pith. sign in

arxiv: 2408.12192 · v2 · pith:RCLMZBIOnew · submitted 2024-08-22 · ❄️ cond-mat.mes-hall · quant-ph

A framework for extracting the rates of photophysical processes from biexponentially decaying photon emission data

Jill M. Cleveland , Tory A. Welsch , Eric Y. Chen , D. Bruce Chase , Matthew F. Doty , Hanz Y. Ram\'irez-G\'omez This is my paper

Pith reviewed 2026-05-25 08:20 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph
keywords biexponential decayphotoluminescenceexciton trappingrate equationssemiconductor heterostructuresCdSeTe/CdScarrier dynamicsoptically inactive states
0
0 comments X

The pith

A model of reversible trapping into inactive states explains biexponential photoluminescence decay and extracts all transition rates without approximations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds a set of linear rate equations that include neutral excitons, radiative and nonradiative paths, and reversible capture into optically dark trap states. This closed system reproduces the biexponential decay routinely seen in low-dimensional semiconductor emitters and supplies likelihood intervals for every rate constant. In the high-temperature limit the same equations yield definite numerical values for the rates, improving on earlier reduced models. The framework is applied to time-resolved photoluminescence data from CdSeTe/CdS heterostructures to obtain radiative lifetime, nonradiative lifetime, and the trapping and release rates that produce the delayed emission component.

Core claim

Biexponential photoluminescence decay arises because carriers reversibly enter and leave optically inactive trap states whose dynamics are fully described by a closed linear rate-equation network; the network permits direct extraction of likelihood intervals for all transition rates, and supplies exact rate values when the high-temperature approximation holds.

What carries the argument

A closed linear rate-equation system coupling neutral excitons to reversible trapping and detrapping by optically inactive states.

If this is right

  • All radiative, nonradiative, trapping, and release rates can be bounded by likelihood intervals from a single biexponential trace.
  • In the high-temperature regime the model returns specific numerical values for every rate, outperforming reduced models used previously.
  • The delayed photoluminescence component is directly attributable to the trapping-release cycle rather than to a second emissive species.
  • The same rate values can be used to predict how photoluminescence efficiency changes with excitation density or temperature.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could be tested by intentionally varying trap density through growth conditions and checking whether the extracted trapping rate scales proportionally.
  • If the model holds, temperature-dependent measurements should show the trapping and release rates approaching each other as thermal energy increases.
  • Extension to more complex heterostructures would require adding additional trap levels while preserving the linear-rate-equation structure.

Load-bearing premise

The observed biexponential photoluminescence decay is produced by reversible trapping into optically inactive states whose dynamics are completely captured by a closed set of linear rate equations.

What would settle it

A measured biexponential decay curve whose shape or temperature dependence cannot be reproduced by any choice of rates inside the four-state linear model, or whose extracted rates disagree with independent measurements of trap occupation times.

Figures

Figures reproduced from arXiv: 2408.12192 by D. Bruce Chase, Eric Y. Chen, Hanz Y. Ram\'irez-G\'omez, Jill M. Cleveland, Matthew F. Doty, Tory A. Welsch.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) States involved in the photoluminescence processes we model. The legend [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) Transition rates involved in the modeled dynamics. (b) Time dependent [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (a) Schematic band diagrams for the two core/rod/emitter heterostructures [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (a) [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (a) [PITH_FULL_IMAGE:figures/full_fig_p039_5.png] view at source ↗
read the original abstract

