11.2.1 Operational Principle and Basic Structures

Figure 11.1 illustrates the operation of a hybrid perovskite solar cell in a simplified picture. Here, the band alignment [i.e. energy positions of valance band maximum (VBM) and conduction band minimum (CBM)] of the solar cell component layers is shown. This solar cell has a basic structure of TCO/ETL/perovskite/HTL/metal, where TCO shows a transparent conductive oxide. For perovskite absorbers with thicknesses of 300–500 nm, a wide variety of perovskite compounds, including MAPbI₃, FAMAPb(I,Br)₃, and CsFAPb(I,Br)₃, have been used (see Figure 4.1). In designing a stable perovskite crystal, the tolerance factor provides a universal guideline (see Figure 3.11). When light is illuminated through the front TCO, the light absorption within the perovskite absorber creates free electrons and holes, which are collected separately in the ETL and HTL (see also Figure 1.1). The choice of ETL and HTL is quite important and these layers are selected such that their energy levels match the CBM and VBM [7, 21]. The example in Figure 11.1 shows a preferable band alignment in which electrons and holes are collected without energy barriers.

Figure 11.2 shows the structures of hybrid perovskite solar cells, which can be categorized into (a) n‐i‐p and (b) p‐i‐n structures. Here, the meanings of “p,” “i,” and “n” differ from those of standard solar cells and, in the hybrid‐perovskite research field, “p” and “n” denote HTL and ETL, respectively, and not the doped perovskite layers. The “i” represents the perovskite absorber layer, which is generally treated as an intrinsic layer with low carrier concentrations. Note, however, that the carrier type and concentration of the perovskite layers vary substantially with the preparation condition (Figure 6.2) and the resulting solar cell performance also changes [22–25]. Figure 11.2c summarizes the molecular structures of representative organic layers used widely as ETL and HTL.

The perovskite single cell is generally formed on a glass substrate (i.e. a superstrate cell). Structurally, the p‐i‐n solar cell is simply an inversion of the n‐i‐p structure, although the selections of ETL and HTL differ due to the difference in their deposition sequences. In particular, a mesoporous TiO₂ (mp‐TiO₂) layer is typically used in the n‐i‐p cell to improve solar cell performance [1, 2, 24]. This layer comprises a continuous structure of anatase TiO₂ with a high porosity of ∼60% (Dyesol) [26, 27]. For both n‐i‐p and p‐i‐n cells, SnO:F and In₂O₃:Sn (ITO) are widely employed as TCO, whereas Ag and Au rear electrodes are commonly adopted to guarantee efficient backside light reflection [28, 29]. In the standard n‐i‐p cell, TiO₂ and spiro‐OMeTAD (or poly(triaryl amine), PTAA) layers are used as the ETL and HTL, respectively. In the p‐i‐n cell, a PTAA or poly(3,4‐ethylenedioxythiophene):poly(4‐styrensulfonate) (PEDOT:PSS) layer is usually employed as the HTL, while (6,6)‐phenyl‐C₆₁‐butyric acid methyl ester (PCBM) combined with a bathocuproine (BCP) interface layer is used as the ETL [30].

In early MAPbI₃ research, n‐i‐p solar cells have been primarily investigated [31–37]. In the cells developed initially, mp‐TiO₂ was incorporated almost entirely into the absorber layers [31–36], but as researches progressed, the mp‐TiO₂ layer thickness was decreased gradually to ∼200 nm. The p‐i‐n cells shown in Figure 11.2b were developed in a later research stage. One disadvantage of the p‐i‐n cell structure is the unfavorable parasitic light absorption in the HTL, located at the light illumination side. Specifically, PTAA and NiO layers, often used as the HTL in the p‐i‐n cell, exhibit strong light absorption in the ultraviolet (UV) region (Figure 11.3), reducing the short‐circuit current density (J_sc) of the cells [10, 38]. In contrast, for the n‐i‐p cells, parasitic absorption is suppressed extremely well because (i) TiO₂ shows a high transparency (see Figure 11.3) and the HTL is placed after the perovskite absorber in the light absorption order. The J_sc reduction in the p‐i‐n cell can be avoided by using a PEDOT:PSS HTL, but the incorporation of PEDOT:PSS reduces V_oc (see Section 11.5).

In Pb‐based perovskite cells, over 20% efficiencies can be obtained in both n‐i‐p and p‐i‐n structures [4, 39]. In Sn‐based perovskite cells, however, p‐i‐n cells show substantially higher efficiencies, compared with n‐i‐p cells (see Table 14.3). This difference has been attributed to the generation of trapping sites at the TiO₂/perovskite interface in the n‐i‐p configuration. In particular, the enhanced SnI₂ formation on the TiO₂ layer in the n‐i‐p structure, which can be avoided in the p‐i‐n configuration, has been proposed as a mechanism of high‐density trap formation (Section 14.5).

