Correction: Influence of permittivity and energetic disorder on the spatial charge carrier distribution and recombination in organic bulk-heterojunctions

Abstract

Correction for ‘Influence of permittivity and energetic disorder on the spatial charge carrier distribution and recombination in organic bulk-heterojunctions’ by Tim Albes et al., Phys. Chem. Chem. Phys., 2017, 19, 20974–20983.

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1 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 have 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 and therefore correspond to 0 meV, 42.4 meV, 70.7 meV, and 99.0 meV, respectively. For readability, we will refer to them as 0 meV, 40 meV, 70 meV, and 100 meV in the following.

The results in the original manuscript are correct as presented but the values for the disorder need to be re-labeled throughout the text and in the figures. This correction does not change the overall implications and conclusions, namely the interface charge accumulation and the increased recombination at low permittivity ε_r in combination with a large energetic disorder.

2 Detailed correction

In Fig. 1, the charge carrier distribution (CCD) is shown for σ ranging from 40 meV to 100 meV; it replaces Fig. 2 of the original manuscript. The figure is identical except for the labelling of σ. The statement of the figure remains, i.e., large values of σ can make the CCD fluctuate by several orders of magnitude locally.

Fig. 1 Electron and hole charge density distributions along a slice through the morphology. All density maps are shown for two cases of low and high permittivity (ε_r = 3 and ε_r = 5), respectively, and the energetic disorder varies from 40 meV (a) via 70 meV (b) to 100 meV (c). In (d), the corresponding charge density scale and its relationship to the energy levels within the Gaussian density of states is shown.

The quantitative evaluation of interface densities vs. bulk densities is shown in Fig. 2 with the corrected axis description for σ; it replaces Fig. 3 of the original manuscript.

Fig. 2 Ratio of interface to bulk charge densities of holes (a) and electrons (b) for different parameter sets of energetic disorder and permittivity (σ, ε_r). High values indicate an inhomogeneous charge distribution with accumulation of charges at the heterojunction interface while a value of 1 represents homogeneous charge distributions of electrons in the acceptor and holes in the donor, respectively. The artificial case of ε_r = ∞ (no Coulomb interaction) is added to be able to interpret the effect of disorder alone.

Fig. 4 of the original manuscript remains unchanged, but shows the absolute CCDs for σ = 100 meV instead of 70 meV.

Fig. 5 of the original manuscript shows the total recombination R_tot and corresponding relative amount of geminate recombination for σ = 100 meV instead of σ = 70 meV. We have added the results for what should have been Fig. 5 in the original manuscript, i.e. R_tot and at 70 meV, in Fig. 3 for an extended parameter set of the recombination rate a_ehr ranging between 10⁴ s⁻¹ and 10⁹ s⁻¹. It can be seen from Fig. 3a that, while R_tot is considerably smaller than at σ = 100 meV, it shows the same trend of being strongly dependent on both ε_r and a_ehr. In particular, also here the change in R_tot between slight changes of ε_r outweighs orders of magnitude of a_ehr and highlights the strong influence of the permittivity on the total recombination. At a disorder of 100 meV, values less than a_ehr ≈ 5 × 10⁴ s⁻¹ were identified at ε_r = 3.5 in order to obtain a sufficiently functioning device with R_tot < 25%. At 70 meV, values up to a_ehr ≈ 10⁷ s⁻¹ (corresponding to 100 ns of pair recombination time) lead to R_tot < 25%, which represent a more realistic scenario according to what is found by transient absorption spectroscopy (TAS) measurements.¹ Even for recombination times of 1 ns (a_ehr = 10⁹ s⁻¹), the device is still reasonably functioning with 37.47% of all charges recombining. From Fig. 3b it is evident that also at σ = 70 meV geminate recombination clearly dominates over nongeminate recombination and cannot be neglected as a major loss mechanism.

Fig. 3 Amount of total recombination R_tot (a) and the corresponding relative part of geminate recombination R_gem/R_tot (b) at σ = 70 meV depending on a_ehr at different values of ε_r. A value of R_tot = 100% means that all charges generated by exciton splitting undergo recombination. A value of R_gem/R_tot = 100% means that from all recombination events, every single one is geminate and none are nongeminate. All recombination that is not geminate is nongeminate recombination.

At last, in order to link σ and ε_r on the device performance, Table 1 shows the effect of σ and ε_r at a_ehr = 5 × 10⁴ s⁻¹ on the short-circuit current j_sc with the corrected values for σ = 0 meV, 40 meV, 70 meV, 100 meV; it replaces Table 1 of the original manuscript. We have furthermore added the dependence of j_sc on σ and ε_r for a larger recombination rate of a_ehr = 10⁷ s⁻¹ in Table 2, in order to show the effect at smaller recombination times. The trend is equivalent (i.e. the anti-correlation of interface accumulation strength and j_sc) but more pronounced, as a larger a_ehr induces faster and therefore more recombination.

Table 1 Effect of permittivity and disorder on short-circuit current density j_sc in mA cm⁻² for a_ehr = 5 × 10⁴ s⁻¹

σ (meV)	ε r
	3	3.5	4	5	∞
100	4.62	5.92	6.77	7.62	8.21
70	7.24	7.59	7.33	7.65	8.11
40	7.31	7.44	7.52	7.71	8.24
0	7.53	7.58	7.65	7.75	8.36

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Table 2 Effect of permittivity and disorder on short-circuit current density j_sc in mA cm⁻² for a_ehr = 10⁷ s⁻¹

σ (meV)	ε r
	3	3.5	4	5	∞
100	0.95	2.08	3.24	5.18	8.08
70	5.08	5.72	6.15	6.85	8.10
40	7.45	7.51	7.54	7.69	8.13
0	7.47	7.51	7.66	7.86	8.35

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There are no qualitative changes in the conclusions of the paper. However, considering the corrected results, we can conclude more suitable recombination rates around a_ehr ≈ 10⁷ s⁻¹ at an energetic disorder of 70 meV and a permittivity of ε_r = 3.5.

Acknowledgements

The authors thank Waldemar Kaiser for spotting the mistake.

The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.

References

1. I. A. Howard and F. Laquai, Macromol. Chem. Phys., 2010, 211, 2063.

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