There is strong interest in designing and realizing optically-active semiconductor nanostructures of greater complexity for applications in fields ranging from biomedical engineering to quantum computing. While these increasingly complex nanostructures can implement progressively sophisticated optical functions, the presence of more material constituents and interfaces also leads to increasingly complex exciton dynamics. In particular, the rates of carrier trapping and detrapping in complex heterostructures are critically important for advanced optical functionality, but they can rarely be directly measured. In this work, we develop a model that includes trapping and release of carriers by optically inactive states. The model explains the widely observed biexponential decay of the photoluminescence signal from neutral excitons in low dimensional semiconductor emitters. The model also allows determination of likelihood intervals for all the transition rates involved in the emission dynamics, without the use of approximations. Furthermore, in cases for which the high temperature limit is suitable, the model leads to specific values of such rates, outperforming reduced models previously used to estimate those quantities. We demonstrate the value of this model by applying it to time resolved photoluminescence measurements of CdSeTe/CdS heterostructures. We obtain values not only for the radiative and nonradiative lifetimes, but also for the delayed photoluminescence originating in trapping and release.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript develops a rate-equation framework incorporating reversible trapping and release of carriers into optically inactive states to model exciton dynamics in low-dimensional semiconductor nanostructures. It claims this closed linear system explains the widely observed biexponential photoluminescence (PL) decay from neutral excitons, enables extraction of likelihood intervals for all transition rates (radiative, nonradiative, trapping, release) without approximations, and in the high-temperature limit yields specific rate values that outperform reduced models. The framework is demonstrated on time-resolved PL data from CdSeTe/CdS heterostructures, providing values for the relevant rates including delayed PL contributions.

Significance. If the derivation and identifiability hold, the framework would be significant for the field, as it targets the extraction of trapping/detrapping rates that are critical for complex heterostructures but difficult to measure directly. The provision of likelihood intervals without approximations and the claimed superiority in the high-T limit, combined with application to experimental data, would represent a useful advance in analyzing biexponential PL signals.

major comments (3)
  1. [model development] The central assumption that biexponential PL decay is generated specifically by a minimal closed linear rate-equation system with reversible trapping into optically inactive states (model development section) is load-bearing for the claim that extracted intervals represent physical transition rates; if inhomogeneous broadening, additional states, or density-dependent processes contribute, the mapping from observed decay constants to microscopic rates is non-unique and the intervals lose their interpretation.
  2. [results] The assertion that the model outperforms reduced models and leads to specific rate values in the high-temperature limit (abstract and results section) requires explicit quantitative comparison, such as fit residuals, R² values, or error metrics between the full model and reduced models; without this, the superiority claim cannot be evaluated.
  3. [abstract] The claim of determining likelihood intervals for all rates without approximations (abstract) depends on the explicit fitting procedure and rate-equation solution; the manuscript must demonstrate how the biexponential parameters map to the full set of rates in a way that avoids circularity or hidden approximations in the likelihood construction.
minor comments (2)
  1. Notation for the transition rates (e.g., radiative vs. trapping) should be defined consistently in the main text with a clear table or diagram of the state diagram to aid readability.
  2. The abstract states the model 'explains' the decay; a brief discussion of why alternative biexponential generators were not considered would strengthen the presentation even if not central to the claims.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive major comments. We address each point below and indicate the revisions that will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [model development] The central assumption that biexponential PL decay is generated specifically by a minimal closed linear rate-equation system with reversible trapping into optically inactive states (model development section) is load-bearing for the claim that extracted intervals represent physical transition rates; if inhomogeneous broadening, additional states, or density-dependent processes contribute, the mapping from observed decay constants to microscopic rates is non-unique and the intervals lose their interpretation.

    Authors: We agree that the extracted intervals are meaningful only under the stated model assumptions. The manuscript presents the framework as a minimal closed linear system capable of producing biexponential decay via reversible trapping; it does not claim this is the sole possible mechanism in all systems. In the revised manuscript we will expand the model development section to state the assumptions more explicitly and add a dedicated paragraph on limitations, including how inhomogeneous broadening, extra states, or density-dependent effects could render the mapping non-unique. This will clarify the conditions under which the reported intervals retain their physical interpretation. revision: yes

  2. Referee: [results] The assertion that the model outperforms reduced models and leads to specific rate values in the high-temperature limit (abstract and results section) requires explicit quantitative comparison, such as fit residuals, R² values, or error metrics between the full model and reduced models; without this, the superiority claim cannot be evaluated.