11.2.2 Band Alignment

Figure 11.4 summarizes the band alignments of MAPbI₃ solar cells with various ETL and HTL, as reported in Refs. [40–42]. The VBM positions (or ionization potentials) in Figure 11.4 were determined using photoelectron spectroscopy, whereas the CBM positions (or electron affinities) were estimated by adding E_g values to the VBM positions [40]. Note, however, that the absolute energy positions vary slightly with sample surface conditions and reference energy; as a result, there are slight inconsistencies among the reported values [2, 7, 21, 33, 35, 38, 42–45]. In Figure 11.4, the conduction‐band edges of all ETLs are slightly lower than that of MAPbI₃, while the valence energies of all HTLs are slightly above the MAPbI₃ valence band. Accordingly, the operation of a perovskite cell can essentially be expressed using the schematic illustrated in Figure 11.1.

Figure 11.5 summarizes the VBM and CBM positions of various halide perovskites. The VBM positions correspond to those determined by photoelectron spectroscopy [46], while the CBM levels have been derived by adding the E_g values listed in Table 4.3 to the VBM energies. The energy‐level diagram for ABX₃ perovskites shows that (i) there are no clear trends in the VBM and CBM with the variation of the A‐site center cation, (ii) the VBM is lifted when the divalent B‐site cation is changed from Pb²⁺ to Sn²⁺, and (iii) the VBM shifts downward and CBM moves upward as the X‐site halide anion is varied in the order I → Br → Cl (see also Figure 4.10). As shown in Figure 5.6, the A‐site cation does not participate in forming the conduction and valence bands and, therefore, the A‐site species indirectly influence the VBM and CBM through the crystal structure alteration. The type‐II (staggered) band alignment of ASnI₃–APbI₃ (Figures 4.10 and 14.17) is particularly important for explaining quite strong E_g bowing observed in their alloys (Figures 4.10 and 18.12). When a hybrid perovskite alloy is employed as the absorber, it is important to consider the relative change of the VBM and CBM in designing and selecting ETL and HTL. In particular, higher solar cell performance can be achieved by improving the energy level matching between the perovskite absorber and ETL/HTL [7, 21] (see Section 13.5 and Chapter 14 for more detail).

11.3.1 Device Simulation

Figure 11.6 shows the band diagrams of n‐i‐p MAPbI₃ solar cells with a structure of glass/SnO₂:F(500 nm)/TiO₂(150 nm)/MAPbI₃(500 nm)/spiro‐OMeTAD (50 nm)/Ag, calculated from a one‐dimensional device simulator (SCAPS [47–50]). In these simulations, the interface recombination was neglected and, for the MAPbI₃ thin layer, a mid‐gap trap density of N_t = 10¹⁵ cm⁻³ was assumed to reproduce the experimental solar cell efficiency of ∼20%. This assumption is, however, quite hypothetical, as the efficiency of the experimental solar cells is limited essentially by the interface recombination, rather than the bulk recombination (Section 11.5.1). Here, the simulation results of Figure 11.6 are shown to explain the overall operation of MAPbI₃ solar cells.

In Figure 11.6a, the band diagram of the n‐i‐p cell under the SC is shown. The dotted line in Figure 11.6a indicates the Fermi level (E_F) and E_F of the TCO locates inside the conduction band when the carrier concentration is ∼10²⁰ cm⁻³. The E_F of the TiO₂ is close to the conduction band edge, while that of the HTL matches the highest occupied molecular orbital (HOMO) level. It can be seen that the conduction and valence bands of the perovskite i‐layer are tilted by the uniform electric field present within the i‐layer (i.e. the i‐layer is depleted completely). In the presence of an electric field, carrier collection is enhanced and, under the SC, the photocarrier collection (i.e. J_sc) can reach almost 100% even in the presence of defects (see Section 11.4.2).

We show the corresponding band diagram under the open‐circuit condition (OC) in Figure 11.6b. The two dotted lines in Figure 11.6b show the quasi‐Fermi levels for electrons and holes. The V_oc of the cell can be described by the splitting of these levels (i.e. quasi‐Fermi‐level splitting). Under the OC, the bands of the perovskite layer become almost flat and the carrier recombination at the interface or within the bulk layer occurs more easily. In other words, the output voltage under this condition (i.e. V_oc) is primarily governed by the recombination characteristics, while J_sc is less sensitive to the recombination behavior due to the electric field carrier collection. Accordingly, V_oc is a good indicator about how significantly carrier recombination occurs within solar cells and the experimental V_oc decreases from its theoretical limit (1.32 V for MAPbI₃ [16, 51, 52] and 1.28 V for FAPbI₃; Table 12.1) with increasing interface and bulk recombinations.

The diffusion length (L_D) is a physical parameter that is inversely related to the recombination (or trap density) in the bulk layer. A significant advantage of hybrid perovskite thin films is very large L_D values (4–23 μm in Table 1.1), which arise from the absence of deep‐level traps (Section 5.6) and the resulting long carrier lifetimes (Section 1.2.1). The L_D of the perovskite layers is sufficiently larger than the solar cell absorber thickness (∼500 nm); in this case, the recombination process is predominantly governed by interface recombination. In hybrid perovskite cells, therefore, the reduction of interface defects is critical to achieving high efficiency (Section 11.5.1).

