How free exciton–exciton annihilation lets bound exciton emission dominate the photoluminescence of 2D-perovskites under high-fluence pulsed excitation at cryogenic temperatures Open Access

Layered two-dimensional (2D) metal-halide perovskites are attracting interest in a variety of application fields including photovoltaics, photon-detectors, light-emitting diodes, and spintronic devices.¹ In terms of enabling these applications, fundamental understanding of charge carrier dynamics and recombination pathways in these 2D materials is still being pursued, for example, how Rashba splitting,^2–6 self-trapped excitons,^7–13 and layer-edge states^14–16 may affect the materials performance. The nature of the excitonic emission lines in these materials is still discussed. The $n=1$ Ruddlesden–Popper (RP, $A2′An−1BnX3n+1$⁠) 2D lead iodide perovskite based on the phenethylammonium (PEA) ligand (PEA$2$PbI$4$⁠, PEPI) that we study is a benchmark 2D perovskite material and its excitonic photoluminescence (PL) continues to be examined in the literature.¹⁷ However, no consensus has been reached on the PL features, especially the similar low energy peaks visible at cryogenic temperatures being ascribed to phonon replica,^18,19 biexcitons,^20–22 triexcitons,²³ and bound excitons,^24–26 in various reports.

We recall that bound excitons are excitons that become trapped by a defect in the semiconductor. A bound exciton has reduced energy compared to a free exciton; due to the interaction with the trapping center, it has no kinetic energy. In traditional semiconductors, the linewidth of excitonic emission is usually limited by the distribution of exciton kinetic energies, and, therefore, the bound exciton emission linewidth is smaller than that of the free exciton and temperature-independent. However, in 2D perovskite semiconductors, wherein the strong exciton–phonon coupling dominates the linewidths, the bound exciton linewidth can be broad and temperature-dependent.²⁷ Also, as the trapping centers all become occupied at high excitation fluences, the ratio of the free-to-bound exciton emission often increases with increasing fluence as there is usually more high energy free exciton emission relative to lower-energy bound exciton emission at higher excitation fluences.

Localized excitons are similar to bound excitons, but rather than being caught by a specific dopant or defect, localized excitons are associated with a region of material whose energy is lower than the surrounding material due to static disorder. In quantum wells with some disorder, emission slightly is lower in energy than the free exciton and with a Gaussian line shape, it is often attributed to localized excitons.^28,29

A biexciton is formed by two excitons that associate to form an energetically stabilized four-particle state. The probability of biexciton formation (and hence, the intensity of biexciton emission) scales with the square of the excitation fluence. As a single exciton is left after the biexciton emission corresponding to the recombination of only two of the carriers involved, the exciton emission intensity remains linear with excitation fluence at low fluences and in the absence of other effects even when biexcitons are formed.

Here, we examine the temperature-dependent PL of two 2D perovskite materials both at $n=1$ composition. The aforementioned RP material, PEPI, is compared with a Dion–Jacobson [DJ (⁠$A′An−1BnX3n+1$⁠)] material based on 1,4-phenyl-enedimethanammonium (PDMA) of PDMAPbI₄ composition. These ligands are chosen for comparison of the corresponding RP and DJ phases due to their structural similarity (as shown in Fig. S1 of the supplementary material). The temperature-dependent PL is recorded under both continuous wave (CW) and pulsed excitation. Surprisingly, the PL below 100 K differs drastically depending on whether the excitation is CW or pulsed, indicating processes that depend differently on the excited-state density in the film are responsible for different parts of the PL spectrum. By using intensity-dependent PL measurements at low-temperature, we show that the high- and low-energy emission features mainly stem from populations of free and bound excitons, respectively, in the RP material, and free excitons and PbI$2$ inclusions in the DJ material. The difference between the PL spectra observed under CW and pulsed excitation is attributed to a reduction in the efficiency of free exciton emission due to exciton–exciton annihilation under pulsed excitation. The bound exciton and the PbI$2$ emission on the other hand are not so reduced by fluence. This explains the dominance of the free exciton PL under CW excitation and the dominance of the bound or PbI$2$ emission under pulsed excitation.

