Quantifying Efficiency Limitations in All‐Inorganic Halide Perovskite Solar Cells

While halide perovskites have excellent optoelectronic properties, their poor stability is a major obstacle toward commercialization. There is a strong interest to move away from organic A‐site cations such as methylammonium and formamidinium toward Cs with the aim of improving thermal stability of the perovskite layers. While the optoelectronic properties and the device performance of Cs‐based all‐inorganic lead‐halide perovskites are very good, they are still trailing behind those of perovskites that use organic cations. Here, the state‐of‐the‐art of all‐inorganic perovskites for photovoltaic applications is reviewed by performing detailed meta‐analyses of key performance parameters on the cell and material level. Key material properties such as carrier mobilities, external photoluminescence quantum efficiency, and photoluminescence lifetime are discussed and what is known about defect tolerance in all‐inorganic is compared relative to hybrid (organic–inorganic) perovskites. Subsequently, a unified approach is adopted for analyzing performance losses in perovskite solar cells based on breaking down the losses into several figures of merit representing recombination losses, resistive losses, and optical losses. Based on this detailed loss analysis, guidelines are eventually developed for future performance improvement of all‐inorganic perovskite solar cells.


Introduction
Lead-halide perovskites exhibit a range of properties that are attractive for optoelectronic and in particular photovoltaic applications. These properties include the ease of fabricating perovskite thinfilms with exceptionally long chargecarrier lifetimes and a steep absorption onset leading to absorption coefficients >10 4 cm −1 only a few meV above the bandgap. [1] Within the family of leadhalide perovskites the best optoelectronic properties are achieved for a range of bandgaps of around 1.5 to 1.8 eV which is a highly useful range for the application as higher-bandgap absorber in tandem or triple-junction solar cells. [2] In this range of bandgaps, perovskites have only III−V semiconductors as viable competition, [3] but have the advantage of substantially lower fabrication cost. While there are many direct semiconductors with good absorption and suitable bandgaps for photovoltaics, [4] there are very few that have so low non-radiative recombination losses and such high luminescence quantum efficiencies as lead-halide perovskites. [5][6][7] This is achieved not only in single crystals but also in polycrystalline thin films. [8] A specific reason for the good performance of these polycrystalline materials is the antibonding valence band of lead-halide perovskites that leads to shallow intrinsic defects [9] and has earned the family of lead-halide perovskites the label "defect-tolerant semiconductor". [10,11] There are two key downsides of the technology that are currently standing in the way of commercialization: [12] One is the long-term stability of the material and the other one is the use of the toxic element lead that is, however, of crucial importance for understanding the superior optoelectronic properties [11] and is therefore difficult to replace. There are various strategies to either replace lead, reduce it or contain it safely inside the film. [13] In terms of improving stability, one major approach of increasing importance in the community is to replace the organic cations methylammonium or formamidinium that are typically used so far with inorganic elements such as Cs. [14] The key challenge here is that the perovskite structure (ABX 3 ) as shown in Figure 1a has to contain A-site cations of an appropriate size to stabilize the BX 6 octaeder at the core of the perovskite structure. Given the relatively large size of Pb and I or (to a lesser degree) Br, the A-site cations have to be large enough.
While halide perovskites have excellent optoelectronic properties, their poor stability is a major obstacle toward commercialization. There is a strong interest to move away from organic A-site cations such as methylammonium and formamidinium toward Cs with the aim of improving thermal stability of the perovskite layers. While the optoelectronic properties and the device performance of Cs-based all-inorganic lead-halide perovskites are very good, they are still trailing behind those of perovskites that use organic cations. Here, the state-of-the-art of all-inorganic perovskites for photovoltaic applications is reviewed by performing detailed meta-analyses of key performance parameters on the cell and material level. Key material properties such as carrier mobilities, external photoluminescence quantum efficiency, and photoluminescence lifetime are discussed and what is known about defect tolerance in all-inorganic is compared relative to hybrid (organic-inorganic) perovskites. Subsequently, a unified approach is adopted for analyzing performance losses in perovskite solar cells based on breaking down the losses into several figures of merit representing recombination losses, resistive losses, and optical losses. Based on this detailed loss analysis, guidelines are eventually developed for future performance improvement of all-inorganic perovskite solar cells.
where r A , r B , and r X are the radii of the corresponding ions [15,16] provides some orientation. If t deviates from the range of 0.8-1.0, the compositions are unlikely to form a stable perovskite phase. [16,17] Figure 1b shows the Goldschmidt tolerance factor varying with A-site cation radius for APbI x Br 3−x perovskites. Though Cs is the largest suitable element with oxidation state +I, it's ionic radius is slightly too small so that Cs-based compositions with Pb and a halogen atom have tolerance factors that are at the lower end of the range of Goldschmidt factors that likely lead to the formation of a stable perovskite phase. By contrast, the MA + leads to a Goldschmidt factor that is in the middle of the stable region while the FA + is a bit too large leading to Goldschmidt factors at the upper end of the stable region. Mixing Cs + and FA + cations can lead to a more suitable tolerance factor and is frequently used in the development of efficient perovskite-based solar cell materials. [18] In addition, from the lines shown in the figure, we can find that the tolerance factor increases when the anion changes from I − to Br − , due to the smaller radius of Br − . As shown in Figure 1c, the tolerance factor of CsPbI 3 is close to 0.8, i.e., close to the lower end of the stable region making it challenging to stabilize the perovskite phase of CsPbI 3 . [19,20] By decreasing the x value, the tolerance factor t of CsPbI x Br 3−x (0 ≤ x ≤ 3) increases, which is beneficial for the phase stability. In 2012, the first all-inorganic halide perovskite solar cells with a structure of indium tin oxide (ITO)/CsSnI 3 /Au/Ti were reported. However, the power conversion efficiency (PCE) was only 0.88%. [22] In 2016, Luther and co-workers have fabricated all-inorganic perovskite solar cells based on CsPbI 3 quantum dots (QDs) with a PCE over 10%. [23] Since this publication in Science, interest in the field of all-inorganic perovskite solar cells has been growing rapidly. As shown in Figure 2a, the numbers of published articles related to all-inorganic perovskite solar cells is steadily increasing. In 2014, only 0.7% of perovskite solar cell related papers focus on all-inorganic perovskites (based on Web of Science database). However, now in 2021, the proportion of articles has risen up to 4.3% and it continues rising. In Figure 2b, the development of champion efficiencies varying with the accumulated number of related articles is presented. We observe that the PCE of all-inorganic perovskite solar cells has increased from 0.09% in 2014 [24] to over 20% in 2021 [25] with ≈950 published articles. This quantity of articles is close to that for the hybrid perovskite solar cells achieving 20% PCE. Moreover, from the experience of the traditional perovskite solar cells development, it is clear that improvements beyond 20% become increasingly difficult and require more additional papers per additional % efficiency (note the logarithmic x-axis in Figure 2b). Hence, while more efforts are needed to further increase efficiencies of all inorganic solar cells, it seems that the development so far did not require a substantially higher amount of work (measured in the number of accumulated publications) than for hybrid perovskites.
Up to now, the champion PCE of CsPbI 3 -based PSC has reached 20.37% which was reported by Sang Il Seok's group [25] while the optimal certified PCE is 18.3%, achieved by Yixin Zhao's group. [26] Apart from CsPbI 3 (whose bandgap (E g ) is estimated to be ≈1.7 eV), all-inorganic perovskite solar cells based on CsPbI 2 Br (E g ≈ 1.9 eV), CsPbIBr 2 (E g ≈ 2.1 eV) and CsPbBr 3 (E g ≈ 2.3 eV) are rapidly developing as well. Figure 2c presents the champion PCE of all-inorganic CsPbI x Br 3−x (0 ≤ x ≤ 3) perovskite solar cells as a function of time. As expected by the optimum bandgap range in the Shockley-Queisser model [27] (see Figure 2d), the composition with the lowest bandgap, i.e., CsPbI 3 , has consistently led the field in PCE, achieving 20.37% PCE, [25] followed by 19.65% [28] PCE for CsPbI x Br 3−x (2 < x < 3) perovskite solar cells and 17.36% [29] PCE for CsPbI 2 Br perovskite solar cells, whereas the CsPbIBr 2 and CsPbBr 3 perovskite solar cells show relatively low PCE of 11.3% [30] and 10.85% [31] respectively. In addition, hybrid perovskite solar cells are shown for comparison (majority of them have been recorded in the Best Research Cell Efficiencies Chart by NREL). [32] It can be found that the PCE of all-inorganic perovskite solar cells is still somewhat behind that of the hybrid species which have already reached 25.5%. [32] Figure 2d depicts the champion efficiency of different solar cells and the Shockley-Queisser limit along with bandgap values. It is clear that there is still large room for efficiency improvement of all-inorganic perovskites, compared with the c-Si, GaAs and hybrid perovskite solar cells. [33] Adv. Mater. 2022, 34, 2108132 Figure 1. a) Structural diagram of APbX 3 perovskite. b) Goldschmidt tolerance factor along with A-site cation radius for APbX 3 perovskite with different X species. c) The partial enlarged details related to pure CsPbI x Br 3−x perovskites. The curve and point values were calculated according to the following cation radii: Cs + ≈169 pm, [20] MA + ≈217 pm, [21] FA + ≈253 pm, [21] Pb 2+ ≈120 pm, [20] I − ≈220 pm, [20] Br − ≈196 pm. [20] It should be noted that as the bandgap increases, both the efficiency limit and actual efficiency decrease. Though the PCE values of all-inorganic perovskite solar cells with high Br contents seem not pretty appealing, it is satisfying that the stability and reliability become better and better. Furthermore, if taking the thermodynamic limits into account, we can find that the η/η SQ values of many all-inorganic perovskite solar cells have approached 70%, which means further performance improvement would become more difficult. Therefore, precise and reliable meta-analysis of performance losses become desiderated, which could be conducted to point out the directions for further optimization.
In the following, we will discuss the material properties of all-inorganic halide perovskites, present the typically used device geometries and then present a detailed meta-analysis of the current state of the art of this technology. The meta-analysis will focus especially on the analysis of different efficiency limitations such as recombination losses, resistive losses and optical losses.