The band diagrams in Figure 11.6c,d show cases in which the perovskite layers are n‐ and p‐type, respectively, with low carrier densities of 10¹⁶ cm⁻³ (i.e. n⁻ or p⁻). As explained in Figure 6.2, the carrier type and concentration of MAPbI₃ change with the precursor ratio (i.e. PbI₂/MAI). In the n‐type perovskite cell shown in Figure 11.6c, the p–n junction is formed at the MAPbI₃/HTL interface and the electric field is concentrated at the HTL interface, while only a weak electric field is present near the ETL as a result of the n–n⁻ band alignment. In this solar cell, due to the flat band formation at the TiO₂/MAPbI₃ interface, the carrier recombination occurs more easily in this region [53, 54]. Moreover, the minority carrier of this solar cell is hole and the conversion efficiency is more influenced by hole mobility. In the n‐p⁻‐p cells, the trend is reversed; the carrier recombination in this case tends to occur at the MAPbI₃/HTL and the electron mobility influences more. Thus, the formation of an n‐ or p‐type perovskite varies the device operation rather significantly.

11.3.2 Experimental Observation

The electric field (or potential) distributions within hybrid perovskite solar cells can be measured directly by using cross‐sectional characterization techniques such as electron beam‐induced current (EBIC) and Kelvin probe force microscopy (KPFM). In this section, we discuss the operation of experimental perovskite devices based on EBIC [55, 56] and KPFM [24, 57–59] characterization results.

Figure 11.7a illustrates the EBIC measurement configuration for a planar‐type hybrid perovskite cell without mp‐TiO₂ [55]. In EBIC, the electron beam of a scanning electron microscope (SEM) is employed to generate the electron–hole pairs and the current flow through the device is characterized. In this technique, therefore, the carrier collection at individual positions can be investigated. Figure 11.7b shows the cross‐sectional SEM and EBIC images of the perovskite cell [55]. In the SEM image, a nonuniform MAPbI₃ layer fabricated by a spin‐coating process can be confirmed. In the corresponding EBIC image, the entire MAPbI₃ layer is brightly displayed due to the uniform carrier collection throughout the absorber layer. The result of the EBIC line scan further shows two shoulders near the HTM/MAPbI₃ and MAPbI₃/ETL interfaces. Based on this observation, Edri et al. concluded that the perovskite cell operates as a p‐i‐n device [55, 56].

In contrast, the KPFM characterization of MAPbI₃ cells has provided controversial results [24, 57–59]. In particular, Cai et al. performed a KPFM measurement of a 20%‐efficient MAPbI₃ cell that shows a high V_oc of 1.12 V in the standard n‐i‐p structure [24]. Figure 11.8a shows a profile of the contact potential difference (CPD) in a standard MAPbI₃ cell [24]. The CPD profile indicates a change in the electrical potential and the magnitude of the CPD is consistent with the V_oc of the device in the same measurement configuration. Note that the electric field is simply given as the change in the voltage with thickness (i.e. E = V/d) and thus the CPD slope reflects the electric field. Importantly, in Figure 11.8a, a large potential drop is observed within the MAPbI₃‐TiO₂ mixed region, indicating that the electric field is concentrated at the MAPbI₃‐TiO₂ interface. Thus, this high‐efficiency cell operates as a simple p–n junction device, whose band profile is represented by that shown in Figure 11.6d. The p–n junction formation is also supported by other KPFM studies [57, 58].

Quite interestingly, in Ref. [24], the large potential drop is always observed within the mesoporous layer, independent of the PbI₂/MAI precursor ratio, and the cell efficiency is rather insensitive to the precursor ratio. In contrast, in planar cells without mp‐TiO₂, the location of the potential drop changes with the PbI₂/MAI precursor ratio. When an n‐type (PbI₂‐rich) MAPbI₃ is applied, the CPD drops in the MAPbI₃/HTL interface region (Figure 11.8b). In this case, therefore, the solar cell is best described by the n‐n⁻‐p type cell shown in Figure 11.6c.

The above results indicate quite important facts that hybrid perovskite cells do not always function as n‐i‐p (or p‐i‐n) devices and the detailed operation of the perovskite cells varies with the solar cell architecture and processing conditions. The interface recombination behavior is also expected to change significantly according to the type of the solar cells (see Figure 11.6).

11.4.1 Carrier Generation and Loss

Here, we discuss the spatial distribution of carrier generation and the influence of carrier recombination in an n‐i‐p MAPbI₃ cell. Figure 11.9 shows the optical simulation results obtained from the optical admittance calculation [17, 29] assuming a flat MAPbI₃ cell [28]. In Figure 11.9a, the solar cell structure and corresponding internal quantum efficiency (IQE) and internal absorptance (IA) spectra of the cell are shown. The IQE and IA are calculated using the relations IQE = EQE/(1 − R) and IA = A/(1 − R), where EQE, R and A indicate the external quantum efficiency, reflectance, and absorptance of the constituent layers, respectively.

