Sustainable A₂B^ⅠB^ⅢX₆ based lead free perovskite solar cells: The challenges and research roadmap for power conversion efficiency improvement

1.   Introduction

A definitive objective of materials utilized in optoelectronic applications ought to be founded on the "triple-E" terms: financially economical, vitality effective, and naturally efficient. Despite their very great execution in lead halide perovskite based solar cells with efficiencies reaching 24.2% and the rising application for lasers ^[1], light-radiating diodes (LEDs) ^[2], field-impact light-producing transistors (FETs) ^[3], organic−inorganic lead halide perovskites experience the ill effects of substances of lethal, contaminating, and bioaccumulative Pb, which may, in the end, hamper their commercialization. Progressively, it turns out to be of essential significance to consider and create alternative classes of lead-free halide double perovskites for various optoelectronic applications ^[4].

The need to create practical advances is dependent on ecologically neighborly, earth-inexhaustible, and financially savvy materials that normally drive the consideration toward the change metals with especially appealing metals (e.g., Fe²⁺, Cu²⁺, Zn²⁺) and post-transition elements ^[5,6]. For example, tin ^[7,8], rubidium ^[9,10], indium-silver ^[11,12], titanium ^[13], bismuth and silver-bismuth ^{[11,14,15,16,17]}, and copper ^[18] based perovskites have been found as potential choices to toxic perovskites. Thanks to their rich science, their utilization may tremendously broaden engineered courses of new halide double perovskites for photovoltaic and light-radiating applications, enhancing the tunability of the material. Moreover, the discovery of lead-free double perovskites provides a feasible way of searching for air-stable and environmentally benign solar cell absorbers ^{[19,20,21,22,23]}. Since the 1970s, a large number of double perovskites (which are well known as elpasolites) with nominal chemical compositions of A₂B^ⅠB^ⅢX₆ (A and B^Ⅰ = Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺, Ag⁺, Tl⁺, etc., B^Ⅲ = Bi³⁺, Al³⁺, Ln³⁺, Ga³⁺, Fe³⁺, etc., and X = F, Cl, Br, or I) have been initially reported as ferroelectric materials ^[24,25]. However, the lead and tin free all-inorganic halide double perovskite solar cell power conversion efficiency is far smaller than the power conversion efficiency (PCE) of lead based perovskite solar cells. The lead and tin free all-inorganic halide double perovskites PCE improvement is too slow compared to lead halide perovskites PCE, which has become a great concern and active research direction for the halide double perovskite scientific community. In conjunction with the advancement of halide double perovskite solar cells, interesting concepts covering cationic exchange, doping, and alloying for engineering the electronic structure of double perovskites ^[26], its crystal structure include preparation approaches, physicochemical properties, and material applications ^[6,27,28] with various strategies such as hetero-substitution of Pb to form quaternary halide double perovskites ^[5] and a strategy for achieving small band gaps in this family of materials ^[29]. Moreover, the PCE of single junction lead based perovskite is now 24.2% ^[30], 25.2% ^[31], and 29.15% ^[32] for the textured monolithic perovskite/silicon tandem solar cell, but the record for lead-free all inorganic cesium tin-germanium triiodide (CsSn_0.5Ge_0.5I₃) solid-solution perovskite is 7.11% ^[33]. According to the simulation results reported, CsSn_0.5Ge0_.5I₃ perovskite material can have a power conversion efficiency of 18.79% ^[34] and 24.63% ^[35]. Furthermore, the CsSn_0.5Ge_0.5I₃/FASnI₃ device architecture is reported with a simulated power conversion efficiency of 31.58% ^[36]. This indicates that the CsSn_0.5Ge_0.5I₃/FASnI₃ device is a promising device for high-performance lead-free solar cells.

This efficiency can be achieved if encapsulation mechanisms, fabrication procedures, and material parameters such as defect density, layer thickness, operating temperature, electron affinity, and potential energy are well optimized during an experiment. Moreover, tin-based perovskite solar cells have promising efficiency next to lead-based perovskite solar cells as devices made of Tin based perovskite materials exhibit insufficient stability ^[37] and contain intrinsically deep defects that are detrimental to the perovskite solar cell performance ^[38]. Even the most stable CsSn_0.5Ge_0.5I₃ based perovskite solar cell showed 10% decay efficiency after 500 h of continuous operation in an N₂ atmosphere under one-sun illumination ^[33]. Hence, to overcome the toxicity of lead and insufficient stability of Tin, efforts to find alternative perovskite materials, which are earth-abundant, non-toxic, stable, and biocompatible, are in progress.

Based on these needs, lead and tin free A₂B^ⅠB^ⅢX₆ based all-inorganic solar cells such as Cs₂AgBiBr₆ and Cs₂TiBr₆ have been reported recently ^[39]. The records for Cs₂AgBiBr₆ and Cs₂TiBr₆ lead and a tin-free, all-inorganic halide double perovskite solar cell are 2.5% ^[40] (current report is 2.81% ^[41] with a photoelectronic conversion efficiency of hydrogenated Cs₂AgBiBr₆ perovskite solar cell of 6.37% ^[42]) and 3.3% ^[43], respectively. These are far less than 24.2% for single junction lead-based halide perovskite solar cells and 29.15% for a tandem solar cell. Consequently, the progress is too slow to reach the hybrid lead halide perovskite solar cells. From a theoretical perspective, simulation results reported that Cs₂TiBr₆ has achieved 11.49% power conversion efficiency ^[44]. This is promising for manufacturing practical lead-free, double halide perovskite solar cells. More recently, an Au/CuSbS₂/Cs₂TiBr₆/CdS/TCO configuration has achieved a power conversion efficiency of 23.77%, as reported by simulated results ^[45]. This is again a more promising result in this field. Unless the real and bottleneck challenges and solutions are clearly identified, the Cs₂AgBiBr₆ and Cs₂TiBr₆ based halide double perovskite solar cell will not be the first alternative solar cell to replace the hybrid lead halide perovskite solar cells. Thus, this review article is designed to identify the challenges and possible solutions for power conversion efficiency improvement of halide, double perovskite solar cells that will be considered a research roadmap for performance improvements in this field. Hence, this is a comprehensive review that concisely reviews the modification strategies from CH₃NH₃PbI₃ into many halide double perovskite materials, the origin of electronic and optical properties variations, and key challenges and areas of research for possible solutions and performance improvement strategies of both Lead and Tin free all-inorganic halide double perovskite solar cells. Moreover, this will provide a new perspective and research roadmap for performance improvement to the scientific community and research industries.

2.   Issue of sustainability in lead-based halide perovskite solar cells

The issue of sustainability in lead halide perovskite solar cells is the biggest challenge. This sustainability concept is not only understood in terms of economic viability, toxicity, and stability but also affordability, availability of materials, energy independence, quality of being able to continue over a period of time, free of hazardous materials, etc. Now, we question whether A₂B^ⅠB^ⅢX₆ such as Cs₂AgBiBr₆ and Cs₂TiBr₆ based perovskite solar cells can answer all concepts of sustainability so that it can revolutionize the photovoltaic field of research or not? We seek to answer this question.

3.   Promising candidate properties to substitute Pb metal

The organic-inorganic halide perovskites become capable of photovoltaic and energy applications beyond photovoltaic. However, the large scale commercialization of the perovskite harvester faces considerable limitations due to the toxicity of lead metal and the perovskite absorber degradation ^[6,46,47,48]. For this reason, there is an interest to discover nontoxic and stable perovskites for the betterment of this field. The degradation concern can be treated by carbon encapsulation, multi-cation substitution, and incorporation of hydrophobic moieties ^[47,49]. On the other hand, substitution of Pb using non-toxic transition metal atoms is the single strategy to overcome the toxicity problems ^[46,50,51]. Consequently, the optoelectronic properties ^[52] such as direct band gaps ^[19,53], electron mobility ^[54], defect tolerance, high absorption coefficient ^[55], small carrier effective masses, intrinsic thermodynamic stability ^[56], long charge carrier diffusion lengths ^[57], low exciton binding energies, higher dielectric constant, and compatibility with low-cost and solution-supported fabrication procedures ^[58] are considered promising candidate properties to replace lead-based solar cell light harvesting materials in perovskite solar cells. Solving the predictable restrictions of solution-processed semiconductors is another important candidate topic that needs to be considered in the lead replacement process ^{[59,60,61,62,63]}. Moreover, there are promising candidate materials that can overcome the issue of toxicity, instability, lifetime, and device deterioration of lead based halide perovskite. Such materials are the topic of this review, with a general formula assigned as A₂B^ⅠB^ⅢX₆ based lead free perovskite solar cells.