Material Properties
Any solar cell absorber material has to fulfil some necessary conditions to allow its use in high-efficiency solar cells. These conditions are to have a suitable absorption coefficient, good charge transport measured via the electron and hole mobilities as well as a long lifetime of charge carriers. [34] The latter argument is often rephrased as having a low defect density because short lifetimes are typically related to a high defect density. In the following, we will therefore give an overview over these three properties and discuss their change with stoichiometry and bandgap as well as compare them with hybrid perovskites.

Absorption Coefficient and Bandgap
Excellent photon absorption is a precondition for perovskites to be used in optoelectronic and photovoltaic applications. Hybrid lead-halide perovskites have been shown to have fairly sharp absorption coefficients that rise quickly above the bandgap to reach values >10 4 cm −1 already few tens of meV above the bandgap. [1] This allows efficient solar cells to have absorber thickness below 1µm and still achieve sharp onsets of the quantum efficiency. For all-inorganic lead-halide perovskites comparably little data is available on the absorption coefficient. Judging from available quantum efficiency data and the typical thicknesses used for efficient devices, the absorption coefficient is likely rather similar to that of hybrid perovskites. However, more detailed studies are missing. This is true for the overall value of the absorption coefficient but also for the shape of the absorption onset and parameters such as the Urbach energy, [63] which can be determined, e.g., from photothermal deflection spectroscopy or sensitive photocurrent spectroscopy methods such as FTPS (Fourier transform photocurrent spectroscopy). [64] Note that Urbach energies cannot reliably be determined from the frequently used UV−Vis transmission (T) & reflection (R) spectroscopy, because this method is not suitable to precisely determine low absorptance (A) values, where A = 1 − R − T is close to zero and R + T ≈ 1. In this case, small errors in R and T, will lead to large relative errors in A that prohibit a precise determination of the Urbach energy.
While there is-to our knowledge-no systematic investigation into the absolute values of the absorption coefficient or the sharpness of the absorption onset as a function of stoichiometry in the family of all inorganic perovskites, it is worth to briefly discuss the obvious change in bandgap that we have already mentioned in the context of Figure 2. Figure 3a presents the bandgap comparison of CsPbI x Br 3−x , MAPbI x Br 3−x and FAPbI x Br 3−x (0 ≤ x ≤ 3) varying with stoichiometric ratio of iodine. Note that the bandgap data for MAPbI x Br 3−x and FAPbI x Br 3−x come from the related references, [35] while those for CsPbI x Br 3−x are calculated by EQE inflection point method. [65] The detailed description of this method can be found in the Supporting Information (Section 1.1). It is observed that the bandgap of Cs + -based perovskite is wider than the MA + and FA + -based samples. Taking x = 3 as an example, the bandgap for CsPbI 3 , MAPbI 3 and FAPbI 3 is ≈1.71 eV, ≈1.58 eV and ≈1.47 eV respectively. In addition, for all the perovskite species, the bandgap decreases with increasing x values. Furthermore, with the cation changing from FA + , MA + to Cs + , the relation between bandgap and x value varies from nonlinear to linear. For all-inorganic perovskites, the relation could be ascribed as: E g ip = 2.314 − 0.205x. The distribution of E g ip for all-inorganic perovskites is shown in Figure 3b. It can be found that the E g ip of CsPbI 3 , CsPbI 2 Br, CsPbIBr 2 and CsPbBr 3 is around ≈1.71 eV, 1.90 eV, 2.11 eV and 2.32 eV respectively, showing that varying x value of CsPbI x Br 3−x (0 ≤ x ≤ 3) is an effective approach for bandgap regulation. The slight difference of E g ip in each group could be due to the fact that the bandgap of the samples would be affected by process technique, component stoichiometry, phase structure and temperature during actual preparation.

Charge-Carrier Mobilities
A further prerequisite for high photovoltaic performance is that the absorber material should have a sufficiently high mobility−lifetime product to allow efficient charge extraction before recombination happens. [34] Depending on the exact device geometry and the presence or absence of electric fields, the mobility lifetime product may be replaced by either the diffusion length or the drift length. [82] Thus, it is not possible to a priori state a certain minimum mobility or lifetime or even mobility−lifetime product necessary to allow efficient photovoltaic energy conversion. However, it is generally true that efficient charge transport is a necessary but not sufficient condition for any solar cell material. Figure 4a gives an overview over the mobility results for lead-halide perovskites. For all-inorganic components, the CsPbIBr 2 exhibit relatively lower mobilities as compared to other compositions. A possible reason could be attributed to worse film quality and higher defects density. [70] CsPbBr 3 presents the maximum mobility value. Song et al. have prepared CsPbBr 3 single crystals (SC), achieving an attractive carrier mobility over 2000 cm 2 V −1 s −1 measured using SCLC methods, [77] which is the highest reported value among all-inorganic perovskites so far. As for comparison between hybrid and all-inorganic perovskites, CsPbI 3 , CsPbI 2 Br and CsPbBr 3 components present competitively high mobilities if compared with FAPbI 3 -and MAPbI 3 -based samples, some of which have reported mobilities beyond 10 2 cm 2 V −1 s −1 . [69,73,75,77] However, it should be noted that at present there are many techniques for mobility measurement, which would therefore result in difference among the reported mobility results. As shown in Figure 4b, the mobilities measured by FET, SCLC and PL-based methods generally present relatively lower values, while those determined by Hall effect measurement, time-resolved microwave current (TRMC) and THz-probe spectroscopy (OPTP) commonly show higher values. Figure 4c shows the average mobility values and standard deviations for each method. Apart from the "else" methods, the THz spectroscopy, SCLC and Hall methods always show larger fluctuations.

