Metal halide perovskites have emerged in recent years as promising photovoltaic materials due to their excellent optical and electrical properties, enabling perovskite solar cells (PSCs) with certified power conversion efficiencies (PCEs) greater than 25%. Provided radiative recombination is the dominant recombination mechanism, photon recycling – the process of reabsorption (and re-emission) of photons that result from radiative recombination – can be utilized to further enhance the PCE toward the Shockley–Queisser (S-Q) theoretical limit. Geometrical optics can be exploited for the intentional trapping of such re-emitted photons within the device, to enhance the PCE. However, this scheme reaches its fundamental diffraction limits at the submicron scale. Therefore, introducing photonic nanostructures offer attractive solutions to manipulate and trap light at the nanoscale via light coupling into guided modes, as well as localized surface plasmon and surface plasmon polariton modes. This review focuses on light-trapping schemes for efficient photon recycling in PSCs. First, we summarize the working principles of photon recycling, which is followed by a review of essential requirements to make this process efficient. We then survey photon recycling in state-of-the-art PSCs and propose design strategies to invoke light-trapping to effectively exploit photon recycling in PSCs. Finally, we formulate a future outlook and discuss new research directions in the context of photon recycling.
Perovskite solar cells (PSCs) have become a leading technology in the photovoltaic (PV) research community owing to the remarkable optical and electrical properties of metal halide perovskites such as a large absorption coefficient, sharp absorption edge, long carrier diffusion lengths, as well as tunable bandgap , , . Owing to these favorable optoelectronic properties, the power conversion efficiency (PCE) of lab-scale PSCs has exceeded 25%, approaching the record PCE for crystalline silicon (c-Si) solar cells, currently at 26.7% , . Notably, after c-Si and gallium arsenide (GaAs), metal halide perovskites are only the third PV material class to obtain a PCE over 25%, and the first polycrystalline thin-film material to reach this milestone (albeit on a smaller active area). Nevertheless, in addition to overcoming challenges in scaling up this technology and demonstrating the stability required for market adoption, further improvements in the PCE of PSCs are required to bring its projected levelized cost of electricity generation (LCOE) to a competitive level . Besides continuous device optimizations, unlocking the potential of photon recycling is one possible path to improve the PSCs’ performance. Optical device design, aimed at exploiting the photon recycling phenomenon, has been crucial for GaAs solar cells to bring their PCE to 29.1%, which is the current record for single-junction solar cells , , , thanks to a significant enhancement in open-circuit voltage (V OC ) , , .
Photon recycling is the physical process that occurs in semiconductors when photons emitted via radiative recombination are reabsorbed by the semiconductor itself, possibly in a repeated process. This event is most efficient in highly luminescent materials such as GaAs, resulting in an effective increase in quasi-Fermi level splitting (Δµ) within the material, and hence a possible increase in the V OC of the device. Although there are essential differences in the structural properties of GaAs and lead halide perovskites, PSC research can benefit from the recent progress in GaAs solar cells and apply that understanding to further improve device performance.
To observe significant effects of photon recycling, a thin-film absorber material must (i) display a high photoluminescence quantum efficiency (PLQE), implying that radiative recombination is the dominant recombination process (compared to Shockley–Read–Hall (SRH) and Auger recombination), thereby favoring materials with low defect densities and a high absorption coefficient; (ii) manifest a minimum Stokes shift, i.e. the energetic difference between the maximum position of absorption and emission spectra should be small (∼4 meV), , , ; and (iii) efficient light management , , . Light-management strategies for conventional solar cells, such as crystalline silicon (c-Si), are usually aimed at enhancing the absorption of external photons due to silicon’s relatively low absorption coefficient, resulting from its indirect bandgap. In the c-Si case, relatively thick wafers (>100 μm) are used, yielding increased light absorption in the wafer . In addition, by texturing the c-Si front surface (often also its rear), using a (random) micron-sized pyramid structure ,  with a typical feature size of few microns, combined with dielectric surface coatings, one can decrease the reflectivity and also randomize the light propagation directions inside the c-Si solar cell. This increases the optical path length inside the active material and substantially enhances the absorption of photons with energies close to the c-Si bandgap. Geometrical or ray optics is used to study light propagation in this type of solar cell. However, this strategy is not suitable for thin-film solar cells, where the absorber thickness is usually comparable to or even smaller than the wavelength of the incident light . Thin-film solar cells, therefore, can benefit from photonic structures on the wavelength scale, such as diffraction gratings , plasmonic structures , and nanoscale structured surfaces  for light-trapping.
Light propagation within such nanoscale devices is explained by wave optics rather than ray optics. In particular, wave optics explain phenomena such as waveguiding (light propagation in a specific direction), diffraction, and plasmonic effects, which cannot be accomplished through ray optics. Another advantage of employing nanoscale features in devices is the possibility to tune the feature geometry to reduce the dependence of light absorption to the incident angle of incoming light . Therefore, nano-photonic structures may be considered as an effective means to enhance light-trapping in the subwavelength regime via spatially trapped resonant optical modes , , , and can aid in exploiting photon recycling to enhance device performance.
In this article, we review the current progress in photon recycling in PSCs. First, we describe the general working principle of photon recycling, followed by its impact on the PCE. We also discuss the primary requirements for efficient photon recycling, with a focus on photon management in PSCs. We then review the recent literature related to photon recycling in PSCs and go on to analyze various light-trapping strategies and device architectures that could yield efficient photon recycling in PSCs. We conclude by providing an outlook and suggesting future research directions.
