Exciton dissociation in 2D layered metal-halide perovskites

Layered 2D perovskites are making inroads as materials for photovoltaics and light emitting diodes, but their photophysics is still lively debated. Although their large exciton binding energies should hinder charge separation, significant evidence has been uncovered for an abundance of free carriers among optical excitations. Several explanations have been proposed, like exciton dissociation at grain boundaries or polaron formation, without clarifying yet if excitons form and then dissociate, or if the formation is prevented by competing relaxation processes. Here we address exciton stability in layered Ruddlesden-Popper PEA2PbI4 (PEA stands for phenethylammonium) both in form of thin film and single crystal, by resonant injection of cold excitons, whose dissociation is then probed with femtosecond differential transmission. We show the intrinsic nature of exciton dissociation in 2D layered perovskites, demonstrating that both 2D and 3D perovskites are free carrier semiconductors and their photophysics is described by a unique and universal framework.

affect the characterization. How did the authors evaluate the impacts? 14. How does halide perovskite superlattice (Nature volume 608, pages 317-323 (2022)) compare with bulk single crystals and polycrystalline thin films in the exciton stability? 15. The image quality of the main text should be improved.
Reviewer #2: Remarks to the Author: The manuscript describes the results of the pump probe measurements of the 2D perovskites, namely PEA2PbI4 in n=1 Ruddlesden-Popper phase, both in single crystal and thin film form. Resonant excitation was used to create cold excitons. The main claim of the manuscript is exciton dissociation in 2D Ruddlesden-Popper layered perovskites, which would make them similar to their 3D counterparts. This is based on the observed splitting into free carriers within 1-2 ps as a consequence of the formation of polarons. The experimental data are interesting, however I do not find that they support the final claim of the manuscript.
1. Why the splitting of the exciton signal in pump probe cannot be attributed to the formation of biexciton? For this polarization resolved measurements should be performed.
2. What are physical evidences of the polaron formation? For this either PL on a very short time scale should be measured (ACS Nano 2022, 16, 12, 21259-21265) or enhancement of the effective mass of the carrier, a characteristic sign of the polaron should be provided.
3. At the same time I do not understand the physical process proposed by authors, is it polaron exciton formation? or is it dissociation and than carrier polaron formation? To which modes in each scenario there sill coupling. This has to be quantified.
4. Temperature dependent measurements should be provided, as coupling with the lattice should have a characteristic temperature dependence. 5. What would be the mechanism of the dissociation of exciton with binding energy of few hundred meV? Why would polaron dissociate the exciton? 6. Just bimolecular decay si not sufficient to claim charge separation, as in 2D TMDS, where we have strongly bound exciton and still Auger effect is observed.
Before providing this extra data and answer to above question, the manuscript is not suitable for publication.
Reviewer #3: Remarks to the Author: The manuscript "Exciton splitting in 2D layered metal-halide perovskites" presents a smart experimental study of dynamics of dissociation of bound excitons in a two-dimensional (Phenethylammonium)2PbI4 perovskite using time-resolved femtosecond differential transmission techniques. The results indicating their dissociation into free carriers within 1-2 ps can be important for understanding of nature of exciton dynamics in 2D Ruddlesden-Popper layered perovskites and implementation of the materials into photovoltaic devices.
Unfortunately, the authors use some jargon in the manuscript, such as "exciton splitting" and "excitons form and then split" which obscures the physics of the processes taking place. It is difficult to imagine that exciton split something or be spatially split in the material. Probably, a splitting of their energy states is meant. In this case, it would be better if the authors used more precise terminology. It also remains unclear from the manuscript the value of this splitting. Does it correspond to the wavelength distance between the maximum and the minima in Fig. 2e? In order for the reader to better perceive the processes that the authors use to explain the experimental results, it is absolutely necessary to give an energy scheme with an indication of transitions on it at different excitations used by the authors in the experiment.
Other comments: Specifying n = 1 in the abstract is not clear and requires an explanation. "PEA": using abbreviation in the abstract is not a good style.
Section Material and methods, first paragraph: "n = 1" is still puzzling, what is n here? A physical value or a number? If latter, in what sequence? Can authors characterize the phase they mention here by more informative terms than "n = 1"?
