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Exciton dissociation in organic solar cells: An embedded charge transfer state model
by Jouda Jemaa Khabthani, Khouloud Chika, Alexandre Perrin, Didier Mayou
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Khouloud Chika |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2407.20839v1 (pdf) |
| Date submitted: | 2024-07-31 10:42 |
| Submitted by: | Chika, Khouloud |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Organic solar cells are a promising avenue for renewable energy, and our study introduces a comprehensive model to investigate exciton dissociation processes at the donor-acceptor interface. Examining quantum efficiency and emitted phonons in the charge transfer state (CTS), we explore scenarios like variations of the environment beyond the CTS and repulsive/attractive potentials. The donor-acceptor interface significantly influences the injection process, with minimal impact from the environment beyond the CTS. Attractive potentials can create localized electron states at the interface, below the acceptor band, without necessarily hampering a good injection at higher energies. Exploring different recombination processes, including acceptor-side and donor-side recombination, presents distinct phases in the energy-injection versus recombination rate. Our study highlights the important role of the type of recombination in determining the quantum efficiency and the existence of hot or cold charge transfer states. Finally, depending on the initial energy of the electron on the donor side, three distinct injection regimes are exhibited. The present model should be helpful for optimizing organic photovoltaic cell interfaces, highlighting the critical parameter interplay for enhanced performance.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
In this article, the authors developed and studied a charge injection model named as "embedded charge transfer state model" at a donor-acceptor interface, typically applicable in organic semiconductors. The dynamic mean-field theory and scattering theory are employed to solve the model. It shows that the coupling between electrons and vibrational modes affects quantum efficiency, introducing the concepts of hot and cold charge transfer states. The efficiency of charge injection in organic solar cells is strongly influenced by the interplay between injection and recombination processes. The interface parameters are crucial for optimizing cell performance and that the interface’s impact is more significant than environmental variations beyond the CTS.
Weaknesses
The paper is theoretical work, all results and conclusions are not compared with experiments. At least, the authors should give some discussions about possible methods to check the results and conclusions.
Report
In this article, the authors developed and studied a charge injection model named as "embedded charge transfer state model" at a donor-acceptor interface, typically applicable in organic semiconductors. The dynamic mean-field theory and scattering theory are employed to solve the model. It shows that the coupling between electrons and vibrational modes affects quantum efficiency, introducing the concepts of hot and cold charge transfer states. The efficiency of charge injection in organic solar cells is strongly influenced by the interplay between injection and recombination processes. The interface parameters are crucial for optimizing cell performance and that the interface’s impact is more significant than environmental variations beyond the CTS. The model is applicable to organic semiconductors, the results and conclusions are meaningful and helpful for understanding of the exciton dissociation process. I think that the work presented in the current manuscript merit publication in the journal after some minor revisions.
Requested changes
1. The units of most physical quantities are unclear. Authors stated all energies are expressed in units of J. The J is the hopping matrix elements of a carrier between nearest neighbors. But typical value of J is not given in the paper.
2. The values of parameters are very important for the results and conclusions. For most calculations, the following parameters are used, g=1 and sqrt(2); w=0.8; eps=1.25x10^(-6), 0.1, 0.2, 0.3; V=-2, 2. But authors didn’t explain reasonability of these values. However, the values g=1 and w=0.8 seems too large for it means energy level of a phonon is similar to a carrier.
3. The paper is theoretical work, all results and conclusions are not compared with experiments. At least, the authors should give some discussions about possible methods to check the results and conclusions.
Recommendation
Ask for minor revision
Report
The charge separation process is one of the crucial processes in organic semiconductors. However, its theoretical understanding has not been well studied, compared to that of charge transport. This paper provides a new approach to analyzing this process and offers detailed analyses, though it has some limitations, such as the assumption of zero temperature. In that sense, this paper likely holds a certain degree of value. If several revisions are made, I believe it would be suitable for publication.
Requested changes
1-This paper can be regarded as a follow-up paper to Ref. 38, while providing more detailed analyses. The authors should address this point in the introduction and clarify the differences and novelty compared to Ref. 38.
2-In Eq. (1), the expression of H_R is not presented. If the recombination is included as a simple self-energy, that should be written explicitly.
3-For better readability, it may be helpful to explain that the sign of V characterizes the electrostatic potential in Section 2.4.
4-In Section 2.4, the authors state "We work in the limit where the temperature is zero, because band energies and phonon energies are well above the thermal energy at room temperature." How can the omission of low-frequency vibrations be justified?
5-The recombination rate \Gamma_R is not defined. The authors must define it clearly.