2 Theory of photon recycling
In an ideal semiconductor (i.e., one where recombination only occurs radiatively) under thermal equilibrium and steady-state illumination conditions, a detailed balance exists between photon absorption (resulting in electron-hole generation) and radiative emission (due to band-to-band recombination). Inside the semiconductor, depending on its absorption properties, emitted photons can potentially be reabsorbed and re-emitted. This iterative reabsorption/re-emission process is known as photon recycling ,  and is sketched in Figure 1. Photons will continue repeating the internal reabsorption/re-emission events until they are internally re-emitted at an angle within the semiconductor’s escape cone (i.e., a reduced solid angle determined by the refractive index difference between the absorber and its surroundings), resulting in their outcoupling without further recycling . In this way, photon recycling enhances the effective density of charge carriers within the absorber layer, resulting in a larger Δµ within the absorber. In a solar cell featuring external contacts, this increases the V OC , and hence the PCE [11, 14, 32, 33].
On thermodynamic grounds, Smestad et al.  estimated the concentration ratio C, quantifying the increase in the number of incident photons when a light concentrator system is employed. By analogy, a solar cell employing light-trapping features essentially also behaves as a concentrator system, where the voltage gain corresponding to an increased photon absorption can be expressed as function of the concentration ratio C :
In this, k B , T, and q, are the Boltzmann constant, absolute temperature, and elementary charge respectively. Hence, using Eq. (1), the net enhancement in V OC by photon recycling is expressed by the equation , :
In this, n is the refractive index of the absorber. Here, it is assumed that the device is optically thin and features Lambertian light-trapping, no external reflection losses, and a perfect back mirror. In such a case radiative recombination is the only energy loss mechanism. Under these assumptions the maximum path length enhancement of light is 4n 2 , which is known as the Yablonovitch limit. Assuming a refractive index of 2.6 near the lead-halide perovskite band edge , this implies that a of 83 mV may be obtained, with perfect photon recycling of internally re-emitted photons. These calculations indicate that photon recycling may be a strategy to further enhance the V OC of PSCs. However, the 4n 2 limit can be further increased by utilizing advanced light-trapping structures which can alter the acceptance angle and exploit photon recycling, as discussed in Section 5 below.
3 Key requirements for efficient photon recycling
As mentioned above, there are three essential requirements to be implemented to achieve efficient photon recycling in thin-film direct-bandgap semiconductors: i) a high radiative emission yield; ii) high reabsorption (i.e., a minimum Stokes shift); and iii) efficient light management. Here, we briefly investigate each of these requirements in more detail within the context of PSCs.
3.1 Radiative emission yield
The primary necessity for efficient photon recycling is a high radiative emission yield. This implies that photogenerated carriers recombine radiatively rather than via competing SRH or Auger recombination processes. A high radiative emission implies that noncollected electron-hole pairs predominantly recombine radiatively, potentially setting off reabsorption/re-emission cycles. The total charge-carrier recombination in a perovskite layer under open-circuit conditions is quantified by the general rate equation :
In this, G ph is the carrier generation rate by absorbed photons, k 1, k 2 and k 3 are rate constants associated with SRH recombination, band-to-band radiative recombination, and Auger recombination, respectively, and R T is the total charge recombination rate; is the charge carrier density.
SRH recombination refers to nonradiative recombination caused by defect states which can be present in both the bulk and at the surfaces. Here, we consider the k 1 factor to be associated with bulk SRH recombination [Figure 2(a)]. Bresnes et al.  showed from device simulations that perovskite films need to have a k 1 value lower than 1 × 104 s−1 to truly benefit from photon recycling to increase the V OC and thus PCE on the device level, as shown in Figure 2(b). If k 1 increases, the presence of photon recycling starts to diminish and becomes insignificant upon reaching the value of 3 × 106 s−1, as depicted in Figure 2(b)–(d). Furthermore, Bresnes et al.  also demonstrated the sensitivity of k 2 on photon recycling, indicating that a value of k 2 = 9.2 × 10−10 cm3 s−1, as measured in state-of-the-art PSCs devices, may be sufficient . Auger recombination is also associated with nonradiative recombination, however it does not play a significant role in PSCs since it is only significant at extremely high carrier injection levels (>1018 cm−3) while being negligible at 1-sun equivalent carrier densities . We note that k 1 can be engineered by defect passivation strategies  whereas k 2 and k 3 are intrinsic material properties. Simulation results revealed that photon recycling only becomes significant if the SRH lifetime, τ SRH, is more than 300 ns which is the typical transient photoluminescence lifetime value of perovskite films on glass . Here, the model was assuming perfectly passivated interfaces (expressed by the surface recombination velocity, S = 0) and used the bulk lifetime as the main parameter (Figure 2(e) and (f)). For lower values of τ SRH, photon recycling is hardly present and does not influence the V OC of the device.