4.   Modification strategies from CH₃NH₃PbI₃ into Cs₂AgBiBr₆ and Cs₂TiBr₆ halide double perovskites

Solar cell devices made of organic-inorganic lead halide perovskite material (CH₃NH₃PbI₃) has been reported in 2009 with a cell efficiency of 3.81% ^[64], indicating that CH₃NH₃PbI₃ with an efficiency of 24.2% ^[30] was achieved in 2019 and has reached 29.15% ^[32]. This is promising if the device made further optimized continuously. Gradually, modification of CH₃NH₃PbI₃ has been done at three sites, as shown in Scheme 1 ^[65]: strategy (1) halogen atoms like chlorine, bromine, and a combination of all these halogens ^{[66,67,68,69]}; strategy (2) organic part ^{[70,71,72,73]}; and strategy (3) at an inorganic Pb metal site such as Ge ^[74], resulting in many derivatives of CH₃NH₃PbI₃ materials classified as organic-inorganic perovskites, fully inorganic perovskites, and halide double perovskites etc. All these modifications are the subject of this section and are classified as cation displacement at A and B site and anion displacement at X-site. Furthermore, all these cation and anion modifications, as well as the tunable structural dimensions, cation-anion order-disorder, distortions, and tilting of the octahedral unit, BX₆, from the ideal structure, are collectively considered as the origin of diversity in materials structure, dimension, and optoelectronic properties. Based on these modifications, iodide, bromide, mixed metals, and mixed I/Br ratio-based double perovskites such as Cs₂AgBiBr₆, Cs₂AgBiCl₆, Cs₂AgInCl₆, Cs₂NaBiCl₆, Cs₂Ag(Sb_xBi_1−x)Br₆, and Cs₂AgBi(Br/I)₆ or Cs₂AgBiBr_6−xI_x, have become widely known double perovskite light absorbing materials ^[75]. The challenge in these materials is the large band gap. To solve this challenge, compositional engineering plays a great role in discovering new optical and electrical properties in these materials. Mixed compositions in the metal and halogen site have been investigated to explore these materials ^[76,77]. This approach helps to discover stable and nontoxic halide double perovskite materials, which are the main focus of this review.

5.   Origin of electronic and optical property variations

In addition to the structural variations, optoelectronic properties such as absorption, electron-hole diffusion length, carrier life time, carrier mobility, charge carrier dynamics, electronic structure such as band structure and density of state, effective mass of electron, thermal properties, and other electrical properties such as ferroelectric, pyroelectric, and piezoelectric properties are the major material properties that cause differences in device efficiency; moreover, everyone wants to deal with this for further energy application of materials ^[78]. Recently, the field of organic-inorganic hybrid halide perovskite has revolutionized the field of photovoltaics. Moreover, modifying the halide perovskites gives new halide double perovskites for which the stated properties are not well studied. Thus, understanding the origin of these optoelectronic property variations would be of great interest for the development of halide double perovskite material performance. In this section, molecular dipoles, tilting of octahedron, transition metal cation size and its oxidation states, band structure, photoluminescence, and other optoelectric properties are considered as potential origins of improvement of the performance for Cs₂AgBiBr₆ and Cs₂TiBr₆ halide double perovskite solar cells.

5.1.   Effect of polarization and molecular dipoles on the dynamics of photo-excitations

Regardless of fast improvements in both photovoltaic and light producing device execution, the comprehension of the optoelectronic properties of halide double perovskites is as yet fragmented. Specifically, the polarization of the material, the nearness of sub-atomic dipoles, and their impact on the dynamics of the photo-excitations remains an open issue to be cleared up. From now on, the imperative subject of discussion has been the seemingly perpetual polarization of the perovskite under connected electric fields ^[79,80]. This impact shows itself as a huge hysteresis in the deliberate current–voltage curve of perovskite sun-oriented cells and LEDs in planar hetero-junction designs, contingent upon the contact materials used ^[79,81,82]. The vast majority of the ongoing work underpins the speculation that particle migration ^[79,82,83] ought to rule any ferroelectric conduct at room temperature ^[84]. In addition to these polarization effects, there is another effect that causes problems in efficiency estimation ^[85]. The hysteresis effect transforms the dominant behavior from normal (Figure 1a−c) to be inverted (Figure 1d−f) owing to the decreasing scan rate with a stabilized current−voltage curve at an equilibrium point ^[86]. The estimated efficiency in the inverted behavior is different from the dominant normal behavior. Those devices showing high efficiency have lower surface recombination that can be a source of the hysteresis effect. Moreover, the presence of the hysteresis effect originates from ion migration, charge carrier trapping/detrapping, and ferroelectric polarization ^[87]. This hysteresis effect is not only affecting device efficiency but also device stability ^[87]. Owing to its negative impact on efficiency and stability, mechanisms to avoid its presence via strategies such as either working on device architecture, increasing grain sizes, interface engineering, and additive doping have been suggested ^[87,88].

Researchers such as Leijtens et al. ^[89] explored the impact of a connected outer electric field on the photograph-energized types of CH₃NH₃PbI₃ thin movies, both at room temperature and at low temperature, by checking the photoluminescence (PL) yield and PL rots. At room temperature, these creators discovered proof for an electric field–incited decrease of radiative bimolecular bearer recombination together with the movement of charged imperfections that influence the non-radiative rot rate of the photoexcited species. This has been allotted to field-incited arrangement of the atomic dipoles, which diminishes the vibrational opportunity of the cross section and the related nearby screening, which results in a more grounded electron gap interaction ^[89].

5.2.   Effects of tilting on the band structure and electron-hole transport

Diverse degrees of tilting of the octahedral structure offer ascent to various precious crystal fields, which results in various electronic and optical properties. The degrees of tilting may influence the band structure, electron transport properties, photoluminescence, and dielectric conduct. Tilting at the organic cage causes distortion of peroveskite lattice either by tilting at PbX₆ octahedra or brings isotropic lattice contractions. In the first case, it increases the band gap by reducing orbital overlap; in the second case, it reduces the band gap ^[90,91,92]. Understanding characteristics of inorganic octahedral tilt is an important issue to understand band structure and electron hole transport in halide perovskite materials. In this case, corner connected octahedral structure where distortion, including octahedral tilting, plays its own role. This lattice distortion brings structural flexibility where various phases are created; not only octahedral tilting but also off-centering at the A and B site of the octahedral inorganic structure, which causes phase transformation to result in high temperature cubic, tetragonal, and a low temperature orthorhombic–phases (Figure 2a). This happens owing to the occurrence of two types of octahedral rotation: in-phase and out-phase rotations (Figure 2b) ^[93]. The cubic aristotype structure happens at a higher temperature, but tetragonal, orthorhombic, and monoclinic phases occur at a lower temperature. This leads to lattice dynamics, resulting in phase diversity ^[94].