Defect Tolerance and Nonradiative Recombination
The concept of "defect tolerance" [11] is a widely used attribute for halide perovskites, as they still possess outstanding optoelectronic properties even if they are processed from solution and form polycrystalline films with micrometer-sized grains and the associated grain boundaries. Originally, based on density functional theory (DFT) calculations, all energetically favorable intrinsic defects in perovskites were considered to be fairly shallow and in consequence were expected to have less impact on photogenerated carrier recombination, which is the so-called "shallow defect hypothesis". [83,84] However, further research found that at least the iodine interstitial should be a deep defect of some concern for the functionality of the device. [85][86][87] Long carrier lifetimes are one of the results of "defect tolerance. Figure 5 shows the relationship between PL lifetime τ and nonradiative open-circuit voltage loss V ∆ oc nonrad . Detailed information of the data points were shown in Table S1 (Supporting Information, Section 2). In addition, the corresponding external luminescence quantum efficiencies Q e lum have also been calculated via the following expression where q is the elementary charge, k is the Boltzmann constant and T is the cell temperature, [88] while oc nonrad oc The details for voltage loss calculation are introduced in Supporting Information (Section 1). We find that the CsPbBr 3 and CsPbIBr 2 groups exhibit shorter lifetime and higher V oc loss as well as lower Q e lum . In contrast, the CsPbI x Br 3−x (2 < x < 3) and   [43,[70][71][72]73] CsPbIBr 2 , [74] and CsPbBr 3 . [68,75,[76][77][78] Mobility of FAPbI 3 [79] and MAPbI 3 [80,81] are also shown for comparison. The color code identifies the mobility characterization method used for each point. b) Mobility distribution of all stoichiometries shown above as a function of measurement method. c) Average mobility and standard error (the value shown in figure) of each measurement method. Please note that in the discussion of (b) and (c), we skip the mobility of CsPbIBr 2 as the values strongly deviated from other compositions. Hall: Hall effect measurement, SCLC: space-charge-limited current, TS: THz spectroscopy (including time-resolved THz spectroscopy and optical-pump THz-probe spectroscopy), TRMC: time-resolved microwave current, PL: photoluminescence spectroscopy (including time-resolved photoluminescence spectroscopy, photoluminescence quenching and electric field-modulated photoluminescence imaging microscopy), TRS: transient reflectance spectroscopy, FET: field-effect transistor, else (including time-of-flight, photoconductivity method, etc. with G ext = Φ/d, where Φ is the absorbed photon flux and d is the thickness. Furthermore, k rad , is the radiative recombination coefficient while p a , and p e are the parasitic absorption and emission probability as defined and discussed in more detail in ref. [90] Note that p e and p a are needed to correctly consider effects of photon recycling as discussed, e.g., in ref. [91] Finally, Equation (3) takes doping into account by allowing to set a value for the equilibrium majority carrier concentration p 0 . Here, we assume implicitly (by naming the variable p 0 ) that holes are the majority carriers but Equation (3) also works for n-type doping. Furthermore, the related results from high-quality organicinorganic hybrid perovskite solar cells have also been shown in the figure. [89] Evidently, as for all-inorganic perovskite solar cells, there is a distinct gap with the hybrid devices in terms of lifetime τ. Even for CsPbI 3 PSC which presented the optimal τ = 374 ns, [38] it is still over an order of magnitude shorter than the comparative optimal hybrid PSC. [92] Such results suggest the large room for PL lifetime improvement of all-inorganic perovskite solar cells, which is the key to achieve small V oc losses and high e lum Q . Long lifetimes, high luminescence quantum efficiencies and high open-circuit voltages are directly connected as discussed in the context of Equations (2) and (3). In order to achieve long lifetimes, a material needs a low defect density and/or a slow capture coefficient of electrons and/or holes by that defect. Thus, measuring and reducing defect densities has been an important topic for essentially all photovoltaic materials. However, in particular the measurement of defects is among the most difficult challenges in the field of material and device characterization for photovoltaics. This is at least partly due to the fact that extremely low densities of defects (relative to the total density of atoms or electrons in a material) may already have a decisive influence on device performance. There exists a multitude of methods that can-under certain conditionsallow the extraction of defect densities. However, these methods have often many caveats and can show features that may be falsely interpreted as trap densities. [93] For CsPbI 3 -based thin films, the trap density of 8.570 × 10 15 cm −3 [25] and 1.6 × 10 16 cm −3 [41] were obtained by the thermally stimulated current (TSC) and transient absorption spectroscopy (TAS) methods. Space charge limited current (SCLC) measurement is the most widely used method for trap density calculation in all-inorganic perovskites. However, the results from SCLC method should be treated with caution, because there are thickness dependent detection thresholds for detecting trap densities. [94][95][96] Thus, trap densities may actually be substantially lower than those measured in SCLC.
For the question of which kind of deep-level defect in allinorganic perovskites should be responsible for nonradiative recombination, the debate still continues and no consensus has been reached. Recent research based on first-principles calculations has demonstrated that iodine interstitials (I i ) and hydrogen vacancies (V H ) are the dominant defects for nonradiative recombination in MA + -containing hybrid perovskite films under I-rich and I-poor conditions respectively. [87,97] By contrast, V H has less effect on nonradiative recombination in FA + -containing perovskites, which might be a reason for why FA + is beneficial for achieving high performance in hybrid perovskites. [87] With regard to all-inorganic perovskites represented by CsPbI 3 , however, the existence of V H can be ruled out since it originates from FA + and MA + organic cations. Nevertheless, studies on I i for all-inorganic perovskite species have not been reported so far. In 2020, Zhang et al. have investigated deep defects Pb I and I Pb in CsPbI 3 . It has been revealed that the formation energy of I Pb is very low for I-rich conditions, while Pb I is energetically favorable under I-poor conditions. [86] In order to find out how detrimental a defect is, DFT calculations can provide access to parameters such as the capture coefficients of specific defects which can then be used to compare their relative impact. Before, we discuss the results of these calculations, let us briefly explain how these quantities affect the recombination rates. The capture coefficients C n and C p are a property of a defect that specifies how efficiently the defect captures either electrons or holes. If one multiplies the capture coefficient with the defect density N def , one obtains the inverse Shockley−Read−Hall lifetimes τ n and τ p for electrons and holes. These lifetimes then enter the Shockley-Read-Hall (SRH) recombination rate (R SRH ) and determine how many recombination events will happen per unit volume and time. The SRH recombination rate is often written as [89]   and valence band edges, n and p are the carrier concentration (for electrons and holes) and n i is the intrinsic carrier concentration. Assuming that the defect levels is sufficiently deep to make thermal detrapping unlikely, we can neglect n 1 and p 1 , as they will then be small relative to either n or p. Thus, Equation (4) is often simplified for deep defects to [89] Then we use the relations of τ n = 1/(C n N def ) and τ p = 1/ (C p N def ) [86,98,99] for the above equation. In case photogenerated or injected carrier concentrations are much larger than the intrinsic carrier concentration, then n i can be ignored. In addition, considering that lead-halide perovskites typically behave as intrinsic or low-doped semiconductors, then n = p can be applied. Thus we obtain [98] which can be rewritten to give [98] , SRH d ef tot t ot n p n p This implies the existence of effective carrier lifetime, defined by Accordingly, we observe that the total capture coefficient C tot is limited by the slowest capture process. In case of high C tot , the defect-assisted SRH recombination rate would increase, leading to a reduction in carrier lifetime τ eff . Figure 6a,b compare the capture coefficient curves of the deep-level defects in CsPbI 3 and MAPbI 3 . The data shown in Figure 6 is based on the calculation of potential energy surfaces and configuration coordinate diagrams of the different states involved in the recombination event using DFT. The DFT was performed using the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional including spin-orbit coupling. [86,87,97,100] Zhang et al. report I i to be the dominant defect in MAPbI 3 films having a low formation energy especially under I-rich condition. As shown in Figure 6a, the process of electron capture by I i + (i.e., C n + ) exhibits the slowest capture coefficient of 0.7 × 10 −8 cm 3 s −1 at room temperature, indicating the same order of magnitude for C tot . [97] As for CsPbI 3 , only I Pb deep defects have been shown to have low formation energies under I-rich condition so far. In Figure 6a, the electron capture by Pb 0 I (i.e., n 0 C ) is the slowest process, which limits the total capture coefficient on the order of 10 −14 cm 3 s −1 at room temperature. [86] On the other hand, Figure 6. a) Nonradiative capture coefficient of I i in MAPbI 3 films and I Pb in CsPbI 3 films as a function of temperature under I-rich condition. The curves were calculated by determining the potential energy surfaces using DFT (upper, Zhang et al., Reproduced with permission. [97] Copyright 2020, American Physical Society; lower, Zhang et al., Reproduced with permission. [86] Copyright 2020, American Chemical Society). b) Nonradiative capture coefficient of V H (N) in MAPbI 3 films and Pb I in CsPbI 3 films as a function of temperature under I-poor condition. (C n : electron capture coefficient; C p : hole capture coefficient.) (upper, Zhang et al., Reproduced with permission. [87] Copyright 2021, The Authors, published by Springer Nature; lower, Zhang et al., Reproduced with permission. [86] Copyright 2020, American Chemical Society). c) Comparison of capture coefficient under room temperature (300 K). the V H (N) in MAPbI 3 possess low formation energy (0.72 eV) under I-poor condition and its C tot curve is affected by both C n and C p . As shown in Figure 6b, the C tot depends on C n at room temperature, suggesting the C tot of 0.8 × 10 −4 cm 3 s −1 for V H (N) under this circumstance. [87] With regard to Pb I deep defects in CsPbI 3 under I-poor condition (Figure 6b), the C tot is limited by the hole capture coefficient of Pb I + (i.e., C p + ), which is only 10 −22 cm 3 s −1 . [86] Evidently, though Pb I and I Pb deep defects in CsPbI 3 possess low formation energy, both of them exhibit extremely slow C tot , which are much slower than the dominant deep defects (I i and V H (N)) in MAPbI 3 . Zhang et al. have attributed the low rates to the presence of strong anharmonicity in the potential energy surfaces that describe the charge-state transitions. [86] However, the dominant defects for nonradiative recombination in CsPbI 3 have not been identified yet. Additionally, it is observed that the capture coefficient for electrons is quite different from that for holes in perovskites, which can be better illustrated in Figure 6c. This result suggests a new route for the improvement of defect tolerance in perovskites. As demonstrated in ref. [101], when the capture coefficient for holes is higher than that for electrons, the recombination could be further reduced by slowing down the electron capture through reducing the electron concentration and increasing the hole concentration, [101] which is feasible during the preparation process. Moreover, as shown in Figure 6c, the C n of I Pb is 9 orders of magnitude lower than the related C p in CsPbI 3 , as well as the C p of Pb I is 14 orders of magnitude lower than the related C n . Such difference is much larger than that of I i and V H (N) in MAPbI 3 , which may be beneficial for the optoelectronic performance of CsPbI 3 -based devices.
Apart from CsPbI 3 , the formation energy and charge transition level of defects in CsPbBr 3 have been investigated by DFT calculation as well. Reported by Kang and Wang, most of the defects in CsPbBr 3 films are shallow, while the two antisite defects Pb Br , Br Pb , and the lead interstitial (Pb i ) can introduce deep transition levels. [83] Fortunately, these three deep-level defects have large formation energies which has been attributed to the lack of bonding−antibonding interaction between the conduction bands and valence bands. [83] In addition, Swift and Lyons have demonstrated that the hydrogen interstitial (H i ) and bromine interstitials (Br i ) are deep-level defects in CsPbBr 3 as well, and show relatively low formation energy under Pb-rich and Br-rich condition respectively. [85] However, their effect on carrier capture process is still unclear.
With regard to mixed halide all-inorganic perovskites, i.e., CsPbIBr 2 , CsPbI 2 Br, and etc., it is believed that phase segregation spontaneously happens when mixing different halogens because of the bonding energy difference between Pb-Br and Pb-I bonds. [102] Unfortunately, few theoretical studies focusing on deep-level defects in mixed halide perovskites have been reported so far and therefore more efforts on this topic are strongly needed.

