Correction to: Charge Pair Separation Dynamics in Organic Bulk-Heterojunction Solar Cells (Advanced Theory and Simulations, (2018), 1, 7, (1800032), 10.1002/adts.201800032)

Publikation: Beitrag in FachzeitschriftKommentar/Debatte

Abstract

Adv. Theory Simul. 2018, 1, 1800032 DOI: 10.1002/adts.201800032 Summary The authors regret a mistake in their previously published paper and would like to communicate a correction. Throughout the manuscript, the values for the energetic disorder σ that had been investigated were stated to be 0 meV, 30 meV, 50 meV, and 70 meV. Due to a mistake in the implementation, these values need to be rescaled by a factor of (Formula presented.) and therefore correspond to 0 meV, 42.4 meV, 70.7 meV, and 99.0 meV, respectively. These values should be replaced throughout the text and figures. For readability, we will refer to the new disorder values as 0 meV, 40 meV, 70 meV, and 100 meV in the following. The change in the values for σ affects the definition of the disorder radii (Formula presented.), i.e., the radii after which the influence of energetic disorder dominates over that of Coulomb interaction, which in turn affects the absolute and relative disorder times extracted from the kinetic Monte Carlo (kMC) simulations. We have re-evaluated all results with respect to the new values of σ. The results show a slight decrease in disorder times (Formula presented.), both in absolute and relative terms, for all investigated parameter combinations with finite σ. There is no change in separation and transport times as well as in the pair lifetimes. Since the changes in (Formula presented.) are only minor, the most relevant changes in the correction represents the re-labeling of the values for σ in the text and figures. The main conclusion of the paper, namely a slow charge pair separation at large disorder and low permittivity, does not change. The re-interpretation of the absolute times with the new values for σ leads to a more realistic quantification of the time-scales involved in the dynamics of electron-hole pair separation. Detailed Correction Table shows the corrected values for (Formula presented.) according to the new values of σ and replaces Table 2 of the original manuscript. Since σ was underestimated, the (Formula presented.) decrease for the corrected values of σ. Overview of disorder radii (Formula presented.) ((Formula presented.)) for different combinations of energetic disorder and permittivity. For comparison, the Coulomb separation radii (Formula presented.) ((Formula presented.)) at room temperature are listed for different values of permittivity (Table presented.) Figure illustrates the evaluation steps at (Formula presented.) instead of (Formula presented.) and replaces Figure of the original manuscript. The trajectory in Figure a shows a single charge pair at 100 meV including the corresponding disorder radius of 4.1 nm instead of previously 5.9 nm. The distribution of disorder times (Formula presented.) in Figure b, the cumulative distribution of the disorder times in Figure c and the 75% (disorder-) threshold times in Figure d, are slightly shifted towards smaller times because a smaller disorder radius is reached faster. (Figure presented.) Illustration of the evaluation steps of charge pair separation dynamics for (Formula presented.) and (Formula presented.). a) shows a typical evolution of (Formula presented.) for a charge pair. The threshold radii (Formula presented.) (red, horizontal), (Formula presented.) (gray, horizontal) and the corresponding times (Formula presented.) (purple, vertical), (Formula presented.) (green, vertical) as well as the pair lifetime (orange, vertical) are indicated. b) distributions of (Formula presented.), (Formula presented.), and (Formula presented.) of all pairs in this dataset. c) cumulative distributions of (b) with 75% threshold. d) threshold values from (c) in comparison for different permittivities, including the interim (between disorder and separation) and transport (between separation and lifetime) times. (Figure presented.) Absolute values for characteristic times: a) disorder-, b) interim-, c) separation-, d) transport-, and e) lifetime in dependence on disorder and permittivity. At (Formula presented.), the disorder- and interim time are not defined. The timeline of a charge pair with the characteristic times is schematically illustrated on the bottom right. Following this evaluation with the updated (Formula presented.), Figure shows the re-evaluated absolute values of the characteristic times with the re-scaled