SbN possesses a band gap close to the optimal value suggested by the SQ model.Furthermore, the absorption coefficient in the visible range of Ba 3 MN is greater than that of GaAs.At thicknesses less than 500 nm, Ba 3 MN has higher SLMEs than GaAs, but Ba 3 SbN and GaAs have comparable SLMEs at larger thicknesses.Recently, Kang has investigated intrinsic defects in Ba 3 SbN [92].The study concluded that Ba, Sb and N vacancies, and N interstitials are the major points defect with low formation energies (<1 eV).Ba-vacancy and N-interstitial defect level occur around the VBM and are not important Shockley-Read-Hall recombination centers.While, electron-phonon coupling at the Sb-vacancy site was very weak.These indicate that Ba 3 SbN anti-perovskite is a defect-tolerant semiconductor with excellent optoelectronic properties, which makes it a suitable candidate for solar cell application.The band gap nature and energy of nitride anti-perovskites are given in table 1.

Anti-perovskites with mixed cations and anions
Mixed anion-based anti-perovskites such as oxyhalide and chalcohalide anti-perovskites are also emerging as efficient photo absorber materials.Zhang et al synthesized three new barium-based chalco-halides Ba 3 (FeS 4 )Cl, Ba 3 (FeS 4 )Br, and Ba 3 (FeSe 4 )Br [84].Optical properties were investigated by UV-visible diffuse reflectance spectroscopy and the results indicate semiconducting nature.The band gap energies of Ba 3 (FeS 4 )Cl and Ba 3 (FeS 4 )Br were obtained using the extrapolation method and the values are 1.65 eV and 1.71 eV respectively.The band gap of Ba 3 (FeS 4 )Cl and Ba 3 (FeS 4 )Br have band gaps close to CH 3 NH 3 PbI 3 .The authors believed that these compounds can be good solar light absorber materials.Xiao et al have recently studied a new chalco-halide Ba 3 (FeS 4 )I and experimental findings propose it as an indirect band gap semiconductor with a band gap of 1.65 eV.Theoretical study also supports the indirect nature of the band gap with a band gap energy of 1.56 eV [85].The abovementioned studies have demonstrated a negligible impact of halides on band gap energy, unlike perovskites.
Liu et al have investigated band gap energy and stability of various oxyhalide and chalcohalide anti-perovskites having chemical composition A 3 YX (A = monovalent cation; Y = O, S, Se; X = Cl, Br, I) [86].All these anti-perovskites predominantly form cubic structures.The computed bandgaps of these anti-perovskites are summarized in figure 5(a) as a function of the calculated lattice constant a.They discovered that the cations at the octahedral corners and anions at the octahedral centers contributed the most to the CBM and VBM of these anti-perovskites.On the other hand, the band edges are not significantly affected by the halogen anions at the cuboctahedral voids.Therefore, whereas element substitutions at cuboctahedral voids have no effect on bandgaps, those at octahedral corners and centers can efficiently engineer bandgaps.Hence, as mentioned in figure 5(a), no significant change in bandgaps of A 3 OX oxyhalide anti-perovskites was observed when X was changed from Cl to Br or I.In contrast, in halide perovskites, halide ions predominantly dictate the band gap of the material.However, the A-site cation situated at the octahedral corner possesses a significant influence on the band gap.Band structures of Na 3 OCl, K 3 OCl, Rb 3 OCl, and Cs 3 OCl is shown in figure 5(b).As the A cation changes from Na to Cs, the bandgaps of A 3 OX decrease monotonically.It can be claimed that as ionic size increases, the A anions' outmost s orbitals become more dispersed and lower-lying, lowering the CBM.Also, as ionic size increases, the lattice constant rises and the Madelung potential falls, assisting in the reduction of the bandgap.They have also shown that the thermodynamic stability of these anti-perovskites is strongly dependent on the constituent ions, for example, as the Y anion changes from O to S and Se.A series of anti-perovskite-derived mixed oxychalogenides are also reported by Wang et al [87].They have calculated the band gap energy of anti-perovskite-derived Ba 2 MQ 3 X (M = As, Sb; Q = S, Se; X = Cl, Br, I) chalcohalides.These materials have band gap energy of approximately 2.5 eV.We expect that ion exchange can serve as a tool to make them an efficient solar light absorber.Sreedevi et al have also shown cation exchange as an effective tool for band gap engineering for mixed anion anti-perovskites [66].They have projected the suitability of anti-perovskites Mg 3 PN, Ca 3 PN, Sr 3 PN, Ba 3 PN, BaSr 2 PN, Ba 1.5 Sr 1.5 PN, and Ba 2 SrPN for usage as the absorbing layers in tandem solar cells using DFTbased calculations.These seven anti-perovskite compounds have direct band gaps with values between 1.1 and 2.3 eV.The absorption coefficient, optical conductivity, and extinction coefficients are all comparatively higher in the visible area.Additionally, the compounds are desirable candidates for photovoltaic absorber materials due to their low visible-range reflectance, low effective charge carrier masses, and low carrier recombination rates.
