Effects of photon recycling and scattering in high-performance perovskite solar cells.

Efficient external radiation is essential for solar cells to achieve high power conversion efficiency (PCE). The classical limit of 1/2n2 (n, refractive index) for electroluminescence quantum efficiency (ELQE) has recently been approached by perovskite solar cells (PSCs). Photon recycling (PR) and light scattering can provide an opportunity to surpass this limit. We investigate the role of PR and scattering in practical device operation using a radiative PSC with an ELQE (13.7% at 1 sun) that significantly surpasses the classical limit (7.4%). We experimentally analyze the contributions of PR and scattering to this strong radiation. A novel optical model reveals an increase of 39 mV in the voltage of our PSC. This analysis can provide design principles for future PSCs to approach the Shockley-Queisser efficiency limit.

INTRODUCTION

Increasing the power conversion efficiency (PCE) of solar cells is crucial for the widespread exploitation of renewable solar energy sources. The famous Shockley-Queisser (SQ) theory () predicts an upper limit for solar cell efficiency based on a radiation balance argument: To approach the SQ limit, solar cells must also have high radiation efficiency, as proven, e.g., for GaAs cells (). Substantial efforts have been devoted in the past decades to improving the PCE of thin-film solar cells, which offer advantages such as low material consumption and flexibility. The most notable example is perovskite solar cells (PSCs), whose PCEs have increased from 3.8% to above 25% in only a decade (–), raising the obvious question of whether PSCs will be able to reach the SQ limit. While state-of-the-art PSCs have already achieved near-unity light absorption and efficient charge collection under short-circuit conditions (–), enhancing electroluminescence (EL) quantum efficiency (ELQE) is believed to be the final key to reducing voltage loss and reaching the SQ limit. However, according to classical optics, the outcoupling efficiency of planar devices is limited to 1/4n2 (n, refractive index of emitter), which increases to 1/2n2 by implementing a back reflector, approximately 7.4% for PSCs (n ~ 2.6) (, ). Regarding recently reported high ELQEs approaching this limit (, , –), classical optics predictions indicate that PSC efficiencies are already near the saturation point.

Therefore, it is important to investigate photon recycling (PR) and scattering, which can surpass the classical limit of ELQE and provide a new pathway toward higher efficiency. For photons in a trapped mode, subsequent events of reabsorption and reemission (i.e., PR), as well as scattering, randomize the emission angle and offer a second chance at outcoupling (–). PR is particularly relevant to metal halide perovskites, which exhibit large overlaps between their emission and absorption spectra. PR has attracted significant attention since its first observation in 2016, and its effectiveness has been investigated in light-emitting diodes (LEDs) (–). On the other hand, the benefits of PR in PSCs have not been clearly quantified for several reasons: (i) The ELQEs of early PSCs were mostly far below 1/2n2 ~ 7.4% and internal radiation efficiency (ηrad) was also low in full devices, where only a few PR events can occur effectively, considering that (ηrad) of the photon flux survives after recursive PR events over N cycles. (ii) It is challenging (, ) to separate the contributions of PR and scattering from the overall emission of perovskites experimentally, which will be detailed later in this paper. (iii) The quantitative analysis of light emission in PSCs is complicated by the fact that the light extraction efficiency (LEE) of radiation significantly deviates from 1/2n2, mainly on the basis of high levels of reabsorption (, ). Compared to LEDs with thin emissive layers, the external radiation of PSCs is more difficult to describe because a high level of light scattering caused by large grains and rough surfaces strongly affects light propagation (, ).