In realistic devices surface recombination is likely to occur, which – as stated – is predominately caused by SRH processes . Figure 2(g) and (h) shows the effect on V OC and PCE as function of the bulk lifetime (τ bulk, denoted as τ SRH in the figure taken from Ref. ), and the impact of S on photon recycling. We can see that above S = 102 cm s−1, the V OC and PCE considerably decrease, even with high values for τ bulk, illustrating that both bulk and surface passivation of metal halide perovskite defects play a crucial role for enhancing photon recycling and thus, considerably impacts the efficiency potential of PSCs. The surface recombination velocity S influences the effective lifetime τ eff which is also influenced by τ bulk (combining the effects of SRH, radiative, and Auger recombination), the diffusion coefficient D and the film thickness W, as:
It should be noted that, under low excitation intensity, τ bulk for lead halide perovskites is primarily determined by τ SRH, due to bulk and grain boundary defects . To increase τ eff, the surface recombination velocity should be decreased and the τ SRH of perovskite films should be increased. To achieve this, several passivation strategies have been reported , as summarized in the sketch in Figure 2(i). After implementing these passivation strategies, contemporary state-of-the-art PSCs exhibit experimental values of k 1 between 1 × 105–1 × 107 s−1 with a trap density of 1015–1017 cm−3 [12, 39, 46]. Comparing these values with those mentioned earlier suggests that a further reduction of nonradiative recombination losses is required to reduce k 1 in order to observe a substantive impact of photon recycling in PSCs. In the context of surface passivation, Yang et al.  reported a value of S ∼ 102 cm s−1 for polycrystalline halide perovskite films coated with polymethylmethacrylate (PMMA). Moreover, Staub et al.  demonstrated the utility of combining time-resolved photoluminescence (TRPL) measurements with analytical models to determine values for S. For materials with high purity and good surface passivation, the estimated S values are in the order of ∼10 cm s−1 for typically observed perovskite TRPL lifetimes (few hundred nanoseconds). Meanwhile, Krogmeier et al.  obtained S ≈ 200 cm s−1 for the interface between the halide perovskite film and PCBM. Recently, Wang et al.  determined S values in the range of 10−1–104 cm s−1 using TRPL for various electron/hole transport and polycrystalline halide perovskite interfaces, values that may be suitable to enable photon recycling, if combined with sufficiently high τ bulk values.
In the context of devices, the requisite high radiative yield for effective photon recycling can be expressed by the need for high internal (Q i ) and external (Q e ) photoluminescence quantum efficiencies [35, 36, 49], determined at open-circuit conditions. Q e is the ratio of the emitted photons per absorbed photons in the material, whereas Q i is the ratio of the radiative recombination rate to the device’s total (radiative and nonradiative) recombination rate . Q e is an important parameter affecting the V OC and thus PCE. If Q e = 1, the V OC is equal to the radiative open-circuit voltage (V OC, rad). The total recombination current (expressing the loss in charge carriers per unit time via radiative and nonradiative processes) increases in case of any additional nonradiative recombination, reducing the V OC and Q e . Similarly, failure to achieve a high Q i is an indicator for high nonradiative recombination losses . To estimate the influence of radiative and nonradiative recombination on device performance, Q e and Q i values should be known. Simulations by Kirchartz et al. , revealed that both a high Q e and Q i are critical parameters in the context of photon recycling and therefore the V OC of the device. The relationship between Q i and Q e can be expressed using the following equation :
Here, p e stands for the probability of emission or outcoupling of photons, p r = 1 − p e − p a is the reabsorption probability in the perovskite, and p a is the probability of parasitic absorption, most prominently via free-carrier absorption within the contact layers of the device. Given that in the case of photon recycling, photons may undergo multiple reabsorption and re-emission events within the absorber and may bounce back and forth may times within a thin-film solar cell, the optical design must play a vital role in curtailing parasitic absorption . Figure 3 clearly shows how Q e depends on Q i and p a , assuming p e = 12.7% for flat PSCs . From Eq. (5), it is clear that Q e increases with the higher p r Q i and thus increased photon recycling. Conversely, an increase in p a results in a substantial decrease in Q e , as shown in Figure 3(a). A reduced Q i directly lowers Q e and hence the as depicted in Figure 3(b). Q i can be calculated with the help of the experimentally given Q e , through rearranging Eq. (5) and assuming that there is no parasitic absorption (p a = 0) :
As introduced by Abebe et al. , a significant enhancement in photon recycling only occurs for very high Q i and p r as per the following equation:
Hence, based on Eqs. (6) and (7), specific knowledge of p e is required to define Q i and thus minimize the nonradiative recombination in PSCs and evaluate the potential for ( ) in PSCs. Moreover, Figure 3(d) displays the increase in photon recycling ( ) over Q i for various p r . For low Q i 40%, is low and similar for all p r , while for higher Q i , the value of more sensitively depends on p r . Hence, the above calculation demonstrates the dependence of Q i on Q e and also highlights the importance of accurately determining p e . In recent reports, p e values are reported between ∼5 and 13% for planar perovskites films [31, 36, 49, 52, 56]. Employing such values in Eq. (7), the noticeable value of = 30 mV can be achieved for Q i ∼ 90% (Q e ∼ 40–50%) in PSCs as shown in Figure 3(c) and (d). The recent advancements in passivation strategies for perovskite absorbers enable lower nonradiative recombination and defect densities, allowing for internal Q i values above 90% . These results underline the promise for realizing photon recycling in practical applications.
3.2 High reabsorption: minimum Stokes shift
Improving only the radiative emission yield is insufficient to observe photon recycling. The increase in is only obtained by reabsorbing internally emitted photons, resulting in an increased carrier concentration within the absorber. If the emitted photon energy is smaller than the perovskite bandgap, or, more specifically, is emitted at a photon energy that corresponds to a negligible absorption coefficient, the emitted photon is unlikely to be reabsorbed. Hence, to enable photon recycling, understanding the reabsorption mechanism is as essential as increasing the radiative emission yield.