Recently, Han et al have proposed a series of quaternary anti-perovskites by anion ordering of X 3 BA as shown in figure 5(c) [83].They have considered 48 pnictogenbased quaternary anti-perovskites.Further, photovoltaic functionality-directed screening of these materials yielded five stable compounds (Ca 6 N 2 AsSb, Ca 6 N 2 PSb, Sr 6 N 2 AsSb, Sr 6 N 2 PSb, and Ca 6 NPSb 2 ) with suitable direct band gaps, small carrier effective masses, low exciton binding energies, and dipole-allowed high optical absorption (figure 5(d)).These 5 compounds have theoretical maximum solar cell efficiencies comparable to halide perovskites.Ca 6 NPSb 2 is the best among them, with a predicted solar cell efficiency of 31.17%.This finding showed that quaternary anti-perovskites based on pnictogen had improved photovoltaic characteristics, paving the way for the development of lead-free, environment-stable perovskite structure-based photovoltaic absorber materials.
The electronic property, static dielectric constant, and exciton binding energy of 6 anti-perovskites X 3 NA (X = Mg 2+ , Ca 2+ , Sr 2+ ; A = P 3-, As 3-, Sb 3-, Bi 3-) were investigated by Zhong and his team, and demonstrated the ability of Mg 3 NAs 0.5 Bi 0.5 as a suitable candidate for absorber material [62].This alloy has a quasi-direct band gap of 1.402 eV.They have investigated the influence of A-and X-site elements on electronic properties.The energy difference between the two conduction band states Γ c and M c is termed as ∆ CBM and the positive and negative value of ∆ CBM refers to direct and indirect band gap respectively.When the X-site element is changed from Sr to Ca to Mg, the value of CBM decreases, indicating a direct-indirect transition.Using Mg 3 NA (A 3-= P 3-, As 3-, Sb 3-, Bi 3-) as a standard system they have also shown that, replacement of Sb 3-with a heavier element causes enhancement in the magnitude of ∆ CBM and replacement of Sb 3-with a lighter element (As 3-and P 3-) changes ∆ CBM from negative to positive indicating restoration of the direct band gap as shown in figure 5(e).Contrary to the halide perovskites, A-site cation significantly influences the electronic properties of anti-perovskites.Copyright (2021), with permission from Elsevier; (c) Schematic of quaternary anti-perovskites (X 6 B 2 AA ′ and X 6 BB ′ A 2 , X = Mg, Ca, Sr, Ba (color coded with green); for X 6 B 2 AA ′ , B = N (color coded with grey), AA ′ = PAs, PSb, AsSb, PBi, AsBi, SbBi (color coded with red); for X 6 BB ′ A 2 , BB ′ = NP, NAs, PAs (color coded with yellow), and A = Sb, Bi (color coded with orange)), (d) screening of materials based on characteristics important to solar performance, Green checks indicate the ideal lead-free quaternary anti-perovskites that meet all the requirements.In the meantime, those with the red X are abandoned; (c), (d) Reprinted with permission from [83].Copyright (2021) American Chemical Society; (e) Schematic band structure of X 3 NA (X = Mg, Ca, Sr; A = P, As, Sb, Bi) by changing the X-and A-sites; (e) Reprinted with permission from [62] .Copyright (2021) American Chemical Society.
