A universal Urbach rule for disordered organic semiconductors

In crystalline semiconductors, absorption onset sharpness is characterized by temperature-dependent Urbach energies. These energies quantify the static, structural disorder causing localized exponential-tail states, and dynamic disorder from electron-phonon scattering. Applicability of this exponential-tail model to disordered solids has been long debated. Nonetheless, exponential fittings are routinely applied to sub-gap absorption analysis of organic semiconductors. Herein, we elucidate the sub-gap spectral line-shapes of organic semiconductors and their blends by temperature-dependent quantum efficiency measurements. We find that sub-gap absorption due to singlet excitons is universally dominated by thermal broadening at low photon energies and the associated Urbach energy equals the thermal energy, regardless of static disorder. This is consistent with absorptions obtained from a convolution of Gaussian density of excitonic states weighted by Boltzmann-like thermally activated optical transitions. A simple model is presented that explains absorption line-shapes of disordered systems, and we also provide a strategy to determine the excitonic disorder energy. Our findings elaborate the meaning of the Urbach energy in molecular solids and relate the photo-physics to static disorder, crucial for optimizing organic solar cells for which we present a revisited radiative open-circuit voltage limit.

Subgap absorption in polymer solar cell D-A blend system has become a highly interesting issue because it contains the information of CT state as well as disorders presented in the materials. Through device measurements on three types of systems ranging from conventional fullerene acceptor to the novel non-fullerene acceptor , the authors applied a number of models to simulate the absorption tails and concluded that the near onset subgap absorption is due to the static disorder of Gaussian type, and the lower energy part is due to the thermal broadening. This finding can clarify the previous view on Urbach energy, a concept borrowed from inorganic semiconductor. I find the corrections are satisfactory. I recommend the publication in the present form.
Reviewer #2 (Remarks to the Author): I'm happy with the responses to my questions and concerns, and would like to compliment the authors with the adequate changes and additions to the manuscript. The work can in my view be published as is. A very minor point: somehow the resolution of Fig. S10 is rather low.
Reviewer #3 (Remarks to the Author): The paper investigates the causes to the lineshape of the absorption at and below the absorption edge in disordered organic semiconductors. The authors show that this is composed of a Gaussian part, attributed to static disorder, and an exponential part, assigned to an Urbach tail with Urbach energy of kT. This is an important and general finding that should be published in Nature Communications. There is only one aspect where the study has some weakness which was already raised by a previous reviewer and which the authors have only partially adressed. The authors use the EQE of solar cells as a proxy for the absorption spectra due to the high sensitivity of EQE measurements. The EQE is the product of absorption times exciton dissociation times charge extraction. Their approach assumes that exciton dissociation and charge extraction are independent of the incident photon energy. I fully agree with the authors that this is valid for efficient solar cells made from blends, but it becomes more debatable when neat donor and acceptor films are investigated, where dissociation is often extrinsic at traps, defects or interfaces to the electrodes. The authors have now stated their underlying assumptions, and that is a valid approach (though repeating this caveat when it comes to the neat film would not harm), and the paper can, in principle, go ahead as it is. Nevertheless, I want to emphasize that the convincing power of the paper would gain substantially, if the authors were to also analyse at least one or two actual absorption spectra, e.g. taken by photothermal deflection spectroscopy (PDS). This could be simply literature data, and an inclusion of such data in the SI would be fully sufficient to swipe away any possible concerns about the approach. I have not done an extensive literature research, yet with a quick superficial check found the PDS spectrum of neat PC60BM ( Fig. 2b in JACS, 2015, 137, 5256) .Is this consistent with the data presented on neat PC70BM in Fig. 2b of the submitted paper? It is up to the authors to which extent they want to follow up these comments and ideas. The submitted manuscript is, in any case, an important and stimulating contribution with a valid approach (as the assumptions are made clear), and I recommend publication in Nature Communications.

Response Letter
Changes made to the revised manuscript and Supplementary Information have been indicated in Red.
Reviewer #1 (Remarks to the Author): Subgap absorption in polymer solar cell D-A blend system has become a highly interesting issue because it contains the information of CT state as well as disorders presented in the materials. Through device measurements on three types of systems ranging from conventional fullerene acceptor to the novel non-fullerene acceptor , the authors applied a number of models to simulate the absorption tails and concluded that the near onset subgap absorption is due to the static disorder of Gaussian type, and the lower energy part is due to the thermal broadening. This finding can clarify the previous view on Urbach energy, a concept borrowed from inorganic semiconductor. I find the corrections are satisfactory. I recommend the publication in the present form.
Answer: We would like to thank the reviewer for their positive feedback on our work. The paper investigates the causes to the lineshape of the absorption at and below the absorption edge in disordered organic semiconductors. The authors show that this is composed of a Gaussian part, attributed to static disorder, and an exponential part, assigned to an Urbach tail with Urbach energy of kT. This is an important and general finding that should be published in Nature Communications. There is only one aspect where the study has some weakness which was already raised by a previous reviewer and which the authors have only partially adressed. The authors use the EQE of solar cells as a proxy for the absorption spectra due to the high sensitivity of EQE measurements. The EQE is the product of absorption times exciton dissociation times charge extraction. Their approach assumes that exciton dissociation and charge extraction are independent of the incident photon energy. I fully agree with the authors that this is valid for efficient solar cells made from blends, but it becomes more debatable when neat donor and acceptor films are investigated, where dissociation is often extrinsic at traps, defects or interfaces to the electrodes. The authors have now stated their underlying assumptions, and that is a valid approach (though repeating this caveat when it comes to the neat film would not harm), and the paper can, in principle, go ahead as it is. Nevertheless, I want to emphasize that the convincing power of the paper would gain substantially, if the authors were to also analyse at least one or two actual absorption spectra, e.g. taken by photothermal deflection spectroscopy (PDS). This could be simply literature data, and an inclusion of such data in the SI would be fully sufficient to swipe away any possible concerns about the approach. I have not done an extensive literature research, yet with a quick superficial check found the PDS spectrum of neat PC60BM (Fig. 2b in JACS , 2015, 137, 5256). Is this consistent with the data presented on neat PC70BM in Fig. 2b of the submitted paper? It is up to the authors to which extent they want to follow up these comments and ideas. The submitted manuscript is, in any case, an important and stimulating contribution with a valid approach (as the assumptions are made clear), and I recommend publication in Nature Communications.
Answer: We would like to thank the reviewer for their very valuable suggestion and positive feedback. In light of this comment, we have added Supplementary Fig. 3 showing that is reobtained from the PDS spectrum of neat PC60BM as taken from the Fig. 2b in the reference JACS, 2015, 137, 5256. Changes the main text: "We note that this is consistent with photothermal deflection spectroscopy results 33 of neat PC60BM (see We amended the method section, because the device fabrication of the neat Y6 device has been missing so far. "Y6 devices: Y6 was dissolved in chloroform solution (16 mg ml -1 ) and spin-coated on ZnO (3000 rpm) to form a 70 nm thick film." We have substituted the word absorbance with the word absorptance in the main text in order to use correct terminology.
"The spectral line-shape of and the absorptance in the sub-gap tail are generally related via a modified Beer-Lambert law, , where is the thickness of the active layer and is an energy-dependent correction factor accounting for optical interference. 27,28 "