Reducing the impact of Auger recombination in quasi-2D perovskite light-emitting diodes

Rapid Auger recombination represents an important challenge faced by quasi-2D perovskites, which induces resulting perovskite light-emitting diodes’ (PeLEDs) efficiency roll-off. In principle, Auger recombination rate is proportional to materials’ exciton binding energy (Eb). Thus, Auger recombination can be suppressed by reducing the corresponding materials’ Eb. Here, a polar molecule, p-fluorophenethylammonium, is employed to generate quasi-2D perovskites with reduced Eb. Recombination kinetics reveal the Auger recombination rate does decrease to one-order-of magnitude lower compared to its PEA+ analogues. After effective passivation, nonradiative recombination is greatly suppressed, which enables resulting films to exhibit outstanding photoluminescence quantum yields in a broad range of excitation density. We herein demonstrate the very efficient PeLEDs with a peak external quantum efficiency of 20.36%. More importantly, devices exhibit a record luminance of 82,480 cd m−2 due to the suppressed efficiency roll-off, which represent one of the brightest visible PeLEDs yet.

Absorption data show that the n=1, n=2 and n=3 phases are intermixed together. Thus, the low temperature PL, show peaks down to 420 nm which are evidence of the non pure perovskite phases. EDS or elemental analysis could show evidence of the structural formula.
The argument here is that your compounds are not one phase so to be able to derive an Eb from the temperature PL data. By the way, the compounds may suffer space group change at low temperature, which could be proven by showing low temperature XRD patterns.
Of course, if you are wondering why you see a single strong red shifting PL peak as you go to high n values at room temperature, this is a manifestation of energy transfer among perovskite crystals. (Of course the room temp. PL data do have "shoulders" especially in the case of p-F-PhE.). The energy transfer effect can be seen nicely in Synthetic Metals 121 (2001) 1339-1340.
(d) Of course as you synthesize high n perovskites, you effectively prepare a compound that has small binding energy. It is possible that the mixture of perovskites does obey some laws regarding the Auger versus Eb relation.
(e) As a side question, how do you measure absorption coefficient data ? Trying to read reference 6, for "The value of absorption coefficient (α(λ)) can be obtained from UV-vis measurements and calculated as follows 6 :", seems to be a dead end since ref. 6 does not seem to have such an analysis. The formula that you use is fairly simple. How do you measure R ? If you do measure absorption coefficient, then why do you provide arbitrary units for the absorbance spectra ? KK method would be better to precisely determine the absorption coefficient, provided that you have enough material.
In conclusion, I would like to see that you address all the previous issues, which mostly regard your explanation of your strong LED action.

Reviewer #1:
The study identifies Auger recombination as a key drawback in perovskite LEDs, directly related to high exciton binding energy Eb of the emitter. Then it finds that replacing conventional ligands with polarizable ones decreases Eg, as well as Auger constant. This also leads to low PLQY, but this issue is then addressed by defect passivation. The LEDs show exceptionally high EQE, and most importantly, slow rolloff of efficiency. This is the only way to make perovskite LEDs useful. The claims are well supported by extensive experimental and theoretical studies. The study is interesting and is timely for the field. The study explains well all aspects of materials science, photophysics and device engineering. The approaches are novel.
A few minor suggestions: Comment 1. Fig. 1g shows that PLQY first increases with n till n = 4, then it decreases.
As it is explained in the text, it might be indeed related to a better energy transfer. It would be help to comment the origin of improved carrier transfer in n = 4 samples.

Response:
Thanks for the reviewer's comment. We have now provided the transient absorption (TA) analysis and space-charge-limited current (SCLC) measurements to better understand the mechanism leading to the high PLQYs of <n> = 4 samples. We confirmed that the efficient energy transfer and high radiative recombination proportion within <n> = 4 perovskite films are main reasons for this case. 1). Decay kinetics of each ground state bleach were extracted from TA spectra (Figs. S6, S7, S8). The decay kinetics in both <n> = 4 quasi-2D perovskite films show obviously faster charge injection processes from donor to acceptor domains than that in <n> = 3 analogs (Figs. S6, S7, S8 and Table S3). Thus, more-graded energy landscape within <n> = 4 quasi-2D perovskite films (Figs. S6, S7, S8) leads to a more efficient energy transfer, facilitating the radiative recombination (Yang, X. et al. Nat. Commun. 2018, 9, 570;Quan, L. et al. Nano Lett. 2017, 17, 3701).