Hexagonal carbide anti-perovskites Ba 6 CCh 4 (Ch = S, Se, Te) have been studied, which reveal that the three compounds are direct band gap semiconductor with strong light absorption in UV-Vis-IR region under AM1.5 irradiance making them promising solar cell absorber materials [88].Manybody perturbation theory-based calculations recently revealed quaternary anti-perovskite Ca 6 N 2 AsSb with a band gap of 1.217 eV.The study predicted the absorption coefficient in the solar spectrum is higher than GaAs and the SLME is 32.13% with a thickness of 500 nm [89].A high-throughput calculation was conducted to search the unexplored anti-perovskites (X 3 B[MN 4 ]) with octahedron [BX 6 ] and tetrahedron [MN 4 ] for light-emitting application [93].They found 266 stable leadfree compounds out of 6320 compounds, out of which four compounds with +1 valence state of the M cations show band gaps in the range of 1-2 eV.Some additional compounds with +2, +3 and +4 valence states of the M cations have also been identified with band gaps suitable for solar cell application.

Conclusion and perspective
This review provides the most recent advancements in antiperovskite materials and their potential as solar light absorbers for photovoltaic applications.For simplicity, the family of anti-perovskite is divided based on the ion placed at the Bposition.The impact of compositional and structural changes on the band gap and stability of anti-perovskites has been discussed.Though device fabrication needs to be evaluated, appropriate band gaps for light absorption, stability, and nontoxic nature could make them potential alternatives to lead halide perovskites.Nonetheless, more investigations need to be carried out in the future on the topics as follows: (1) Device fabrication: One of the main reason of the popularity of perovskite solar cell is easy, low-cost solutionbased fabrication techniques [12,16,26,[94][95][96].Unlike perovskite, anti-perovskite materials are hardly explored experimentally.Synthesis of these anti-perovsites often require harsh conditions.For example, synthesis of silver chalcohalide anti-perovskites, a relatively unexplored substitute for lead halide perovskites, require long reaction time and high temperature.Low cost processing, thin film fabrication, optimization of passivating agents, search for appropriate transport layers etc. should be investigated simultaneously in order to make anti-perovskites a commercially viable photovoltaic material.(2) Structural variations: In contrast to perovskites, some transition metals can be positioned at both the A and X sites in the anti-perovskites; therefore, benefit from accepting more types of components than perovskites while maintaining structural resemblances.In comparison to halide perovskites, the development of double antiperovskites greatly expands the compositional space for solar absorbers [83].Double anti-perovskites with the formula X 6 B 2 AA ′ or X 6 BB ′ A 2 can also be generated from X 3 BA [101].In addition to double anti-perovskites, organic-inorganic hybrid anti-perovskites also can be explored as photo absorber material.The incorporation of organic components further diversifies the structural tunability [102].Anti-perovskites having A 3 BX 5 and AB 2 X 5 phases (Cs 3 ZnBr 5 and CsPb 2 Br 5 ) were also discovered, further expanding the family of anti-perovskites [103,104].Anti-perovskites/perovskites and anti-perovskites/antiperovskites heterostructures are also an unexplored avenue for photovoltaic application.Recently Quintela et al have demonstrated a unique class of sharp heterointerfaces formed by nitride anti-perovskite and oxide perovskite [105].This study opens the door for more investigation into these kinds of interfaces.(3) Exploration of dimensionality variation: The performance of perovskites as solar materials is significantly impacted by their dimensions.Both 2D and 3D perovskites are extensively explored as absorber materials [106].Though 3D halide perovskites are preferred in terms of efficiency, the stability of these materials remains a serious issue.Mixed dimensional 2D/3D hybrid perovskites are emerging as absorber materials for photovoltaic applications, because of the excellent moisture stability provided by 2D perovskites as they are rich in water-repelling organic components.In Anti-perovskites, both 3D and 2D structures are observed.Unlike perovskites, 3D antiperovskites do not face stability issues.Also, 2D antiperovskites are rich in inorganic components and less explored in terms of optoelectronic properties [52].(4) Stability: In terms of solar cell efficiency, iodide-based perovskites are currently leading the race.However, they suffer from thermal, photo, and moisture instability, which hinders their commercialization.Moisture instability results from the weak electrostatic attraction between cations and anions, which makes the accommodation of water molecules viable.Decomposition of perovskites also occurs at moderate temperatures causing an irreversible drop in device performance.Exposure to light also brings instability in perovskites.e.g.Photo instability of CH 3 NH 3 PbI 3 is predicted due to the oxidation of iodide to iodine by the photogenerated holes.A smaller ionic size of iodine than iodide causes it to exit the lattice, leaving vacancies in the perovskites and making them unstable [107,108].and have shown that the photoexcited electrons and holes occupy two distinct atomic sites and are thus spatially well separated from one another in these anti-perovskites [66].