Structure
At present, the typical layer stack of all-inorganic perovskite solar cells is identical to that of many organic-inorganic hybrid perovskite solar cells, which commonly includes FTO (or ITO) glass substrate, perovskite absorber layer, HTL, ETL and electrode, as illustrated in Figure 7. To be specific, it can be classified into several types, i) mesoscopic; ii) planar regular (n−i−p) and iii) planar inverted (p−i−n) structures. Many highly efficient CsPbBr 3 and CsPbIBr 2 perovskite solar cells with wide bandgaps have adopted carbon-based HTL-free structure, [103] which is partly because of the lack of highly efficient HTLs for them. For all-inorganic perovskite solar cells, fewer works with planar inverted structure have been reported, which results from the fact that the conventional organic transport layer materials (e.g., poly(triaryl amine) (PTAA) and poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS)) cannot withstand the typical temperatures of 200 °C to 250 °C used for annealing of inorganic perovskites. In this case, inorganic NiO x film is the most commonly used HTL for planar inverted devices. Alex K. Y. Jen's group has made substantial contributions to the field of inverted all-inorganic perovskites. The best efficiencies obtained in this structure was 16.10% (certified: 15.6%) using the layer stack ITO/NiO x /CsPbI x Br 3−x :6TIC-4F/ZnO/C 60 /Ag. [104] High PCE up to 20.37% has been reported for all-inorganic PSC with planar regular structure, [25] as well as 17.16% PCE for that with mesoscopic structure, [47] suggesting the large room for planar inverted all-inorganic perovskite solar cells improvement. Thus, more  efforts on inverted all-inorganic perovskite solar cells are needed, as well as on highly efficient inorganic HTLs exploration. Figure 8 illustrates energy levels of typical transport layer materials for highly efficient all-inorganic perovskite solar cells, along with that of perovskite absorber layers. For ETLs, TiO 2 , SnO 2 , ZnO and c-TiO 2 /m-TiO 2 are most commonly used for highly efficient perovskite solar cells, which are inorganic materials and have been fully investigated and optimized for hybrid perovskite solar cells. For perovskite solar cells with regular or mesoscopic structure, HTLs would not be affected by the high-temperature process, leading to a large variety of materials to choose. Apart from the most frequently used 2,2,7,7-tetrakis(N,N-dimethoxy-phenylamine)-9,9-spirobifluorene (spiro-MeOTAD) films, other organic materials, such as poly[bis-(4-phenyl)-(2,4,6-trimethylphenyl)-amine] (PTAA), poly(3-hexylthiophen-2,5-diyl) (P3HT) and poly[5,5′-bis(2butyloctyl)-(2,2′-bithiophene)-4,4′-dicarboxylate-alt-5,5′-2,2′bithiophene] (PDCBT), have also been reported for highefficient all-inorganic perovskite solar cells. Niu et al. have explored some D−A−π−A−D-type hole-transport materials which have advantages of dopant-free, low-cost and stable, and applied for CsPbI 2.5 Br 0.5 perovskite solar cells, achieving a PCE of 17.0%. [105] However, the conventional hole-transport materials are not suitable for CsPbBr 3 and CsPbIBr 2 perovskite solar cells. In consequence, HTL-free carbon electrode structure has been developed and new-type of inorganic transport layer materials have been explored basing on such structure. Tang's group have successively developed Cu(Cr,Ba)O 2 nanocrystals (NCs), [60] CuInS 2 /ZnS quantum dots (QDs) [31] and brominated graphene oxide (Br-GO) [109] materials to act as HTLs for CsPbBr 3 perovskite solar cells.

Device Fabrication
Most all-inorganic perovskite solar cells reported in the literature so far have been prepared using solution processing methods such as spin-coating, spray coating and blade coating. So far, most highly efficient all-inorganic perovskite solar cells have been prepared by spin-coating, including the devices with a PCE over 20%. Spray coating and blade coating are in general more suitable to prepare devices that exceed the areas <1 cm 2 typically used in research.Up to now, larger-area all-inorganic perovskite solar cells with PCE of 13.82% (112 cm 2 , regular CsPbI 3−x Br x (2 < x < 3) solar cell) [110] and 10.73% (8 cm 2 , regular CsPbI 3 solar cell) [111] have been reported by using spray coating and blade coating, respectively. A challenge for depositing multinary semiconductors on larger areas can be lateral inhomogeneities in thicknesses but also in composition, bandgap or other film qualities such as stress or strain or the density of recombination active defects. Specific research on upscaling and avoiding of spatial inhomogeneities in all-inorganic perovskite solar cells is so far still scarce. Early examples are the demonstration of Mai and co-workers who showed that increasing the transport layer thickness can relieve the leakage loss to some extent leading to a PCE of 12.19% for a 10.92 cm 2 area achieved (inverted CsPbI 2 Br solar cell), however, still by spin-coating. [71] Another challenge for the upscaling and technological maturity of solution processing is to find alternatives for the toxic solvents that are used in the large majority of academic research efforts on lead-halide perovskites. While there have been sufficient investigations on "green" solvents for hybrid perovskites in general, [112] we just find very few investigations in the context of all inorganic perovskites and the performance is still not as   [20,40,41,49,56,60,61,[105][106][107][108], which were mainly obtained from absorption spectra and photoelectron spectroscopy. Note that the valence and conduction band levels as well as the work function may vary depending on the exact stoichiometry but also on the mode of preparation and surface treatments.
good as the traditional solvents. [113] Vapor deposition methods such as evaporation have advantages with regard to the absence of any solvents but have the disadvantage of requiring costly vacuum equipment as well as fairly long deposition times as compared to solution processing. Until now, the champion efficiency of all-inorganic perovskite solar cell prepared by vapor deposition is 13% (0.051 cm 2 , regular CsPbI 2 Br solar cell). [114] Furthermore, a small amount of studies on large-area devices were reported, among which the highest PCE of 9.4% (1 cm 2 , regular CsPbI 2 Br solar cell) was achieved by single source evaporation. [115]