We examine the temperature dependence of the PL of RP PEPI thin films under CW and pulsed laser excitation (Fig. 1). The excitation power density for the CW excitation is 165 mW cm$−2$ at 405 nm, and the pulsed excitation provides an energy density of 48 $μJcm−2$ per pulse at 430 nm with a repetition rate of 20 kHz and a pulse length of 260 fs. For comparison, this corresponds to a peak power of around 185 MW cm$−2$⁠. The samples are stable under both CW and pulsed excitation, as determined by the invariant PL spectrum and intensity for prolonged illumination time at a given temperature (Fig. S2 of the supplementary material). The layer thickness for the PEPI samples is $55±2$ as determined with a profilometer and the morphology has an RMS of 2.0 nm (Fig. S3 of the supplementary material). It is known from the literature that the thickness of PEPI minorly influences the PL emission peak, with reabsorption in thicker materials causing a peak shift of up to 30 meV from the true single-layer emission.³⁰ 

As immediately apparent upon the comparison of Figs. 1(a) and 1(b), there is a difference between the PL at lower temperatures when the material is excited with CW or pulsed radiation. This is attributable to the significantly different excited state densities under these conditions. The excited-state density under CW excitation can be approximated utilizing the monomolecular lifetime determined below 704 ps, to be around $1.74×1013$ cm$−3$⁠. On the other hand, the initial excited-state density under the pulsed excitation is $7.2×1018$ cm$−3$⁠.

Under CW excitation presented in Fig. 1(a), a seemingly single band around $2.34$ eV dominates the PL at all temperatures. We will assign this band to free exciton (FE) emission, and for simplicity refer to it with that name henceforth. We note that the FE peak position varies with temperature as the bandgap of the material shifts with temperature; the electron–phonon coupling causes an increase in emission energy with decreasing temperatures from room temperature down to 140 K, then the effects of lattice contraction dominate, causing the bandgap to decrease with decreasing temperature. This is consistent with literature reports^31–34 and fully explained below. From room temperature, the FE emission first increases in intensity with decreasing temperature until around 120 K, then the intensity decreases with decreasing temperature until around 20 K, and finally, it increases again with further temperature reduction. This unique temperature dependence will be discussed later, in terms of a shifting equilibrium between free and bound excitons, wherein the rate of transition from localized/bound excitons to free excitons is temperature-activated, as are the nonradiative rates of the free and bound exciton states.

Contrary to the observations under CW excitation, under pulsed excitation below approximately 120 K, two distinguished peaks are observed in the PL. The higher-energy peak of these is similar in energy to the FE peak observed under CW excitation. However, at low temperatures, it is the lower energy peak that dominates the PL [as shown in Fig. 1(b)]. This lower energy emission overlaps with the bound exciton band observed under CW excitation, albeit with a slightly smaller linewidth of approximately 20 meV FWHM compared to 35 meV FWHM for the CW case, and a 40 meV redshift from the center of the FE emission as compared to 32 meV for the CW case at 5 K. Based on its line shape, lifetime, and intensity-dependence presented in this work and based on its similarity to the literature,^24,25 we assign this lower energy emission to bound excitons (BE) in both the CW and pulsed cases. We also note that in 3D-perovskite films reabsorption by the Urbach tail can lead to an apparent double peak in the observed PL spectrum, although the true emission spectrum inside of the film has only a single peak.³⁵ Such an artifact does not explain the double peak that reproducibly and reversibly arises upon varying the excited-state density in the films described in this work.

To examine the intensity, peak width, and peak position of each spectral component in the data presented in Figs. 1(a) and 1(b), we fit the PL spectrum at each temperature to either one Voigt peak at higher temperatures, two (pulsed), or three (CW) Voigt profiles at lower temperatures. We note that a third peak between the FE and BE peaks is necessary to fit the CW data. This peak has a more Gaussian shape than the lower energy BE peak (see Figs. S4 and S5 of the supplementary material) and also is suppressed rather than enhanced at high excited-state densities. We speculate that this may be caused by localized excitons in lower energy areas of the quantum wells, which would be consistent with the more Gaussian shape and the evidence is presented later in the paper regarding the mechanism by which the BE emission is enhanced at higher excitation densities. Nonetheless, this assignment to localized excitons is not definitive and warrants further study in the future. We also note this from room temperature to 120 K, where we use a single Voigt profile to fit the data. We note that at high temperatures, the observed PL peak becomes asymmetric, with the PL at the high energy side dropping off more quickly than the lower energy side. This is shown in Fig. S6 of the supplementary material and can be explained by an increased effect of reabsorption at high temperatures as the increased FWHM of the FE emission leads to more reabsorption of the high energy PL.³⁶ 