    Authors: The referee correctly notes that quantitative metrics are required to substantiate the outperformance claim. The original text relied on the additional physical rates obtained and qualitative statements. We will revise the results section to include a direct comparison table (or supplementary figure) reporting fit residuals, R², and information criteria (e.g., AIC) for the full model versus the reduced models on the experimental CdSeTe/CdS datasets, thereby providing the requested quantitative evidence. revision: yes

  3. Referee: [abstract] The claim of determining likelihood intervals for all rates without approximations (abstract) depends on the explicit fitting procedure and rate-equation solution; the manuscript must demonstrate how the biexponential parameters map to the full set of rates in a way that avoids circularity or hidden approximations in the likelihood construction.

    Authors: The mapping follows directly from the exact analytic solution of the linear rate equations, which yields closed-form relations between the observed biexponential amplitudes/decay constants and the four microscopic rates; the likelihood is then evaluated on these exact relations. No further approximations are introduced. To eliminate any ambiguity, the revised manuscript will add an explicit worked example (main text or supplementary information) that takes one fitted biexponential dataset, applies the algebraic mapping step by step, and constructs the likelihood intervals, thereby demonstrating transparency and absence of circularity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is standard forward modeling from rate equations

full rationale

The paper constructs a closed linear rate-equation system (bright exciton plus optically inactive trap states) whose solution yields a biexponential form for the photoluminescence decay. Observed decay constants are then mapped to the microscopic rates via fitting or likelihood analysis. This is a conventional forward-modeling procedure in which the functional form is derived from the assumed Markov chain and the rates are outputs of the fit to data; no step reduces a claimed prediction to a fitted input by construction, nor does any load-bearing premise rest on self-citation. The abstract and model description contain no self-definitional relations, smuggled ansatzes, or uniqueness theorems imported from prior author work. The derivation remains self-contained against the experimental time-resolved PL traces.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of a linear rate-equation description that includes reversible trapping; no new physical entities are postulated beyond standard trap states already used in the field. Free parameters are the individual transition rates that are fitted to data.

free parameters (1)
  • transition rates (radiative, nonradiative, trapping, release)
    These rates are the quantities whose values or intervals are extracted by fitting the model to measured decay curves.
axioms (1)
  • domain assumption Carrier dynamics in the nanostructure are fully described by a closed linear system of rate equations that includes optically inactive trap states.
    This modeling premise is invoked to derive the biexponential form and to enable rate extraction.

pith-pipeline@v0.9.0 · 5781 in / 1414 out tokens · 38321 ms · 2026-05-25T08:20:44.907695+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

84 extracted references · 84 canonical work pages

  1. [1]

    our model allows us to understand clearly how the presence of a trapping state creates biexponential decay dynamics and 2) our model reduces to the well-known monoexponential behavior in the absence of the trapping state. Finally, given the biexponential decay of the exciton population shown by equation (4), the corresponding quantum yield can be written ...

    work page

  2. [2]

    Utzat, W

    H. Utzat, W. Sun, A. E. K. Kaplan, F. Krieg, M. Ginterseder, B. Spokoyny, N. D. Klein, K. E. Shulenberger, C. F. Perkinson, M. V. Kovalenko, and M. G. Bawendi, Science363, 1068 (2019), https://www.science.org/doi/pdf/10.1126/science.aau7392

    work page doi:10.1126/science.aau7392 2019

  3. [3]

    H. Y. Ramírez, Y.-L. Chou, and S.-J. Cheng, Scientific Reports9, 1 (2019)

    work page 2019

  4. [4]

    X. Ma, Y. Wang, J. Zide, and M. Doty, Phys. Rev. Applied13, 064029 (2020). 24

    work page 2020

  5. [5]

    F. P. G. de Arquer, D. V. Talapin, V. I. Klimov, Y. Arakawa, M. Bayer, and E. H. Sargent, Science 373, eaaz8541 (2021), https://www.science.org/doi/pdf/10.1126/science.aaz8541

    work page doi:10.1126/science.aaz8541 2021

  6. [6]

    Q. Liu, Y. Sun, T. Yang, W. Feng, C. Li, and F. Li, Journal of the American Chemical Society 133, 17122 (2011), pMID: 21957992, https://doi.org/10.1021/ja207078s

    work page doi:10.1021/ja207078s 2011

  7. [7]

    Cotrino-Lemus and H

    J. Cotrino-Lemus and H. Y. Ramírez, Journal of Physics: Conference Series 864, 012081 (2017)

    work page 2017

  8. [8]

    Y. Chen, S. Zhao, X. Wang, Q. Peng, R. Lin, Y. Wang, R. Shen, X. Cao, L. Zhang, G. Zhou, J. Li, A. Xia, and Y. Li, Journal of the American Chemical Society138, 4286 (2016), pMID: 26998730, https://doi.org/10.1021/jacs.5b12666

    work page doi:10.1021/jacs.5b12666 2016

  9. [9]

    Albers, E

    A. Albers, E. Chan, P. McBride, C. Ajo-Franklin, B. Cohen, and B. Helms, J Am Chem Soc 134, 9565 (2012)

    work page 2012

  10. [10]

    C. C. Milleville, E. Y. Chen, K. R. Lennon, J. M. Cleveland, A. Kumar, J. Zhang, J. A. Bork, A. Tessier, J. M. LeBeau, D. B. Chase, J. M. O. Zide, and M. F. Doty, ACS Nano13, 489 (2019), https://doi.org/10.1021/acsnano.8b07062

    work page doi:10.1021/acsnano.8b07062 2019

  11. [11]

    Amani, D.-H

    M. Amani, D.-H. Lien, D. Kiriya, J. Xiao, A. Azcatl, J. Noh, S. R. Madhvapa- thy, R. Addou, S. KC, M. Dubey, K. Cho, R. M. Wallace, S.-C. Lee, J.-H. He, J. W. Ager, X. Zhang, E. Yablonovitch, and A. Javey, Science 350, 1065 (2015), https://www.science.org/doi/pdf/10.1126/science.aad2114

    work page doi:10.1126/science.aad2114 2015

  12. [12]

    D. F. Macias-Pinilla and H. Y. Ramírez, Phys. Rev. A102, 033731 (2020)

    work page 2020

  13. [13]

    Y. He, J. Yan, L. Xu, B. Zhang, Q. Cheng, Y. Cao, J. Zhang, C. Tao, Y. Wei, K. Wen, Z. Kuang, G. M. Chow, Z. Shen, Q. Peng, W. Huang, and J. Wang, Advanced Materials33, 2006302 (2021), https://onlinelibrary.wiley.com/doi/pdf/10.1002/adma.202006302

    work page doi:10.1002/adma.202006302 2021

  14. [14]

    BECKER, Journal of Microscopy 247, 119 (2012), https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1365-2818.2012.03618.x

    W. BECKER, Journal of Microscopy 247, 119 (2012), https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1365-2818.2012.03618.x

    work page doi:10.1111/j.1365-2818.2012.03618.x 2012

  15. [15]

    J. R. Lakowicz, chapter 4, in Principles of fluorescence spectroscopy (Springer, 2016) p. 141–142, 3rd ed

    work page 2016

  16. [16]

    Jones, S

    M. Jones, S. S. Lo, and G. D. Scholes, The Journal of Physical Chemistry C113, 18632 (2009), https://doi.org/10.1021/jp9078772

    work page doi:10.1021/jp9078772 2009

  17. [17]

    K. Gong, Y. Zeng, and D. F. Kelley, The Journal of Physical Chemistry C117, 20268 (2013), https://doi.org/10.1021/jp4065449

    work page doi:10.1021/jp4065449 2013

  18. [18]

    Zhang, X

    J. Zhang, X. Zhang, and J. Y. Zhang, The Journal of Physical Chemistry C113, 9512 (2009), 25 https://doi.org/10.1021/jp9026354

    work page doi:10.1021/jp9026354 2009

  19. [19]

    D. C. Hannah, N. J. Dunn, S. Ithurria, D. V. Talapin, L. X. Chen, M. Pelton, G. C. Schatz, and R. D. Schaller, Phys. Rev. Lett.107, 177403 (2011)

    work page 2011

  20. [20]

    X. Li, Y. Wu, S. Zhang, B. Cai, Y. Gu, J. Song, and H. Zeng, Advanced Functional Materials 26, 2435 (2016), https://onlinelibrary.wiley.com/doi/pdf/10.1002/adfm.201600109

    work page doi:10.1002/adfm.201600109 2016

  21. [21]

    Huang, J

    H. Huang, J. Raith, S. V. Kershaw, S. Kalytchuk, O. Tomanec, L. Jing, A. S. Susha, R. Zboril, and A. L. Rogach, Nature Communications8, 996 (2017)

    work page 2017

  22. [22]

    L. Y. Karachinsky, S. Pellegrini, G. S. Buller, A. S. Shkolnik, N. Y. Gordeev, V. P. Evtikhiev, and V. B. Novikov, Applied Physics Letters84, 7 (2004), https://doi.org/10.1063/1.1637962

    work page doi:10.1063/1.1637962 2004

  23. [23]

    Q. Wang, S. Stobbe, and P. Lodahl, Phys. Rev. Lett.107, 167404 (2011)

    work page 2011

  24. [24]

    C. J. Bhongale, C.-W. Chang, C.-S. Lee, E. W.-G. Diau, and C.-S. Hsu, The Journal of Phys- ical Chemistry B109, 13472 (2005), pMID: 16852685, https://doi.org/10.1021/jp0502297

    work page doi:10.1021/jp0502297 2005

  25. [25]

    Coppens, J

    P. Coppens, J. Sokolow, E. Trzop, A. Makal, and Y. Chen, The Journal of Physical Chemistry Letters 4, 579 (2013), pMID: 26281869, https://doi.org/10.1021/jz400013b

    work page doi:10.1021/jz400013b 2013

  26. [26]

    Mayer, B

    G. Mayer, B. Maile, R. Germann, A. Forchel, and H. Meier, Superlattices and Microstructures 5, 579 (1989)

    work page 1989

  27. [27]

    V. B. Verma, M. J. Stevens, K. L. Silverman, N. L. Dias, A. Garg, J. J. Coleman, and R. P. Mirin, Journal of Applied Physics109, 123112 (2011), https://doi.org/10.1063/1.3599889

    work page doi:10.1063/1.3599889 2011

  28. [28]

    H. Geng, Q. Liu, Y. Tang, and K. Wei, Photonics11, 10.3390/photonics11040358 (2024)

    work page doi:10.3390/photonics11040358 2024

  29. [29]

    Oreszczuk, W

    K. Oreszczuk, W. Pacuski, A. Rodek, M. Raczyński, T. Kazimierczuk, K. Nogajewski, T. Taniguchi, K. Watanabe, M. Potemski, and P. Kossacki, 2D Materials11, 025029 (2024)

    work page 2024

  30. [30]

    W. M. Sanderson, J. Hoy, C. Morrison, F. Wang, Y. Wang, P. J. Morrison, W. E. Buhro, and R. A. Loomis, The Journal of Physical Chemistry Letters11, 3249 (2020), pMID: 32255643, https://doi.org/10.1021/acs.jpclett.0c00489

    work page doi:10.1021/acs.jpclett.0c00489 2020

  31. [31]

    Kuno, The Journal of Physical Chemistry Letters12, 4024 (2021), pMID: 33880921, https://doi.org/10.1021/acs.jpclett.1c00811

    Z.Zhang, S.Zhang, I.Gushchina, T.Guo, M.C.Brennan, I.M.Pavlovetc, T.A.Grusenmeyer, and M. Kuno, The Journal of Physical Chemistry Letters12, 4024 (2021), pMID: 33880921, https://doi.org/10.1021/acs.jpclett.1c00811

    work page doi:10.1021/acs.jpclett.1c00811 2021

  32. [32]

    E. Y. Chen, T. A. Welsch, J. M. Cleveland, C. C. Milleville, K. R. Lennon, H. Y. Ramírez, J. M. O. Zide, D. B. Chase, and M. F. Doty, The Journal of Physical Chemistry C125, 17183 (2021)

    work page 2021

  33. [33]

    Zhang, Y

    X.-X. Zhang, Y. You, S. Y. F. Zhao, and T. F. Heinz, Phys. Rev. Lett.115, 257403 (2015). 26

    work page 2015

  34. [34]

    Labeau, P

    O. Labeau, P. Tamarat, and B. Lounis, Phys. Rev. Lett.90, 257404 (2003)

    work page 2003

  35. [35]

    Gokus, L

    T. Gokus, L. Cognet, J. G. Duque, M. Pasquali, A. Hartschuh, and B. Lounis, The Journal of Physical Chemistry C114, 14025 (2010)

    work page 2010

  36. [36]

    X. Wu, M. T. Trinh, D. Niesner, H. Zhu, Z. Norman, J. S. Owen, O. Yaffe, B. J. Kudisch, and X.-Y. Zhu, Journal of the American Chemical Society137, 2089 (2015)

    work page 2089

  37. [37]

    S. G. Motti, D. Meggiolaro, S. Martani, R. Sorrentino, A. J. Barker, F. De Angelis, and A. Petrozza, Advanced Materials 31, 1901183 (2019), https://onlinelibrary.wiley.com/doi/pdf/10.1002/adma.201901183

    work page doi:10.1002/adma.201901183 2019

  38. [38]

    Bao and F

    C. Bao and F. Gao, Reports on Progress in Physics85, 096501 (2022)

    work page 2022

  39. [39]

    Hauswald, T

    C. Hauswald, T. Flissikowski, T. Gotschke, R. Calarco, L. Geelhaar, H. T. Grahn, and O. Brandt, Phys. Rev. B88, 075312 (2013)

    work page 2013

  40. [40]

    Krishnamurthy, A

    S. Krishnamurthy, A. Singh, Z. Hu, A. V. Blake, Y. Kim, A. Singh, E. A. Dolgopolova, D. J. Williams, A. Piryatinski, A. V. Malko, H. Htoon, M. Sykora, and J. A. Hollingsworth, ACS Nano 15, 575 (2021), pMID: 33381968, https://doi.org/10.1021/acsnano.0c05907

    work page doi:10.1021/acsnano.0c05907 2021

  41. [41]

    Sabzevari, R

    Z. Sabzevari, R. Sahraei, N. N. Jawhar, A. F. Yazici, E. Mutlugun, and E. Soheyli, Journal of Applied Physics129, 063107 (2021), https://doi.org/10.1063/5.0038696

    work page doi:10.1063/5.0038696 2021

  42. [42]

    R. Jain, R. Sinha, M. K. Sahu, and M. Jayasimhadri, Luminescence 36, 1444 (2021), https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/pdf/10.1002/bio.4085

    work page doi:10.1002/bio.4085 2021

  43. [43]

    Chang, J

    Q. Chang, J. Sui, Z. Chai, and W. Wu, Nanomaterials11, 10.3390/nano11071761 (2021)

    work page doi:10.3390/nano11071761 2021

  44. [44]

    Soheyli, S

    E. Soheyli, S. Zargoush, A. F. Yazici, R. Sahraei, and E. Mutlugun,54, 505110 (2021)

    work page 2021

  45. [45]

    Berstermann, T

    T. Berstermann, T. Auer, H. Kurtze, M. Schwab, D. R. Yakovlev, M. Bayer, J. Wiersig, C. Gies, F. Jahnke, D. Reuter, and A. D. Wieck, Phys. Rev. B76, 165318 (2007)

    work page 2007

  46. [46]

    Gorgis, T

    A. Gorgis, T. Flissikowski, O. Brandt, C. Chèze, L. Geelhaar, H. Riechert, and H. T. Grahn, Phys. Rev. B86, 041302(R) (2012)

    work page 2012

  47. [47]

    A. J. Goodman, A. P. Willard, and W. A. Tisdale, Phys. Rev. B96, 121404(R) (2017)

    work page 2017

  48. [48]

    C. Zhao, C. W. Tang, G. Cheng, J. Wang, and K. M. Lau,7, 115903 (2020)

    work page 2020

  49. [49]

    G. Yang, M. Kazes, D. Raanan, and D. Oron, ACS Photonics 8, 1909 (2021), https://doi.org/10.1021/acsphotonics.1c00399

    work page doi:10.1021/acsphotonics.1c00399 1909

  50. [50]

    D. G. Sellers, J. Zhang, E. Y. Chen, Y. Zhong, M. F. Doty, and J. M. Zide, Solar Energy Materials and Solar Cells155, 446 (2016)

    work page 2016

  51. [51]

    E. Y. Chen, C. Milleville, J. M. Zide, M. F. Doty, and J. Zhang, MRS Energy & Sustainability 27 5, E16 (2018)

    work page 2018

  52. [52]

    E. Y. Chen, J. Zhang, D. G. Sellers, Y. Zhong, J. M. O. Zide, and M. F. Doty,Photovoltaic Specialist Conference, 1 (2015)

    work page 2015

  53. [53]

    Zhang, E

    J. Zhang, E. Y. Chen, M. F. Doty, and J. M. O. Zide, Journal of Applied Physics126, 044301 (2019)

    work page 2019

  54. [54]

    N. Meir, I. Pinkas, and D. Oron, RSC Adv.9, 12153 (2019)

    work page 2019

  55. [55]

    Deutsch, O

    Z. Deutsch, O. Schwartz, R. Tenne, R. Popovitz-Biro, and D. Oron, Nano Lett.12, 2948 (2012)

    work page 2012

  56. [56]

    Deutsch, L

    Z. Deutsch, L. Neeman, and D. Oron, Nat. Nanotechnol.8, 649 (2013)

    work page 2013

  57. [57]

    R. E. Bailey and S. Nie, J. Am. Chem. Soc.125, 7100 (2003)

    work page 2003

  58. [58]

    Carbone, C

    L. Carbone, C. Nobile, M. De Giorgi, F. D. Sala, G. Morello, P. Pompa, M. Hytch, E. Snoeck, A. Fiore, I. R. Franchini, M. Nadasan, A. F. Silvestre, L. Chiodo, S. Kudera, R. Cingolani, R. Krahne, and L. Manna, Nano Letters 7, 2942 (2007), pMID: 17845067, https://doi.org/10.1021/nl0717661

    work page doi:10.1021/nl0717661 2007

  59. [59]

    D. V. Talapin, J. H. Nelson, E. V. Shevchenko, S. Aloni, B. Sadtler, and A. P. Alivisatos, Nano Letters 7, 2951 (2007), pMID: 17845068, https://doi.org/10.1021/nl072003g

    work page doi:10.1021/nl072003g 2007

  60. [60]

    D. Kim, Y. K. Lee, D. Lee, W. D. Kim, W. K. Bae, and D. C. Lee, ACS Nano11, 12461 (2017)

    work page 2017

  61. [61]

    Reiss, M

    P. Reiss, M. Protière, and L. Li, Small 5, 154 (2009), https://onlinelibrary.wiley.com/doi/pdf/10.1002/smll.200800841

    work page doi:10.1002/smll.200800841 2009

  62. [62]

    J. Cui, A. P. Beyler, L. F. Marshall, O. Chen, D. K. Harris, D. D. Wanger, X. Brokmann, and M. G. Bawendi, Nature Chemistry5, 602 (2013)

    work page 2013

  63. [63]

    D. L. Ferreira, R. N. Maronesi, S. O. Ferreira, A. G. Silva, and M. A. Schiavon, The Journal of Physical Chemistry C123, 24289 (2019)

    work page 2019

  64. [64]

    Gao and X

    Y. Gao and X. Peng, Journal of the American Chemical Society137, 4230 (2015)

    work page 2015

  65. [65]

    J. E. Thomaz, K. P. Lindquist, H. I. Karunadasa, and M. D. Fayer, Journal of the American Chemical Society 142, 16622 (2020)

    work page 2020

  66. [66]

    Y. Li, S. Natakorn, Y. Chen, M. Safar, M. Cunningham, J. Tian, and D. D.-U. Li, Frontiers in Physics 8, 10.3389/fphy.2020.576862 (2020)

    work page doi:10.3389/fphy.2020.576862 2020

  67. [67]

    A. F. van Driel, I. S. Nikolaev, P. Vergeer, P. Lodahl, D. Vanmaekelbergh, and W. L. Vos, Phys. Rev. B75, 035329. 28

    work page

  68. [68]

    Gryczynski, I

    Z. Gryczynski, I. Gryczynski, and J. R. Lakowicz, inMolecular Imaging, edited by A. Peri- asamy and R. N. Day (American Physiological Society, San Diego, 2005) pp. 21–56

    work page 2005

  69. [69]

    R. Howl, C. Sabín, L. Hackermüller, and I. Fuentes, Journal of Physics B: Atomic, Molecular and Optical Physics51, 015303 (2017)

    work page 2017

  70. [70]

    N. R. Fino, A. S. Camacho, and H. Y. Ramírez, Nanoscale Research Letters9, 297 (2014)

    work page 2014

  71. [71]

    Ravindran, A

    T. Ravindran, A. K. Arora, B. Balamurugan, and B. Mehta, Nanostructured Materials11, 603 (1999)

    work page 1999

  72. [72]

    Brunhes, P

    T. Brunhes, P. Boucaud, S. Sauvage, A. Lemaître, J.-M. Gérard, F. Glotin, R. Prazeres, and J.-M. Ortega, Phys. Rev. B61, 5562 (2000)

    work page 2000

  73. [73]

    Jasieniak, L

    J. Jasieniak, L. Smith, J. van Embden, P. Mulvaney, and M. Califano, The Journal of Physical Chemistry C 113, 19468 (2009)

    work page 2009

  74. [74]

    H. Y. Ramírez and A. Santana, Computer Physics Communications183, 1654 (2012)

    work page 2012

  75. [75]

    Planelles, J

    J. Planelles, J. I. Climente, and C. Segarra, The Journal of Physical Chemistry C116, 25143 (2012)

    work page 2012

  76. [76]

    H. Y. Ramírez, J. Flórez, and A. S. Camacho, Phys. Chem. Chem. Phys.17, 23938 (2015)

    work page 2015

  77. [77]

    J. I. Climente, C. Segarra, and J. Planelles, New Journal of Physics15, 093009 (2013)

    work page 2013

  78. [78]

    Aghoutane, L

    N. Aghoutane, L. Pérez, D. Laroze, M. El-Yadri, and E. Feddi, Results in Physics44, 106158 (2023)

    work page 2023

  79. [79]

    Sabah, I

    A. Sabah, I. Shafaqat, A. Naifar, H. Albalawi, M. S. Alqahtani, M. Ashiq, and S. A. Shabbir, Optical Materials 142, 114065 (2023). 29 Appendix A: Amplitudes, ND limit and PLQY

    work page 2023

  80. [80]

    Population amplitudes The amplitudesA− X,A + X,AT, A− D, A+ D, A0 D, A0 D, A− G, A+ G and A0 G appearing in the time dependent population functions at equations (4), are given by the expressions A− X = 1 2−ΓPL + ΓXT−(ΓTX + ΓTD ) 2Γ2 , A+ X = 1 2 + ΓPL + ΓXT−(ΓTX + ΓTD ) 2Γ2 , AT = 4Γ2 0ΓXT [ ΓTD (Γ1−ΓTD )−Γ2 0 ] Γ2 [ Γ2 2 (Γ1−ΓTD )2− ( Γ1ΓTD−Γ2 1 + 2Γ0 )2...

    work page

Showing first 80 references.