Stability
Though all-inorganic perovskites are facing phase transition issue as mentioned above, however, they still possess satisfying stability, particularly the thermal stability. It is known that organic-inorganic hybrid perovskites cannot endure high-temperature treatment because of the existence of MA + and FA + organic cation. It has been reported that MAPbI 3 have the risk of decomposition at temperatures of 85 °C, [118] while the decomposition temperature for FAPbI 3 is approximately 150 °C. [119] In general, 250-350 °C is required for inorganic materials preparation via regular thermal processes and satisfyingly, Cs + -based all-inorganic perovskites would not occur decomposition issue under this circumstance. Such favorable thermal stability could not only improve the durability of the whole device, but also be able to adapt to more high-temperature technologies. This is especially useful for constructing devices with complex structures (e.g., tandem devices). Many reviews outlining the status, mechanism and optimization process of stability for allinorganic perovskite devices have been reported. [119,120] Here we just list some typical works to reveal the status of stability for allinorganic perovskite solar cells with different x values. Required by the International Electrotechnical Commission, the assessment criteria for photovoltaic stability should meet that both moisture (80% relative humidity) and heat (80 °C) stabilities are more than 2000 h. Compared to the organic-inorganic hybrid perovskites, the all-inorganic species are apparently closer to these requirements. Chen et al. have developed a PbI 2 ·Nmethyl-2-pyrrolidone (NMP)-assisted growth method for highquality α-CsPbI 3 films and used 18-crown-6 ether to suppress water invasion and passivate defects, and thus achieved stable α-CsPbI 3 perovskite solar cells, which readily maintained ≈91% of the initial PCE for more than 1000 h (85 °C, N 2 ) and even ≈90% for up to 2000 h (25 °C, 20% relative humidity) without encapsulation (Figure 9a). [111] Furthermore, a stability performance that retained ≈95% of the original value for over 500 h (operating conditions, 60% relative humidity) with encapsulation has also been achieved. [111] As shown in Figure 9b, Han et al. have reported CaCl 2 -doped CsPbI 2 Br devices which maintains ≈90% of its initial efficiency after 1080 h when stored and tested in air (≈25% relative humidity). [116] Zhu et al. fabricated unencapsulated CsPbIBr 2 devices maintaining ≈90% of the initial PCE after storing for 60 days (1440 h) at 25 °C and 45% relative humidity (Figure 9c), as well as ≈97% PCE after storing for 7 days (168 h) at 85 °C with water content below 1 ppm. [52] With regard to CsPbBr 3 perovskite solar cells, as they are usually fabricated using carbon electrodes rather than Au or Ag electrodes Adv. Mater. 2022, 34, 2108132 Figure 9. Storage stability measurement results of the representative unencapsulated all-inorganic perovskite solar cells. All figures are replotted based on the data in the following publications: a) CsPbI 3 PSC reported by Chen et al., [111] b) CsPbI 2 Br PSC reported by Han et al., [116] c) CsPbIBr 2 PSC reported by Zhu et al., [52] d) CsPbBr 3 and the reference MAPbI 3 perovskite solar cells reported by Liang et al. [117] and getting rid of organic HTLs, which is beneficial to avoid moisture absorption and thermal decomposition of organic HTLs and oxidation of metal electrodes, CsPbBr 3 devices exhibit superior stability among all-inorganic perovskites. Early in 2016, Liang et al. have investigated CsPbBr 3 device with FTO/c-TiO 2 /m-TiO 2 /CsPbBr 3 /carbon structure. The unencapsulated PSC showed none degradation after storing for 3 months (2640 h) at 25 °C and 90-95% relative humidity, while the reference MAPbI 3 devices degraded to ≈10% of its initial value after storing for ≈720 h (Figure 9d). [117] Furthermore, they have also demonstrated that the use of organic spiro-MeOTAD HTL would fasten the degradation of device performance. Furthermore, in high-temperature and high-humidity conditions (100 °C, 90-95% relative humidity), the unencapsulated CsPbBr 3 PSC still presented no degradation after 840 h storage, while the MAPbI 3 device with the same structure could only remain stable in the initial 20 h. [117] These results suggest that apart from considering film quality, grain boundary and phase stability, substitution of organic HTLs is a promising strategy for PSC stability improvement.

Performance
In this section, we review the key photovoltaic performance indicators (i.e., J sc , V oc , FF, and η) of high-quality CsPbI x Br 3−xbased perovskite solar cells and mainly focus on the comparison between the experimental values and the corresponding SQ limits. Also, we discuss surface and interface passivation approaches for the devices. Detailed performance indicators are shown in Figure 10, Figure 11 and Tables 1-5 while the correspondence between data points and authors being found in Figure S4-S8 in Supporting Information (Section 3). We mainly focus on the perovskite solar cells with the best PCEs in their own group. As shown in Tables 1-5, it can be seen that the bandgaps of materials or devices as well as the accurate calculation process have not been performed in many publications, leading to the difficulty for sensible loss analysis and straightforward performance comparison for the all-inorganic perovskite solar cells. Fortunately, the dataset of external quantum efficiency has been provided in the vast majority of publications, making it pretty possible for the calculation of  reasons for the deviation could be attributed to the followings, i) the effect of functional layers such as transport layers and interfacial layers. Absorbance by the functional layers broadens the absorption range, which would have effect on the bandgap of the devices in the case of constant perovskite-layer bandgap. ii) the effect of subsequent processes. The preparation of transport layers, interfacial layers and electrodes via chemical and heating processes would affects the perovskite layers which cannot be reflected by the conventional Tauc method. iii) calculation errors. The stated E g values using Tauc method is determined by a fit of the linear region of (αhν ) 2 versus hν and extrapolation to the x-axis, which is more error prone as compared to the calculation of g ip E values. Hence, we conclude that it would be more sensible to use the g ip E values for the performance loss analysis in these cases. Figure 10 and Figure 11 summarize the distribution of the parameters efficiency (a); short-circuit current density (b); open-circuit voltage (c), and fill factor (d) as a function of g ip E .