The Stokes shift is a useful figure of merit to estimate the influence of reabsorption on photon recycling, and is defined as the energy difference between the maximum positions of the emission and absorption spectra as sketched in Figure 4(a) . To effectively reabsorb the re-emitted photons (a necessary condition for photon recycling), the Stokes shift must be minimal. In other words, a significant overlap between the absorption/emission spectra is essential for the reabsorption mechanism to occur . Lee et al.  demonstrated that decreases exponentially with increasing Stokes shift, as shown in Figure 4(b). In Table 1, we summarize the reported Stokes shift in GaAs and perovskites. For GaAs, the Stokes shift is quite small (4 meV) compared to perovskites. A small Stokes shift implies that the bandgap of the absorber is direct. In addition, Wong et al.  demonstrated that the smaller the Urbach energy (γ) of a semiconductor, the smaller the Stokes shift, where the Urbach energy is extracted from the logarithmic slope of the absorption coefficient below the band edge and is indicative of the material’s static and dynamic disorder. In the case of γ < kT, the absorption and emission spectra are overlapping and this leads to a minimal Stokes shift. However, in the case of γ > kT, the emission spectra are notably broadened and move away from the absorption band edge, resulting in a larger Stokes shift as shown in Figure 4(c). With the presence of deeper, yet nonlocalized bandedge states, radiative recombination of electrons and holes populating these deeper states results in a redshifted emission of photons with energies below the absorption band edge [Figure 4(d)].
Practically, at room temperature, γ is about 15 meV for lead-halide perovskites, compared with GaAs = 7 meV , which likely explains also the difference in Stokes shift for these materials. It is of note that the Urbach energy scales with temperature . Therefore, with increasing temperature the Stokes shift will also increase, likely impairing photon recycling. This further underlines the importance of addressing parasitic heating of solar cells; the hotter the devices, the less photon recycling will be present, due to the increased Urbach energy . Overall, γ can be used as be metric for the material’s high structural quality, with small values leading to a smaller Stokes shift . We note that different perovskite compositions and the use of various additives may be explored to improve the material’s quality, expressed through γ and ΔE stokes, which may aid in enhancing photon recycling in these materials.
3.3 Efficient light management
Apart from radiative emission and reabsorption, light management also plays an essential role in thin-film solar cells for effective photon recycling. Figure 5(a), shows the optically ideal structure for photon recycling which minimizes the escape-cone angle from the front side of the cell and increases the photon concentration by perfectly internally reflecting all the emitted photons that reach the rear side of the device. In particular, following Snell’s law, the large refractive index contrast between the absorber and free space leads to a narrow escape cone angle . To analyze the impact of optical design on photon recycling in PSCs, Abebe et al.  discussed three types of light interaction with semiconductors [Figure 5]. The first possible light interaction is perfect incoupling of light (ideal case of a perfect antireflective coating, ARC), where the absorption response is based on the Beer–Lambert law but without considering light-trapping effects [Figure 5(c)]. A second interaction is light propagation in a multilayer medium where constructive and destructive interference effects occur. The interference effect is produced only if each layer’s (optical) thickness in the thin-film stack is on the order of the wavelength of light. In general, the transfer matrix method (TMM) is used to model such structures. The TMM relies on wave optics, in which a matrix represents the propagation of the electromagnetic field (light) through each layer of the device. The matrices associated with each layer are multiplied together to achieve a global matrix and is used to calculate the electromagnetic field on each side of the layer that allows to calculate reflection and transmission coefficients . Essentially, with the TMM, the absorptance of a planar experimental solar cell device can be calculated [Figure 5(b) and (d)].
Thirdly, light may interact at the interface in which a Lambertian light-trapping structure is implemented, as shown in Figure 5(e). Here, the frontside-textured surface is considered to allow complete randomization of the direction of transmitted light and results in an absorptance enhancement by a factor up to the Yablonovitch limit, assuming the absorption in the active layer is weak. The absorption spectra were calculated with thickness h = 300 nm of the perovskite absorber at normal incidence.
To analyze the performance of these designs, Abebe et al.  derived an explicit expression to predict the . They also derived an expression to describe the dependence of on Q i , the probability of parasitic absorption of radiatively emitted photons (p a ), and the escape probability of emitted photons (p e ), respectively, as defined earlier. In particular, they calculated p e without any angular restriction ( θ out = 90°, angle-independent) while comparing the impact of the various absorption responses on photon recycling in a solar cell.