Reviewer #1 (Remarks to the Author): In this manuscript, the authors utilize 2D Ruddlesden-Popper halide perovskite to discuss the exciton stability. The ultrafast spectroscopy experiment based on differential transmission and photoluminescence is demonstrated. Spontaneous exciton splitting is observed and interpreted as a generation of polarons. The authors conclude that 2D halide perovskite is a free carrier semiconductor like their 3D structures, although with larger exciton binding energy. The experiment and discussion in this manuscript are insightful and convincing. The authors are recommended to address the following comments to further improve the quality of this work.
1. In line 42, edge states and dangling bonds could also exist on single-crystal surfaces. (Na Quan, Li et al. "Edge stabilization in reduced-dimensional perovskites." Nature communications 11.1 (2020): 1-9.) We thank the Reviewer for the comment and agree that our statement could be made more precise. In this specific case, we mean that the concentration of surface defects in the polycrystalline film is much higher than in the single crystal due to the presence of grain boundaries [Blancon et al., Science 355,1288-1292(2017]. The assumption is corroborated by experimental data (Fig. S6, Supporting Information): the long-lived TA signal at cryogenic temperature, attributed to temperature-activated trapping, is clearly visible only in the case of poly-crystalline thin film, while it has negligible amplitude in the case of single crystal. We have modified and extended the manuscript to clarify our statement and motivate our assumption.
2. In line 61, page 3, it says, "PEA is the only cation." But lead also serves as a cation in the structure. In the following sentence, "in the absence of a second shorter organic cation," it is not only organic cation that could occupy the position, like PEA2CsPb2Br7. It is suggested that the authors make the sentence clearer and more accurate.
We appreciate the carefulness of the Referee: we now added in the manuscript a more precise description of layered perovskite structures and clarified what was the actual meaning of this sentence, that was not accurate enough. Fig 1a is usually not sufficient to prove the crystalline structure of 2D halide perovskite for its layered structure. It is recommended that the authors take small-angle X-ray scattering images to discuss its structures better. More information will be revealed.

The XRD pattern in
We thank the referee for the suggestion. In the original manuscript only the XRD powder pattern was recorded and compared to literature, since the PEA2PbI4 perovskite has a well known crystal structure and several cif files have been already deposited in the main database. Nevertheless, the authors have considered the reviewer's suggestions to characterize the structure more in depth and performed single crystal diffraction on a small PEA2PbI4 crystal with a Bruker D8 Venture diffractometer equipped with Incoated microsource (Mo Kα, λ = 0.71073 Å) and a PHOTON II detector. A suitable crystal of 0.05 x 0.13 x 0.15 mm 3 was selected and mounted on a MiTeGen loop (50 µm in diameter). Two sets of ω scans (12 frames each, 0.5 °/frame) were collected using a detector to sample distance of 50 mm and 5 s/frame. A total of 113 reflections with I/σ ≥ 20 were found and were indexed with the Fast Fourier Transform Method. The initial unit cell parameters were then refined and the Bravais lattice determined using the APEX 3 plugin. The measurements confirm the symmetry and structure as triclinic with space group P-1 and the following lattice parameters: a = 8.680 Å, b = 8.682 Å, c = 16.418 Å and α = 94.512°, β = 100.618°, γ = 90.559°, with disordered cations. Our results are in agreement with a crystal structure deposited on the CCDC with refcode BARHOU for the same layered perovskite (Nano Res. (2017), 10, 2117, DOI: 10.1007/s12274-016-1401-6). Fig. 1a has been updated with the new sketch of the structure from experimental data. Table with refined cell parameters has been added in the SI. Figure 1b, the XRD of the polycrystalline thin film had fewer peaks than the single crystalline sample. However, there should be more than one orientation in polycrystalline samples, which contributes to more XRD peaks. The authors should explain why there are more peaks in the single crystalline sample.

In
The comment of the referee is correct: XRD patterns on single crystals should have fewer peaks than the polycrystalline one. However, the XRD pattern shown in the manuscript is obtained from a finely ground crystal which is analogous to a polycrystalline powder. The new single crystal diffraction measurements mentioned at point n.3 confirm as much. On the other hand, the polycrystalline film has a preferred orientation out of plane along the 00l direction while it is reasonably randomly oriented inplane, for this reason, in theta-2theta geometry it is possible to see only the 00l peaks. In the modified manuscript we now include a full discussion of the issue. 5. The authors should distinguish whether their thin films are single-crystalline or polycrystalline in the main text.