Performance Variations with Stoichiometry
In Figure 10, we show the absolute values of the four parameters, while in Figure 11 we normalize each parameter to the corresponding value in the SQ model. In Figure 10 the trends for efficiency, J sc and V oc are dominated by the trends inherent to the SQ model. Efficiencies decrease strongly with bandgap, because the loss in J sc for higher bandgaps overcompensates any gains in V oc . The only part of the stoichiometry range that severely underperforms relative to the rest is CsPbI 1 Br 2 . To compensate for the SQ-inherent trends with bandgap, the normalized values are shown in Figure 11. Here, the most noteworthy aspect is the anticorrelation between the normalized V oc (Figure 11c) and the normalized J sc (Figure 11b). The normalized V oc decreases and the normalized J sc increases with bandgap. Thus, the normalization inverses the trends seen in Figure 10.
Because of the significant effect of the stoichiometry of the perovskite characterized by the x value on the bandgap, stability and photovoltaic performance of the devices, we discuss the present high-quality all-inorganic perovskite solar cells in detail as a function of the x value. As shown in Figure 11a, the champion η of present all-inorganic perovskite solar cells approaches 70% of the SQ limit. Nevertheless, only a few high-quality CsPbI 3 -based have approached such a ratio. As for the majority of devices, the ratio of η/η SQ is around 60-70% (x ≥ 2 and x = 0), while the ratio is even lower than 60% when x = 1 or 1.5. Furthermore, most of the samples exhibit high-level J sc performance, with / sc sc SQ J J ratio achieving to 90% or even higher (Figure 11b). Some devices show ultrahigh values close to or above 1 which seem unreasonable and will be discussed later. As shown in Figure 11d, the variation of FF/FF SQ ratio with bandgap is similar to that of η/η SQ , with the majority of data points being in the 80-95% range. In Figure 11c [25] This is the only one with η/η SQ ratio exceeding 70% so far. In addition, Yu  PSC with η of 11.1% and η/η SQ of 53.9%. [56] As the bandgap is relatively wide for pristine CsPbIBr 2 devices, many publications have mainly focused on narrowing the bandgap by Sndoping and co-absorber layer processes. These devices normally exhibit higher J sc and η but lower / sc sc SQ J J and η/η SQ values. The optimal PSC with a η of 11.53% was achieved by Sn-doping accompanying with low annealing temperature (150 °C). [123] As for high-quality CsPbBr 3 -based perovskite solar cells, we find that the ratios of η/η SQ exhibit high values above 60%, which is much better than that of CsPbIBr 2 -based devices. Meanwhile, the average FF/FF SQ ratio is as high as around 90%. However, all / oc oc SQ V V values are less than 82%. Yuan et al. have prepared CsPbBr 3 perovskite solar cells with PCE of 10.26%, with an optimal η/η SQ of 67.0% in this group. [59] Additionally, Duan et al. have reported the champion PCE of 10.85%. [31] However, due to the lack of EQE dataset, we are not able to make a further analysis.

Performance Variation As a Function of Transport Layer
In this section, we analyze the device performance depending on the types of ETL and HTL materials. To be specific, the ETL materials have been classified into 5 groups: TiO 2 , SnO 2 , ZnO, m-TiO 2 /c-TiO 2 and others; while the HTLs have been classified into spiro-MeOTAD, NiO x , other organics, other inorganics and HTL-free. The power conversion efficiency distributions with different transport layers are shown in Figure 12 as well as Figure S4-S8 (with more details) in Supporting Information (Section 3). As shown in Figure 12a, ETL materials are dominated by inorganic films, especially the TiO 2 and SnO 2 films. For HTLs, a larger variety of materials have been used (Figure 12b). Specifically, spiro-MeOTAD films play a leading role for perovskites with smaller g ip E , while more inorganic materials or HTL-free structure have been adapted for larger g ip E perovskite devices.
With regard to CsPbI 3 perovskite solar cells, all the samples have been fabricated with a regular planar structure and have employed spiro-MeOTAD as HTLs. In terms of ETLs, the majority of publications used TiO 2 films, including the champion 20.37% PCE reported by Yoon et al. [25] and 20.08% PCE reported by Yu et al. [41] Furthermore, Chang et al. have used SnO 2 ETL and achieved 19% PCE. As for the CsPbI x Br 3−x (2 < x < 3) group, SnO 2 films have been used as ETLs for most of the devices. Nevertheless, the optimal 19.65% PCE has been achieved by utilizing TiO 2 ETL. [28] ZnO ETL for inverted planar PSC has been reported by Wang et al. [104] Furthermore, spiro-MeOTAD films have been the predominantly used HTL  [47] In addition, though spiro-MeOTAD has still been the predominant HTL material, other organic HTL materials, such as PDTDT, P3HT, poly(N,N″bis-4-butylphenyl-N,N″-bisphenyl)benzidine (PolyTPD) and PTAA, have also shown satisfying performance. The perovskite solar cells which utilized PDTDT, P3HT and PolyTPD as HTLs have reached PCE of 17.36%, [29] 17.16% [47] and 16.84% [49] respectively, higher than that of 16.6% [48] using spiro-MeOTAD film. Regarding CsPbIBr 2 and CsPbI 1.5 Br 1.5 perovskite solar cells, we find that both TiO 2 and SnO 2 films have been generally used relative to the others, among which TiO 2 containing perovskite solar cells exhibited better performance in terms of PCE. As for HTLs, besides of the predominantly used spiro-MeOTAD films, inorganic NiO x , [30] (NiCo) 1−y Fe y O x -GO [57] materials and carbonelectrode-based HTL-free perovskite solar cells [52,54] have also been reported. For the CsPbBr 3 group, m-TiO 2 /c-TiO 2 , TiO 2 , and SnO 2 have been the main ETLs, while there is little performance difference among these devices. In addition, the carbonelectrode-based HTL-free structure is the most popular device geometry for CsPbBr 3 perovskite solar cells. Based on this,  [59] MnS, [61] Cu(Cr,Ba)O 2 NCs, [60] CuInS 2 /ZnS QDs [31] and Br-GO GO. [109] However, though the utilization of new transport layer materials have achieved favorable performance, they show a limited effect (with PCE just increase from 10.14% to 10.85%, less than 1%) and thus more efforts are still urgently needed.

Surface and Interface Passivation
Tables 1-5 list the key aspects of the device stack and the processing condition that define the unique aspects of the different publications. We observe that surface and interface passivation methods are among the most frequently used strategies to improve performance beyond the state of the art. Especially, in hybrid lead-halide perovskites, the detrimental effect of surfaces and interfaces leading to enhanced carrier recombination, short photoluminescence lifetimes and lower external luminescence quantum efficiencies as well as open-circuit voltages has been thoroughly investigated. [134] Defect passivation could effectively reduce the defect density at the surfaces/interfaces, which has been of major importance for the device performance improvement of hybrid [135] but also all-inorganic perovskite solar cells in recent years. The passivation techniques applied to all-inorganic perovskite solar cells include the following types, 1) Induced 2D layers: It has been reported that OAI, [25] PEAI [40] and GABr [122] could have a passivation effect due to the formation of a 2D  [36] CHI, [26] PTACl, [37] 6TIC-4F [104] and CsBr [128] has been used for perovskite surface treatment to passivate defects. 3) Interfacial layers: The preparation of interfacial layers, e.g., LiF, [125] EDEA [48] and PBAI, [48] between perovskite and transport layer has been proven to be effective in defect passivation. Nevertheless, improper surface/ interface passivation may cause an increase of the series resistance R s , or even interface deterioration, and thus can lead to a reduced J sc and FF. It should be noted that passivation can not only reduce defect density and improve device performance, but also enhance the stability simultaneously. For instance, 2D perovskite layer capping can improve V oc due to the passivation effect as well as prevent moisture and oxygen ingress by forming a compact layer on the surface of the 3D perovskite. [25,38,40,122] In addition, as mentioned above, CsPbI 3 exhibits a relatively low tolerance factor which means phase transitions may easily occur. Fortunately, it has been demonstrated that interface passivation can effectively enhance the phase stability. Zhao and coworker have reported that using PTABr, [36] CHI, [26] and PTACl [37] reagents can passivate surface defects and improve the phase stability of CsPbI 3 perovskites at the same time. Introduction of hydrophobic groups on perovskite surface can further prevent moisture penetration. Apart from that, lowering Adv. Mater. 2022, 34,2108132    the surface energy by interface engineering is also promising strategy for improving the phase stability of CsPbI 3 . [136]