The Lambertian response leads to a higher and ideal absorption response but results in a lower V OC = 1290 mV at Q i = 1 [Figure 5(e)], and [green plots in Figure 5(g) and (h)] compared to the Beer–Lambert and wave-optics response [red and blue plots in Figure 5(g) and (h)]. This relates to the high escape probability of the Lambertian scheme (p e = 17.8%) as compared to the Beer–Lambert (p e = 5.32%) and wave optics (p e = 3.32%) responses. The Lambertian response shows the highest p e due to the lack of total internal reflection inherent for such an idealized front texture. Figure 5(g) and (h) show the V OC of the PSC as a function of Q i and the obtained maximum V OC of 1317 and 1305 mV for the PSCs including charge-transport layers (wave optics) and Beer–Lambert cases at Q i = 1, respectively. The Beer–Lambert response leads to a higher absorption compared to the wave-optics analysis but provides less V OC and . Following this, the authors argued that the perfect incoupling of light through the Beer–Lambert response results in a larger escape probability of re-emitted photons compared to the wave-optics analysis and hence to a less as shown in Figure 5(h). Indeed, the wave-optics case results in a larger V OC when Q i > 0.95, where the photon recycling impact is sufficiently large. Moreover, they have calculated based on different escape-cone angles ( θ out) and found that at θ out = 2.5°, one could reach = 240 mV, as shown in Figure 5(i). The increase in is mainly due to re-emitted photons having a lower escape probability due to a smaller escape cone. Note that upon introducing parasitic absorption p a , even though Q i approaches unity, the increase in substantially reduces [Figure 5(h)]. This is because the parasitic absorption probability p a profoundly affects the probability of reabsorption of photons within the perovskite. Furthermore, parasitic absorption’s unfavorable influence on photon recycling is more obvious in the case of varying θ out [Figure 5(i)]. Therefore, dedicated attention must be given to light management to minimize p a to exploit photon recycling in PSCs.
In practical terms, rugate structures could establish a narrow θ out angle over a broader wavelength range , . This structure relies on dielectric coatings, such as a solar cell with an ARC (which simultaneously may act also as transparent electrode, depending on its electrical conductivity) with a refractive index equal to the geometric mean of that of its adjacent materials, i.e. glass (n = 1.5) and the absorber material (the optical thickness of the ARC then dictates the minimum of reflection via quarter-wavelength conditions). The refractive index of the ARC could also be made gradual, e.g. by SiO2/TiO2 codeposition , . However, light-trapping strategies that involve narrowing θ out, compared to Lambertian light-trapping concepts, come at the cost of reducing J sc of the device due to the optical reciprocity principle.
These results show the importance of photon management in PSCs toward efficient photon recycling. In addition, the authors’ theoretical analysis of photon management for photon recycling has assessed only planar PSCs while the optical treatment of nanostructure-based PSCs is yet to be reported. In particular, the analysis could be extended to perform a precise photon-recycling treatment in PSC designs that feature nanoparticles, nanowires, grating structures, or nanopatterned active layers.
In recent times, similar models were also demonstrated by Kirchartz et al. , who studied systems in the framework of ray optics. Furthermore, several groups have also investigated both randomly-textured and planar structures to quantify the impact of photon recycling for PSCs by using both simulations (ray-optics and statistical models) and experimental analyses , , . Nevertheless, Abebe et al.  reported that conventional light-trapping structures that are based on Lambertian light scattering will not be applicable for efficient photon recycling in PSCs. For thin-film planar stacks and nanostructured solar cells, interference and light–matter interactions at the nanoscale need to be considered. Therefore, the PSC community should explore other light-trapping strategies for excellent light-trapping in PSCs. Some potential light-trapping structures are discussed in Section 5.
4 Photon recycling in PSCs
In 2016, Pazos-Outon et al.  reported one of the first demonstrations of photon recycling in lead iodide-based PSCs by studying a thin film of perovskite (∼100 nm) on a glass substrate and measuring the spatial distribution of photogenerated emission via confocal optical microscopy [Figure 6(a)] .
The authors observed a change in the normalized photoluminescence (PL) spectrum while increasing the separation distance between excitation and collection lenses that probe the perovskite film, as presented in Figure 6(b). At a separation distance greater than 5 μm, the PL spectrum red-shifted beyond 800 nm, accompanied by a weaker peak close to the original emission at 765 nm, as shown in Figure 6(c). The authors attributed this shift to the guided re-emitted but nonabsorbed photons scattered out from the perovskite film. The authors also fabricated an interdigitated back contact (IBC) PSC with electron- and hole-transport layers. They observed the extraction of charge >50 μm away from the contacts as exhibited in Figure 6(d), which arises from repeated photon recycling events.
Likewise, Dursun et al.  experimentally demonstrated photon recycling via two photon-excitation measurements on perovskite microwires. The team observed that the PL spectrum leads to a red-shifted secondary emission peak accompanying the primary PL emission, as shown in Figure 6(e) and (f), a finding that became more apparent when the detector was further moved away from the excitation source. Similar behavior was also observed by Wang et al.  in perovskite nanowire arrays. Braly et al.  passivated polycrystalline perovskite (CH3NH3PbI3) thin films by an electron-donating molecule n-trioctylphosphine oxide (TOPO) and utilized a multimetal back reflector substrate [Figure 7(a)–(f)] to experimentally evidence a Q i of over 90% [Figure 7(g) and (h)]. These passivated perovskite films showed one of the highest Δµ of ∼1.28 eV, approaching 97.1 ± 0.7% of the radiative limit, which is close to the best performing GaAs solar cells . Since such a high Q i implies negligible nonradiative recombination, the authors predicted through simulation that the PCE values can be improved from 24.3 to 27.9%, which can be ascribed mainly to increases in (by 130 mV) and fill factor of the device.
With a similar approach, this time with superoxide ion (O2 •−) defect passivation, Brenes et al.  demonstrated Q i ∼89% and calculated a potential short-circuit current density (J SC) and V OC enhancement of 90 mV resulting in a predicted PCE increase of 1.4%.