It is anticipated that the recombination rate between the carriers will be extremely low for all of the compounds, which is advantageous for higher-efficiency solar cells.(6) Environmentally benign: Degradation of organicinorganic iodide perovskites releases Pb 2+ ions, which have a high solubility in water (K s : 1 × 10 8 ) and accumulate inside the human body without natural removal [110].Other divalent metal cations such as Sn 2+ , Ge 2+ , and Bi 3+ have been investigated, but they fall far behind Pb-based perovskites in terms of stability and PCE.In this aspect, anti-perovskites serve as a Pb-free, environmentally beneficial substitute for Pb-based perovskites.
(7) Understanding the influence of defects and surface and interface passivation: It is well known that defects reduce the efficiency of perovskite solar cells by triggering decomposition.Defect management is mainly done by chemical passivation of the surface and interface of antiperovskites [95,111].However, this field needs more research because it has not yet been fully investigated.The above-mentioned directions are summarized in figure 6. (8) Anti-perovskite as a potential photovoltaic material: The study of anti-perovskites is still in its infancy but is quickly gaining attention for photovoltaic applications owing to the following properties  [66].As the photoexcited electrons and holes occupy two distinct atomic positions and are thus widely apart spatially, it is anticipated that the recombination rate between the carriers will be extremely low for all these compounds.• Anti-perovskites also benefit from the inherent potential of the perovskite-type structure and diverse opportunities for structural variations.
Given the enormous potential of anti-perovskites in solar cells, additional investigation is anticipated to widen the structural diversity of the perovskites and their dimensionality.The connectivity between different types of perovskites and functional viewpoints discussed in this study significantly advances the field of material sciences.

Figure 1 .
Figure 1.(a) Structural representation of perovskite and anti-perovskite materials, (b) elemental constituent of anti-perovskite materials reported so far.

Figure 2 .
Figure 2. Structural representation of certain anti-perovskite materials.Carbon, Nitrogen, Hydrogen, Oxygen, and Sulfur are represented in grey, blue, white, red and yellow respectively; halogens are represented in green and selenium or telurium are represented in brown respectively.Tolerance factor for (MA) 3 OI, (MA) 3 SI, (MA) 3 FTe, (MA) 3 TeBr, and (MA) 3 ITe are 0.90, 0.79, 0.58, 0.68 and 0.71 respectively.The alternative CaIrO 3 phase has been observed in (i), (j) for t <0.76, in most of the cases.It is found that O and S remain as protonated species (H 2 O and HS−).The B-site protonation reduces the ionic character shown in figures 2(a)-(c) for O.In general, MA ions situated on the X-sites are tilted, which allows to form hydrogen bonding between two B-site oxygens to the CH 3 and the NH 3 groups.(a)-(l) Reprinted with permission from [37].Copyright (2018) American Chemical Society.