Overview
In this section, we analyse the loss sources and the underlying physical mechanisms for all-inorganic perovskites. As discussed in last chapter, we find that the / oc oc SQ V V values of most of the present all-inorganic perovskite solar cells are at a relatively low level, indicating that the performance is mainly restricted by substantial voltage losses. Figure 13 shows the distribution of ≈ 5% for completed MAPb(I 0.8 Br 0.2 ) 3 perovskite solar cells (E g = 1.725 eV) with 1.35 V V oc , which is higher than any all-inorganic perovskite solar cells. [88] Noting that all the e lum Q values mentioned here were based on completed devices and thus these values were lower than those reported by other publications which were obtained from perovskite films. [88] For CsPbI 3 perovskite solar cells, Ye et al. have fabricated 3D/2D mixed CsPbI 3 devices achieving an optimal V oc of 1.33 V under 1.749 eV g ip E , [38] as well as a calculated e lum Q ≈1.13% which is the highest value among the discussed all-inorganic perovskite solar cells. It is worth noting that the position of this data point in the figure is slightly lower than the reference line of e lum Q = 1%. This situation also happens to some other samples. Such difference could be attributed to the non-negligible radiative recombination for actual devices, which cannot be took into account in the calculation of the reference lines. For the recorded device (PCE = 20.37%) reported by Yoon et al., [25]  ≈0.21% among the CsPbI x Br 3−x (2 < x < 3) group with a relatively low bandgap of 1.754 eV. [122] The maximum e lum Q value for CsPbI 2 Br group is calculated to be ≈0.54% using the results reported by Guo et al. [29] As for CsPbIBr 2 perovskite solar cells, Yang et al. have designed novel transport layers to narrow down the bandgap to 1.961 eV (obviously lower than the intrinsic value) and obtained a high 1.32 V V oc , [130] resulting in an optimal  Tables S3-S7 in Supporting Information (Section 5). The V ∆ oc nonrad therein originates from the nonradiative recombination in the bulk and at the interfaces, which has been widely focused on by the academic community and can be suppressed by film quality improvement and interface optimization. Figure 14a provides an overview over the distribution of , which can be lower than 200 mV. Nevertheless, such nonradiative loss is still pretty large compared with high-quality hybrid perovskite solar cells, whose can be suppressed to below 100 mV. [88,137,138] Figure 14b  for all-inorganic perovskite solar cells. Obviously, there is a negative correlation between current loss and voltage loss, which means that it is difficult to achieve a low current loss and a low voltage loss at the same time.  Though the voltage loss is high for CsPbIBr 2 -based perovskite solar cells as mentioned above, they exhibit a low current loss. The CsPbI 3 -based and CsPbI x Br 3−x -based (2 < x < 3) perovskite solar cells present a higher current loss, which could be attributed to the V oc optimization process. For instance, interface passivation is an effective mechanism to reduce oc nonrad V ∆ , which would increase series resistance at the same time because of the addition of dielectric interface layer and in consequence has a negative effect on the short-circuit current density J sc .
There are several possible reasons for the relatively high / sc sc SQ J J ratios of perovskite solar cells with larger bandgap (e.g., CsPbI 2 Br): 1) Absorption below g ip E . We compare the absorption of an ideal step function with a step at g ip E to calculate SQ limit with the actually measured EQE spectra. For bandgaps substantially above the maximum of the efficiency versus bandgap curve predicted by the SQ model, the below g ip E absorption becomes relatively more important. 2) Measurement errors. We find frequent disagreements between the stated J sc from J−V curves compared to the J sc obtained from the integration of the EQE spectrum. We will discuss it later (Section 4.7). Furthermore, the calibration of the solar simulator is often done with Si photodiodes. Given that the risk of calibration and measurement errors increases if the bandgap of the device under test and the reference photodiode are different, [139] it is conceivable that the occurrence of measurement errors increases for higher bandgaps.
In the following, we break down the efficiency losses into five figure of merits (FoMs) to reveal the physical mechanism via the following equation, [6,140] where F sc = sc real J / sc SQ J and FF res F = FF real /FF 0 ( oc real V ). FF 0 (V oc ), the value without resistive losses, can be calculated as following, [6,140] The corresponding physical loss mechanisms are shown in Table 6. The details have been introduced in the Supporting Information (Section 1.4). Figure 15 presents the energy loss comparison of the representative all-inorganic perovskite solar cells in each group. There are also three high-quality hybrid perovskite solar cells with low oc nonrad V ∆ shown for comparison. We find that all-inorganic perovskite solar cells present larger energy losses compared with the hybrid perovskite solar cells. Especially, the CsPbIBr 2 -based perovskite solar cells possess the largest energy losses, following by CsPbI 1.5 Br 1.5 -based and CsPbBr 3 -based perovskite solar cells, whose η/η SQ values are much lower than that of hybrid perovskite solar cells. For the CsPbI 3 and CsPbI x Br 3−x (2 < x < 3) devices, the related η/η SQ values tend to be close to hybrid perovskite solar cells, benefiting from the similar or even smaller loss in FF res F . However, there is still large room to catch up with the hybrid devices with respect to the oc real V / oc rad V loss. For the complete set of all-inorganic perovskite solar cells shown, the energy losses are dominated by the FoMs of oc real V / oc rad V and FF res F , indicating severe nonradiative recombination loss, high series resistance and poor ideality factor. In addition, for the devices with x > 2, the F sc , which is due to the photocurrent loss, also accounts for a large proportion of the total efficiency loss. Nevertheless, its effect would be weakened along with increasing of bandgap energy, while the effect of oc    the following, we discuss the physical loss mechanisms for each group of all-inorganic perovskite solar cells in detail. V ∆ of 116 mV by fabricating a 2D/3D mixed-dimensional perovskite structure, which is the lowest value among all the discussed devices in this paper. However, the current performance has been sacrificed for the voltage optimization and the / sc sc SQ J J value was only 84.4%, which is lower than its competitors. [38] Apart from this device, we find that the / presented a decreasing trend, from the initial 336 mV to 264.4 mV. [26,36,37] It is observed that the efficiency of CsPbI 3 -based perovskite solar cells has been satisfyingly improved from 17.06% to 20.37% within 3 years, which could be due to the successful optimization for nonradiative voltage loss   [137,138] The respective g ip E for each device has been marked.

CsPbI 3 -Based (x = 3) Perovskite Solar Cells
losses by nonradiative recombination, photocurrent and series resistance together with ideality factor. By contrast, the green bar is the largest in terms of the area for most devices, namely, the nonradiative voltage loss is the dominant factor for performance difference, indicating that the main strategy for performance improvement should focus on suppressing carrier nonradiative recombination, which is consistent with the above discussion. Although Ye et al. have reported the best oc real V / oc rad V factor, both the F sc and FF res F losses are pretty large compared with the others and thus limits the efficiency. For further performance improvement, efforts on balancing nonradiative voltage loss and resistive loss should be done.  [122] Similar to Ye et al. [38] and Liu et al. [40] [126] These two studies have adopted similar device structures but focused on the upper and lower surfaces of perovskite films respectively and both exhibited favorable effect on reducing nonradiative recombination. There is no obvious conflict of these two technologies and it seems possible to combine them together to further reduce ∆ oc nonrad V , aiming to achieve ∆ oc nonrad V that could as low as that for hybrid perovskite solar cells. Ye  F , which represents smaller series resistance and better ideality factor for the devices. While the device from Wang et al. (2020) existed fewer photocurrent loss due to the smaller area of F sc . Similar to CsPbI 3 -based perovskite solar cells, a balance between the indicators is the key for further performance improvement.

CsPbI 2 Br-Based (x = 2) Perovskite Solar Cells
The comparison of losses for CsPbI 2 Br-based perovskite solar cells is presented in Figure 18a. Guo   indicating that suppression of carrier nonradiative recombination is significant for performance improvement. The related FoMs loss analysis is shown in Figure 18b. On the whole, the green bar is the largest in terms of the area, suggesting that more efforts on suppressing nonradiative recombination should be done. In addition, the distinct red area indicates the deficiency of series resistance and ideality factor for present CsPbI 2 Br-based perovskite solar cells.  [43] performed ultralow short-circuit current density loss. In addition, Patil et al. [46] have achieved the best oc rad V / oc SQ V value by Nb-doping process, demonstrating that the actual shape quantum efficiency is much close to the ideal step-function assumed in the SQ limit. In a brief, apart from the others factors, suppression on nonradiative recombination loss is the primary task for CsPbI 2 Br-based perovskite solar cells performance improvement. 3%. [106] However, it seems hard to make a balance between voltage and current losses for most CsPbIBr 2 -based perovskite solar cells. To be specific, Yang et al., [130] Liang et al., [129] and Li et al. [123] have achieved low oc nonrad V ∆ , while the optimal / sc sc SQ J J value among them was just 81.2%. Noted that all of them have adopted regulation process to narrow bandgaps and in consequence broadens the response range of external quantum efficiency and improves short-circuit current density J sc and the power conversion efficiency η. It is surprising that such regulation could obtain lower oc nonrad V ∆ than the others, rather than higher / sc sc SQ J J value.  That means, though the range of external quantum efficiency has been broadened, more efforts are needed to effectively convert them into current and thus improve the ratio of , indicating that nonradiative recombination loss is the primary factor limiting device performance in this group. Noted that some devices exhibit ultrahigh / sc sc SQ J J value of approximately 1. They will be discussed later. As shown in Figure 19b, the FoM of oc real V / oc rad V dominates the energy losses overall, following by FF res F . For the devices from Yang et al., [130] Liang et al., [129] and Li et al. [123] with smaller bandgaps, despite the effect of oc real V / oc rad V has been reduced at a certain extent, the loss caused by F sc increase significantly. For the CsPbI 1.5 Br 1.5 device reported by Zhang et al., [106] it presented lower loss overall, and the oc real V / oc rad V is the dominated factor. It is noted that the devices shown in Figure 19b have been arranged depending on bandgap energy from small to large. We conclude that the main factor affecting energy losses changes from F sc to oc real V / oc rad V along with increasing bandgap energy, suggesting that targeted optimization approach should be performed. In addition, the FF res F occupied large percentage for all devices, indicating that series resistance reduction and ideality factor improvement are needed as well. in this group is still as high as 332 mV. [60] The other devices exhibit more severe nonradiative recombination loss, [58,59,61] which is consistent with FoMs loss analysis shown in Figure 20b. Obviously, the green bar, which is related to oc real V / oc rad V representing nonradiative recombination loss, is the largest. Note that Yuan et al. [59] have fabricated solar cells with the structure