We thank the referee for the question, that induced us to improve the "visualization" of the samples. While thin films are polycrystalline, they grow with a spontaneous preferred orientation along the 001 direction during the spin coating process. The main text has been modified with a more detailed description, as well as small insets in Fig. 1b to help the reader visualize the two different kind of samples that were studied in this work.
6. It would be more straightforward for bandgap discussion if the authors could integrate photoluminescence and absorption into one figure in Fig 1c. We thank the referee for the suggestion, the Figure has been modified by integrating absorption with PL spectrum in Fig. 1c, as proposed by the reviewer. 7. In line 70, page 3, the authors need a reference to support that PEA2PbI4 has the largest exciton binding energy of the whole RP series with PEA.
We thank the referee for the careful observation, and agree that this statement needs a supporting reference. We also realized the sentence was misleading, since the n=1 PEA2PbI4 has the largest exciton binding energy in its own RP series, thus we modified the text and added a reference to the paper [Gao, X. et al. Advanced Science 6, 1900941 (2019)] where a comprehensive list of layered perovskite in the Ruddlesden-Popper phase is provided, along with their bandgaps and exciton binding energies. We inserted a brief discussion illustrating that, being quantum confinement strongest for the n=1 layered compound, it is natural that also the exciton binding energy has the largest value.
8. In line 121, page 6, how and by what data could the authors derive a "5%" bleaching?
The fraction is calculated as the ratio between the spectral integrals of the absolute value of the DT signal and its relative (signed) value; as such, it measures the mismatch between the positive and negative parts of the signal. Pure bleaching would generate 100% positive signal, pure broadening would generate zero mismatch between positive and negative signal, since broadening does not alter the overall oscillator strength of the optical transition. We recognize that the number was quoted without enough explanation, which we have now explicitly added to provide context. 9. In line 122, the authors should briefly describe the phenomenon of coherent oscillations and why it appears here. And the authors use citations 40 and 63 to explain the coherent oscillations. The authors also claimed that the appearance of polarons might come from the deformation of the crystal lattice in line 250. The authors should further explain the relationship between them.
We thank the referee for carefully reading and pointing out this ambiguity, as we figured out that this needed to be emphasised. In line 122 we are referring to the phenomenon of ground state coherent phonon oscillations, as a result of lattice oscillations in the fundamental state triggered by a Raman process occurring during the pump pulse. In order to clarify if the observed oscillation is indeed coming from ground state coherent phonon oscillations, we performed DT measurements at different excitation photon energies, in resonance with the exciton peak, below and above it, with one and two photon excitation. The results are reported in Fig. S2, showing picosecond-scale oscillations at different excitation wavelengths, and temperature dependent behaviour with 2-photons resonant excitation. It is evident that in the resonant case oscillation amplitude is amplified and damping is much slower, while their period and phase are not depending on excitation energy. Furthermore, the observed period (around 1ps) corresponds to a well-known Raman mode (30 cm-1) of PEA 2 PbI 4 , providing further confirmation of the ground-state nature of coherent oscillations.
We have now inserted a discussion to clarify that polaron formation is an excited-state phenomenon caused by lattice deformation in the presence of optical excitations, while the observed coherent oscillations are a ground-state phenomenon, caused by the Raman excitation of the lattice without a population in the excited state. Thanks to the observation of the Referee, we noticed that there can be a minor difference in the background noise, but none of the reported signal was subjected to smoothing or data processing. The difference in signal-to-noise ratio (SNR) can be attributed to higher thickness of the crystal with respect to that of thin film, which translates, through Lambert-Beer law, in a higher absorption. The thickness of the crystal is in fact approximately one order of magnitude higher than that of the thin-film, leading to a higher DT signal and a lower SNR. We have now inserted a comment to briefly clarify this point.
11. In line 143, the authors said the one-photon excitation could create the maximum carrier density of carriers and make it easier for opposite charge carriers to split at the surface trap states. The "opposite charge carriers" may be ambiguous because the authors said the carriers could split. And the "split" is only used to describe excitons instead of carriers in this manuscript. In the reviewer's opinion, the authors are trying to express that free carriers were generated and combined into excitons. Those excitons close to the surface tend to split at the surface trap states, which causes the broadening and redshift in the DT signal.