Figs. S6, S7, S8
TA spectra at different wavelength as a function of delay time for 4 and 5) perovskite films.

Figs. S6, S7, S8 Relative presence of different n-value phase within different quasi-2D perovskite films, which
were extracted from the amplitude of the GSB peaks.
Figs. S14, S19 Current-voltage (J-V) response for  and 5) perovskite films in space charge limited current (SCLC) measurements. Meanwhile, the exciton binding energy (Eb) is largely reduced as the <n>-value increased (Fig. S1), leading to reduced exciton recombination rates. Thus, the synergy between the faster trap-assisted recombination rates and slower exciton recombination rates leads a significant decline for <n> = 5 perovskite films' PLQY. In brief, we confirmed that the more-graded energy landscape in both <n> = 4 quasi-2D perovskite films is the foundation for their high PLQYs, which ensures more efficient energy transfer process and higher radiative recombination proportion.

Action:
We have now provided the TA analysis for quasi-2D perovskite films with different <n>-values in Supplementary Information Figures 6, 7, 8. We have now provided the SCLC measurements for quasi-2D perovskite films with different <n>values in Supplementary Information Figures 14, 19. The relevant discussion was provided in Supplementary Information Note 1.

Comment 2.
It would help to directly show how Eb is related with k3, with an equation or a schematic. This will make the connections clearer.
Response: Thanks for the reviewer's comment. We have now provided the schematic relating to the relation between Eb and Auger recombination rate (k3), to make the connections clearer. The relative equations as well as detailed description are also provided. In reduced-dimensional perovskite materials, since the strong Coulomb interaction between electrons and holes, the electron density in the vicinity of a hole is increased while it is decreased for another electron (Hangleiter, A. et al., Phys. Rev. Lett. 1990, 65:2, 215). As well known, Auger recombination rate strongly depends on the particle density, this nonuniform distribution can induce to Coulomb-enhanced Auger recombination (Fig. S1a). The Auger recombination rate ( Auger ) can be written in the form (Hangleiter, A. et al., Phys. Rev. Lett. 1990, 65:2, 215): where Auger 0 is the band-to-band Auger recombination rate for noninteracting particles; cn is the Auger coefficient; n and p are the density of electrons and holes respectively; geeh is the Coulomb enhancement factor. Keeping this in mind, reducing Eb is a promising strategy to suppress Auger recombination rates theoretically (Fig. S1b).

Fig. S1
Schematic relating to the relation between exciton binding energy and Auger recombination rate.

Action:
We have now provided relative schematic, equation and detailed description about the relation between Eb and k3 in Supplementary Information Figure 1.
Comment 3. The stability is enhanced by ~10 times (Fig. 4e) the loss of devices' efficiency is attributed to the chemical instability at the interface between perovskite and charge transport layers.