In addition, Fassl et al.  developed a curve-fitting model to determine p e accurately (and thereby Q i ) from the experimentally accessible Q e spectrum of perovskite films, measured with the help of a confocal microscope. The PL spectra associated with photon recycling can be explained by light propagation and scattering events, as shown in Figure 8(a). The authors claimed that the initially trapped photons are scattered out before being reabsorbed and re-emitted, giving rise to the red-shift in the PL spectra, indicative of photon recycling [Figure 8(b) and (c)]. Furthermore, the team pointed out that not considering the scattering events diminishes the p e by more than 10% in absolute terms and hence overestimates the Q i and underestimates the effect of photon recycling on the PCE of PSCs. A recent article by Wang et al.  introduced an analytical expression to define photon recycling in halide perovskite films. Their model has successfully quantified the increase in Δµ in the presence of photon recycling with a k 1 value as low as 7 × 105 s−1 in halide perovskite films. Their findings give insight into how Δµ depends on photon recycling, a requirement for PSCs’ future developments.
Furthermore, Gan et al.  aimed to isolate the contributions of carrier diffusion and photon recycling to understand carrier dynamics and long-range transport in perovskite single-crystals [Figure 9(a) and (b)]. Although both mechanisms were observed to a certain extent, photon recycling seems to be the main effect responsible for the red-shifted emission and enabling long-distance transport of energy in both two-dimensional (2D) and three-dimensional (3D) halide perovskites. On similar grounds, Yamada et al. , showed the role of photon reabsorption and re-emission in PL spectra, using Bi3+ doped samples, where the Bi3+ ions act as a dopant resulting in a reduced photon-recycling effect. The exploitation of photon recycling may also be used to further enhance the performance of perovskite-based tandem solar cells [51, 81, 82]. Sheng et al.  proposed a design strategy that involves integrating a low refractive index layer between the subcells of III/V tandem solar cells to trap the re-emitted photons and improve photon recycling. This strategy enabled increasing the V OC and an enhancement in the overall PCE of the device. In a similar context, Steiner et al.  demonstrated enhanced photon recycling by implementing a low-index transparent epoxy to join the subcells of mechanically stacked multi-junction solar cells, fabricated on GaAs and InP substrates. In particular, a low-index transparent epoxy reflects a substantial portion of light toward the GaAs subcell while transmitting the rest of the sub-bandgap light.
The current literature studies imply the role of photon recycling and its impact on metal halide-based perovskite absorbers. A few reports based on simulations have gone further and investigated the potential for photon recycling to push the PCE of PSCs, and the extent of its contribution for high performing device requires further studies. More importantly, PSCs are nicely poised to exploit photon recycling with novel light-trapping strategies and which may be able to further increase their performance in the future.
5 Light-trapping for efficient photon recycling
The optical design of solar cells largely depends on the absorber layer’s optical properties, particularly the real and complex parts of the refractive indices. The real part directly relates to reflectance at interfaces which can be minimized by ARCs . To effectively couple light into a macroscopically thick semiconductor, it may also be beneficial to use micron-scale texture, such as is the case of silicon solar cells. The refractive index contrasts at the interfaces also regulates the total internal reflection, by which the optical path length can be increased, and which holds relevance to exploit photon recycling in the case of thin-film direct-bandgap semiconductors such as lead halide perovskites. To exploit photon recycling, light-trapping should aim to keep the re-emitted photons inside the cell until they are finally reabsorbed, effectively resulting in an optical path enhancement (α ope). This parameter can also be regarded as a simple metric to quantify the effectiveness of distinct light-trapping schemes . Following, we discuss the three fundamentals light-trapping concepts that could be used to exploit photon recycling by maximizing the optical path enhancement of re-emitted photons.
5.1 Lambertian light-trapping
Lambertian light-trapping is based on the complete randomization of incoming light directions after entering the absorber. By definition, an ideal Lambertian scatterer works independently of the angle of incidence of incoming light  resulting in an upper limit of light path enhancement to be α ope = 4n 2 for weakly absorbed light ,  [Figure 5(e)], as defined above. For example, for silicon and lead halide perovskites, α ope values of ≈50 and ≈21 are theoretically possible respectively.
However, the theoretical photon recycling models of Abebe et al.  and Kirchartz et al.  explained that Lambertian light trapping would undesirably improve light out-coupling (through optical reciprocity) and thereby actually reduce the amount of reabsorbed photons, and hence relatively reduce the carrier concentration and thus the V OC of the device. Nevertheless, the optical benefits of Lambertian light-trapping via the increase in absorption and so J sc outweigh these shortcomings. Consequently, a solar cell with a Lambertian light trapping [Figure 5(e)] structure can be of interest in those cases where the photon recycling effect is anyway relatively weak (e.g. when using an absorber with indirect bandgap or relatively large Stokes shift, possibly caused by high environmental temperatures).