RESULTS AND DISCUSSION

Highly radiative perovskite solar cell

To investigate the role of PR and scattering processes in practical devices, we prepare a highly radiative PSC with the following structure: glass/fluorine-doped tin oxide (FTO)/SnO2/octylammonium (OA) bromide (OABr)–passivated (FAPbI3)0.95(MAPbBr3)0.05 perovskite [formamidinium (FA) and methylammonium (MA)]/2,2′,7,7′-tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9′-spirobifluorene (spiro-OMeTAD)/Au (Fig. 1A and fig. S1), by integrating up-to-date strategies for suppressing nonradiative losses. To improve band alignment and reduce nonradiative quenching, the SnO2 electron-selective layer is grown via chemical bath deposition (, , ). An OA-based two-dimensional (2D) perovskite is formed on top of the 3D perovskite to passivate defects (, ) and form an appropriately coordinated 2D/3D heterojunction (). Figure 1B and fig. S2 present the emergence of new x-ray diffraction (XRD) peaks and a textured surface morphology corresponding to the formation of OA-based 2D perovskite (). The PCEs are measured to be 24.1 and 24.0% with and without an aperture mask, respectively (Fig. 1C), which clearly exceed the 22.1% efficiency of a device without OABr (fig. S3). The open-circuit (OC) voltage (Voc) of 1.21 V in the fully illuminated device slightly decreases with the use of a mask based on reduced effective current density.

Fig. 1.

Device performance.

(A) PSC device configuration and schematic. (B) Ratio of XRDs of perovskites with and without OABr passivation [inset: scanning electron microscopy images of perovskite surfaces]. (C) Measured J-V curves of our PSC with and without an aperture mask (device area, 0.205 cm2; mask area, 0.093 cm2). (D) Measured EQE and EL spectra. A.U., arbitrary units. (E) Measured PLQEs (film) and ELQEs (device) at various excitations. The dashed line corresponds to 1-sun excitation. (F) J-V curve calculated from the Shockley equation (295 K) in comparison to the measured curve. (G) Ratio of self-excited photocurrent densities of pixels 2, 3, and 4 to the injected current density of pixel 1.

Figure 1D presents the measured spectra of the external quantum efficiency (EQE) and EL, which exhibit significant overlapping. The photoluminescence (PL) of the perovskite film and EL of the full device are measured under various optical and electrical excitations, respectively, and their efficiencies are presented in Fig. 1E. Instead of reaching the steady state, ELQE is swept in both forward and reverse directions to keep the consistent condition as that for the solar simulator. At low intensities (below 1 sun), both PLQE and ELQE increase as excitation increases on the basis of the bimolecular behavior of radiative recombination in 3D perovskites (). At a 1-sun equivalent excitation of Jph/q = 1.55 × 1021 m−2 s−1 (Jph = 24.8 mA cm−2), the film and device exhibit a high PLQE of 40% and ELQE of 13.7% (dual-sweep average), respectively. The maximum ELQE of 14.2% appears at a higher excitation of 2.9 × 1021 m−2 s−1.

On the basis of well-passivated defects and reduced quenching, our PSC’s ELQE is among the highest values reported for PSCs (, ). While many of previous studies reported high PSC ELQEs (5 to 10%) at the maximum point, achieved mostly at a high J of ~102 mA cm−2 (, –), it is noteworthy that our ELQE at Jph is already as high as the maximum value, hence, more effective in solar cell performance. This ELQE value significantly exceeds the classical limit of 1/2n2 ~ 7.4%, which implies the presence of additional effects such as PR and scattering. We emphasize that although there have been several reports of LEDs exceeding this limit, this could be related to additional benefits such as the use of microcavities, dipole alignment, and plasmonic effects, resulting from their thin emitter thickness (<100 nm) in addition to PR (, , –). It is remarkable that we observe a violation of this classical ELQE limit in a PSC with a thicker active layer (~500 nm), which causes high reabsorption losses and excludes the aforementioned optical benefits (, ), as well as interfaces for charge extraction, which can quench radiative recombination.

According to the EQE, a radiative limit for Voc (Vrad) (, ) of 1.27 V can be obtained (fig. S5). The nonradiative voltage loss [Vnr = (kBT/q) ln(ELQE) (, –), where kB is the Boltzmann constant, T is the temperature (295 K), and q is the electron charge] is calculated to be 50 mV at OC, which is the lowest value among reported PSCs. Figure 1F demonstrates that the measured J-V curve can be easily reconstructed using the Shockley equation (, , ) with the measured ELQE(J) and Vrad as inputs and without any arbitrary fitting, except for the series resistance (Rs = 18 ohms; see the Supplementary Materials). The result proves the reciprocal relationship in the device physics for light emission and solar cell operation.