1).
To evaluate the effect of Auger recombination on the devices' stability, a high initial luminance or current density should be set to ensure the exist of Auger recombination. Furthermore, efficient PeLEDs with high luminance of 10 3 -10 4 cd m -2 are still urgently needed in solid-state-lighting (Shirasaki, Y. et al., Nat. Photonics 2013, 7, 13). Thus, evaluating the device stability at the initial luminance of 10,000 cd m -2 processes practical significance.
2). It has been reported that the interfacial contact between the perovskite and charge transport layers is a key factor for the device's operational stability (Quan, L. et al., Nat. Commun. 2020, 11, 170). As shown, CF3KO3S-p-FPEA perovskite coated on ZnO/PVP layer remains 90% of its initial the PL intensity for even 120 min (Fig. S30).
However, PL intensity of the perovskite coated on PEDOT:PSS/PFN-Br layer displays a sharp decline. It has been demonstrated that the acidic nature of PEDOT:PSS could significantly corrode the active layers. Thus, we attributed the loss of devices' efficiency to the chemical instability at the interface between perovskite and charge transport layers, rather than to perovskite degradation itself (Quan, L. et al., Nat. Commun. 2020, 11, 170;Wang, H. et al., Nat. Commun. 2020, 11, 891).  Comment 4. Verb tenses can be changed from past to present.
Response: Thanks for the comment. We have revised the manuscript thoroughly, and tried to avoid any grammar or syntax error to meet the high criteria of Nature communications.
Action: The manuscript has been revised thoroughly.
Improved efficiency roll-off has also been observed, which was attributed to the reduced Auger recombination. Transient measurements and simulations based on rate equations were presented together for further understanding of the results. This is a very nice work, with both high performance and new understanding of the device physics/ photophysics. I would hence strongly recommend to accept the ms after the authors address the following questions: 2). It should be point out that, it is difficult to precisely correlate the charge-carrier density in the perovskite film produced by laser pulse with that in the LED device produced by continuous charge injection (Chen, Z. et al. Adv. Mater. 2018, 1801370).
As well known, in addition to the Auger recombination rate of active materials, efficiency roll-off is attributed by several conditions, such as leakage current, imbalanced charge injection, Joule heating, etc. (Kim, H. et al. Nat. Commun. 2018, 9, 4893).
3). SEM images confirmed the uniform and dense morphology of perovskite films ( Fig. S25), demonstrating that the leakage current between charge transport layers was largely inhibited. Furthermore, the extremely low current density (< 10 -3 mA cm -2 ) at ohmic response reconfirmed the ignorable leakage current (Fig. 4b).
The low charge mobility as well as the conductivity can be attributed to two mean reasons: i) Presence of insulative large organic cation within quasi-2D perovskite films.
ii) High charge injection barrier induced by the large bandgap of low n-value domain within Br-based quasi-2D perovskites. Synergistically, the threshold of our greenemission quasi-2D PeLEDs is slightly lower than that in green-emission 3D and near- infrared-emission quasi-2D PeLEDs (Chen, Z. et al. Adv. Mater. 2018, 1801370;Zou, W. et al. Nat. Commun. 2018, 9, 608). In brief, we have obtained PeLEDs with higher efficiency based on twodimensional perovskite materials. By further molecular and passivation engineering, we reported the brightest visible PeLEDs together with high efficiency (EQE > 15%).
However, additional efforts on material science and device engineering are still required for further suppressing the efficiency roll-off and increasing the brightness. Comment 2. The PLQY will not be higher than 40% if we consider outcoupling of perovskite film. Considering that the optimal film here does not show microstructures (hence no coupling enhancement), can the authors comment why the PLQY value is over 80%?

Action:
We have rechecked the PLQYs of the perovskite films. We have provided the updated PLQYs in Fig. 1 and Table 1. We have added relative references about the PLQY test methods and light-outcoupling techniques in the revised manuscript.
Comment 3. I would suggest the authors to add more discussions on Figure 1f. I was not able to really follow how to extract the binding energy from the absorption.

Response:
Thanks for the reviewer's comment. We have provided the updated absorption spectra for PEA2PbBr4 and p-FPEA2PbB4 single crystals to facilitate understanding. We have provided more detailed discussion. Fig. 1, the optical absorption spectra can be characterized by an excitonic peak at lower energies and an extended absorption edge representing to the band-to-band electronic transitions. Particularly, we resolved the low-energy excitonic contribution in the optical absorption spectra for each single crystal (Stoumpos, C. et al. Chem 2017, 2, 427). As expected, an obvious excitonic absorption peak can be observed at around 3.08 eV for PEA2PbBr4, demonstrating a pronounced excitonic resonance (Saba, M. et al. Acc. Chem. Res. 2016, 49, 166;Ishihara, T. J. Lumin. 1994, 60, 269). In contrast, the excitonic contribution only displays a kink at around 3.04 eV for p-FPEA2PbBr4, which undoubtedly indicates the decreased exciton binding energy (Cao, D. et al. J. Am. Chem. Soc. 2015, 137, 7843).

2).
We also tried to extracted the actual Eb values from the optical absorption spectra. Unfortunately, the free electron-hole transition in optical absorption spectra could not be quantitatively resolved under room temperature (Ishihara, T. et al. Solid State Commun. 1989, 69:9, 933;Ishihara, T. J. Lumin. 1994, 60, 269). Nevertheless, attributed to the temperature-dependent PL measurements, the extracted Eb was estimated to be 347 and 195 meV for PEA2PbBr4 and p-FPEA2PbBr4, respectively.