Figure 5 .
Figure 5. (a) Predicted bandgaps of A 3 YX (A = Na, K, Rb, Cs, Cu, and Ag; Y = O, S, and Se; X = Cl, Br, and I) as a function of the calculated lattice parameter a; (b) Calculated band structures of Na 3 OCl, K 3 OCl, Rb 3 OCl, and Cs 3 OCl; (a), (b) Reprinted from [86],Copyright (2021), with permission from Elsevier; (c) Schematic of quaternary anti-perovskites (X 6 B 2 AA ′ and X 6 BB ′ A 2 , X = Mg, Ca, Sr, Ba (color coded with green); for X 6 B 2 AA ′ , B = N (color coded with grey), AA ′ = PAs, PSb, AsSb, PBi, AsBi, SbBi (color coded with red); for X 6 BB ′ A 2 , BB ′ = NP, NAs, PAs (color coded with yellow), and A = Sb, Bi (color coded with orange)), (d) screening of materials based on characteristics important to solar performance, Green checks indicate the ideal lead-free quaternary anti-perovskites that meet all the requirements.In the meantime, those with the red X are abandoned; (c), (d) Reprinted with permission from[83].Copyright (2021) American Chemical Society; (e) Schematic band structure of X 3 NA (X = Mg, Ca, Sr; A = P, As, Sb, Bi) by changing the X-and A-sites; (e) Reprinted with permission from[62] .Copyright (2021) American Chemical Society.

Figure 6 .
Figure 6.Research direction in the field of anti-perovskite materials.

Table 1 .
List of anti-perovskite materials with their band gap and type.

Table 1 .
[79,80]ued.)full-potential linear muffin-tin method within the local density approximation (LDA) by using GGA and found that Mg 3 AsN has a direct band gap of 1.332 eV and Mg 3 SbN has an indirect band gap of ∼0.623 eV[75], which is in good agreement with the investigation provided by Okoye, using the full-potential augmented plane wave plus local orbital (APW + lo)[76].They have also theoretically investigated the optical properties of these materials.The calculated static dielectric constants ε 1 (0) are 10.8843 and 13.296 and refractive index n(0) are 3.29 and 3.64 for Mg 3 AsN and Mg 3 SbN respectively.The maximum reflectivity of both compounds occurs in the range of 5 and 10 eV, which is in the ultraviolet range.This indicates that both of these compounds absorb or transmit visible and infrared spectra, and hence they possess a high potential as absorber materials in tandem solar cells.Optical properties of Mg 3 AsN and Mg 3 SbN were also investigated by Bouhemadou et al[77,81]and resemble well with Okoye[76].Amara et al and Basit et al have also theoretically investigated Mg-rich nitride anti-perovskites[79,80]. Mg 3 PN and Mg 3 AsN have direct band gaps of 2.60 eV and 2.41 eV respectively.However, Mg 3 SbN and Mg 3 BiN have indirect band gaps of 1.48 eV and 1.42 eV respectively.While Basit et al found almost similar results with direct band gaps of 2.62 eV and 2.43 eV for Mg 3 PN and Mg 3 AsN respectively and indirect band gaps of 1.61 eV and 1.51 eV for Mg 3 SbN and Mg 3 BiN respectively, which almost resembles the results of Amara et al.They studied the optical properties of these materials, which have static refractive index n(0) for Mg 3 PN, Mg 3 AsN, Mg 3 SbN, and Mg 3 BiN are 2.61.2.70, 2.93, and 3.07 respectively.The maximum reflectivity is in the range of 4.0-12.2eV for Mg 3 PN, 3.8-12.0eV for Mg 3 AsN, 3.4-11.8eV for Mg 3 SbN, and 3.1-11.4 eV for Mg 3 BiN, which are in the range of near-visible and ultraviolet.Recently, Heinselman et al synthesized a thin film of Mg 3 SbN deposited on Eagle XG glass and indium tin oxide coated glass by sputtering [82].The achieved optical band gap value is close to 1.3 eV.
a Experimental Values.the This ink can be deposited on a film by using a low-cost spin coating technique.These developments pave the way to develop new low cost, fast and scalable deposition techniques, needed for device fabrication.
