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

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.


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 s 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 ffiffi ffi 2 p 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 e r in combination with a large energetic disorder.

Detailed correction
In Fig. 1, the charge carrier distribution (CCD) is shown for s ranging from 40 meV to 100 meV; it replaces between 10 4 s À1 and 10 9 s À1 . It can be seen from Fig. 3a that, while R tot is considerably smaller than at s = 100 meV, it shows the same trend of being strongly dependent on both e r and a ehr . In particular, also here the change in R tot between slight changes of e 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 E 5 Â 10 4 s À1 were identified at e r = 3.5 in order to obtain a sufficiently functioning device with R tot o 25%. At 70 meV, values up to a ehr E 10 7 s À1 (corresponding to 100 ns of pair recombination time) lead to R tot o 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 = 10 9 s À1 ), the device is still reasonably functioning with 37.47% of all charges recombining. From Fig. 3b it is evident that also at s = 70 meV geminate recombination clearly dominates over nongeminate recombination and cannot be neglected as a major loss mechanism.
This journal is © the Owner Societies 2019 Phys. Chem. Chem. Phys., 2019, 21, 11488--11490 | 11489 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 (e r = 3 and e 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. At last, in order to link s and e r on the device performance, Table 1 shows the effect of s and e r at a ehr = 5 Â 10 4 s À1 on the shortcircuit current j sc with the corrected values for s = 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 s and e r for a larger recombination rate of a ehr = 10 7 s À1 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.
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 E 10 7 s À1 at an energetic disorder of 70 meV and a permittivity of e r = 3.5.

References
1 I. A. Howard andF. Laquai, Macromol. Chem. Phys., 2010, 211, 2063. Fig. 3 Amount of total recombination R tot (a) and the corresponding relative part of geminate recombination R gem /R tot (b) at s = 70 meV depending on a ehr at different values of e 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.