6-How many basis sets are used for vibrations?
7-Why does the axis in Fig. 5 point downward?
8-It would be helpful to explain why the density of states presents the localized peaks in Fig. 9(c).
9-Which model is used for Fig (10)?
10-In Fig. (17), the label of the y-axis is missing.
Recommendation
Ask for minor revision
Author: Khouloud Chika on 2024-11-12 [id 4957]
(in reply to Report 1 on 2024-10-17)
Attached are the answers to the questions, numbered according to the corresponding questions: 1- Indeed, we studied the model in its simplest form in reference [34] (The reference 38 has become 34). We explained in the introduction (page 3) what new developments we presented in this work by adding the following paragraph: “A first analysis of charge injection was presented in our previous work \cite{chika2022model}. Here we enlarge our approach by considering several types of recombination processes, various type of environments, attractive or repulsive potential and by analyzing more deeply the process of injection and its interdependence with phonon emission on the CTS”. This addition highlights the differences and the extended scope of our current work compared to Ref. 34, as suggested.
2- The Hamiltonian HR describes the recombination processes. As stated above these processes can be represented by a coupling to a continuum of states and in the formalism used here we just need to model the self-energy ∆R(z) that represents this coupling to a continuum. We consider the cases where the continuum is a wide band (∆R(z) = −iΓR) and narrow band as discussed in Section 5.2. All energies are expressed in units of J, which is typically of the order of 0.2 eV. All parameters are chosen to fall within a realistic experimental range [30–32, 41–44].
3- The sign of V characterizes the sign of the electrostatic potential: if V>0 then the potential is repulsive and if V<0 then the potential is attractive. This has been added to the text in the last paragraph (page 5).
4- We have added a sentence in the introduction in section 2.4.”The Hamiltonian H of our model takes into account a tight-binding hopping model for the electron and includes the essential coupling with local vibration modes, as is common for molecular solids [21].”
5- This definition of Gamma_R was clarified on page 6 at the end of section 2.4.
6- In this model, we consider one orbital per site, and for each phonon mode, we account for coupling with multiple phonons. Typically we take into account at least the emission of ten phonons which is largely enough here to get a good convergence of the computation.
7- Thank you for your remark. It's a mistake; we have corrected the figure.
8- As explained now “These states are analogous to bound electronic states in atoms or impurity states in semiconductors and are geometrically localized around the CTS. Although an infinite series of such states might be expected near the minimum energy of the continuum, their weights are too low to be detected numerically.”
9- In Figure 10, we present the results for the N phonon modes (Model A).We added “Model A” in the sentence just before the figure.
10- You're right, the y-axis is the spectral density n(E).This is now shown.
Author: Khouloud Chika on 2024-11-12 [id 4958]
(in reply to Report 2 on 2024-10-18)Attached are the answers to the questions, numbered according to the corresponding questions:
1- We have addressed this point at the end of Section 2 with the following sentence “All energies are expressed in units of $J$, which is typically of the order of $0.2$ eV. All parameters are chosen to fall within a realistic experimental range [30–32, 41–44]“ and at the beginning of section 5 with the sentence “Note that the parameters of the Hamiltonian are given in units of J which is typically of the order of 0.2 eV. All are chosen such that they are in a realistic experimental range to model the prototypical PCMB and C60 acceptor systems [30–32, 41–44]”
2- This remark is connected to the previous one. We have addressed this point in Section 5 by adding the following paragraph: “Note that the parameters of the Hamiltonian are given in units of $J$ which is typically of the order of $0.2$ eV. All are chosen such that they are in a realistic experimental range to model the prototypical PCMB and C60 acceptor systems \cite{zheng2019charge,d2016electrostatic,faber2011electron,castet2014charge,antropov1993phonons,d2014electronic,richler2019influence}. These molecular solids have electronic bands which are narrow (typically 4J which is less than one eV) and have molecular vibration modes of high frequency which can be of the order of 0.1/0.2 eV. ”
3- We appreciate the reviewer's suggestion regarding the need for experimental comparisons. In the revised manuscript, we emphasize that in the conclusion (last paragraph) “Although a detailed comparison with a given system is beyond the scope of this work, we believe that the present model offers a simplified but comprehensive approach to advanced analyses of experimental results [11]. It should be helpful for a better understanding of the exciton dissociation process and for finding ways to improve the organic solar cells. The present embedded charge transfer state model could still be improved by considering several orbitals and several modes per site and even finite temperature. We emphasize that the modeling of the dynamics of the recombination process is also an essential ingredient.”