5.2 Resonant light-trapping
Light-trapping structures that can achieve a larger redirection of path lengths are diffractive elements such as diffraction grating structures. A possible light path of emitted photons involving a diffraction grating in a solar cell is shown in Figure 10(a). In principle, the grating structure, placed on the front side, diffracts the light into at least one diffraction order m (…−2,−1,1,2…) other than the 0th order in the case where the grating period (d) is larger than the effective wavelength of light in the absorber (at normal incidence) . The diffraction efficiency (the ratio between the diffracted and incident light intensity) is responsible for the amount of light energy going into a particular diffraction order m, which essentially relies on the grating structure’s geometry , . In particular, for gratings with a periodicity d ≤ λ r (λ r is the wavelength of re-emitted photons), internally emitted photons can couple into a particular diffraction mode in air i.e. the 0th or the principal diffraction order. As the refractive index of the absorbing medium is higher than air, re-emitted photons can couple to the available propagating diffraction modes in the absorber . Hence, the re-emitted photons can couple to a higher number of propagating diffraction modes inside the absorbing medium, compared to only one diffraction mode in air. Therefore, such gratings can act as an efficient light-trapping scheme for photon recycling. However, as the number of allowed propagating diffraction orders in air increases with an increased grating period, so does the light out-coupling efficiency. Therefore, the grating design is critical for maximizing the V OC improvement by photon recycling.
Peters et al.  derived the maximum optical path enhancement for a diffraction-based light-trapping structure to be α ope = 893n . In addition, Eq. (2), describing can be rewritten with the optical path enhancement of diffraction-based light structure and described as follows:
Assuming n = 2.6 near the perovskite band edge  implies α ope ≈ 2053 for lead halide perovskites and that of 200 mV may be obtained, with perfect absorption of re-emitted photons. Thus, this approach constitutes a diffraction-based theoretical upper limit and emphasizes the higher potential to trap the re-emitted photons via diffraction gratings, compared to Lambertian trapping concepts, albeit at the cost of restricting the acceptance angle to normal incidence, which will come at the expense of the J sc of the device.
In addition to diffraction gratings, in literature various other concepts are suggested based on resonant structures including dielectric , , , , , ,  as well as metallic nanoparticle arrays for light-trapping, as shown in Figure 10(b). Utilizing metallic nanoparticles allows efficient light scattering via localized surface plasmon resonances that originate from collective oscillations of free electrons in a metal . The surface plasmon resonance condition can be tuned by varying the particles’ size, shape, and distribution. Although solar cell results based on plasmonic light-trapping have been reported by several research groups , , , , , the absolute PCE values are usually limited by dissipative losses, such as parasitic absorption within the metallic nanoparticle array . Furthermore, parasitic absorption, i.e., photons that are absorbed within the material without resulting in collected charge carriers, can be detrimental for photon recycling. Recently, to overcome parasitic absorption and bring novel functionalities, dielectric Mie resonators can be used for photon recycling, where light can be confined via geometrical resonances . However, the challenge when incorporating Mie resonators is to make their relatively narrowband resonances more broadband for covering the entire wavelength spectrum to overlap with the emission within the perovskite material’s bandgap. Moreover, extensive optimization of the particle size, shape, and distribution is required to adjust the desired range of wavelength spectrum. 3D photonic crystal structures are also excellent candidates for photon recycling as they combine the properties of a grating and a mirror . However, apart from the recent work of Chen et al. , little effort has yet been made toward using 3D photonic crystals combined PSCs, where these challenge consists of implementing 3D photonic crystals with a photonic bandgap around the perovskite electronic bandgap.
5.3 Angular selective light-trapping
Another potentially useful light-trapping scheme consists of merging light scattering with an angularly selective optical filter [85, 104, 105]. The working principle of this concept is shown in Figure 10(c). Incoming light is allowed within the angular acceptance angle θ a of the system. Once light enters the device, it scatters due to the surface’s roughness, where isotropically scattered light is confined by total internal reflection. In particular, the scattered light is trapped in case of light incident on the optical filter with an angle larger than θ a . This mechanism achieves α ope = 4n 2 /sin θ a with a Lambertian-scatterer and an ideal mirror at the rear side of the cell. Inserting θ a ∼ 1°, a higher optical path enhancement can be realized; for silicon α ope ≈ 20,000 and lead halide perovskites α ope ≈ 15,000 is theoretically possible. In addition, Eq. (2) of can be rewritten with optical path enhancement of angularly limiting light-trapping structure as follows:
Assuming a refractive index of 2.6 near the perovskite band edge , this implies that a of 240 mV may be obtained, with perfect absorption of re-emitted photons.
Angular selective light-trapping concepts restrict the escape cone angle, creating thereby a situation where the emitted photons are recycled back into the cell. Two components are required to accomplish such a system: a surface to induce a scattering mechanism and an appropriate angularly selective optical filter. Well-known possibilities to realize the first component includes the introduction of substrate roughness in the case of thin-film solar cells ,  or front/backside texturing of a silicon solar cell , . However, texturing the surface of perovskite films is not trivial , . Since most perovskite films are deposited on glass superstrates, the best approach is to texture either the glass surface or the transparent conducting oxide (TCO) electrode or have a detached rear Lambertian reflector (like spectralon , or a textured Si wafer with a reflector for the relevant wavelengths on top). Recently, several works successfully explored the possibility to deposit solution-processed perovskite films on a textured TCO , . Furthermore, vacuum-deposition approaches can also be utilized to deposit perovskite films on textured glass substrates . In addition, solution-processed perovskite films on textured silicon tandems have been successfully demonstrated, paving the way for applications on textured glass [110, 115, 116]. The challenges in realizing an angularly selective light-trapping structure lie in the second component, which is finding the appropriate optical element. Peters et al.  suggested that a Bragg-like filter or opal (3D photonic crystal) could be used as a suitable optical filter to restrict the angular confinement of light. However, as also noted above, reducing the acceptance angle comes at the cost of reducing the J sc and hence reducing the PCE of the device. When the acceptance angle is restricted, the angles at which light can go out of the cell are also limited due to optical reciprocity. As such, this approach may be compatible with concentrated PV designs which inherently limit the incoming light to direct radiation. In these cases, combining moderate-angle restriction with moderate concentration can offer more flexibility in system design, enabling higher PCEs. Besides, this method needs a solar tracking system on to which the solar cell is installed so that light always comes within the same acceptance angle. However, the concentration or tracking systems increases balance of the system (BOS) costs. In terms of angular restriction light-trapping structures, a low parasitic absorption probability p a is required, i.e., at least in the range of 0–2% for efficient photon recycling [Figure 5(i)]. Achieving such low values of p a is certainly challenging; however, devices with thicker absorber layers can usually support longer optical path lengths and offer low values of p a , .