To understand the surface structure relaxation process in organic inorganic hybrid 2D perovskite, Yan Shao et al. studied how to unlock the surface octahedral tilt in Ruddlesden-Popper perovskites ^[95]. The result indicated that surface-enhanced octahedral tilt is correlated with excitonic redshift, which enhances inversion asymmetry normal to the direction of a quantum well and promotes Rashba spin splitting for n > 1. The surface structure relaxation is related to the exfoliated monolayer surface and bulk interface (Figure 2c) while the surface-enhanced octahedral tilt is related to a rotation of the anion cage classified as out-of-plane and in-plane tilt (Figure 2d). Furthermore, the characteristic inorganic octahedral tilt affects the optoelectronic properties such as charge carrier lifetime and band gap ^[96]. This long charge carrier lifetime in halide perovskite is owing to the presence of octahedral tile, related to dynamic disorder, which impacts the optoelectronic performance ^[97].

6.   Energy applications of halide double perovskites

The key point that researchers deal with regarding materials property is to obtain promising material property for certain promising applications ^[20]. Thus, many researchers are working on the halide double perovskites for some applications ^[98] because these materials show promising solar cell absorbers ^[20,99], tandem solar cells ^[32,99,100], photocatalytics ^{[20,27,101,102,103]}, and light emission devices ^[20]. Moreover, the applications of halide double perovskites for energy storage systems such as batteries have shown promising research progress ^{[104,105,106,107]}. In this regard, vacancies are observed to facilitate ion conductivity, surface area, and ion migration, which are vital to energy storage systems such as batteries ^[108]. Furthermore, MA₂SnCl₆ as a cathode demonstrates the highest specific capacity of 589.98 mAh·g⁻¹ while Cs₂NaBiCl₆ as an anode demonstrates over 99% Coulombic efficiency with a specific capacity of about 300 mAh·g^{–1 [105]}. Thus, Cs₂NaErCl₆: Li⁺ as the negative electrode achieves a coulomb efficiency of nearly 100% with specific capacity of 120 mAh·g^–1 at 300 mA·g^–1 after 500 cycles ^[107]. Although it is believed that halide double perovskites are suitable for energy storage systems such as batteries, research will continue to confirm whether this progress is confidential enough to use them in batteries in the practical work. Until this practical application of halide double perovskites is confirmed, this application will be debatable in the research world. Another application of halide double perovskites such as the Cs₃Bi₂Cl₉ electrode for thin film based supercapacitor achieved a higher specific surface area (26.4 m²·g⁻¹), areal capacitance of 64 mF·cm⁻², and 6.6 μWh·cm⁻² energy density much higher than the lead-based devices ^[109]. With this perspective, halide double perovskites have achieved many possible applications but limited research in fuel cell applications. Hence, new possible breakthroughs are expected to become great research news for the proposed fuel cell applications. Furthermore, X-ray detectors require high sensitivity and acceptable doses applied in security screening, nondestructive industrial inspection, and imaging ^[110]. Moreover, imaging and self-powered X-ray detection use halide double perovskites such as Cs₂AgBiCl₆ with a limit of detection of 241 nGy·s^–1 and sensitivity of 325.78 μCGy·air^–1·cm^{–2 [111]}. Valuable characteristics such as lower trap density (1.18 × 10⁹ cm^–3), high carrier mobility-lifetime product (5.36 × 10^–4 cm²·V^–1), and the high dark resistivity (3.1 × 10¹⁰ Ω·cm) presented in halide double perovskites make them possible candidates for X-ray detector applications ^[111]. Finally, opportunities and challenges remain that are addressed elsewhere for possible application of halide double perovskite materials in X-ray detectors ^[112].

7.   Challenges in lead and tin free all-inorganic halide double perovskite solar cells

As a result, revolutionary advances have been claimed in lead halide perovskite photovoltaic, i.e., PCE has reached greater than 24.2% ^[30] for a single junction organic inorganic halide perovskite in only a few years of development ^[61,113,114] and 29.15% for a textured monolithic perovskite/silicon tandem solar cell ^[31], rendering lead halide perovskites a unique type of material for solar energy capture; however, the record for lead free all inorganic halide perovskite is 7.11%, and for both lead and tin free all inorganic halide double perovskite solar cells, the record is 2.8% ^[33] and 3.3% ^[43,115], which is far less than 24.2% for a single junction and 29.15% for a tandem solar cell. Unlike their encouraging efficiency, lead and tin based perovskite solar cells face both the toxicity of Pb metal and device instability ^[47,116,117], which limits the practical applications. Consequently, a great deal has been dedicated to find alternative perovskite materials such as lead and tin free halide double perovskites and lead and tin free all inorganic perovskites ^{[118,119,120,121]}. The great opportunity to use double halide perovskites is because of the following important points ^[122,123]: (1) more stable to moisture compared to (MA)PbI_3. A 30-day exposure to 55% humidity ^[99] causes no decomposition in the material, whereas (MA)PbI₃ is mostly converted to PbI₂ ^[20,124]. (2) Halide double perovskites are more stable to heat compared to (MA)PbX₃. Volatile organics in (MA)PbX₃ perovskites leave the material at low temperatures. Although CsPbI₃ is more thermally stable, it does not form a 3D perovskite under ambient conditions. In contrast, the Bi-containing perovskites can be heated to 350 ℃ without decomposition ^[28,125,126]. Furthermore, (3) long photoluminescence lifetimes (660 ns), which are very promising for solar-cell applications and band gap, are ideal for pairing with Si absorbers in a dual-absorber tandem solar cell ^[125]. On the other hand, halide double perovskites have challenges relating to their physical chemistry and chemical physics, to date, which need further investigations for more advancement. The big challenge in halide double perovskites is a larger band gap causing poor light absorption and low efficiency. This creates a big question and concern that can cause A₂B^ⅠB^ⅢX₆ based lead-free double perovskites solar cells to be an acceptable alternative to replace organic inorganic halide perovskite solar cells in the market in order to realize the practical applications ^{[127,128,129]}. The key challenging mechanisms during performance improvements are suggested as follows, which will be considered core ideas for advancement. These forward-looking points of discussion are expected to improve the photovoltaic performance in addition to the questions raised elsewhere ^[128].

7.1.   Discouraging power conversion efficiency

Regardless of the quick development of halide double perovskite solar cells, the cell power conversion efficiency remains about 2.5%, which was achieved using Cs₂AgBiBr₆ ^[33] and 3.3% using Cs₂TiBr₆ ^[43]. Furthermore, the strategy to improve both material and device efficiency made of these materials becomes a great concern. Moreover, looking at halide double perovskite light absorbers of high-quality with high absorption coefficient, longer diffusion length, and free of defects, trap states with less radiative centers are concerning. In accordance with the Shockley-Queisser limit, a theoretical maximum PCE of 16.4% can be obtained with an E.g. of 2.2 eV, thus holding promise for working double perovskite based photovoltaics ^[129]. Even though the theoretical maximum PCE of Cs₂AgBiBr₆ does not reach the highest reported PCEs of single-junction MAPbI₃-based photovoltaic cells, Cs₂AgBiBr₆ is a promising candidate for applications in tandem solar cells, as was already shown for MAPbBr₃, which features a slightly larger E.g. of 2.3 eV ^[130]. Not only are the energy alignment and band gap with the charge extraction layers important, but the charge collection efficiency is vital to manufacture high-efficiency solar cells ^[40].

7.2.   Mismatch among various interfacial layers of the device architecture

This is another key challenge in halide double perovskite solar cells that remains an unexplored area of research. Furthermore, poor interfacial integration might lead to broadening of the depletion width, poor band alignment, inefficient charge collection, enhanced recombination, insufficient charge transport, and poor overall device performance. For instance, such mismatch in energy levels has occurred in materials such as (MA)₂AgBiI₆ and Cs₂PdBr₆. For example, (MA)₂AgBiI₆ was observed as not compatible with TiO₂ but was well-matched with SnO₂ and C₆₀ ^[131].