The IQE spectrum has a rectangular shape, in which the short‐wavelength (λ) response is limited by the light absorption in the SnO₂:F and TiO₂ top layers. The upper bound of the IQE (λ ∼ 800 nm) is simply determined by the E_g of the MAPbI₃ layer. Remarkably, the absorption effect of spiro‐OMeTAD is almost completely negligible because (i) the E_g of spiro‐OMeTAD (2.95 eV) [29] is higher than that of MAPbI₃ and (ii) the spiro‐OMeTAD layer is placed after MAPbI₃ in the order of light absorption.

Note that the maximum IQE in the visible region (λ = 400–750 nm) is limited by the free carrier absorption in the SnO₂:F layer. Free carrier absorption increases strongly with carrier density [60, 61] and, in Figure 11.9, a TCO carrier density of 1.2 × 10²⁰ cm⁻³ is assumed. This density is much lower than those of widely used TEC substrates (5 × 10²⁰ cm⁻³) [60, 62] and, when a TEC substrate is adopted, the maximum IQE (or EQE) decreases due to enhanced free carrier absorption [54].

In Figure 11.9b, the light absorption in 1‐nm‐thick MAPbI₃ sublayers (partial IQE) is shown. Integration of these partial IQE spectra reproduces the IQE spectrum in Figure 11.9a. The arrows in the figure denote the λ positions of the E₀ (E_g), E₁, and E₂ transitions in MAPbI₃ (see Figure 4.4). At E ≥ E₁, the partial IQE exhibits rapid decay because of the strong light absorption within MAPbI₃. In the region E_g ≤ E < E₁, however, the IQE is low due to the smaller absorption coefficient (α) in this region and photocarriers are generated uniformly throughout the entire MAPbI₃ layer with the appearance of the optical interference effect. In this region, the electrons and holes need to travel through the entire MAPbI₃ layer and high J_sc observed experimentally for hybrid perovskite cells confirms the quite efficient carrier collection within the whole absorber layer [28].

In Figure 11.9b, the integrated J_sc relative to the depth and incident light (λ) is also shown. Because of the assumed flat structure, the absolute J_sc value is relatively low (∼20 mA/cm²) as compared to the cells with natural textures (∼24 mA/cm²) [1, 2, 16]. The calculation result shows the intense carrier generation near the TiO₂ interface and a gradual increase in J_sc with depth. The contribution of J_sc at λ ≥ 500 nm accounts for 73% of the total J_sc, indicating that the longer λ response is critical to achieving high J_sc. In the MAPbI₃ cell, the effect of metal‐electrode backside reflection is large and the light is absorbed effectively even when the MAPbI₃ layer is thin [28]. When a MAPbI₃ absorber thickness is varied, J_sc saturates at a thickness of 400 nm [28], which is consistent with a general absorber thickness employed in perovskite cell fabrication.

Figure 11.10 further shows the EQE response when interface recombination at the front or rear interface is assumed. In Figure 11.10a, the α spectrum of MAPbI₃ (Figure 4.4) and the corresponding penetration depth of light, calculated from d_p = 1/α, are indicated. The d_p is very small (<70 nm) in the high‐α region (λ < 500 nm), but increases drastically in the longer λ region. Figure 11.10b shows the depth‐resolved light absorption (partial absorptance) of the MAPbI₃ layer in the n‐i‐p cell. Here, the white line indicates the 3d_p position, which corresponds to the upper limit of light absorption in the depth direction.

To visualize the influence of carrier recombination, we assume a dead layer in the front or rear interface region [29, 54]. The dead layer represents the carrier recombination region located at the front (rear) interface with a thickness of d_front (d_rear). In this simulation, all carriers generated in the dead layer are simply lost due to an intense recombination. The dotted lines in Figure 11.10b show the assumed dead layer thickness and the corresponding EQE spectra, obtained by varying d_front and d_rear, are shown in Figure 11.10c,d, respectively. These EQE spectra were calculated using the e‐ARC software [63] (Section 11.4.3).

It can be seen from Figure 11.10c that a slight increase in d_front up to 40 nm decreases the short‐λ EQE response significantly due to the strong light absorption near the TiO₂/MAPbI₃ interface. In contrast, the increase in the rear recombination deteriorates the EQE in the long‐λ region, but with a more moderate EQE variation due to uniform carrier generation in this λ region. Consequently, the effects of the front and rear interfaces appear primarily in the short‐ and long‐λ regions, respectively.