We are grateful for this suggestion by the Referee, which was remarked by Referee 3 as well. Having realized that our phrasing may be ambiguous and in conflict with other terminology, we decided to edit the manuscript by replacing expressions as "exciton splitting" or "carrier splitting" with "exciton dissociation", even in the title. We believe that this modification is greatly improving the clarity of the whole manuscript and of the scientific claims.
12. In line 257, the authors claimed that the fast initial decay corresponds to polaron formation. Because the temperature would influence on the speed of lattice deformation, the initial decay will also be influenced by temperature. The authors should supplement the experiments by comparing the initial decay with different temperatures.
We thank the Referee for raising this point and accept the suggestion of additional measurements as a function of temperature. We analysed the ultrafast transient in the DT signal as a function of the sample temperature, as reported in the newly added Fig. S12, Supporting information. The initial ultrafast dynamics of DT signal at cryogenic temperatures is found to be comparable in magnitude and dynamics to what measured at room temperature. The measurements demonstrate that the spontaneous polaronic deformation is not temperature activated, which may be related to the absenceor a very low value -of an energy barrier between the excitonic and polaronic states. We have now included an additional discussion and we believe that the additional measurements have significantly enhanced the manuscript insight.
13. Do the authors attempt to improve the quality of the polycrystalline thin film? According to the methods part, utilizing DMSO to dissolve the precursors is rare for iodic 2D perovskite. Meanwhile, the spin coating and annealing parameters are also critical to the film quality. Comparing single crystals and polycrystals is unfair when one is in poor condition. Also, the PMMA treatment could potentially affect the characterization. How did the authors evaluate the impacts?
Various sample preparation techniques have been explored, and we have now revised the manuscript to account for it. Our choice for the solvent can be supported by a comparison between the performance of thin films obtained from DMSO and DMF. If we consider the photoluminescence lifetime (in the low excitation regime) as an indicator of the quality of the thin film, we found that in the considered excitation range (below 1µJ/cm 2 /pulse) samples prepared with DMSO have a PL decay around 200 ps, compatible with what reported in literature. Lifetimes for films prepared with DMF are substantially shorter, as reported in Fig. S14, Supporting Information. On the other hand, PL spectra are not noticeably affected by the chosen solvent.
Regarding the concerns about PMMA, we also compared the quality and reliability of the samples with and without PMMA deposition. We thus added in Fig. S14, Supporting information, a comparison between films with and without a PMMA protective capping layer. The TA spectra and lifetimes are unaltered, while we experienced a faster degradation of the sample without PMMA that, at highest excitation power, can become visible during the TA measurement (typically 15-30 minutes). Thin films covered with PMMA show better performance comparing PL lifetime at the same excitation energy, and have a better stability, allowing to perform multiple measurements without evident signs of alteration in the considered excitation range (below 10µJ/cm 2 /p at 430nm excitation wavelength).
Perovskite superlattice is indeed an interesting material, characterized by a lower exciton binding energy, with respect to the case of polycrystalline material or conventionally grown single crystals, showing a much higher mobility as well as higher and less-power dependent carrier lifetime. We did not explicitly consider superlattices in our study, so our observation may be speculative, still we can suggest that, since exciton are proven to be unstable "regardless" of morphology, we may expect superlattice material to have a behaviour analogous to what is reported in this work. We realize this material is worth a mention, thus we added a reference in the introduction of the manuscript.
15. The image quality of the main text should be improved.
We thank the reviewer for the note, we now uploaded new higher resolution images in the main text in place of the previous ones.

Reviewer #2 (Remarks to the Author):
The manuscript describes the results of the pump probe measurements of the 2D perovskites, namely PEA2PbI4 in n=1 Ruddlesden-Popper phase, both in single crystal and thin film form. Resonant excitation was used to create cold excitons. The main claim of the manuscript is exciton dissociation in 2D Ruddlesden-Popper layered perovskites, which would make them similar to their 3D counterparts. This is based on the observed splitting into free carriers within 1-2 ps as a consequence of the formation of polarons. The experimental data are interesting, however I do not find that they support the final claim of the manuscript.
1. Why the splitting of the exciton signal in pump probe cannot be attributed to the formation of biexciton? For this polarization resolved measurements should be performed.