The high ELQE of our PSC facilitates the demonstration of self-excitation effects, which are the primary evidence for PR. When the left-most pixel (P1) is excited by an external bias, the radiated photons propagate laterally mainly through the substrate mode and excite the next pixels through reabsorption (), as shown in Fig. 1G. The quantum efficiencies, the generated photocurrents over the injected current, are measured to be <0.50% (P2), <0.24% (P3), and <0.12% (P4), respectively.

Elucidating the effects of PR and light scattering

Both PR and scattering can contribute to the high ELQEs by breaking the trapped modes. To separately highlight the roles of PR and scattering in PSCs, we design an intensity-dependent spatially resolved PL experiment, as shown schematically in Fig. 2A. The excitation beam is focused on a specific spot on the PSC, and PL is measured at various lateral distances from the excitation spot. During lateral propagation in the waveguide mode, the spectrum becomes red-shifted as high-energy photons are preferentially absorbed by the perovskite. While photons in the perfect waveguide mode cannot outcouple, they become measureable when they undergo a PR or scattering event. Because scattering (assumed to be elastic) only changes the propagation angle, the red-shifted spectrum is directly recorded. On the other hand, PR resets not only the angle but also the spectrum based on the fast thermalization of excited charge carriers; hence, the photons outcoupled through PR have a spectrum identical to the initial PL (, ), more blue than those from scattering.

Fig. 2.

Excitation-dependent spatially resolved PL.

(A) Schematic of the setup for spatially resolving PL on the full device stack, excluding the Au electrode. (B) Relative intensities of PL at various wavelengths when R = 0 is excited by a focused pulse laser (12.5 nJ). PL is multiplied by R to compensate for radial dilution. (C) Absorption coefficient of OABr-passivated (FAPbI3)0.95(MAPbBr3)0.05 perovskite. (D) PL intensities at various R values and a wavelength of 790 nm with varying excitation intensities to distinguish PLs broadened by diffused excitation (30 μm) and PR (70 and 120 μm). (E) Measured PL at 0 μm (PL0) and 70 μm (PL70). PL70 − PL0 is plotted to approximate the spectrum of scattered light.

Figure 2B presents the measured PL as a function of the distance (R) from the point of excitation. At R > 50 μm, the curves for 790, 820, and 860 nm are split and decay on different slopes according to the different absorption coefficients (Fig. 2C). At 860 nm, where the absorption is only ~3 cm−1, the measured slope of 240 cm−1 can be mainly attributed to light scattering occurring in the waveguide mode (). The PL intensities become flattened at distances over 120 μm, mainly on the basis of photons returning from the surface of the glass substrate via Fresnel reflection ().

Because of the absorption coefficients larger than the decay from scattering (240 cm−1), the decay slope increases for shorter wavelengths of 790 and 820 nm. At 790 nm, the curve is broadened to 60 μm and decays as slowly as that at 860 nm in the range of 60 to 120 μm, despite the short absorption length (<1 μm). This can occur if 790-nm photons are generated at a greater distance by recycling long-wavelength photons in the waveguide mode. Therefore, such spatially broadened PL has been presented as evidence of PR in several pioneering reports on PR effects (, ). However, we note that another possible cause of PL broadening, one that has not been studied thus far but must be excluded to conclusively demonstrate PR, must be considered. Under highly focused excitation, the PL in the central region is inefficient because of, among other reasons, Auger recombination. In comparison, areas at greater distances are under weaker excitation based on the Gaussian excitation profile and can have a higher radiation efficiency. Therefore, the spatial distribution of the directly excited PL is already broader than the spatial resolution of the focused excitation, even in the absence of contribution from PR and scattering.