The results of the peak fitting are presented in Fig. 1(d) for the CW data and in Fig. S7 of the supplementary material for the pulsed data. The peak position of the FE can be described by the effects of lattice expansion and electron–phonon coupling. The energy of the valence band maximum and the conduction band minimum depends on the overlap of the metal s- and halide p-orbitals and the overlap of the metal p- and halide p-orbitals, respectively.³⁷ An increase in metal–halide orbital overlap leads to a stronger increase of the valence band energy relative to the conduction band and, therefore, to a decrease of the bandgap energy. It follows that lattice expansion increases the bandgap energy. On the other hand, electron–phonon coupling leads to bandgap renormalization, which decreases the bandgap energy. With increasing temperature, the bandgap energy first increases due to lattice expansion and then decreases due to electron–phonon coupling. This interaction can be described with Eq. (1),

where $E0$ is the unrenormalized bandgap, $ATE$ and $AEP$ are the weights of the thermal expansion and electron–phonon coupling, respectively, and $ℏω$ is the average optical phonon energy.^31–34 Electron–phonon coupling also leads to an increase in the FWHM, which can be described by (2)

where $Γ(0)$ is the inhomogeneous broadening, $γLO$ is the electron–phonon coupling strength for Fröhlich scattering with the longitude optical phonon and $ELO$ is the energy of the phonon.³⁸ The fits are shown in Fig. 1, and the parameters for the FWHM agree well with those in the literature,³⁸ and reveal consistent electron–phonon couplings of 23 meV and 22 meV for pulsed and CW excitation, respectively. Full details of the extracted parameters can be found in Fig. S7 of the supplementary material and Tables 1 and 2 of the supplementary material.

The PL intensity for the FE and BE emission under CW excitation is temperature-dependent. As the temperature decreases from 300 to 120 K, the FE emission intensity steadily increases, and no BE emission is observed. This can be explained by a temperature-activated nonradiative rate for FE decay that has an activation energy of approximately 125 meV from an Arrhenius fit of the data in this region, and the fact that there is sufficient thermal energy present that BE can separate easily, i.e., the equilibrium between FE and BE established by the rates of BE formation from FE, and FE reforming from BE strongly favors FE in this temperature regime. Therefore, above 120 K FE dominate the excited-state population and suffer from a temperature-activated nonradiative rate. This energy is consistent with many vibrational modes of organic molecules, and we postulate that increasing molecular vibrations contribute to the nonradiative deactivation at higher temperatures.

With decreasing temperature (120 to 30 K) the FE emission under CW excitation begins to decrease, whereas the BE emission begins to increase with a similar slope to the decrease of the FE emission. This is indicative of a shift in the equilibrium population of free vs bound/localized excitons. The temperature-dependent rate with which BE can return to FE begins to decrease. The decrease in the rate of BE to FE transition relative to the rate of FE to BE transition will shift the equilibrium away from the FE population and toward the BE population, explaining the decrease in intensity of the former and increase in the intensity of the latter. Finally, at temperatures below 30 K the FE emission begins to increase again, which we interpret as being caused by a necessary activation energy for excitons to be bound. So with increasing temperature, the probability of an exciton to be bound first increases and then decreases again.

We now compare the temperature dependence under CW excitation to that under intense pulsed excitation (48 $μJcm−2$⁠, 430 nm, 260 fs). Whereas the position of the FE peak is consistent with that under CW excitation, the emission intensity of the FE (peak area) behaves significantly differently with temperature under pulsed excitation. The total FE emission stays relatively constant with temperature down to $≈160K$⁠, then decreases as the BE emission starts to dominate under 160 K. The decrease in FE emission and the concurrent increase in BE emission is consistent with the CW data; the explanation is that this is due to a decrease in the FE population and an increase in the BE population because BE no longer have sufficient thermal energy to return to the FE population.

The peak position of the BE emission is slightly different in the pulsed and CW cases. The BE emission peak shifts as a function of pulsed excitation fluence (Fig. S8 of the supplementary material, and below). At lower pulsed excitation fluences, the BE emission peak agrees well with that observed under CW excitation.