Action:
We have provided the updated absorption spectra for perovskite single crystals.
We have provided more detailed discussion on Fig. 1f in Page 8. Comment 4. It is a critical issue to manipulate the distribution of different-n-value nanoplates within a quasi-2D perovskite film, toward efficient charge transport or light emitting performance. In this manuscript, different ligands were compared in view of exciton binding energy that is related to Auger recombination. But the nanoplates distribution seems to be also important in determining the roll-off performance, and I hence suggest the authors to add more discussions.
Response: Thanks for the reviewer's comment. We have provided the relative presence of different n domain for <n> = 4 quasi-2D perovskite films according to TA spectra.
We now confirm that the n domain distribution within PEA and p-FPEA perovskite films are similar; and the reduction of Eb enabled by introducing high-polarizable organic cation is the main reason for suppressed Auger recombination. We have also provided the TRPL spectra, TA measurements and PLQYs under various excitations for higher <n>-value quasi-2D perovskite films (<n> = 5), to understand the effect of n domain distribution on photophysical characters. 1). We qualitatively evaluated the relative presence of different n domain according to the amplitude of GSBs in TA spectra (Quan, L. et al. Nano Lett. 2017, 17, 3701;Yuan, S. et al. Adv. Mater. 2019, 31, 1904319). As shown, PEA and p-FPEA quasi-2D perovskite films displayed an almost similar domain distribution (Fig. S7).
Furthermore, we also extracted the energy transfer kinetics for each perovskite films.
We found that the whole energy transfer kinetics for both perovskite films occurred within sub-ps, which was significantly faster than the Auger recombination process (sub-ns) (Xing, G. et al. Nat. Commun. 2017, 8, 14558;Zou, W. et al. Nat. Commun. 2018, 9, 608). Thus, we confirmed that the reduction of Eb enabled by introducing highpolarizable organic cation is the main reason for the suppressed Auger recombination, rather than the difference domain distribution or energy transfer kinetics. 2). In addition, we also obtained the high <n>-value quasi-2D perovskite films (<n> = 5) by simply modifying the stoichiometry ( Table S1). As expected, compared with <n> = 4 analogy, the flatted energy landscape composed by high n value domain (n > 5) was largely increased, leading to an increased recombination center (Fig. S8). 3). It has been reported that Auger recombination can be suppressed by increasing width of lower-bandgap quantum wells (Zou, W. et al. Nat. Commun. 2018, 9, 608).
Furthermore, the exciton binding energy (Eb) of the perovskite film could be sequentially reduced with <n>-value increasing (Fig. 1g). Thus, compared with <n> = 4 analogies, higher thresholds for PLQY declining were found in both CF3KO3S treated <n> = 5 perovskite films. These results demonstrate that simply increasing the large n domain is do an effective approach for reducing the PLQY declining.

4).
It is worth mentioning, we found that the maximal PLQYs for <n> = 5 perovskite films were significantly sacrificed, even though after passivation engineering by CF3KO3S additive (Fig. S20). SCLC techniques were then employed to evaluate the defect state density. In particularly, compared with <n> = 4 perovskite films, <n> = 5 analogies display almost 2-times higher density of defect state (Fig. S19).
These results clearly indicate that a mass of defect states is inevitably introduced with the increasing proportion of large n-value domain (Fig. S8), resulting in faster trapassisted recombination rates. (Milot R. et al., Nano Lett. 2016, 16, 7001).
However, the k1 of CF3KO3S-PEA (<n> = 5) also display a significant decline due to the reduced Eb. The k1 of CF3KO3S-p-FPEA (<n> = 5) increases probably due to the enhanced trap-assistant recombination (Milot R. et al., Nano Lett. 2016, 16, 7001). The extracted kinetics were consistent well with the experimental results.
Furthermore, we confirmed that simply increasing the large n domain can inevitably introduce a mass of defect states and sacrifice the PLQYs, though it is do an effective approach for reducing the Auger recombination.

Action:
We have provided the relative presence of different n domain in Supplementary Information Figures 7, 8, 9. We have provided the SCLC measurements, PLQYs, TRPL spectra and TA measurements for quasi-2D perovskite films (<n> = 5) with high n domain in Supplementary Information Figures 19, 20,

21, 22.
Detailed discussion has been provided in Supplementary Information Note 2.
Comment 5. In general, there are quite some PL lifetime curves, which I am not sure are necessary. In addition, the simulation of Figure 2h is not new. Maybe the authors can consider moving some of these curves to the SI?
Response: Thanks for the reviewer's comment. We have revised the Fig. 2 and moved some PL-decay curves to the Fig. S12. Furthermore, we consider that Fig. 2f should be the significant connection for the research process. Thus, we hope to keep this figure in the main text.

Action:
We have now moved the previous Fig. 2b, c to Supplementary Information   Fig. 12 in revised manuscript.

Comment 6. Some information is missing: i) corresponding carrier density value to
PLQYs in the caption of Figure 1g. ii) information for excitation pulsed lasers for trPL and TA measurement such as repetition frequency and pulse width. iii) the consistency between experimental results and carrier dynamic simulations (how accurate the simulation is).
Response: Thanks for the reviewer's comment. We have now provided the corresponding carrier density value to PLQYs measurements. We have now provided the detailed test parameters for transient spectra measurements in revised manuscript.
We have now provided the standard error for each recombination rate (k1, k2 and k3).
Detailed discussion on the recombination simulations has also been provided.

1).
Carrier densities of around 1.2 × 10 5 cm -3 was adopted for the perovskite films PLQYs measurements, to evaluate the perovskite films' emission properties preliminarily.
2). The excitation source used in TRPL measurements was picosecond pulsed laser with a pulse width of below 100 ps and a repetition rate of 800 kHz at 355nm. The pump pulse used in TA measurements was generated by an optical parametric amplifier with a pulse width of around 100 fs and a repetition rate of 1 kHz at 365. Detailed information for the transient spectra measurements have been provided in revised manuscript.

3).
We have now provided the standard error for each recombination rate, to enhance the scientificity of the carrier dynamic simulation ( Table 1). Numerical simulation was then conducted by using the kinetics as parameters (Fig. S16)

Action:
We have now provided the corresponding carrier density value to PLQYs measurements in the caption of Fig. 1g. We have now provided more detailed test information for TRPL and TA measurements in Method Section. We have now provided the standard error for each recombination rate. More discussion on the recombination simulations has been provided in Supplementary Information Figure   16. For publishing this article, I would like to ask you to have some issues addressed and resolved.
Comment 1. Your expressions should be revised in multiple locations within the text.
For example, even the abstract text needs to be revised. You write, "Further passivate the deep-level defects, trap-assistant recombination thus be greatly suppressed, which enable the film's PLQY becoming insensitive to reduced exciton recombination rates." Personally, I can understand the implied meaning, but the sentence structure is wrong.
As another example, in page 4 of the submitted pdf file, you write "Auger recombination rate was proportional to the cube of carrier density in theoretical; thus, the amplified carrier density lead to enhanced Auger recombination rate.", which is not a correct English sentence.
Similar issue arises with the sentence "However, the problem has yet to fully solve due to the limited numbers of solution.", which also does not make sense, although I can sense what you would like to say.

Response:
Thanks for the reviewer's comment. We have revised the manuscript thoroughly, and tried to avoid any grammar or syntax error to meet the high criteria of Nature communications.
In view of the concern raised by the reviewer, we have added the following justification to the manuscript: 3). In original manuscript, "However, the problem has yet to fully solve due to the limited number of solutions." was changed to "However, the problem has yet to be fully solved due to the limited numbers of solution." Furthermore, we have revised the manuscript thoroughly, and tried to avoid any grammar or syntax error.

Action:
The manuscript has been revised thoroughly.  Communications, Vol. 91, No. 9, pp. 695-698, 1994. I would assume that these compounds would also "see" the effect of a reduced Eb, which is not the case. Thus, it is possible with the arguments presented until now, that it may well be that the reduced Eb is not due to the organic's dielectric constant, ie. Fluorine atoms, alone.
Response: Thanks for the reviewer's comment. We agree with the reviewer that the decreased dielectric confinement is the main reason, but not the only reason, for the reduced exciton binding energy (Eb) within 2D perovskites. We have now added the relative references and acknowledged these in the revised manuscript. We have now revised a part of description about the exciton binding energy measurements. We have now provided more information about the single crystal structure of 2D perovskites.
However, as the temperature is decreased, the perovskites undergo a slight structural phase transition, as a consequence of the changes in materials' band structure (Hong, X. et al. Phys. Rev. B 1992, 45:12, 6961). It should be noted that, the step-like peak within absorption spectra, which is ascribed to the free electron-hole transition, is difficult to be resolved at room temperature (Ishihara, T. J. Lumin. 1990, 60, 269).
We have simulated the dipole moment of the large organic cations through density function theory; and the values were determined to be 2.39 D and 1.28 D for p-FPEA + and PEA + , respectively. Thus, the increased dipole moment of p-FPEA + facilitated the increased dielectric constants, leading to reduced Eb within 2D perovskites theoretically.

4).
Nevertheless, we have still tried to estimate the Eb of the 2D perovskite single crystal from the diffuse reflection absorption spectra and the temperature-dependent photoluminescence spectra. We resolved the low-energy excitonic contribution in the absorption spectra for each perovskite single crystals (Fig. 1f) (Stoumpos, C. et al. Chem 2017, 2, 427). As expected, an obvious excitonic absorption peak can be observed at around 3.08 eV for PEA2PbBr4, demonstrating a pronounced excitonic resonance even at room temperature (Saba, M. et al. Acc. Chem. Res. 2016, 49, 166;Ishihara, T. J. Lumin. 1994, 60, 269). In contrast, the excitonic contribution only display a kink at around 3.04 eV for PEA2PbBr4, which undoubtedly indicate the decreasing exciton binding energy (Cao, D. et al. J. Am. Chem. Soc. 2015, 137, 7843).
Temperature-dependent PL measurements have employed to extract the relative Eb (Figs. 1d, e and S3). The extracted Eb was estimated to be 347 and 195 meV for PEA2PbBr4 and p-FPEA2PbBr4, respectively. Combining with the results of absorption spectra, we confirmed that dielectric-confinement in p-FPEA2PbBr4 has been largely reduced. Fig. 1f Absorption spectra of PEA2PbBr4 and p-FPEA2PbB4 single crystals.

Figs. 1d, e and S3 Temperature-dependent PL spectra and corresponding integrated PL intensity at different
temperature for PEA2PbBr4 and p-FPEA2PbBr4 perovskite single crystals 5). Furthermore, the width of the inorganic and organic layers of PEA2PbBr4 and p-FPEA2PbBr4 perovskite has also been calculated from the single crystal structure (Fig.   S2) (Ishihara, T. et al. Solid State Commun. 1989, 69:9, 933 In brief, we agree with the reviewer's concern that the decreased dielectric confinement attributed by para-fluorine atoms is the main reason, but not the only reason, for the reduced exciton binding energy (Eb) within 2D perovskites.

Action:
We have now added the relative references in the revised manuscript. We have now revised the description about the exciton binding energy measurements in Page 9.
We have now provided more information about the single crystal structure of 2D perovskites in Supplementary Information Figure 2.
Comment 3. Let us assume for a moment, that the arguments in Comment 2 before, do not completely change your approach to your reduced Eb ideology.
The compounds that you prepare are not distinct n = 1, n = 2, n = 3, n = 4 and so on phases. One would argue that the XRD patterns could confirm this, but it is crucial to point that your XRD figures do not show the low angle peak which is evident in the previous references written in Comment 2 above, but also for the PbBr4 2D material in 10.1021/acsanm.8b00207.
Even if the XRD patterns do not include the low angle peak, it is obvious from the absorption data that the compounds that you prepare so meticulously, are not composed from one phase only, since you see the absorption peak of the n = 1 phase in almost all but the n = 5 phases.
Absorption data show that the n = 1, n = 2 and n = 3 phases are intermixed together.
Thus, the low temperature PL, show peaks down to 420 nm which are evidence of the non-pure perovskite phases. EDS or elemental analysis could show evidence of the structural formula.
The argument here is that your compounds are not one phase so to be able to derive an Eb from the temperature PL data. By the way, the compounds may suffer space group change at low temperature, which could be proven by showing low temperature XRD patterns.
Of course, if you are wondering why you see a single strong red shifting PL peak as you go to high n values at room temperature, this is a manifestation of energy transfer among perovskite crystals. (Of course, the room temp. PL data do have "shoulders" especially in the case of p-F-PhE.). The energy transfer effect can be seen nicely in Synthetic Metals 121 (2001) 1339-1340.
Response: Thanks for the reviewer's comment. We agree with the concern from the reviewer. To avoid misunderstanding, we have adopted that 'n' stands for the species with a fixed composition but '<n>' represents a quasi-2D perovskite domain. We have added relevant reference (Papavassiliou, G. et al. Synthetic Met. 2001, 121, 1339 in the revised manuscript.

4).
Thus, the Eb obtained from the temperature-dependent PL largely reflect the complex Columbic electron-hole interactions within the whole quasi-2D perovskite film, which is severely restricted by the dielectric environment at recombination center (Yuan, M. et al. Nat. Nanotechnol. 2016, 11:10, 872;Ban, M. et al. Nat. Commun. 2018, 9, 3892). Furthermore, as the concern from the reviewer, the perovskite materials generally undergo a slight structural phase transition with the decreasing of the temperature. However, this aspect does not influence the dielectric confinement problem at hand. (Hong, X. et al. Phys. Rev. B 1992, 45:12, 6961). Nevertheless, we agree with the concern from the reviewer that the exact Eb value of the perovskite films is difficult to be obtained or calculated. We still tried to qualitatively evaluate the relative Eb, and confirmed that introducing the fluorine atom at para-position of phenyl group did decrease the Eb within the quasi-2D perovskite films.

Action:
We have adopted that 'n' stands for the species with a fixed composition but '<n>' represents a quasi-2D perovskite domain. We have added relevant reference in the revised manuscript.
Comment 4. Of course, as you synthesize high n perovskites, you effectively prepare a compound that has small binding energy. It is possible that the mixture of perovskites does obey some laws regarding the Auger versus Eb relation.

Response:
Thanks for the reviewer's comment. We have provided the relative presence of different n domain for <n> = 4 quasi-2D perovskite films according to TA spectra.
We confirmed that the n domain distribution within PEA and p-FPEA perovskite films are similar; and the reduction of Eb enabled by introducing high-polarizable organic cation is the main reason for the suppressed Auger recombination. We have also provided the TRPL spectra, TA measurements and PLQYs under various excitations for higher <n>-value quasi-2D perovskite films (<n> = 5), to understand the effect of n domain distribution on photophysical characters. 1). As shown, the PEA and p-FPEA quasi-2D perovskite films display an almost similar domain distribution (Fig. S7) (Quan, L. et al. Nano Lett. 2017, 17, 3701;Yuan, S. et al. Adv. Mater. 2019, 31, 1904319). Furthermore, the whole energy transfer kinetics for both perovskite films occur within sub-ps, which is significantly faster than the Auger recombination process (sub-ns) (Xing, G. et al. Nat. Commun. 2017, 8, 14558;Zou, W. et al. Nat. Commun. 2018, 9, 608). We confirmed that the reduction of Eb enabled by introducing high-polarizable organic cation was the main reason for the suppressed Auger recombination, rather than difference of the domain distribution or energy transfer kinetics. 2). We also prepared the high <n>-value quasi-2D perovskite films (<n> = 5) (Table S1), to preliminarily understand the effect of n domain on photophysical characters. Compared with <n> = 4 analogy, the flatted energy landscape composed by high n domain (n > 5) is largely increased, leading to an increased recombination center (Fig. S7). 3). It has been reported that the Auger recombination can be suppressed by increasing width of lower-bandgap quantum wells and then reducing the local carrier density (Zou, W. et al. Nat. Commun. 2018, 9, 608). Furthermore, the exciton binding energy (Eb) of the perovskite film could be sequentially reduced as <n>-value increased (Fig. 1g). Thus, as expected, higher threshold for PLQY declining are found in both CF3KO3S treated <n> = 5 perovskite films than that of <n> = 4 (Fig. S20). These results demonstrate that simply increasing the large n domain distribution is do an effective approach for reducing the PLQY declining.

4).
However, we also found that the maximal PLQYs for <n> = 5 perovskite films were significantly sacrificed, even though after passivated by CF3KO3S additive (Fig.   S20). Compared with <n> = 4 perovskite films, <n> = 5 analogs display almost 2-times higher density of defect state (Figs. S14, S19). This result clearly indicate that a mass of defect states is inevitably introduced with the increasing proportion of large n-value domain (Fig. S7), resulting in faster trap-assisted recombination rates in perovskite films. (Milot R. et al., Nano Lett. 2016, 16, 7001).

Action:
We have provided the relative presence of different n domain in Supplementary Information Figure 6. We have provided the SCLC measurements, PLQYs, TRPL spectra and TA measurements for quasi-2D perovskite films (<n> = 5) with high n domain in Supplementary Information Figures 19, 20, 21, 22. Detailed discussion has been provided in Supplementary Information Note 2.
Comment 5. As a side question, how do you measure absorption coefficient data?
Trying to read reference 6, for "The value of absorption coefficient (α(λ)) can be obtained from UV-vis measurements and calculated as follows 6:", seems to be a dead end since ref. 6 does not seem to have such an analysis. The formula that you use is fairly simple. How do you measure R? If you do measure absorption coefficient, then why do you provide arbitrary units for the absorbance spectra? KK method would be better to precisely determine the absorption coefficient, provided that you have enough material.
Response: Thanks for the comment. We have provided the transmission and reflection spectra for all the perovskite films. We have provided the corresponding absorption spectra through the following equation: α(λ) = -(1/l)ln [T/(1-R)]. We have checked and revised the citations thoroughly, and tried to avoid error. 1). As shown, we provided the transmission and reflection spectra for all the perovskite films through a dual beam UV-vis-NIR spectrophotometer (Cary 5000, Agilent) ( Fig. S5 and Fig. S18 a-d). In order to obtain the transmission and reflection coefficient as precise as possible, the incident beam is adjusted to be basically perpendicular to the sample.  2). As shown in Fig. S4a, b and Fig. S18 e- where A is absorbance, T is transmittance, R is reflectance, and l is the average film thickness of layers (Milot, R. et al. J. Phys. Chem. Lett. 2016, 7:20, 4178). The l is obtained from the cross-section SEM images. It is worth mentioned that, this method is a universal and convenient technology to evaluate the absorbance coefficient for the film samples and crystals (Song, T. et al. J. Am. Chem. Soc. 2017, 139:2, 836;Wenger, B. et al. Nat. Commun. 2017, 8, 590). The unit of the absorbance coefficient has been revised to be cm -1 . We have checked and revised the citations thoroughly, and tried to avoid error.

Fig. S18
The absorption coefficient curves of the quasi-2D perovskite films, which were calculated from transmission and reflection spectra.

Fig. S18
The absorption coefficient curves of the CF3KO3S treated quasi-2D perovskite films, which were calculated from transmission and reflection spectra.
3). We also tried to precisely determine the absorption coefficient through Sci. Technol. 2003, 15:2, N17.). As the reviewer concern, we have described this method and added relevant references in the revised manuscript. revised to be cm -1 . We have checked and revised the citations thoroughly, and tried to avoid error.

Action
Comment 6. In conclusion, I would like to see that you address all the previous issues, which mostly regard your explanation of your strong LED action.
Response: Thanks for the reviewer's comment. We herein reported a concept to suppress the efficiency roll-off in quasi-2D PeLEDs, and achieved one of the most efficient green devices with a record luminance. We showed that introducing high polarizable organic cation into the 'A-site' of the structure can be an effective method for reducing the exciton binding energy, and then suppressing the Auger recombination constant within quasi-2D perovskite films.
Reviewer #1 and Reviewer #2 also valued our strategies and scientific methods.
They commented "The claims are well supported by extensive experimental and theoretical studies." AND "The study explains well all aspects of materials science, photophysics and device engineering." AND "This is a very nice work, with both high performance and new understanding of the device physics/ photophysics." Furthermore, thanks to the suggestion from the Reviewer #3, we now provided more complete and more scientific comprehension for our strategy. We hope that our justifications could satisfy the referee concerns.
Action: According the suggestion from Reviewer #3, we have provided more detailed discussion in the revised manuscript.