To resolve this issue and identify the contributions of PR, we vary the intensity of laser excitation, making it possible to distinguish between the two possible physical origins of PL at large distances, as shown in Fig. 2D. When the excitation is low, the 790-nm PL at 0 μm is in the range of 104 to 105 and follows a logarithmic slope of 1.5, which is larger than 1 because of the bimolecular nature of radiative recombination. The same phenomenon can be observed for PL at 30 μm, which also exhibits a slope of ~1.5 at PL intensities of 104 to 105 (i.e., the curve for 30 μm can be fitted by laterally shifting the curve for 0 μm). This observation implies that the PL at 30 μm is predominantly associated with excitation by diffused direct light rather than PR. In contrast, at 70 and 120 μm, the slopes at PL values of 104 to 105 (at excitation ~10 nJ) are much smaller than that at 0 μm, implying that direct excitation does not play a dominant role at these distances. Therefore, by excluding all these possibilities, we can conclude that the emission at 790 nm at 70 and 120 μm originates from PR. The slope at 10 nJ is 0.5, which is consistent with the slope of the PL source (equal to 0.33, for 0 μm at a given excitation) multiplied by the slope for the reradiation (equal to 1.5, for 0 μm at a given PL intensity), representing the physics of a single event of PR. The slope slightly decreases for 120 μm at 10 nJ because of the influence of photons that are generated at 0 μm and traveled the substrate by Fresnel reflection at the surface. Figure 2E compares the measured spectra at 0 and 70 μm. At 70 μm, the spectra from PR (identical to PL0) and scattering (PL70 − PL0) are clearly distinguishable in the mixed spectrum, demonstrating that both mechanisms contribute to the external emission of PSCs.

Figure 3 presents the spatially resolved EL as direct evidence for the contribution of PR and scattering to practical solar cell operation. Photons are generated by current injection, and those in the trapped mode can propagate to the outside of the cell area (Fig. 3A). As shown in Fig. 3B, the laterally diffused EL is similar to the previously described PL. While the EL at 790 nm can be mainly attributed to PR, the EL at 820 and 860 nm appears broader on the basis of the lower reabsorption at these wavelengths, making the contribution of light scattering relatively stronger. The role of PR is further investigated through additional experiments on spatially resolved EL in the backward direction and photocurrent measurement in response to backward optical excitation. The results are presented in figs. S6 and S7.

Fig. 3.

Spatially resolved EL.

(A) Schematic of the setup for spatially resolving EL near the edge of the Au electrode on the full device. The Au-covered area is excited by current injection of 52 mA cm−2. (B) Spatial profile of forward EL at various wavelengths. The gray line represents the transmission profile of a backlight (wavelength, 900 nm) illuminated from the electrode side.

Quantification of PR and scattering effects

Despite rapidly growing interest in the EL of PSCs, a suitable method for modeling the EL of these devices has yet to be developed. In particular, as we have shown experimentally, the recent success of highly efficient PSCs cannot be explained without quantitatively understanding the role of PR and scattering processes. Here, we establish an optical model that is generally applicable for quantifying various optical parameters in PSCs, thereby providing important insights into solar cell design that should allow new devices to reach the SQ limit. The electromagnetic fields at each interface in a PSC stack are calculated using a method that was recently presented for LEDs with reabsorbing emitters (, ). However, the method developed for LEDs assumes that all layers in a device are perfectly smooth and homogeneous, whereas in PSCs, which have a thicker active layer, larger grains, and rough interfaces, scattering effects must be considered for accurate modeling. To resolve the complicated optical behavior of scattering, we propose an effective scattering coefficient (S0) for quantification. In this model, which assumes an infinite lateral dimension, a photon in the trapped mode is eventually either reabsorbed by perovskite (Aact) or parasitic layers (Apara) or scattered at a rate of S0 (Fig. 4A). A photon is replaced by a new dipole with a random orientation at the same wavelength at each scattering event. This model cannot fully reflect all of the physical processes in a real system, such as the nonisotropic angular distribution of scattered light. However, it is plausible to select an effective value of S0 that represents the equivalent quantity of apparent light scattering and approximates its contribution to outcoupling efficiency. In our PSC, an S0 value of 3.2 × 103 cm−1 can be derived from the measured decay slope of 240 cm−1 at a wavelength of 860 nm (Fig. 2B) and assumed outcoupling efficiency of 1/2n2 (n = 2.6). Figure 4B presents the calculated fractions of outcoupling, Aact, Apara, and scattering in our PSC at each wavelength. PR and scattering recursively generate new dipoles until no photons remain in the trapped mode. While Aact is more relevant for short wavelengths, the contribution of scattering is greater at long wavelengths, where Aact is small. These spectral characteristics result in external EL red shifting from the internal spectrum. Figures S9 and S10 show additional details.

Fig. 4.

Quantification of PR and scattering effects in practical device operation.

(A) Schematic of light emission and trapped modes in PSCs. (B) Calculated fractions of outcoupling, scat, Aact, and Apara at each wavelength (background). The external EL spectrum is obtained by considering PR and scattering effects for an ηrad of 78%. (C) Calculated ELQEs of a full device as a function of ηrad, including and excluding PR and scattering effects. The brown dashed line is derived from a classical calculation ignoring Apara and scattering. (D) Voltage, ηrad, ELQE, −ΔVnr, and ratio of photons undergoing given number of recursive PR and scattering events in external EL as functions of J for our PSC. MPP, maximum power point. (E) Benefits of PR and scattering in Vnr as a function of ηrad.

Figure 4C presents the calculated external ELQE, which has a nonlinear relationship to ηrad based on PR effects (). The measured 1-sun equivalent ELQE of 13.7% in our PSC corresponds to an ηrad of 78%. The ELQE from direct outcoupling is calculated to be only 3.1% at ηrad = 78%, indicating that PR and scattering enhance the ELQE of the PSC by a factor of 4.5. The maximum ELQE at the radiative limit is 34%, which still does not reach unity on the basis of the losses stemming from Apara (, ). For comparison, Fig. 4C also presents the results of a classical ray optics calculation for PR that assumes a direct LEE of 1/2n2 and ignores Apara and scattering (, , ). The exclusion of Apara results in a considerable overestimation, particularly at high ηrad values, demonstrating the necessity of our comprehensive modeling approach.

While PR and scattering significantly improve the ELQE of our device in operation as an LED, the enhancement needs to be translated into the power output to evaluate their effectiveness in photovoltaic operation because Vnr is proportional to log(ELQE). Figure 4D presents the contributions of PR and scattering at each J in the PSC. The ELQE(J) under illumination is assumed to be the same as the ELQE(J + Jph) measured under dark conditions. The ηrad and direct ELQE (excluding the effects of PR and scattering) are obtained using the relationship shown in Fig. 4C. Upon increasing the external bias, more charge carriers are injected and ηrad increases. While scattering improves ELQE by 73% (e.g., 3.1 to 5.3% at OC) and reduces Vnr by 14 mV regardless of ηrad, the contribution of PR increases as J increases on the basis of the enhanced reradiation efficiency. At OC, more than 78% of outcoupled photons have undergone at least 1 PR or scattering event, and 8% of these photons have experienced at least 10 of these events. These effects reduce the Vnr of our PSC by 39 mV (from 89 to 50 mV), which is not as marked as the ELQE enhancement but still considerable.

It should be noted that the contribution of scattering to the reduction of Vnr may not lead to a real increase in Voc because Voc is equal to Vrad − Vnr and Vrad can also be affected by scattering. Light scattering increases the optical path length of incoming light and enhances band-edge absorption, resulting in a reduction in the apparent bandgap and Vrad (). The decreases in Vrad and Vnr compensate for each other, keeping Voc unchanged (, ). This means that scattering processes enhance the photocurrent without voltage loss, unlike in the case of a real bandgap reduction, resulting in a trade-off between Jph and Voc. Therefore, it is reasonable to suppose that the reduction of Vnr caused by scattering still causes a net increase in PCE in addition to that caused by PR, which enhances Voc without changing Vrad or the photocurrent.

The first panel in Fig. 4D compares the J-V curves with and without the benefits of PR and scattering. While PR and scattering enhance Voc from 1.17 to 1.21 V (an increase of 3.3%), the PCE increases from 23.3 to 24.0% (an increase of 3.1%). The small reduction in the fill factor from 80.1 to 79.9% stems from the lower ELQE (8.4%) and corresponding smaller PR contribution at the maximum power point (MPP) when compared to the OC condition. Although a high ηrad of 78% is already achieved at OC, this result indicates that there is more room for enhancing ηrad at the MPP, which is more directly relevant to PCE.