7.3.   Unclear charge-transport properties of these materials

Whether or not they are as favorable as lead-based perovskites is not well known. The optoelectronic properties of Cs₂AgBiBr₆ and Cs₂AgBi_1−xSbxBr₆ have displayed a comparable rate-transport mechanism, which can act as an alternative absorber to lead-based perovskites ^[15]. The charge carrier density of both Cs₂AgBiBr₆ and Cs₂AgBi_1−xSb_xBr₆ is limited to 10¹⁶ cm⁻³ and a mobility of 0.8 cm²/Vs as well as tunable band gap of 2.0 to 1.6 eV ^[132,133]. Thus, this charge transport property requires greater attention for further improvement of the field. The carrier mobility of Cs₂AgBiBr₆ is 0.3–11 cm²/Vs with electron and hole mobility of 17 and 14 cm²/Vs, respectively ^[134]. Other charge transport properties of Cs₂AgBi_1−xSb_xBr₆ have not been reported. Thus, further study is required to clarify and fill the limitation not yet reported.

7.4.   Quantum confinement effect

The quantum confinement effect in the last shells due to restricted orbital interactions of the adjacent cations, particularly B′ and B″ cations in the cubic unit cell of the AB′B″X₆ double halide perovskite materials, might result in a narrow and localized conduction band edge as well as a broad energy gap, which deteriorate the device performance ^[27,127]. Consequently, finding a way to move into another unite cell structure is expected to overcome such challenges.

7.5.   Low electronic dimensionality

Halide perovskites have both low and higher dimensionality. Such dimensions have their own electronic and optical properties that impact the efficiency and stability of halide perovskites. This structural dimension at the molecular level ranges from 0D to 3D (Figure 3, Table 1), where D stands for the word 'dimension'. High dimensionality, i.e., 3D lead halide perovskites, achieved high performance. The majority of these materials demonstrated 3D dimensionality ^[28]. On the other hand, halide double perovskites showed broad band gaps, which means structural dimensionality is a factor affecting PCE in addition to the electronic band gap that is affected by the electronic dimensionality. This might make halide double perovskites inappropriate for a single junction solar cell function though these materials crystallize into 3D ^[119]. Furthermore, the most explored halide perovskite are 2D and 3D, while those least explored are 0D and 1D. The reason why they are unexplored lower dimensional halide perovskites is because of site isolation and strong confinement ^[135].

7.6.   Indirect and wide band gaps

The higher performance of organic, inorganic halide perovskites was achieved due to their direct and lower band gap, but halide double perovskites possess indirect and wide band gaps which limit the absorption of light for solar cells and is not ideal for thin film PV applications cases, and this field needs band gap engineering. For instance, in recent times, bismuth and silver based perovskites were anticipated as a choice to replace MAPbI₃ ^[51,125]. The band gaps are indirect, which is not ideal for single junction solar cell applications, though bismuth/silver based double perovskites absorb 1.9 to 2.2 eV ^[145]. The reason that indirect semiconductors are not preferable compared to direct semiconductors is due to the weak oscillator strengths for radiative recombination and for optical absorption, which might be a challenge if there is low carrier mobility. Similarly, Cs₂AgBiBr₆ has a 1.95−2.19 eV indirect band gap ^[146,147], showing a comparable lifetime with optimized lead halide perovskite films ^[148,149]. Solving the issue of non-radiative recombinations from its indirect band gap makes them promising for photovoltaic application. The charge mobility in the polycrystalline Cs₂AgBiBr₆ is 1 cm²·V⁻¹s^{−1 [135]}, while in the single crystal it is 11.81 cm²·V⁻¹s⁻¹, indicating that charge transport property is superior in single crystals.

7.7.   Energetic disorder

The energy state of a given semiconductor is described via energy disorder since it impacts charge transport, carrier mobility, and recombination rate ^[117,150]. Such disorder may be dynamic (caused by carrier phonon interactions) and/or static (caused by impurities or defects) disorder, which influence inter-band structure as shown in Figure 4 ^[151]. In organic solar cells, energetic disorder is caused by the synergy of intra- and intermolecular interactions that originated from intermolecular disorder, the unfavorable molecular packing behavior ^[152]. In mixed halide perovskites, the origin of the disorder would be compositional disorder causing inhomogeneity of halide ions ^[153,154]. The great debate here is: which type of energy disorder matters for carrier recombination dynamics, charge transport, band-tail structure, carrier mobility, carrier trapping, and ultimately device performance? Thus, understanding energetic disorder in halide double perovskites becomes necessary of the time scales connected with atomic and molecular motions as well as the variation of the disorder from a single crystal to the thin film ^[155]. Knowing the variations might also be vital during the processing of these light-absorbing materials and hence strongly correlated with the device performance.

7.8.   Geometrical constraints

There are variations reflecting the coordination and local chemistry. As these uncertainties transfer to the octahedral and tolerance factors, the stability ranges proposed so far are descriptive rather than predictive. There are some geometric factors restricting the formation of stable 3D halide double perovskites. Many promising routes towards Pb-free halide double perovskites have been explored to replace Pb by elements such as germanium ^[74], bismuth, or antimony and noble metals ^[126,131]. However, the geometrical constraints imposed by the necessity of forming an ideal perovskite lattice, in addition to the common oxidation states of these optional cations (e.g., +3 of Bi and Sb), still cause this to be a difficult discovery of lead-free materials that could rival the optoelectronic properties of prototypes such as MAPbI₃.

7.9.   High processing temperature

While organic inorganic halide perovskites need annealing temperatures usually less than 100 ℃, the halide double perovskites are fabricated only at a higher annealing temperature up to 285 ℃ ^[40,156]. Such prerequisites for fabrication might damage the integration of the device architecture and further restrict wide range function of these materials. Additionally, such high energy consumption for materials fabrication is not economically cost-effective, environmentally none green, and is not sustainable. As a result, looking for alternative methods that could minimize such higher processing temperature becomes an impressive research area in this field.

7.10.   Shortage of a broad-spectrum of speculative guidelines

In spite of considerable contributions, there is no well-refined guideline and theoretical understanding for what kind of mixed B-site cation halide double perovskites should be used and how to design Pb and Sn free halide double perovskites for enhancing collective optical, electrical, thermal, and mechanical properties and long term stabilities of these materials for wide range applications. In order to minimize such bottleneck challenges, detailed knowledge of the electronic structures of these materials with respect to B'/B'' cation arrangement and design become attractive research directions in the field of halide double perovskites.

7.11.   Lack of stoichiometric design and compatibility of various layers

Stoichiometric design of the perovskite ^[156] has been known as a strategy to develop solar cells with enhanced performance. Moreover, unique stoichiometric design and compatibility of various interfacial device layers are essential aspects that require more attention ^[19,26,157].

7.12.   Incomplete order

Elucidating the arrangement and position of the ions is another concern in halide double perovskites. Because the B cations generally determine the physical properties of double perovskites, there are three B-cation sublattice types known for double perovskites: random, rock salt, and layered. The latter two are ordered arrangements. In some situations, it is observed that the order is not complete, especially in the A'A''B'B''X₆ structure. Interestingly, order-disorder effects are mainly encountered when the charge variation between B' and B" is two or less. Although the degree of order is an important subject, the dynamic nature of order-disorder behavior is a quite useful parameter ^{[11,46,158,159]}.

7.13.   Challenges in achieving high quality films

Unlike organic inorganic halide perovskites, achieving high quality film in halide double perovskites becomes a challenge. High quality film might be defined as a material with excellent crystallinity, uniform morphology, less defects, high absorption coefficient, superior ambipolar carrier transport ability ^[160], and high coverage or pinhole-free film ^[161,162]. All these parameters are well known to deter both materials and device performance in halide double perovskite solar cells if the quality of these materials is not well optimized during processing steps. For that reason, the light harvesting and active layer that is the halide double perovskite monolayer in the perovskite solar cells is one of the very important research topics that researchers deal with. Moreover, controlling and designing the colloidal properties of the precursor and solvent engineering ^[60,163,164] should get considerable attention to enhance the required film with high quality ^{[165,166,167]}.

8.   Suggested research roadmap engineering strategies for material and device performance improvement

In order to overcome the key challenging mechanisms faced by halide double perovskite solar cells, suggesting key areas of research that will be considered as research roadmap for improvement of both material and device performance is quite important. These include engineering microstructure, surface and bulk properties, grain boundary and domain wall engineering, polar order engineering, band gap and band structure engineering, colloidal engineering, composition engineering, optoelectronic engineering, device architectural engineering, interface and defect engineering, equilibrium and non-equilibrium quantum transport, and ferroelectric engineering, as shown in Figure 5.

8.1.   Engineering materials microstructure, surface, and bulk properties

Engineering microstructure, surface, and bulk properties of halide double perovskites are important mechanisms and research areas for improvement for both materials and devices ^{[20,50,124,168,169]}. Microstructure influences virtually all aspects of the behavior of materials. Moreover, it is the spatial distribution of material in the useful object that is the goal of the endeavor and is the most richly variable; thus, this is the most susceptible to control of the elements in the materials structural hierarchy. Engineering microstructure of materials ^[168,170] comprises the concepts of morphology or topological properties and geometry, thermodynamic properties, surface and bulk properties, and grain growth as well as bulk and nano-scale domain structures.

8.2.   Engineering domain wall and grain boundaries

The halide double perovskite microstructure might offer optional lanes for conductivity and electron−hole disjointing. Because grain boundaries have an impact on the long-term stability along with the ferroelastic domain boundaries that might be different from regular grain boundaries, the finding of ferroelasticity offers a novel parameter to pursue in favor of enhancing their stability as well as facilitating their extensive implementation ^[171]. Additionally, grain engineering and morphology control through the introduction of additives to the perovskite precursor is another way for performance improvement ^[31]. Sub-micron-sized crystal grains in perovskite thin films, on the other hand, have been obtaining considerable attention due to their fundamental morphological properties in the course of twin domains ^[172,173], which are highly essential for understanding the basic mechanisms, for instance, of low recombination rate and long diffusion length of the device's high performance ^[174]. Moreover, the presence of charged domain walls will significantly reduce the band gap by 20%−40% and can serve as segregated channels for the motions of charge carriers, while the presence of uncharged domain walls has no substantial impact on the band gap ^[175].

8.3.   Polar order engineering

Effect of polarization, molecular dipoles, tilting of octahedron and transition metal cation size, and its oxidation states on photo-excitation, band structure, and photoluminescence are not well investigated. Notwithstanding the microscopic model, polar order is accepted to recline at the center of the ferroelectric photovoltaic impact ^[176]. Besides, it is outstanding that interactions between lattice, orbital, and polarization order parameters in ferroelectric materials initiate upgrades of their physical properties close to phase boundaries ^[177]. On the road to advanced performance, conventional approaches focus on reducing the band gap to superior fit the solar spectrum, while reducing the basic relation between polar order and photovoltaic effect is ignored ^[177]. Hence, spotlighting both narrowing the band gap and basic relation between polar order and photovoltaic effect has become an attractive research topic.

8.4.   Band gap and band structure engineering

The fundamental bottleneck restraining the function of halide double perovskites is their bigger energy gap. The most favorable band gap for the single junction solar cells ought to be close to 1.3 eV ^[178]. As a result, band gap and band structure engineering are vital if halide double perovskites are to be suggested optional contender materials as shown in Figure 6. On the other hand, Cs₂Ag_0.95Ga_0.05BiBr₆ based double halide peroveskite solar cells show a small performance improvement of 4.52% via band gap reduction ^[179]. If the suggested engineering strategies are implemented, it is promising to maximize the power conversion efficiency of these solar materials.

As shown in Figure 6, the band gap and band structure of various Cs₂AgBiBr₆ derivatives are shown as indirect band gap semiconductor materials, substituting Bi using Sb and In elements. Bi 6p orbitals are the conduction band minimum for Cs₂AgBiBr₆ (Figure 6a), while the Bi 6s orbitals construct their valence band maximum with a calculated indirect band gap of 2.0 eV. Furthermore, a valence band maximum is constructed by the Sb 5s orbital observed above the Bi 6s orbitals for Cs₂AgBi_0.75Sb_0.25Br₆ (Figure 6b) whiles its conduction band minimum is constructed from the Sb 5p orbital. The 1.58 eV indirect band gap is obtained from this calculation. The conduction band minimum for Cs₂AgSbBr₆ is derived from Sb 5p orbitals, but its valence band maximum is derived from Sb 5s orbitals (Figure 6c) with a calculated band gap of 1.67 eV. Further substitution with In metal results in a new band structure, introducing 4s orbital in the lower conduction band, but Bi 6s orbitals drives the valence band maximum with an indirect band gap structure. Thus, a larger band gap of 2.28 eV has been calculated for Cs₂AgBi_0.25In_0.75Br₆ (Figure 6d, e), which is larger than that of Cs₂AgBiBr₆. Increasing In concentration leads to strong coupling in the [InBr₆] octahedral, resulting in a reduced gap caused by the In 5s-derived conduction band. These band structures obtained by Sb and In atomic substitution suggest that every atom introduced has its own band structure and unique optoelectronic properties with unique optical and electrical performance. Thus, understanding band structure matters for optoelectronic properties and the application of a given semiconductor.

8.5.   Crystallization process and colloidal engineering

The nucleation and growth, coordination chemistry, and coordination engineering of halide double perovskites need to be studied: In addition to the photophysics properties, the nucleation and growth, coordination chemistry, and coordination engineering concepts are equally important and quite essential for developing new halide double perovskite materials ^[181]. Therefore, colloidal engineering, colloidal chemistry, and ion exchange reactions during synthesis of halide double perovskites are important ideas that need to be controlled for synthesizing high quality thin film for high performance.

8.6.   Composition engineering

The computational details on the structure of Cs₂AgBiBr₆ double perovskites were reported recently, as shown in Figure 7a, b ^[182]. This structure is taken as the starting material for its derivatives such as Cs₂AgSb_0.5Bi_0.5Br_6, Cs₂Ag(Bi_1−xTl_x)Br₆, etc. From these reports, Cs₂AgBiBr₆ crystalizes as a face-centered cubic structure with a space group of Fm3m, as shown in Figure 7a. The atomic positions of the Ag atom is at (4a) (0, 0, 0), Cs atom is at (8c) (0.25, 0.25, 0.25), Br is at (24e) (ux, 0, 0), and Bi atom is at (4b) (0.5, 0.5, 0.5). Its tetragonal structure (Figure 6b) crystalizes at low temperatures with the atomic position of Br₂ atom at (4e) (0, 0, uz), Br1 atom at (8 h) (ux, uy, 0), Ag atom at (2b) (0, 0, 0.5), Bi atom at (2a) (0, 0, 0), and Cs atom at (4d) (0.5, 0, 0.25) ^[182]. Furthermore, the band structure of Cs₂AgBiBr₆ with an indirect band gap character is shown in Figure 7c, d. The band edges are mostly formulated from Br, Bi, and Ag states. The Bi–p states contribute to the conduction band while Ag–d and Br–p hybridized states contribute to the formation of a valence band. The band edges are made of Br, Bi, and Ag states. Bi–p states contribute to the formation of conduction bands while Br–p and Ag–d hybridized states contribute to the formation of valence bands. The possible electron transition occurs in Ag–s and Bi–p antibonding states from Br–3p and Ag–4d bonding. Thus, the optoelectronic properties of Cs₂AgBiBr₆ are influenced by Ag, Bi, and Br atoms. Furthermore, all possible compositional displacements and addition of atoms at a given ratio can take place at these atoms for possible modifications of the electrical and optical properties as well as other applications.

Cation and anion displacement, cation-anion order-disorder effects, cation size mismatch, distortion, tilting, ordered vacancies, hydrogen bonding, charge disproportionation, and stereochemistry or lone pair effects need to get more attention in order to improve stability, inferior material, device performance, and engineering a new halide double perovskite material ^{[13,119,152,153,154]}. In addition, the creation of new chemical compositions using new elements in the mixed halide double perovskite structure is an acceptable strategy to tune the band gap and other optoelectronic properties ^[183]. Currently, Cs₂AgBiBr₆ and Cs₂TiBr₆-based lead and tin-free all-inorganic halide double perovskites are reported as alternative types of perovskite solar cells. The latter has an energy gap of 1.8 eV in addition to its > 100 nm carrier diffusion length ^[43]. The composition engineering due to modifications at the halide anion from Br to I results in the reduction in band gap ranging from 1.8 to 1.0 eV ^[37]. This band gap is suitable for single junction halide double perovskite solar cells ^[37]. Furthermore, modifications at the cation site, A-site, and B site are not confirmed. Similarly, Cs₂AgBiBr₆ has a high band gap, tunging from 1.83 to 2.21 eV ^[125,40,184]. Composition engineering at the A, B, and X sites may reduce the band gap to make it more suitable for single-junction halide double perovskite solar cells ^[185]. Recently, precursor engineering has been suggested as a route to enhance the power conversion efficiency of Cs₂AgBiBr₆ materials, showing 40% enhancement ^[186]. This result indicates that precursor engineering is one type of composition engineering that is responsible for obtaining smooth, large grains, and high-coverage Cs₂AgBiBr₆ films.

The indirect band gap characteristics of the inorganic double perovskite band structure have been reported as shown in Figure 8 ^[77]. In this report, pure Sb(Cs₂AgSbBr₆, Cs₂AgSb_0.5Bi_0.5Br₆) and pure Bi(Cs₂AgBiBr₆) double perovskites have been studied (Figure 8). Electronic band structures were computed employing the TB09 method, considering both the inclusion of spin–orbit coupling (depicted by the black lines) and its exclusion (represented by the red lines). Materials under investigation include pure Sb alloy Cs₂AgSbBr₆ (Figure 8a), mixed alloy Cs₂AgSb_0.5Bi_0.5Br₆ (Figure 8b), and pure Bi alloy Cs₂AgBiBr₆ (Figure 8c). The valence band maximum (VBM) of these three compounds is situated at the X point, whereas the conduction band minimum is positioned at the L point in the reciprocal space. This observation signifies the indirect band gap nature of these compounds. Band gaps obtained from calculation inclusion with SOC are lower than that of exclusion with SOC. This results from SOC leads to band degeneracy resulting in a reduction of the band gap. Band gaps calculated with the inclusion of SOC are lower than those obtained without SOC. This discrepancy arises because SOC introduces band degeneracy, consequently decreasing the band gap in these systems. Indirect band gaps calculated by TB09-PBE (excluded SOC) of pure Cs₂AgSbBr₆, mixed Cs₂AgSb_0.5Bi_0.5Br₆, and pure Cs₂AgBiBr₆ are 1.69, 1.96, and 2.17 eV, respectively.

The indirect band gaps of 1.69, 1.96, and 2.17 eV are reported for pure Cs₂AgSbBr₆, mixed Cs₂AgSb_0.5Bi_0.5Br₆, and pure Cs₂AgBiBr₆, respectively ^[77]. The conduction band of these materials is dominated by the Ag–d orbitals while the valence band is dominated by Sb–p orbitals in pure Cs₂AgSbBr₆ and Cs₂AgSb_0.5Bi_0.5Br₆ but Br–p orbitals in pure Cs₂AgBiBr₆ ^[77]. Hence, it is possible to investigate photoactive materials for various applications as a function of compositional engineering in the field of lead-free halide perovskite materials.

8.7.   Engineering photoelectric properties

Ferroelectrics, dielectrics, piezoelectric, pyroelectrics, electro- and photocatalytic properties, thermoelectric properties, electrical transport properties, and other optoelectric properties have not been studied ^{[11,20,171,187,188]}. Optical transition in identical inversion symmetry is symmetry forbidden, leading to poor optical absorption, as shown in Figure 9a ^[189]. For instance, in Cs₂AgTlCl₆ the band gap transition at contains the A_1g orbital in the CB and E_g orbital in the VB (Figure 9b) owing to grade symmetry, which results in forbidden band gaps. Furthermore, the optical transition from to L progressively becomes allowed (Figure 9c). Such isoelectronic properties are observed in Cs₂AgInCl₆, where Figure 9d shows the formation of a new conduction band owing to increasing Tl³⁺ concentration in Cs₂Ag(Bi_1−xTl_x)Br₆. Introducing Tl³⁺ reduces the band gap of Cs₂Ag(Bi_1−xTl_x)Br₆ since the Cs₂AgBiBr₆ band includes Tl³⁺ 6s orbitals (Figure 9d) ^[189]. From this perspective, the band structure depends on the composition of metal atoms incorporated in the structure of the semiconductor.

Moreover, the microscopic physics related properties that mater the photovoltaic effect are vital properties in the field of photovoltaics. This property becomes inadequately known and tarnished when we discover the double perovskite solar cells. Furthermore, diverse methods have been suggested to explain research outputs in a variety of device architectures, such as asymmetric momentum distribution of the non-equilibrium carriers ^[190,191], shift in current through coherent evolution ^{[192,193,194]}, polarization-dependent interfacial band bending ^[195,196], and bulk depolarization field ^[195].

From a material properties and applications perspective, understanding and extracting information on the presence or absence of ferroelectrics in halide perovskite materials will greatly contribute to multifunctionalities in the field of electronics beyond photovoltaic; additionally, symmetry and structure of the crystalline unit cell determines the ferroelectricity of materials ^[197]. For ferroelectricity to be detected, the primary requirement is the presence of a non-centrosymmetric unit cell. According to the definition of Anderson and Blount ^[198], a ferroelectric material has to encompass several criteria: (1) a continuous structural transition; (2) a non-centrosymmetric low temperature structure; and (3) a structure with a unique polar axis (a rotational axis of symmetry without a mirror plane perpendicular to it) at low-temperatures ^[199,200]. All these properties clarify the origin of ferroelectricity ^[201]. Whether or not a material has such a polar axis is decided exclusively by its crystal structure and creates the delicate variation between pyro- and piezoelectric. LiOsO_3, whose existence was first predicted half a century ago ^[202] has been identified ^[203] as an example of a ferroelectric metal, and has been established. It is likely that materials in this class could show some attractive physical properties. For instance, at enhanced temperatures, the existence of ferroelectric-like soft phonons can stabilize non-centrosymmetric superconductivity ^[204].

In addition to this, there are essential situations for bulk ferroelectricity to be present ^[205]: (1) noncentrosymmetric properties without inversion symmetry; (2) characteristic polarity; (3) an assembly of polar unit cells facing a similar direction that can make a "polar domain"; and (4) polarization switching. In addition to the electrical responses, ferroelectricity can be structurally explained using periodically ordered polar domains. Like the other ferroelectric materials, the relationship between the crystal thickness, D, and domain periodicity, ω, obey the Landau–Lifshitz–Kittle model scaling relationship as ω ~D^0.6 for MAPbI₃ perovskites. Due to differences in doping, the crystal synthesis could affect the ω–D relation. Derived from the periodic structure and etching, the domains appear to develop a head-to-head orientation.

Based on these facts, ferroelectricity in halide perovskites remains elusive. Inorganic materials with ferroelectric properties like BiFeO₃ have revealed a huge possibility in many other functionalities beyond photovoltaic ^[206]. At this time, application in optoelectronic devices and the related semiconducting properties of stannate or hybrid organo-plumbate become burning issues. With respect to their structural properties, these materials are appropriate for investigation regarding ferroelectricity ^[207]. As a result, the architecture of molecular ferroelectric semiconductors based on these materials demonstrates an opportunity to get novel or high-performance semiconductor ferroelectrics. In this section, we will address ferroelectric properties in both halide perovskite and fully inorganic perovskites. Until now, since this is a greatly arguable matter, additional proof for ferroelectricity of the material has to be present and is, therefore, shown. With the application of steady-state conditions, very important points become energetic as follows ^[205,208]:

(a) Buildup of unlike charged species at the outer surface of the polar bulk (e.g., adsorption of free charges or charged molecules from the adjacent electrodes or environment, respectively). This event, known as "pyroelectricity", is straight confirmation for accessible polarity. Previously, a clear experimental proof demonstrated that at room temperature (RT), cubic MAPbBr₃ is not pyroelectric ^[209]. In addition, it has been evidenced practically that tetragonal MAPbI₃, is pyroelectric ^[205].

(b) Buildup of mobile holes and electrons from the polar bulk material can happen if the bulk materials is adequately conductive, beyond ~10⁻⁶ S·cm⁻¹, a sensible value for a low bandgap semiconductor, like that of MAPbI₃. Thus, leakage currents ought to govern the dielectric response and are influenced by the bulk overall polarization ^[205].

(c) Stacking of domains of contrary polarity to reduce Coulomb repulsion, except at the price of creating a "domain-wall". For several famous ferroelectric materials, the periodicity between the domains, ω, scales with the crystal thickness the length of its polar axis, D, as ω ~ D^γ, where γ is the power reliance that is hypothetically equivalent to 0.5 ^[210,211]. The tetragonal MAPbI₃ follows this rule ^[205].

(d) Accordingly, the quarrel on ferroelectricity in MAPbI₃ has not been concluded with clear termination, which inspires us to review ferroelectric behavior of various perovskite materials such as MAPbI₃, FAPbX₃, CsSnI₃, RbSnI₃, and layered and double perovskites in the next subsections.

Domains created by the sharing of spontaneous polarization in space are important to characterize ferroelectric materials. These domains, in a given ferroelectric material, are illustrated in Figure 10. Arrows point out the trend of net polarization in domains and the constituent of the polarization vector. The constituent of the polarization at a 90° angle to the domain boundary leads to a bound charge at the boundary, as shown in Eq 1 ^[212,213]:

where, ρ_pol is the bound charge density. This bound charge gives rise to a depolarizing electric field in a reverse direction to the spontaneous polarization. The existence of strongly-ordered polarized domains in the perovskite gives rise to the formation of channels for minimizing charge recombinations and efficient charge transports in the device, which result in a high short-circuit current (JSC) and fill factor (FF). This important domain ordering is, nevertheless, doubtful to take place in actual devices. In the case of arbitrarily interrelated polarization in domains, a realistic scenario, it has been illustrated that holes and electrons emerge to pursue pathways or channels in the perovskite, leading to lower charge recombinations and efficient charge transports in the photovoltaic cell as proved by high FFs ^[213].

The P_i (C·m⁻²) polarization is produced in dielectric and insulating materials with the application of the electric field vector E_i (V·m⁻¹) (Eq 2):

where χ_ij (F·m⁻¹) is the 2^nd-rank tensor identified as the material's dielectric susceptibility. Eq 2 is valid only in a linear limit for nonlinear materials or for linear materials. Generally, the polarization, P_i, depends on higher-order terms of the field. Similarly, the total surface charge density induced in the material by applying the applied field is obtained using the dielectric displacement vector, D_i (C·m⁻²), shown in Eq 3:

Scalar ε₀ = 8.854 × 10⁻¹² F·m⁻¹ and is called the dielectric permittivity of a vacuum. Thus, Eq 4 is obtained from Eqs 2 and 3, that:

where δ_ij is Kronecker's symbol and ε_ij = ε₀δ_ij + χ_ij is the material's dielectric permittivity. δ_ij = 0, for i ≠ j; δ_ij = 1 for i = j. In most ferroelectric materials, ε_ij ≠ χ_ij and ε₀δ_ij ≪ χ_ij. In fact, the comparative dielectric permittivity, k_ij = ε_ij/ε₀, identified as a material dielectric constant is usually taken compared to the dielectric permittivity. Taking free energy opinion, it can simply be illustrated that χ_ij (also ε_ij and k_ij) have to be a symmetrical tensor (χ_ij = χ_ji) with only six autonomous mechanisms ^{[214,215,216]}.

Like ferroelectrics, it would of great interest to deal with and understand piezoelectric properties and applications of halide perovskite materials. The word piezoelectrics is used to explain attractive properties of technological important classes of materials with a diversity of functionalities, ranging from ultrasound transducers, fuel injectors, and waveguide devices to gyroscopes and accelerometers ^{[217,218,219]}. It is of high technological interest to explore the piezoelectric properties of the hybrid perovskites for applications such as piezoelectric generators or energy harvesting devices ^[220,221]. In this section, origin of piezoelectrics, the sunrise of piezoelectrics, methods to enhance hybrid perovskite piezoelectrics, possibility of constructing dampers, and low loss piezoelectrics are issues that should not be missed while studying piezoelectrics. Other important points are also discussed.

The piezoelectric effect consists of strain development under the application of an electric field. Moreover, piezoelectricity is a basic procedure that includes multiple piezoelectric equations and diverse electromechanical effects. The direct piezoelectric effect relates to the produced polarization that builds up in i direction (ΔPi) with an applied stress in direction j (σ_j in Voigt notation) as in Eq 5 ^[222]:

where, d_ij is 3rd-rank tensor, and every d_ij is typically called a piezoelectric coefficient or direct piezoelectric strain coefficient in units of pC/N. An additional piezoelectric equation between the polarization with the strain η is specified by Eq 6 ^[222]:

where the e_ij is the piezoelectric stress coefficient in the unit of C/m². It is indicated that the d_ij and e_ij parameters are associated with each other using stiffness and/or elastic compliances, though d_ij is simple to determine experimentally. The total generated polarization articulated in the c direction is given by Eq 7 ^[222]:

where, Eqs 8 and 9 are obtained:

are strains along the x, y, and z axis, with x₀, y₀, and z₀ as lattice constants for a structure not strained.

In order to disclose the source of piezoelectricity ^[223], it is important to split the total polarization originated from contributions of the (1) A-site MA cations and (2) B-site Pb atoms. The Pb atom induced polarization is measured using D(Pb)/Vu × P_Pb = Z₃₃ ^[222], where Z₃₃ is the Born effective charge of Pb, D(Pb) is the average displacement of Pb alongside the c axis with respect to the center of its I₆ cage, and Vu is the volume of the primitive unit cell. Thus, +4.24 is the measured value from the contribution of Z₃₃, which is considerably greater than the supposed charge of Pb (+2.0) in a pure ionic image ^[222] that implies the presence of a dynamic charge transfer coupled with the change of Pb–I bond length and the strong covalence of the Pb–I bonds. It is obvious that both molecular dipoles and Pb displacements are in charge of the total polarization in which Pb atoms contributes nearly all the piezoelectric response with negligible contribution from the MA⁺ molecules.

In perovskites with unusual atomic substitutions in the ABX₃ architecture, the competition between B–X metal-halide bond and A–X hydrogen bond monitors the piezoelectric characteristics, drawing attention to the perspective of a halide perovskite design for manipulative and useful photopiezoelectrics and photoferroelectrics ^[222], such as applications in sensors, actuators, and energy harvesting ^{[219,224,225,226]}. Because of the pairing of semiconducting properties with its piezoelectrics, micro- and nanowires of piezoelectric semiconductors have been utilized as fundamental building blocks for developing ground-breaking devices ^[227], including piezo-phototronic devices ^[228,229], piezoelectric diodes ^[230], piezoelectric field-effect transistors ^[231], piezoelectric chemical sensors ^[232], and nanogenerators ^{[233,234,235]}.

Thus, halide perovskites possess a cubic crystal structure that gives rise to ferroelectric polarizations similar to other classes of perovskites with identical structural characters ^{[180,236,237,238,239]}. Coll et al. have demonstrated the polarization switching and light-enhanced piezoelectricity of CH₃NH₃PbI₃ materials ^[240]. Furthermore, an output piezoelectric of 2.7 V and 140 nA·cm⁻² have been reported ^[241], hindering the practical functionalities due to its modest output performance. Moreover, the highest piezoelectric current density and output voltage of 3.8 μA·cm⁻² and 8.5 V have been demonstrated from the piezoelectric nanogenerator under periodically vertical compression. Multilayered halide perovskites even have large polarization or strong piezoelectricity ≈1540 p·CN^{−1 [242]}. This output is quite promising compared to other literature reports ^[243]. This could help charge LED and capacitors through a bridge rectifier.

8.8.   Interface and defect engineering

In the field of halide double perovskites, the interfacial properties, especially those between the active perovskite layer and hole transporting layers, are not well touched. Recently, using Cu₂O as hole transporting material, a power conversion efficiency of 11.32% Cs₂AgBiBr₆ based solar cell was achieved, as indicated by the numerical simulations ^[244]. This indicates that the hole transport layer with a suitable alignment to the active layer makes an efficient charge transport process that can improve the challenges faced by Cs₂TiBr₆ and Cs₂AgBiBr₆. Furthermore, the grain boundary interfaces present in the active perovskite layer in addition to the other grain boundary interfaces present between various layers is a vital research lesson for improving the PEC and the performance. This is because considerable detrimental trap states in the electronic state of the valence and conduction band states of the halide double perovskite semiconductors might exist, which increases the carrier recombination rate and reduces the open circuit voltage significantly. Therefore, the engineering of the grain boundaries to eliminate the detrimental trap states in polycrystalline thin films becomes a long-standing and important issue for high performance optoelectronic devices ^{[245,246,247,248,249]}. In addition to the detrimental trap states, understanding the defect properties of the surface and bulk perovskite films, grain boundary, and surface passivation mechanisms, defect properties of the interface during engineering the device architecture is quite a crucial aspect that needs serious interface and defect engineering ^[245,246].

Moreover, Cs₂TiBr₆ is reported as a sensitive material to defect density ^[44,250,251] though it demonstrates a power conversion efficiency of 14.8% ^[252]. If all possible solar parameters are optimized, this solar material is a promising candidate for the future of peroveskite solar cells. Moreover, the numerical approach shows that a power conversion efficiency of 24.49% can be achieved by Cs₂PtI₆-based Cs₂TiBr₆ perovskite solar cells while Cs₂TiBr₆ is just 9.81% if it is well optimized ^[253]. Furthermore, the poor device performance of Cs₂TiBr₆ based peroveskite solar cells is because of the bulk defect present within the Cs₂TiBr₆ active light absorbing layer. Hence, defect passivation approaches are expected to solve defect related challenges in these materials. Thus, based on this defect optimization method, 9.9% efficiency has been achieved for Cs₂TiBr₆-based peroveskite solar cells ^[254]. Defects are also important to reconstruct band edges as shown in Figure 11. Such defects are intentionally incorporated defects useful to create new semiconducting materials ^[245]. The dominant metal orbital character of the bands is shown in color. Arrows show the direct (Figure 11a, b, (MA)₂TlBiBr₆) and indirect (Figure 11c, Cs₂AgBiBr₆) band gap transitions. In the primitive unit cell of 1 the VBM appears at X, however, in the conventional setting shown in Figure 11 the VBM is at Γ owing to band folding.

8.9.   Device architectural engineering

Engineering the light harvesting active halide double peroveskite layer and interface between the active layer and different charge transporting layers as well as between the transporting layers and the charge collecting electrodes are indispensable prerequisites for appreciable performance. However, engineering the materials and the interface among various layers is not adequate. This is because the closing stages are eventually paying attention to the device performance for a specific application. As a result, engineering appropriate device architecture ^{[255,256,257]} is mandatory.

8.10.   Doping engineering

Halide double perovskites become less suitable solutions to replace the unstable organic-inorganic halide perovskite solar cells. This is due to their indirect or direct as well as larger band gaps ^[18,40,147]. Therefore, doping engineering ^[18,200] is another strategy to achieve a band gap, which is suitable for light harvesting applications ^{[23,185,258,259,260]} This along with a chemical substitution approach might be done in all lattice sites of the double perovskite (A₂(B⁺, B³⁺)X₆) available for substitution ^[23,185,258]. In this case, the degrees of freedom, with over 34 choices of trivalent metals available for selection, are mostly provided from the B³⁺ lattice site ^{[259,260,261]}.

8.11.   Equilibrium and non-equilibrium quantum transport

These transport properties and the effect of the spin-orbit on these properties is unclear: Studies on these properties could shed light to provide insightful understanding on why inferior device performances of halide double perovskites solar cells are happening.

9.   Conclusions

A₂B^ⅠB^ⅢX₆ based lead-free halide double perovskite solar cells have been reported as promising nontoxic and stable candidates to replace organic-inorganic halide perovskite solar cells. Thus, such lead-free halide double perovskites have a (1) diversity of various families, (2) diversity of structural, optical and electrical properties, and (3) wide range of energy applications. Furthermore, the key origins of these diversities and variations are: cation displacement, cation anion ordering, ordered vacancies, tuneability of structural dimension, octahedral distortions, and tilting from the ideal structure. In addition, polarization, molecular dipoles, and tilting on the band structure are key origins of optoelectronic properties in halide double perovskites. Although lead-free halide double perovskite solar cells have promising opportunities such as a relatively longer photoluminescence lifetime and higher stability towards moisture, temperature, and light compared to lead halide perovskites, these solar cell devices have bottleneck challenges at material, interface, and device levels. Such challenges include: (a) inferior material and device power conversion efficiency, which is 2.5% using Cs₂AgBiBr₆ and 3.3% using Cs₂TiBr₆; (b) limited integration with interfacial materials; (c) quantum confinement effect of interacting orbitals of adjacent cations, which might result in broader band gaps and localized conduction bands; (d) high processing temperature, which may limit the diverse applications; and (e) low electronic dimensionality, making them less appropriate for single junction solar cell functions. Thus, it is suggested that material surfaces and bulk engineering, device architectural engineering, interfacial engineering, composition engineering, band gap engineering, doping engineering, polar and domain order engineering, etc., may be possible mechanisms to overcome the challenges. In addition, promising candidate characteristics, for instance, long charge carrier diffusion lengths, defect tolerance, low exciton binding energies, small carrier effective masses, intrinsic thermodynamic stability, direct band gaps, high absorption coefficient, and compatibility with low-cost and solution-supported fabrication procedures are highlighted for further considerations. This review will serve as a research roadmap for performance improvement for the lead and tin free halide double perovskite solar cell scientific community, research institutions, and commercial enterprises. Moreover, the challenge in most solar cells is the issue of sustainability.

With this in mind, the sustainability issue of A₂B^ⅠB^ⅢX₆ such as Cs₂AgBiBr₆ and Cs₂TiBr₆ perovskite solar cells shall be analyzed not only in terms of the balance among environment, equity, economy, affordability, energy independence, availability of desirable materials, and conditions over the long term but also the quality of being able to continue over a period of time. Thus, the researchers have to work in a way that they can confirm the sustainability issue of A₂B^ⅠB^ⅢX₆ based perovskite solar cells.

Use of AI tools declaration

The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.

Author contributions

The first author, Etsana Kiros Ashebir, is responsible for manuscript writing, literature review, and the conceptualization, while Berhe Tadesse Abay is participated as a co-member of the project, bringing in expertise in materials properties and assisting with data analysis. Taame Abraha Berhe is main advisor of the research project, providing guidance and expertise in the field of halide double perovskite solar cell as well as serving the corresponding author of the idea and content designer. All authors have read and approved the final manuscript.

Conflicts of interest

The authors declare no conflict of interest.