In Pb‐based perovskite cells, EQE variations in both short‐λ [54, 64] and long‐λ [3] regions have been observed, which can be interpreted by the change in interface recombination, provided that L_D is sufficiently long. In MAPbI₃ cells without HTL (i.e. n-i cells) [65, 66], the absence of an electric field in the rear interface enhances the carrier recombination at the MAPbI₃/metal interface, making the EQE spectrum similar to that observed at d_rear = 200–300 nm in Figure 11.10d. A large EQE reduction in longer λ has also been confirmed for Sn‐based solar cells [67, 68] (see Figure 14.18), due to the significant recombination in the solar cell bottom region. These results demonstrate the usefulness of EQE simulation analysis in finding the dominant carrier recombination region in solar cells. Note, however, that many high‐efficiency solar cells show 100% carrier‐collection efficiency in the short‐circuit condition (see Section 11.4.2).

11.4.2 Power Loss Mechanism

This section presents a detailed power‐loss analysis performed for a state‐of‐the‐art perovskite cell (η ∼ 20%) with a triple‐cation‐mixed Cs_0.05FA_0.8MA_0.15Pb(I_0.95Br_0.05)₃ absorber (see Figure 4.14). Figure 11.11 shows (a) the optical model (structure) of the analyzed cell and (b) the EQE analysis result. This solar cell has an n‐i‐p structure of glass/ITO/Sb‐doped TiO₂(ATO)/TiO₂/mp‐TiO₂/perovskite/PTAA/Au. In the analysis, to simplify the simulation, the optical effect of the mp‐TiO₂ is neglected while maintaining the total perovskite thickness. The EQE analysis was performed based on the ERS method [17, 28], which performs the EQE analysis by incorporating experimental reflectance spectra (ERS).

As shown in Figure 11.11b, the calculated EQE (red line) shows almost complete agreement with the experimental EQE (open circles), demonstrating a 100% carrier collection under the EQE measurement (short‐circuit) condition, as observed earlier [28]. Note that a strong electric field is present in the perovskite layer under the short‐circuit condition and the photocarriers are collected relatively easily, as discussed in Figure 11.6. In Figure 11.11a, the J_sc of the perovskite absorber and the J_sc losses induced by the R and A of the component layers are summarized. When 1‐sun illumination is converted completely into J_sc, we obtain J_sc,1sun = 28.9 mA/cm² for E_g = 1.55 eV. Among the J_sc losses, the R loss is the largest (2.9 mA/cm²), followed by the TCO loss (2.1 mA/cm²). Remarkably, the optical losses in the ETL, HTL, and Au metal electrode are almost zero, resulting in a very high optical gain (i.e. g = J_sc/J_sc,1sun) of g = 81%. This optical gain is higher than those of other thin‐film devices including CuInGaSe₂ and CdTe solar cells [54], but lower than those of crystalline Si devices (g = 86–89%) [15].

The above EQE analysis can further be combined with the J–V analysis to determine the precise power loss mechanism in the solar cell. Figure 11.12a shows the J–V curves obtained experimentally (open circles) and analytically (solid lines) for the CsFAMAPb(I,Br)₃ cell. When the resistance within solar cells is neglected, the J–V curve is given simply by

(11.1)

where J₀, q, k_B, and T denote the saturation current density, electron charge, Boltzmann constant, and temperature, respectively [14, 69]. The J–V curve denoted by the blue area in Figure 11.12a is obtained from Shockley-Queisser (SQ) theory (Section 12.2) [70] assuming E_g = 1.55 eV. In this case, two parameters J₀ = J_0,SQ and J_sc = J_sc,SQ can be calculated from the blackbody radiation at 300 K (ϕ_BB) and 1‐sun illumination (ϕ_1Sun), respectively (see Section 12.2).

In the SQ calculation, however, the parasitic light absorption is not considered and J_sc,SQ is notably higher than the experimental J_sc. In the next simulation step (green J–V area), J_sc obtained experimentally (J_sc,ex) is applied for Eq. (11.1) (i.e. J_sc = J_sc,ex, J₀ = J_0,SQ). From the experimental EQE spectrum and ϕ_BB, the radiative saturation current (J_0,rad) can further be estimated from Eq. (12.17). For the assumption of J₀ = J_0,rad, however, the calculated V_oc (1.27 V) is much higher than the experimental value (1.08 V). To adjust the theoretical V_oc to the experimental V_oc (V_oc,ex), the nonradiative recombination (i.e. defect‐induced recombination current) in the experimental cell is considered and the dark current is increased according to

(11.2)

where J_0,nonrad is the nonradiative dark current. The J–V curve obtained by adding the J_0,nonrad term is shown as the orange region in Figure 11.12.

In the next analysis, the series resistance (R_s) and shunt resistance (R_sh) of the solar cell are considered by the following equation [14]:

(11.3)

where n represents the diode factor. The J–V curve with the red region indicates one obtained assuming R_s = 1.8 Ωcm² and R_sh = 1.3 kΩcm² while using n = 1 in Eq. (11.3). In the final fitting analysis, n is varied and the experimental J–V curve (yellow region) is reproduced almost perfectly when n = 1.6 (red line in Figure 11.12a). In this case, J_0,nonrad is modified slightly by

(11.4)

assuming that V_oc/R_sh → 0. The numerical values of the above analyses are summarized in Table 11.1.