Figure 4E presents the contribution of PR and scattering to the reduction of Vnr as a function of ηrad. The benefit increases as ηrad increases on the basis of the enhancement of PR. In an ideal PSC that exhibits an ηrad of 100% and an Rs of 0 ohms, a benefit of 55 mV and a maximum PCE of 27.4% could be achieved (device B in Fig. 5 and fig. S11). This provides a practical upper bound of PCE for PSCs in their current form, leaving only small room for the enhancement of state-of-the-art PCE (>25%) (, ).

Fig. 5.

Calculated ELQE, Voc, and PCE with (light + dark) and without (dark) PR and scattering for various ideal PSCs.

(Left) Rectangular EQE and corresponding EL spectrum assumed for devices C and D.

Additional breakthroughs will require fundamental changes in device and material properties. Device C (Fig. 5 and fig. S12) assumes an ideally rectangular EQE [i.e., zero Urbach energy for band edge at 807 nm (unchanged Vrad of 1.27 V)], resulting in an enhanced Jph and perfect overlap of EL (assuming Boltzmann distribution of free charges). Increased reabsorption results in increased benefits of PR and scattering of 71 mV and a PCE of 30.7%. While the ELQE still does not reach unity because it is limited by Apara even for an ηrad of 100%, future research to reach the SQ limit must be accompanied by optical approaches to overcome this limitation, including plasmonic nanostructures, microtextured surfaces, and novel device architectures suppressing Apara (, , –). Device D (Fig. 5 and fig. S13), which has no parasitic layers, exhibits a maximum ELQE of 100% and a PCE of 31.3%, where PR and scattering contribute a Voc of 79 mV and a PCE of 2.1%. Likewise, unlike in early PSCs with low ELQEs, understanding and using the effects of PR and scattering will play a key role in developing future PSCs to approach the SQ limit. This research represents a first step in this direction.

MATERIALS AND METHODS

Materials

Lead halides (PbI2 and PbBr2) were purchased from Tokyo Chemical Industry. Formamidinium iodide (FAI), methylammonium bromide, and OABr were purchased from Dyesol. Methylammonium chloride (MACl), lithium bis(trifluoromethanesulfonyl)imide salt (Li-TFSI), anhydrous dimethylformamide (DMF), anhydrous dimethyl sulfoxide (DMSO), chlorobenzene, acetonitrile, and 4-tert-butylpyridine (tBP) were purchased from Sigma-Aldrich. Last, 2,2′,7,7′-tetrakis(N,N-di-p-methoxyphenylamino)-9,9′-spirobifluorene (spiro-OMeTAD) and tris(2-(1H-pyrazol-1-yl)-4-tert-butylpyridine)-cobalt(III)tris(bis(trifluoromethylsulfonyl)imide)) salt (Co-TFSI) were purchased from Lumtec.

Sample preparation

Perovskite preparation

The 3D perovskite solution was prepared by dissolving FAI (1.37 M), PbI2 (1.37 M), MAPbBr3 (0.07 M), and MACl (0.5 M) into a mixed solvent consisting of DMF:DMSO = 8:1 (volume ratio). The solution was spin-coated at 1000 rpm (ramp 1000 rpm/s for 5 s) followed by 5000 rpm (ramp 1500 rpm/s for 30 s). Ten seconds after reaching 5000 rpm, diethyl ether (1 ml) was poured onto the spinning substrate. Next, the spin-coated yellow film was annealed at 150°C for 10 min. Then, 12.5 mM OABr in chloroform was spun at 5000 rpm for 60 s. Last, the FTO/SnO2/3D perovskite/OABr film was heat-treated at 100°C for 5 min to form an OA-based 2D perovskite via reactions with the 3D perovskite surface.

Device fabrication

An FTO substrate with dimensions of 1 inch by 1 inch was cleaned via sonicating in deionized water, acetone, and IPA (Isopropyl alcohol) for 15 min. A SnO2 layer was grown on the cleaned FTO in accordance with previous reports (). Next, the FTO/SnO2 substrate was cleaned with ultraviolet/O3 for 15 min before coating the 3D perovskite. A 3D perovskite film was fabricated using the abovementioned perovskite preparation method. A spiro-OMeTAD solution was prepared by dissolving spiro-OMeTAD (90.9 mg ml−1) in chlorobenzene with 20.9 μl of Li-TFSI solution (540 mg ml−1 in acetonitrile), 9.1 μl of Co-TFSI (375 mg ml−1 in acetonitrile), and 35.5 μl of tBP. Next, a 60-nm-thick Au counter electrode was deposited via thermal evaporation. A film with an antireflection coating was then attached to the device.

Characterization

Photoluminescence

PLQE was characterized in an integrating sphere (Labsphere Inc.) connected to a spectrometer (Ocean Optics QE65Pro), as reported previously (). The excitation flux density was calculated by dividing the continuous-wave laser power by the photon energy and spot area (wavelength, 532 nm; diameter, 2 mm). Before sweeping the laser power, the film was exposed to 5-mW excitation for approximately 30 min to reach the saturation of the light soaking effect.

Transmission, reflection, and absorption coefficient

Transmission and reflection were measured using an ultraviolet-visible spectrometer (Shimadzu UV-3100) and were used to fit the refractive index of the perovskite. The absorption coefficient was obtained from the imaginary part of the fitted refractive index.

Device efficiency

J-V curves were measured in air using a solar simulator (ABET Technologies, Sun 3000) under AM1.5G illumination at a room temperature of ~295 K. For measurement without an aperture, the effective device area was defined by Isc (short-circuit current, measured without an aperture) over Jsc (measured with an aperture) to eliminate the possible overestimation of photocurrent. The EQE was measured using a QuntaX-300 device (Newport).

Film thickness

The thicknesses of the FTO (600 nm), perovskite (500 nm), and spiro-OMeTAD (260 nm) layers were measured using a Dektak 150 surface profiler and double-checked using a scanning electron microscopy (SEM) cross-sectional image (fig. S1). The thickness of the SnO2 (80 nm) was obtained from the SEM image.

Electroluminescence

ELQE was measured by directly attaching a calibrated silicon photodiode that was sufficiently large to cover the cell area. The current injection for PSC and photocurrent collection from the photodiode were controlled by two separate source measure units (SMUs) using the software “SweepMe!”. The edge sides of the substrate were blocked using aluminum tape to avoid overestimation. To ensure the reliability of measured values, the measured ELQEs were confirmed by (i) double-checking using an independent setup with a calibrated integrating sphere (Labsphere Inc.) and (ii) comparing the measured J-V curves under 1-sun excitement to the Shockley equation based on the measured ELQE (Fig. 1F). The EL spectrum was measured in an integrating sphere (Labsphere Inc.) using a spectrometer (Ocean Optics USB4000).

Self-excitation

For self-excitation measurement, two SMUs were connected to pixel 1 (for excitation) and pixel 2, 3, or 4 (for measuring photocurrent). Pixels 2, 3, and 4 were under short-circuit conditions (V = 0). The width of each pixel and the gap between the pixels were 4.2 and 0.8 mm, respectively. The SMUs were controlled using SweepMe!.

Spatially resolved PL/EL

PL signals were excited and collected using high–numerical aperture objective lenses. A second lens on the collection side projected the signal into a spectrometer equipped with an array of a cooled charge-coupled device cameras so that both spatial and spectral information could be recorded simultaneously. For PL excitation, a 1.3-ns pulse laser (532 nm and 10 kHz) was focused on a spot size at the diffraction limit. The lateral waveguide mode is mostly confined in the perovskite (n ~ 2.6), while the refractive indices of spiro-OMeTAD (n ~ 1.6), FTO (n ~ 1.5), and SnO2 (n ~ 1.9) are similar to those of glass (n ~ 1.5) in the given spectral range and rarely trap photons. In our analysis, the small absorption potentially arising from traps or quenching states and skin-depth parasitic absorption during propagation was assumed to be negligible compared to the measured decay slope of 240 cm−1. EL was measured by applying a DC current (52 mA/cm2) to the electrodes. For backward spatial EL shown in fig. S6, the device was moved laterally to cover a longer distance range.

Photocurrent from backward excitation

The device was excited by a highly focused continuous-wave light with an arbitrary intensity from the back side (i.e., electrode side). The photocurrent was then recorded at each step, while the device was moved laterally.

Optical modeling

An effective scattering coefficient is added to a recently presented optical model containing PR effect (, , ). Refer to the Supplementary Materials for the details.