Another major difference is the appearance of an emission band at 2.5 eV under pulsed excitation. This emission feature, along with a broad emission around 2 eV is also clearly observable in a pure PbI$2$ film (Fig. S9 of the supplementary material). Furthermore, we observe the same temperature-dependence (Fig. S10 of the supplementary material) and power-dependence (Fig. S11 of the supplementary material) of the 2.5 eV peak in the perovskite as in a pure PbI$2$ film. Based on this, we conclude that at high excitation power densities weak emission features from PbI$2$ inclusions become observable. The PbI$2$ inclusions are not created by the intense excitation, as there is no irreversible sample change. When the excitation is reduced after intense excitation, the same spectrum as before the intense excitation is observed (Fig. S2 of the supplementary material).

On the low energy side, a broad but very weak peak can be seen under both CW and pulsed excitation, which is assigned to surface defects of the PbI$2$ inclusions.³⁹ We also observe that the broad emission quickly decays with rising temperature similarly in the perovskite and PbI$2$ films (Fig. S12 of the supplementary material).

Following these observations, the questions that must be answered are: Why, under pulsed excitation, is the FE emission relatively constant with the temperature above $≈160K$ and why is the BE emission more intense than the FE emission at low temperatures? The answer to both of these questions, presented by the following time-resolved and intensity-dependent experiments, is that exciton–exciton annihilation of the FE population significantly reduces its lifetime (at all temperatures) under high-fluence pulsed excitation. At high temperatures, this means that the FE lifetime is dominated by exciton–exciton annihilation. As the rate of exciton loss due to annihilation is so much faster than the nonradiative rate (see time-resolved PL below), the changes in the nonradiative rate only have a minor effect on the total FE lifetime and, therefore, FE emission intensity. Similarly, because the free exciton emission is suppressed due to annihilation, the emission of the BE states can overwhelm the FE emission.

To get further insight into this material, we provide fluence-dependent measurements of the PL at 5 K varying the pulse energy from 0.12 to 48 $μJcm−2$ (430 nm, 260 fs, 20 kHz). These data are shown in Fig. 2(a). For fluences up to 12 $μJcm−2$⁠, the peak emission of the FE exceeds that of the BE emission. However, the increase of the time-integrated FE emission is sublinear while the increase in the BE emission is linear [as illustrated in Fig. 2(b)], leading the BE emission intensity to exceed the FE emission intensity at fluences over 12 $μJcm−2$⁠.

These fluence-dependent observations could be explained by lower mobility of BE leading to a less significant reduction of their population by exciton–exciton annihilation, coupled with some extent of direct formation of BE from free charge carriers. BE cannot exclusively be a product state of FE, as if this were the case the BE emission should also decrease in the same way as the FE emission. Therefore, it is likely that BE are also formed from the initially-created free charge carriers. In their short lifetime, one carrier may be trapped at a defect center, and subsequently captures another carrier of opposite charge to form a BE. Such generation of BE from free charge carriers could be promoted by exciton–exciton annihilation in the following fashion. The product of an exciton–exciton annihilation event is a highly-excited, $Sn$⁠, state that exceeds the energy of band edge free charge carriers. Therefore, we suggest it is possible (as in organic semiconductors)⁴⁰ that highly excited excitons that are created after annihilation can briefly separate into free charge carriers similar to those formed upon initial high-photon-energy excitation.

In Fig. 2(c), a schematic model summarizes the initial formation of free charge carriers, the formation of both FE and BE from free charge carriers, the rate of free to BE transition, the temperature-activated return of a BE to FE, and the fluence-dependent rate of exciton–exciton annihilation in the FE population leading at least partially to the recreation of free carriers. This model is sufficient to explain the key observations of this work.

To establish the existence of exciton–exciton annihilation and its effect on the FE and BE populations, we examine the time-resolved PL dynamics. To do this with sufficient time resolution to measure the FE dynamics over a range that also includes low enough pulse energies to monitor population decay before exciton–exciton annihilation sets in, we turn to a streak camera and a Ti:sapphire oscillator based system [100 fs, 435 nm (second harmonic generated by lithium triborate crystal), 80 MHz] and take measurements at 77 K. Exemplary streak images at various fluences are shown in Fig. S13 of the supplementary material. From these images, the time-resolved PL intensity of the FE emission can be determined by integrating over the wavelength range 516–530 nm for each excitation fluence. These data are shown in Fig. 2(d). At the lowest fluences here, the decay of the FE emission is mostly monoexponential but as the fluence is increased, the decay becomes dominated by a shorter-lived component, a sign typical of exciton–exciton annihilation.

Approximating the decay from the FE population by $dn/dt=−k1n−k2n2$⁠, we can use an analytical solution of a combination of mono- and bimolecular decay to do a global fit of the data presented in Fig. 2(d),⁴¹ 

where $N$ is the exciton density and $k1$ and $k2$ are the respective mono- and bimolecular decay rates and $N(0)$ is the initial exciton density. We get an estimate of $k1=(1.42±0.03)×109s−1$⁠. In order to estimate $k2$⁠, we make the assumption that the FE can annihilate with all excited states present in the film (including BE) and, therefore, estimate $N(0)$ simply based on the total density of photons absorbed (38% in the 55 nm thick film). This estimate leads to $k2=(1.4±0.01)×10−6cm3s−1$ or $(2.4±0.2)×10−1cm2s−1$ depending on whether volumetric or areal density is considered. Recent measurements in PEPI single crystals at room temperature lead to much lower monomolecular and bimolecular recombination rates of $3.5×107s−1$ and $(3.4±0.2)×10−4cm2s−1$⁠.⁴² The much faster monomolecular and bimolecular rates in our materials compared to the single crystal are consistent with the much smaller areas of our crystals, increasing monomolecular nonradiative rates such as defect-related quenching and increasing bimolecular rates due to the restriction of diffusion.⁴³ 

The observed lifetimes for the BE and FE are the same for low fluences (Fig. S14 of the supplementary material), supporting our conclusion that the equilibrium between these states is an important factor determining the temperature dependence of the FE. However, at high fluences, the BE emission decays faster than the FE emission (Fig. S15 of the supplementary material), but its total contribution to the emission increases because the maximum instantaneous emission rate from the BE increases superlinearly [Fig. 2(e)].

These data are consistent with the model presented above. BE can be preferentially made from free carriers. This allows an increase in their formation rate during EEA and explains the superlinear increase of their maximum instantaneous emission rate observed in the streak data. The lower quantum yield of the BE is consistent with a faster nonradiative decay channel. When many BE are created at early times through the more efficient channel presented by EEA then this faster decay of the BE population is visible before equilibrium is established. Thus, we conclude that a temperature-dependent equilibrium between BE and FE and efficient EEA explain the variety of spectra that are observed from PEPI as a function of temperature and excited-state density.

We now compare the results for the Ruddelson–Popper PEPI material to the Dion–Jacobson perovskite using PDMA spacers. The results are presented in Fig. 3.

At first sight, the results look very different as we have a broad emission around 2 eV with an FWHM of $≈350$ meV at temperatures less than $≈70$ K. This is just apparent in the CW data but dominates the emission in the case of pulsed excitation. As explained above we are confident that this emission comes from surface defects of PbI$2$ inclusions in the material. Under pulsed excitation, the excitonic peak of these inclusions at 2.5 eV is also visible (Fig. S16 of the supplementary material). Looking at the excitonic peak of the DJ-perovskite, we can fit three peaks again. They are, however, not as distinguished as in the RP-perovskite. Importantly, the dominance of BE is not observed, even under high fluence pulsed excitation. Furthermore, the dominant FE peak monotonically increases in intensity with decreasing temperature [Fig. 3(a)] in contrast with the more nuanced behavior in PEPI. These two observations are consistent with fewer BE states being present in the PDMA-based material and, therefore, FE emission playing a more dominant role in this material under almost all conditions.

In summary, similar to the PEA system, FE emission dominates at room temperature. At lower temperatures (less than $≈70$ K), the FE emission is reduced by exciton–exciton annihilation. In this case, BE emission does not dominate the spectrum, rather when the efficiency of FE emission is suppressed by EEA, the broad weak low-energy emission from PbI$2$ becomes more dominant.

The RP material that we study, PEPI (PEA$2$PbI$4$⁠), is a benchmark 2D perovskite material and has been scrutinized in the literature. However, no clear consensus has been reached on the PL features, with similar low energy peaks being ascribed to biexcitons, triexcitons, BE, and phonon replica in various reports.^{18–26,38,44,45} Biexcitons have been shown to exist, though at lower energies than the peaks we observed.²⁵ 

In 2004, Fujisawa et al. observed two emission peaks in PEPI under intense pulsed excitation and noted that the ratio of the low energy peak intensity to the high energy peak intensity increased with increasing excitation pulse fluence.²⁰ From this, they concluded that the lower energy peak at $2.31$ eV is due to biexcitons with a peak at 2.306 eV being attributed to amplified spontaneous emission from the biexcitons. A biexciton is two excitons that associate to form an energetically stabilized four-particle biexciton. The probability of biexciton formation and hence the intensity of biexciton emission scales with the square of the excitation fluence. The higher energy peak at 2.35 eV was attributed to FE. Although the ratio of the low-energy peak to high-energy peak shifted in favor of the low energy one at higher excitation fluences, both were observed to depend sublinearly on excitation fluence, not following the linear and quadratic dependence on fluence expected for exciton and biexciton emission, respectively.²⁰ Interestingly, they showed that doping PEPI with bismuth leads to a higher ratio between the low and high energy peaks,²⁰ supporting our assignment of the low energy emission to BE.

Gauthron et al. also observed two emission peaks in PEPI at low temperatures in their work in 2010.¹⁸ They found peak positions of 2.355 and 2.337 eV and concluded that the two peaks came from the same excited state (i.e., could be phonon-replica) because they observed that the two peaks scaled with the same power dependence under CW excitation (over a limited range).¹⁸ They also discuss exciton localization—the trapping of excitons in a disorder potential—which is much more consistent with our observations.

Chong et al. revisited the temperature and power dependence of the PEPI emission spectrum in their work, considering the challenges of achieving ASE in 2D perovskites.²⁵ They also observed high and low energy peaks around 2.35 and 2.32 eV and an additional third peak at very high pulse fluences at 2.27 eV, which they ascribe to biexcitons that we do not see up to our most intense pulsed excitation. The other two peaks correspond to our observations of the FE and BE emission under high-fluence pulsed excitation, and our explanation of exciton–exciton annihilation significantly reducing the intensity of the FE peak with increasing fluence explains the atypical change in the ratio between these two peaks. Instead, one would normally expect the free to BE emission ratio to increase with increasing excitation fluence as the BE sites become saturated. This is not the case in this material because the reduction in FE PL due to exciton–exciton annihilation overwhelms the contribution of site saturation reducing the BE PL while simultaneously aiding the formation of further BE.

In this study, we examine the PL of (PEA)$2$PbI$4$ (an RP material) and (PDMA)PbI$4$ (a DJ material). We study them with temperature, fluence, and time-dependent PL measurements.

The (PEA)$2$PbI$4$ results can be understood with the framework: (1) an equilibrium is established between free and bound/localized excitons. Above $≈140$ K, the bound/localized excitons can easily dissociate from FE, so emission is dominated by the FE. The net increase in the PL with increasing temperature from 50 to 140 K supports this hypothesis. The atypical increase in the total emission intensity with increasing temperature can be explained by the equilibrium between BE and FE shifting to the more efficiently emitting FE. (2) At temperatures lower than $≈100$ K, the bound/localized exciton population becomes high enough that PL can be observed from these states. (3) Exciton–exciton annihilation is very significant in these materials, suppressing the intensity of FE emission at all temperatures under pulsed excitation. At temperatures below $≈100$ K under pulsed excitation, this suppression of the FE emission can allow the BE emission to become the dominant emission. Also, the weak emissions from PbI$2$ inclusions become relatively more dominant at these high excitation densities.

(PDMA)PbI$4$⁠, on the other hand, is less affected by BE emission. At high excitation densities in this material, the EEA does still reduce the FE emission efficiency significantly, again leading to an increase in the relative dominance of emission from PbI$2$ inclusions.

In terms of material design for maximizing PL in these materials at room temperature, we suggest that suppression of nonradiative recombination of the FE is essential. Potentially designing ligands with reduced vibrational degrees of freedom could help in this direction. To achieve higher luminescence at low temperatures, understanding and removing the sites that allow BE is essential. PL spectroscopy at high fluences is also shown to be sensitive to small fractions of PbI$2$ inclusions and could be used to guide efforts to further optimize the material quality.

See the supplementary material for various findings discussed in this work that support our conclusions.

We acknowledge the funding by the Helmholtz Association through the Initiative and Networking Fund (PEROSEED [ZT-0024], Innovationpool), Research Field Energy – Program Materials and Technologies for the Energy Transition – Topic 1 Photovoltaics, and also the Helmholtz Energy Materials Foundry (HEMF).

The data that support the findings of this study are available from the corresponding author upon reasonable request.