From the step‐by‐step analyses described above, the exact power loss mechanism in the solar cell can be determined (Figure 11.12b). The SQ limit for E_g = 1.55 eV is η = 31.44%, where the experimental cell shows η = 19.95%. The difference between these efficiencies (Δη = 11.5%) can be decomposed into the loss contributions arising from J_sc, J₀, R (R_s and R_sh) and n. Roughly half of the efficiency loss (4.17%) is caused by the dark current generation due to the nonradiative recombination (i.e. J_0,nonrad). The relatively large loss arising from n (Δη = 1.1%) can also be interpreted as a result of the recombination within the cell. The second largest loss originates from the J_sc reduction due to the light reflection (Δη = 2.4%), whereas the influences of R_s and R_sh are also notable (Δη = 1.6% in total). The above analysis results indicate clearly that the 19.9%‐efficient CsFAMAPb(I,Br)₃ solar cell is limited essentially by the nonradiative recombination and unoptimized high reflectance of the cell. For this cell, it is most likely that intensive recombination occurs predominantly in the interface regions, as discussed in Section 11.5.

11.4.3 e‐ARC Software

Many analyses described in Section 11.4 can be performed based on a Windows‐based free computer software (e‐ARC software) [63]. Figure 11.13 shows the screenshot of the e‐ARC software, which indicates the analysis example for a MAPbI₃ cell. This software allows the complete analysis of the optical gain/loss as well as the calculation of the maximum conversion efficiency for designed solar cell structures. In the software, the EQE spectra of various solar cells can be calculated by applying e‐ARC method, in which the absorptance of submicron‐textured thin film structures can be deduced by applying the antireflection condition [54] (see Figure 12.10). This software also enables an EQE analysis based on the ERS method [17, 54], which was adopted in the EQE analysis of Figure 11.11. The carrier recombination effect within solar cells can explicitly be incorporated into the analysis, as performed in Figure 11.10. The software is quite easy to operate and is recommended for those who wish to gain a better understanding of the carrier generation/loss and theoretical limit of solar cells.

11.5.1 Effect of Interface

Carrier recombination in hybrid perovskite solar cells occurs predominantly at the interfaces [40, 78–82], limiting the V_oc of high efficiency cells. The V_oc reductions caused by individual interfaces formed with the ETL and HTL have been investigated quantitatively based on photoluminescence (PL) emission measurements [40, 81, 82]. In this method, V_oc loss is characterized analytically by observing the PL quantum yield (Q_PL) under a 1‐sun illumination condition. An important physical concept underlying this technique is the fact that good solar cells are essentially good photo emitters (i.e. light‐emitting diodes) [83–85] and thus shows high Q_PL. The V_oc loss in solar cells can uniquely be related to Q_PL by considering the diode equation written simply as

(11.5)

where J_rad is the radiation current density, which is equivalent to the current contributing to light emission, and J_0,rad is the prefactor. For simplicity, the “−1” term in Eq. (11.1) is omitted in Eq. (11.5). By setting V = V_oc in Eq. (11.5), we obtain

(11.6)

Here, we consider the current density contribution generated by light absorption (J_ab) and modify the above equation as follows:

(11.7)

Now, the ratio of J_rad/J_ab represents the current density ratio of light emission and absorption and defines Q_PL (i.e. Q_PL = J_rad/J_ab). Moreover, in solar cells, J_ab = J_sc. Accordingly, from Eq. (11.7), we obtain the following relation [83, 85]:

(11.8)

where V_oc,rad is V_oc originating from J_0,rad, thus the theoretical V_oc limit. Note that Q_PL < 1 and, therefore, the term k_BTlnQ_PL/q shows the negative contribution to V_oc. In other words, the detrimental effect of the perovskite interface on V_oc can be determined explicitly by measuring Q_PL. A significant merit of this method is that V_oc reductions induced by the ETL and HTL can be evaluate separately based on the obtained Q_PL even for structures that are not solar cells. For example, by measuring the Q_PL of a substrate/perovskite/PTAA structure, the V_oc reduction due to the perovskite/PTAA interface can be assessed.

Figure 11.15 shows the effect of interface recombination on V_oc in CsFAMAPb(I,Br)₃, determined analytically from Q_PL measurements using Eq. (11.8) [40]. In Figure 11.15, the V_oc potential values obtained for each interface formed with the HTL or ETL are summarized. The V_oc indicated as “Pero” (1.23 V) is extracted from a substrate (fused silica)/perovskite structure, showing a reference level without a significant influence of interface recombination.

When a perovskite/ETL(HTL) interface is formed, Q_PL decreases rather drastically, leading to a notable reduction in the implied V_oc. The Q_PL reduction by the interface formation is consistent with the general observation that the carrier lifetime is shortened drastically by the ETL (or HTL) interface formation (Figure 6.5b) [86–88]. For the HTL in Figure 11.15, the V_oc becomes low when PEDOT:PSS and P3HT layers are adopted, while PTAA provides the best interface with a smaller V_oc loss. The V_oc characteristic of spiro‐OMeTAD is slightly inferior to that of PTAA. For the ETL, the direct formation of the perovskite on ITO increases the V_oc loss. The recombination at the PCBM and C₆₀ interfaces is also relatively strong, whereas SnO₂ and TiO₂ provide much better interfaces with higher V_oc.

The result of Figure 11.15 is of critical importance, as it provides a general guideline for perovskite cell design. In particular, a systematic Q_PL measurement shows that the V_oc decreases sequentially as the ETL and HTL interfaces are formed. Figure 11.16 shows an example of how V_oc is reduced by the formation of ETL and HTL [81]. It can be see that the V_oc losses at the ETL and HTL interfaces add up to determine the final V_oc of the cell.

The characterization results in Figure 11.15 show that, for the n‐i‐p configuration, the TiO₂/perovskite/PTAA structure ensures low interface recombination at both interfaces, highlighting why this structure has become the standard for hybrid perovskite cells. Moreover, a high V_oc of 1.23 V is reported for an n‐i‐p SnO₂/perovskite/spiro‐OMeTAD cell [72], which is consistent with the result of Figure 11.15. For the p‐i‐n configuration, the application of PEDOT:PSS/perovskite/PCBM leads to a low V_oc due to the strong interface recombination occurring at both ETL and HTL interfaces and the PTAA/perovskite/PCBM structure outperforms both PEDOT:PSS and P3HT cells. Note, however, that the overall results shown in Figure 11.15 have been obtained for specific process conditions, and the optimization of layer processing improves the absolute V_oc values of Figure 11.15. In fact, a remarkably high V_oc of 1.26 V has been reported for a p‐i‐n PTAA/MAPbI₃/PCBM cell [10]. For MAPbI₃ cells, V_oc,rad = 1.32 V, resulting in a simple relation of V_oc = 0.026lnQ_PL + 1.32 V from Eq. (11.8). The V_oc of 1.26 V observed in the MAPbI₃ cell corresponds to Q_PL = 0.1, indicating that, even in over 20% efficiency perovskite cells, Q_PL is rather small and many carriers still recombine nonradiatively at the interfaces.

11.5.2 Effect of Passivation

As we have seen in Section 11.5.1, interface recombination leads to a substantial V_oc reduction, limiting the efficiency of perovskite solar cells. Fortunately, the intense carrier recombination at the perovskite interfaces can be suppressed effectively by providing sophisticated passivation layers [89–108]. In fact, when a MAPbI₃ layer is terminated by a Lewis‐base ligand (tri‐n‐octylphosphine oxide; TOPO), a drastic improvement of Q_PL from 0.03 to 0.35 has been reported [78, 79]. An extremely long PL lifetime of 8 μs has also been observed for the TOPO‐passivated surface [78] (see Figure 1.6). Accordingly, the passivation of a hybrid perovskite surface (i.e. perovskite rear interface in a cell) has a dramatic impact on suppressing nonradiative recombination, which is presumably induced by vacancies of organic cation and halide atoms [39, 103, 104].

A significant passivation effect has been observed when a wide‐bandgap halide (WBH) perovskite layer is introduced at the perovskite/P3HT rear interface (Figure 11.17a) [93]. In this structure, a thin WBH layer (12 nm) consisting of a double‐layered perovskite crystal is formed by treating a FAMAPb(I,Br)₃ absorber layer with n‐hexyl trimethlyammonium bromide (HTAB). The P3HT polymer on the WBH is further self‐organized along the preferred direction. By introducing the WBH passivation layer, the V_oc improves drastically by 227 mV from 0.925 to 1.152 V, while the cell efficiency also increases remarkably from 15.8% to 23.3%. Recall from Figure 11.15 that the perovskite/P3HT interface is particularly defective, compared with the perovskite/PTAA interface, and thus the passivation effect is more drastic. The mechanism for the suppression of nonradiative interface recombination is illustrated in Figure 11.17b. The photoelectron characterization of the layers, however, indicates the formation of small energy barrier for holes at the perovskite/WBH interface [93]. The above study shows the exciting result that high efficiency cells can still be fabricated using an inexpensive P3HT HTL by effectively passivating the perovskite rear interface, while avoiding the use of an expensive spiro‐OMeTAD.

Table 11.2 summarizes the results of different passivation approaches performed for the n‐i‐p and p‐i‐n cells. The η and V_oc in the table show those obtained by introducing a passivation layer (or reactant) indicated by a square bracket, whereas ΔV_oc represents the V_oc improvement obtained through the introduction of the passivation layer; V_oc − ΔV_oc in the table corresponds to the V_oc of the unpassivated cells. The basic concept of passivation involves the introduction of a thin wide‐gap perovskite (a 2D planar‐type perovskite crystal) [89–93] or an insulating layer. As insulating passivation layers, various organic materials (polymers [95–101], organic salts [102–104], molecules [105, 106]), and inorganic layers (LiF [107] and Al₂O₃ [108]) have been adopted. In Table 11.2, the largest ΔV_oc is obtained for the n‐i‐p cell shown in Figure 11.17. The passivation effect is smaller in the n‐i‐p cells with spiro‐OMeTAD HTLs (ΔV_oc ∼ 50 mV). For a p‐i‐n cell, treatment of the perovskite rear surface by choline chloride [103] or guanidinium bromide [94] is particularly successful with a large ΔV_oc exceeding 100 mV.