[86]he class of anti-perovskites provides more options without the halogens and band gap tailoring is not severely impacted by halides, they are expected to provide a more stable alternative for solar cells.Recently, Liu et al have shown that the thermodynamic stability of antiperovskites having chemical formula A 3 YX (A = monovalent cation; Y = O, S, Se; X = Cl, Br, I) decreases as we move from O to Se[86].However, a lot of investigations must be conducted to evaluate the moisture, thermal, and photo-stability of anti-perovskites.(5)Bandgapnature,tunability: Like perovskites, antiperovskites benefit from having direct band gaps because they can efficiently absorb sunlight without losing solar energy to thermal radiation.These anti-perovskites are more appealing to employ in photovoltaics because they have a straight band gap and can easily be tuned across a wide range of values[86].Contrary to halide perovskites, band gap tunability is not primarily halide ion-dependent.Iodide-based perovskites are the most effective among the halide perovskites in terms of efficiency.However, as previously mentioned, these perovskites are quite unstable in ambient conditions.Anti-perovskites are favored over halide perovskites because they can obtain an adequate band gap for photovoltaics without iodide ions.Band gap tunability with O, N, and mixed anions is shown in section 3.Recently Liang et al have shown the potential of P-based anti-perovskites for solar cell applications [109].They have shown that Ca 3 SbP, Sr 3 SbP, and Ba 3 SbP are direct bandgap semiconductors having bandgap values of 1.52 eV, 1.35 eV, and 0.98 eV respectively.These materials are effective at absorbing light in the visible and ultraviolet ranges and also exhibit low energy loss and reflectivity in the visible light spectrum.Anti-perovskites have effective charge separation capabilities in addition to having high light absorption capabilities.Sreedevi et al have investigated a series of anti-perovskites (Mg 3 PN, Ca 3 PN, Sr 3 PN, Ba 3 PN, BaSr 2 PN, Ba 1.5 Sr 1.5 PN, and Ba 2 SrPN) • Perovskites used for solar cell applications are predominantly Pb-based, harmful effect of which is well known.Anti-perovskites provide a non-toxic alternative to Pbbased perovskites • Unlike perovskites, anti-perovskites are stable towards prolonged exposure to moisture and heat.• As mentioned in table-1, most of the anti-perovskites have direct band gap appropriate for solar cell applications.E.g.Sr 6 N 2 PAs is a direct band gap anti-perovskite having band gap of 1.58 eV [83].In addtion, band gap of anti-perovskites can be tuned easily.e.g.Sr-substitution can be used to tune the band gap of Ba 3 PN so that the band gaps of BaSr 2 PN, Ba 1.5 Sr 1.5 PN, and Ba 2 SrPN are 1.27 eV, 1.12 eV, and 1.38 eV, respectively [66].Also, they have high absorption co-efficients.• Low effective masses of electrons and holes in antiperovskites make them appropriate materials for solar cells.Smaller effective mass indicates high charge carrier mobility, a prerequisite for solar cell applications.Recent reports evident high charge carrier mobility for anti-perovskites.E.g.Thin films of Ag 3 SI have shown high charge carrier mobility of 49 cm 2 V −1 s −1 [99].Guo et al have reported high charge carrier mobility of 195-289 cm 2 V −1 s −1 for Sr-and Ca-based antiperovskites Ca 6 CSe 4 , Ca 6 CTe 4 , Sr 6 CSe 4 , and Sr 6 CTe 4 , which is comparable with MAPbI 3 (197 cm 2 V −1 s −1 ), a well-known photovoltaic material [112].Sreedevi et al have reported lower recombination rate of charge carriers for a series of anti-perovskites such as Mg 3 PN, Ca 3 PN, Sr 3 PN, Ba 3 PN, BaSr 2 PN, Ba 1.5 Sr 1.5 PN, and Ba 2 SrPN