Based on a similar concept, Figure 10(d) illustrates the schematic design of dielectric double-array cone-like structures. In particular, the design comprises of a closely packed double array of cones set apart by a broadband band reflector shown in Figure 10(d). The radiatively emitted photons are reflected by the ideal broadband reflector. This kind of design has already been successfully implemented in GaAs solar cells to demonstrate photon recycling, inspiring its utilization in PSCs . Another possible configuration to induce light-trapping is to nanopattern the active layer itself, such as by the use of cylindrical nanopatterned perovskite thin-films . In this design, the light-trapping of re-emitted photons is achieved through the excitation of waveguide modes. Here, a significant portion of re-emitted photons are reabsorbed through the nanopatterned perovskite layer.
To date, there are no reports yet published that demonstrate the use of either a grating structure, a nanoparticle array or an angular-selective filter in the context of photon recycling for PSCs. However, in terms of optical path enhancement, the angular-selective light-trapping structures outclass both Lambertian and resonant light-trapping structures. Generally, these approaches aim at elevating the device-level J SC by curtailing front-side reflection losses while concurrently increasing the optical pathlengths of the weakly absorbing in-coupled photons. Analogous to c-Si devices, numerous light management strategies have also been explored for improving the performance of perovskite-based single-junction and tandem solar cells. Typically, for light management, surface corrugations or periodic features are introduced in either the device stack’s supporting layers or within the photoactive layer itself. Examples of the former case include the use of fiber-array based anti-reflection electrodes which provide a lensing effect for realizing multiple reflection minima in the 360–750 nm wavelength interval , incorporating nanostructured frontside electrodes which address both anti-reflection and light-trapping aspects by allowing an increased number of higher order diffraction modes in the active layer while limiting those in the air  and the application of micro-pyramidal textured polydimethylsiloxane (PDMS) anti-reflection coating on an incident glass medium for improving the transmission to reflection ratio at the air/PDMS interface by means of multiple reflections at pyramid facets and refracting light at larger angles .
6 Summary and outlook
Optimizing a solar cell’s design to enhance the V OC is a hurdle that requires a clear and in-depth understanding of the structural and material properties of the absorber. In particular, with lead halide perovskites, nonradiative recombination losses in the bulk and at the surface have to be suppressed relative to radiative recombination for optical effects like photon recycling to manifest a significant role. The primary benefit of photon recycling as applied to solar cells is the enhancement of the V OC . Such a benefit is achieved by increasing the quasi-Fermi level splitting (Δμ) within the absorber material via reabsorption of radiatively emitted photons. The increased Δμ results in a higher maximum power point voltage and, therefore, a more efficient light-to-electricity conversion system. Apart from higher radiative recombination rates, a minimal Stokes shift and efficient light trapping are required to observe efficient photon recycling in PSCs. In particular, it is vital to understand the potential of light trapping to maximize light path enhancement for internally emitted photons. We have shown that light trapping in perovskite solar cells could be accomplished by following several strategies. We demonstrated three fundamental types of light-trapping concepts and explained their potential in terms of light path enhancement. In particular, the light path enhancement by resonant and angle-selective light-trapping structures is superior to the Lambertian scattering based structures (Yablonovitch limit). Moreover, despite having the highest theoretical upper limit for light-path enhancement, the experimental implementation for angularly selective structures, suitable for concentrator applications, is still lacking. Similarly, resonant and angularly selective light-trapping structures hold promise for enhancing the path length in perovskite solar cells, but there are no reports yet published that demonstrate their use in the context of photon recycling for PSCs.
While simulations have predicted considerable potential gains in PCE for PSCs via the incorporation of photon recycling, this has yet to be demonstrated at the experimental device level. One limitation is that the phenomenon relies on high-quality perovskite films and contact interfaces. In this context, the immediate future requires further development of efficient strategies to passivate the surface and bulk defects in perovskite films. Passivation strategies based on Lewis-acid/Lewis base molecules, long-chain alkyl amines, 2D passivation, and various other additives are being explored continuously toward this purpose.
Funding source: King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR)
Award Identifier / Grant number: IED OSR-2019-4208
Award Identifier / Grant number: OSR-CARF URF/1/ 3079-33-01
Award Identifier / Grant number: KAUST OSR-CRG2018-3737
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: This research was funded by King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research, (OSR), IED OSR-2019-4208, OSR-CARF URF/1/ 3079-33-01, KAUST OSR-CRG2018-3737.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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