Effect of J sc Reporting Method on the Performance Loss Analysis
In the process of meta-analysis, we have found that many devices show ultrahigh / sc sc SQ J J values, i.e., ultralow F sc loss in the FoMs loss analysis figures. This phenomenon is usually observed for the CsPbI x Br 3−x perovskite solar cells with small x value which have a relatively wide bandgap. We hold the opinion that such ultralow F sc loss should be considered with caution. Almost all the stated J sc (denote as sc sta J ) are from the champion devices measured by the J-V measurement system with a standard solar simulator. These sc J on the performance loss distribution, as shown in Figure S17 and S18. The results show that the J sc calculation method have significant influence on the F sc loss but little influence on oc

Conclusions and Outlook
We have performed a detailed meta-analysis of key performance parameters of all-inorganic CsPbI x Br 3−x (0 ≤ x ≤ 3) perovskitebased solar cells and absorber materials. Given that all-inorganic perovskites cover a wide range of bandgaps that go up to values of 2.3 eV, i.e., much higher than ideal for single junction solar cells, it is imperative to correct device performance data for the influence of bandgap. Therefore, we used a consistent way of determining the bandgap from the inflection point of the quantum efficiency that is in line with other efforts such as the emerging-PV project. [7] Using the bandgap, we determined performance parameters in the SQ model and referenced all experimental data to the respective values in the SQ model. From this data and meta-analyses of the material parameters such as mobility and photoluminescence lifetime, we can make conclusions on the whole material family as well as obtain more detailed insights as a function of stoichiometry. Independent of the I to Br ratio, CsPbI x Br 3−x perovskite layers show similar carrier mobilities as compared to hybrid lead-halide perovskites but so far shorter photoluminescence lifetimes and lower external photoluminescence quantum efficiencies. Thus, allinorganic perovskite solar cells have more severe nonradiative recombination losses over the whole range of bandgaps, and hence lower / oc oc SQ V V and η/η SQ ratios in devices as compared to hybrid perovskites. However, we also note that given the current level of work (measured in the accumulated number of publications) invested into the material system, all-inorganic perovskite solar cells don't perform worse than hybrid ones at a similar stage in their development.
While V oc losses are the largest fraction of the total losses for basically all studied devices, fill factor losses are also quite substantial in particular in case of higher-bandgap perovskites. This suggests that tackling resistive limitations is important for a further improvement of efficiencies. Photocurrent losses are overall the least significant in most of the devices that are best of their respective bandgap range. While this is generally a good sign and an indication of a high absorption coefficient and sufficient mobilities of absorber and contact layers, we note that the losses get significantly lower with higher bandgap with some of the cells having values above the SQ model. While this is not technically impossible given the definition of the bandgap via the inflection point, those cells often have discrepancies between the current densities derived from quantum efficiency measurements and the current densities derived from current-voltage curves. This suggests that at least some of the values might be affected by calibration issues. A further trend seen as a function of bandgap is a decrease of PL lifetime of films with increasing bandgap. This trend is consistent with the trend in non-radiative recombination losses in full devices. Here, we note that in both cases, the CsPbIBr 2 -based devices break the trend as they show even higher voltage losses and lower lifetimes than the higherbandgap CsPbBr 3 -based samples. Achieving an improved balance between voltage and photocurrent losses is another key requirement for better performance. Our meta-analysis shows a trade-off between these two factors. The lowest Finally, we also performed a meta-analysis of the used contact layers. Given the higher annealing temperatures, all-inorganic perovskites are mostly prepared in the structure that is often called the regular structure and that starts the deposition with an ETL that is normally a metal oxide (TiO 2 or SnO 2 ) that can withstand the required higher annealing temperatures much better than the organic HTLs that are typically used for inverted geometries. Here, we want to point out that there is over all rather little variation in the used contact layers, with Spiro-OMeTAD dominating the used HTLs over the whole range of I to Br ratios. However, given the large range of bandgaps covered, it is likely that perfect (or even good) band alignment can only be achieved by a tiny subsection of the studied compositions while many of the layer stacks may suffer from additional recombination losses at interfaces. As TiO 2 /SnO 2 and Spiro-OMeTAD have been shown to be compatible with high-efficiency lower-bandgap hybrid perovskites, [138,141] it is likely that especially the higher-bandgap all-inorganic perovskite solar cells suffer from this effect.
To achieve a higher degree of technological maturity and improved device performance in all inorganic perovskites, understanding of carrier recombination processes in the bulk and at the interfaces is essential. All-inorganic perovskites have shorter photoluminescence lifetimes and lower photoluminescence quantum efficiencies than the best hybrid leadhalide perovskites. While there are already many experimental studies on the topic, theoretical work on the dominant defects and their impact on the recombination rates and lifetimes is so far relatively scarce. We think theoretical work, identifying the dominant defects and their associated capture coefficients and formation energies would be highly valuable. [87] If we know the dominant defect species, we can adjust processing conditions to eliminate the source of defect formation. An example for a such a change in processing conditions could be, e.g., a change in the ratio of precursors to achieve a stoichiometry that has an excess of a certain element which is harmful as a vacancy. Furthermore, changes in stoichiometry can also lead to changes in formation energies of defects and may therefore be a feasible way to reduce the densities of certain defects. In addition, calculated capture coefficients are often (but not always) fairly different for electrons and holes(see Figure 6). [87] Assuming for instance that the electron capture rate is much slower than the hole capture rate, the entire recombination process would be rate limited by electron capture. Thus, if one was able to further slow down electron capture, the whole process could be further slowed down and efficiency would increase. Such a slowing down of the rate could be achieved by reducing the density of (in this example) electrons, e.g. by introducing doping or by adjusting the properties of the electron injecting contacts relative to the hole injecting contacts such that one type of carrier is present in excess of the other. [101] Another major aspect that will help direct process and device optimization will be to develop a suitable set of characterization methods to identify the dominant efficiency limiting mechanisms in all-inorganic but also in hybrid perovskites. The determination of many key parameters such as defect densities, recombination lifetimes or the efficiency of charge extraction that are necessary for improving our understanding of charge-carrier recombination could be improved. So far, defect densities are frequently measured using the trap-filled regime in single carrier devices, which is highly problematic due to electrostatic limitations [96] of the method and the dangers associated with neglecting the influence of injection barriers [142] and moving ions. [94,143] Steady-state and transient photoluminescence are frequently used to study recombination. However, often also information about charge extraction or charge collection are derived from photoluminescence. For instance, the quenching of the steady-state photoluminescence when attaching electron-or hole-transport layers is often considered a way of identifying efficient charge extraction. [144][145][146] However, in fact this only clarifies that the electron-or hole-transport layer will increase charge recombination and is hence a clearly negative factor that should correlate with losses in open-circuit voltage. A better way of extracting information on charge collection from photoluminescence is to compare PL at short circuit and open circuit [144] or to even measure voltage-dependent photoluminescence in complete devices. [145] Furthermore, it may be possible to develop new experimental methods sensitive to charge extraction and collection based, e.g., on the rise of the photovoltage in different transient methods. [146] Thus, we hope that the technological development of all inorganic perovskite solar cells will be enabled and accompanied by improvements in theoretical understanding and characterization of efficiency limiting processes.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.