axis description for σ ranging from 0 meV to 100 meV; it replaces Figure of the original manuscript. For finite values of disorder, the results show a slight decrease of (Formula presented.) compared to the previous results. At a small disorder of 40 meV, (Formula presented.) is also of the order of ns and varies between (Formula presented.) at (Formula presented.) and (Formula presented.) at (Formula presented.) (instead of previously (Formula presented.) at (Formula presented.) and (Formula presented.) at (Formula presented.) for (Formula presented.)). At a large disorder of 100 meV, (Formula presented.) increases to μs and varies between (Formula presented.) at (Formula presented.) and (Formula presented.) at (Formula presented.) (instead of previously (Formula presented.) at (Formula presented.) and (Formula presented.) at (Formula presented.) for (Formula presented.)). For the separation-, transport- and lifetimes no changes are obtained compared to the previous evaluation. The decrease in disorder times shifts in favor of increased interim times. The effect of the wrong (Formula presented.) on the absolute times is therefore only small and affects only the disorder and interim times. (Figure presented.) Relative values for characteristic times normalized to the respective lifetime for the investigated values of disorder and permittivity. For no disorder (top), the disorder time is not defined, therefore only separation (blue) and transport times (orange) are shown. For finite disorders, the first bar represents the disorder time (red), the middle bar is the interim time (purple) and the last bar the transport time (orange). The ratio of each time with respect to the lifetime is indicated in the bars in percent. The relative times for σ ranging from 0 meV to 100 meV are shown in Figure for the re-evaluation of the data; the figure replaces Figure of the original manuscript. Also here, for finite values of disorder, the relative disorder time decreases and shifts in favor of the relative interim time. The sum of disorder and interim time (the relative separation time) remains unchanged, and with it the relative transport time. At a small disorder of 40 meV, the relative disorder time decreases by up to 16% compared to the previous results, while the relative interim time increases by the same ratio. At a large disorder of 100 meV, the difference to the previous results is as little as 3%, where the relative disorder time is now 68.1% (instead of 70.8%) at (Formula presented.) and 17.0% (instead of 19.8%) at (Formula presented.). (Figure presented.) Electron (solid lines) and hole (dashed lines) mobilities vs. energetic disorder for different permittivities. The inset shows the inverse transport time of the charge pair statistics for the same parameters. Neither the charge mobility nor the inverse transport time are affected by the updated (Formula presented.) and their correlation remains. The mobility values discussed for large disorder, (Formula presented.) and (Formula presented.), keep the same values but represent the mobilities at a disorder of 100 meV instead of 70 meV. Figure replaces Figure 5 of the original manuscript. In the figure, only the label for the disorder axis (also in the inset) is re-scaled according to the corrected values for σ. The results about geminate recombination presented are for the large disorder case, i.e. 100 meV instead of 70 meV, but remain unchanged otherwise. The recombination times should be compared with the extracted disorder times, which are (Formula presented.) - (Formula presented.) instead of previously (Formula presented.) - (Formula presented.). Figure 6 of the original manuscript shows the ratio between the number of geminate recombination events and the total number of pairs that can recombine (a) and the 75% time after which geminate recombination occurs (b) for (Formula presented.) instead of 70 meV. There are no qualitative changes in the conclusions of the paper. Reference In reference no. 42, volume and page number are missing. The correct reference is W. Kaiser, T. Albes, A. Gagliardi, Phys. Chem. Chem. Phys. 2018, 20, 8897–8908. Acknowledgements The authors thank Waldemar Kaiser for spotting the mistake and apologize for any inconvenience to the readers. Conflict of Interest The authors declare no conflict of interest.

OriginalspracheEnglisch
Aufsatznummer1900100
FachzeitschriftAdvanced Theory and Simulations
Jahrgang2
Ausgabenummer8
DOIs
PublikationsstatusVeröffentlicht - 1 Aug. 2019

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