We thank the referee for carefully reading our manuscript, and considering mechanisms that were not explicitly discussed in the submitted version. Two are the basic reasons for which the formation of biexcitons (BX) must be ruled out. 1) Emission of one photon from a BX state would occur at the exciton (X) energy minus the BX binding energy. We never observed such emission. Furthermore, BX formation requires pairing of two Xs. BX emission should therefore overcome X PL at high excitation fluence. Again, experimental evidence of such a behaviour was never observed. 2) The fact that the transient PL intensity is proportional to the square of the transient DT signal is not consistent with the formation of BXs. If a population of BX existed, two cases would be possible. BXs are the minority species and Xs the majority one. In this case, the overall PL intensity would be proportional to the overall population of photoexcitations (i.e., Xs plus BXs), so would be DT. In other words, the PL transient would be proportional to DT, and not to DT squared as observed experimentally. If Xs were the minority species and BXs the majority ones, same conclusions are drawn.
However, we also believe that polarization-resolved measurements provide a direct and useful proof that biexcitons are not involved. Therefore we performed on thin film and single crystal samples additional DT and PL measurements with the control of circular polarization of both pump and probe. The results, that we report in Fig. S7, Supporting Information, show that there is no evidence of an effect on the DT signal or PL with pump and probe polarization, further excluding a biexciton explanation for the observed spectra.
We remark that such findings are not in disagreement with other measurements at liquid He temperatures that have shown biexciton formation, since at such very low temperature, excitons may very well be stable and then pair to form biexcitons. We also added a discussion and a relevant reference in the main text.
2. What are physical evidences of the polaron formation? For this either PL on a very short time scale should be measured (ACS Nano 2022, 16, 12, 21259-21265) or enhancement of the effective mass of the carrier, a characteristic sign of the polaron should be provided.
The main finding in our work is that excitons are unstable and dissociate, notwithstanding their very large binding energy. As a mechanism responsible for such a dissociation, we invoke the only one that is known to play a role, namely polaron formation. Such explanation is consistent with all our observations, time resolved DT spectra and DT vs PL decays; ultrafast transient absorption has been similarly interpreted in literature. Femtosecond PL has also been measured, but it provided no further direct evidence.
However, we do not claim to observe directly polaron formation. Ultrafast X-ray and electron diffraction measurements are the tools recognized as useful for providing direct evidence for polaron formation, 3. At the same time I do not understand the physical process proposed by authors, is it polaron exciton formation? or is it dissociation and than carrier polaron formation? To which modes in each scenario there sill coupling. This has to be quantified.
Our measurement demonstrate that excitons dissociate, therefore the formation of a majority of exciton-polarons are ruled out, because they would still be bound electron-hole states. The mechanism proposed to explain the observed dynamics is therefore exciton dissociation into unbound polarons, meaning that one exciton generates one positive and one negative polaron.
On the other hand, bound exciton-polarons have been reported in literature, especially through measurements at liquid helium temperatures (see eg. [Thouin et al, Nat. Materials 18,pp 349-356, 2019]). Such observations are not in contrast with ours, on the contrary it is perfectly reasonable that if the polaronic deformation is strong enough to dissociate the exciton at liquid nitrogen temperature, even if the binding energy is hundreds of meV, then some significant polaronic deformation persists even at liquid helium temperatures, when the exciton is stable against dissociation, giving rise to exciton polarons.
Stimulated by the Referee's comment, we therefore introduced in the main text the possibility that, when equilibrium is established, it may involve a majority of unbound polarons and a minority of exciton-polarons. Quantifying their ratio certainly warrants further investigation and may require applying the radiometric time-resolved photoluminescence we have recently demonstrated [Simbula et al. Adv. Optical Mater. 2021, 2100295].
4. Temperature dependent measurements should be provided, as coupling with the lattice should have a characteristic temperature dependence.
We welcome the Referee's suggestion and we have performed additional DT measurements at low temperature. Part of the answer to this question is bound to questions 2 and 3, and question 11 of Referee1. We thus refer to the new data reported in Fig. S2, Supporting Information, showing DT on a picosecond timescale and its oscillations. Another interesting evidence is reported in Fig. S12, Supporting Information, that compares the DT signal evolution at room and at cryogenic temperature, showing that the dynamic is not affected in the sharp drop of intensity, that happens on the same timescale at the different temperatures. This indicates that the mechanism of exciton dissociation is quite not evidently dependent on temperature, for the considered temperature range. 5. What would be the mechanism of the dissociation of exciton with binding energy of few hundred meV? Why would polaron dissociate the exciton?