The results of Table 11.2 demonstrate that the passivation of the perovskite rear surface is a very important approach for achieving high V_oc. Note, however, that very high V_oc values of 1.23–1.26 V have been reported for the n‐i‐p and p‐i‐n cells without the introduction of passivation layers [10, 72]. Accordingly, detailed processing is also of critical importance in improving an absolute V_oc. In fact, the V_oc increases largely by adopting a process that enhances the ordering of PCBM molecules [109] or by minimizing the HTL doping concentration [72]. Nevertheless, the incorporation of a passivation layer is an effective approach for fabricating higher efficiency cells, enabling more effective control of the nonradiative recombination occurring at the interfaces. Moreover, the introduction of a passivation layer leads to the significant improvements in fill factor (FF), cell stability, and a reduction in unfavorable J–V hysteresis characteristics [89, 91, 93]. A state‐of‐the‐art passivation technique has also been incorporated in the fabrication of a FAPbI₃‐based perovskite cell that shows a high efficiency of 24.66% [6].

11.5.3 Effect of Grain Boundary

In general, the grain boundary formation is detrimental for solar cells and the V_oc of Si solar cells, for example, increases as grain size becomes larger [110]. Remarkably, even though the grain sizes of hybrid perovskite polycrystals are relatively small (∼1 μm), a very high carrier lifetime (∼8 μs) [78] and a quite high V_oc [10] have been observed. Thus, nonradiative recombination at grain boundaries is suppressed extremely well in hybrid perovskite thin films. This is a characteristic that can be considered as a key factor in achieving >20% efficiencies in polycrystalline devices. In fact, efficient carrier extraction in the grain boundary region has been confirmed experimentally (Chapter 9).

Figure 11.18 shows the influence of average grain size on V_oc, FF, and the diode factor n in hybrid perovskite cells with η ∼ 20% [6–8, 91, 94, 104, 111]. The n values in Figure 11.18 are extracted from the reported J–V characteristics by applying Eq. (11.3). Although data shown in Figure 11.18 are obtained from different perovskite materials and structures, the implications of the results are quite clear; (i) V_oc is essentially independent of the grain size and remains unchanged unless the grain size is very small (∼100 nm) [111, 112] and (ii) FF improves markedly as the perovskite grain size increases, reaching 86% in a large‐grain MAPbI₃ cell reported in Ref. [8]. The constant V_oc observed at different grain sizes indicates that V_oc is limited by the surface (interface) recombination and the grain boundary plays a minor role for nonradiative recombination. For the increase of FF with grain size, the improvement of n is mainly responsible and we observe n = 1.46 at large grain sizes. The results of Figure 11.18 demonstrate that perovskite polycrystals with larger grains are preferable for improving the cell efficiency.

It should be emphasized that the grain boundary significantly hinders the carrier transport in the perovskite thin films. Indeed, in‐plane carrier mobility [∼5 cm²/(V s)] is much lower than the intragrain mobility [∼30 cm²/(V s)] (see Figure 6.4). However, when the grain size exceeds the film thickness, there is no grain boundary in the carrier transport direction (i.e. vertical direction) of the cells [111] and thus the detrimental effect of the grain boundary is minimized.

For the exact grain‐boundary structures of the perovskite films, however, controversial results have been reported [11, 94, 113]. In an early report [113], it was suggested that the grain boundary is predominantly composed of PbI₂ and that the perovskite grains are surrounded by thin PbI₂ shells. The perovskite growth under a PbI₂‐rich condition is often considered to be beneficial to enhance the grain‐boundary passivation through the PbI₂ component. Nevertheless, more recent studies have shown that an excess PbI₂ component is present as isolated PbI₂ grains and does not exist selectively in the grain boundary region [11, 94]. To date, several attempts have been made for “grain‐boundary engineering,” in which the grain‐boundary chemical structures are modified, and the improved solar cell efficiency has been attained (see Chapter 9).

For the p‐i‐n cells with PCBM ETLs, it has been proposed that PCBM molecules diffuse from the ETL back interface into the perovskite absorber through the grain boundary region, which in turn passivates the grain‐boundary trap states [30]. As discussed above, however, the perovskite/PCBM interface shows relatively strong interface recombination and the diffusion of disordered PCBM molecules is expected to enhance the nonradiative recombination by widening the n‐type interface region. In fact, when a chemical barrier layer (i.e. passivation layer) is placed at the perovskite/PCBM (or C₆₀) interface, V_oc improves effectively (see Table 11.2). Thus, the beneficial role of PCBM diffusion into the grain boundary region is questionable.