The Referee's comment highlights the major novelty of our findings: the experimental evidence demonstrates that excitons dissociate, even though their binding energy estimated from absorption measurements is several hundreds of meV, at least an order of magnitude larger than thermal energy KT at room temperature. The mechanism we invoke to explain the observation is that the polaron stabilization energy, i.e. the energy gained through lattice relaxation in presence of optical excitations, is comparable to the exciton binding energy. Therefore, the energy difference between bound excitons and unbound polarons is not the exciton binding energy anymore, and is instead the difference between the exciton binding energy and the polaron relaxation energy. Such mechanism is explained in detail, together with the modified Saha equilibrium condition and a rate equation model that describes the experimental observations, in Simbula et al. Adv. Optical Mater. 2021, 2100295. Following the Referee's comment, we therefore modified the discussion in the manuscript and provided a less ambiguous and more clear description of the invoked mechanism to dissociate the exciton.
6. Just bimolecular decay si not sufficient to claim charge separation, as in 2D TMDS, where we have strongly bound exciton and still Auger effect is observed.
The Referee is indeed right, bimolecular decay alone is not sufficient to draw conclusions on exciton dissociation. This is the reason why we combine PL and DT in a "tandem" setup where PL and DT are measured on the same spot of the sample, and show that PL is proportional to the square of DT -as reported in Fig. 4 and Fig. S5, Supporting information. Such evidence is conclusive for charge separation and for the fact that an equilibrium is established between a majority of unbound carriers (the polarons) and a minority of bound excitons. The two different power laws of the d(PL)/dt vs PL and d(DT)/dt vs DT identify the dominant decay process for polarons and excitons as the monomolecular decay of excitons. Because of Saha equilibrium, such a decay results in a bimolecular deple tion of polarons. Auger would instead result in a cubic rate for polarons and a quadratic one for excitons, as experimentally observed and discussed in Simbula et al. Adv. Optical Mater. 2021, 2100295. Following the Referee's comment, we improved the discussion of the implication of our measurements to clarify any possible misunderstanding.
Before providing this extra data and answer to above question, the manuscript is not suitable for publication.
Reviewer #3 (Remarks to the Author): The manuscript "Exciton splitting in 2D layered metal-halide perovskites" presents a smart experimental study of dynamics of dissociation of bound excitons in a two-dimensional (Phenethylammonium)2PbI4 perovskite using time-resolved femtosecond differential transmission techniques. The results indicating their dissociation into free carriers within 1-2 ps can be important for understanding of nature of exciton dynamics in 2D Ruddlesden-Popper layered perovskites and implementation of the materials into photovoltaic devices.
Unfortunately, the authors use some jargon in the manuscript, such as "exciton splitting" and "excitons form and then split" which obscures the physics of the processes taking place. It is difficult to imagine that exciton split something or be spatially split in the material. Probably, a splitting of their energy states is meant. In this case, it would be better if the authors used more precise terminology. It also remains unclear from the manuscript the value of this splitting. Does it correspond to the wavelength distance between the maximum and the minima in Fig. 2e? In order for the reader to better perceive the processes that the authors use to explain the experimental results, it is absolutely necessary to give an energy scheme with an indication of transitions on it at different excitations used by the authors in the experiment.
We sincerely thank the Referee for pointing out a source of possible misunderstanding in the terminology and phrasing we have been using. We have therefore thoroughly revised the manuscript, including its very title, and avoided the wording 'exciton splitting' that generated some ambiguity to the Referee, since we do not describe any energy splitting. In place, we refer to the process as 'exciton dissociation', meaning that a bound exciton dissociates into one positive and one negatively charged carrier, holes, and electrons, or more accurately positive and negative polarons, that are not bound to each other.
After revising every instance in the manuscript where we refer to the process and carefully avoiding sources of possible confusion, we believe the manuscript is now compliant with the broadly adopted terminology and avoid conflicts with other definitions in literature [Han, Y. et al. Nat. Mater. 21, 1282-1289(2022].
Other comments: