Influence of static disorder of charge transfer state on voltage loss in organic photovoltaics
Disorder in the energies of charge-transfer (CT) states can be induced by the complex phase behaviour of bulk heterojunctions in organic semiconductors. Here, we propose a model to help to quantify and understand the impact of CT state energetic disorder on voltage losses in organic photovoltaics.
The application of organic electronic materials to photovoltaic energy conversion has stimulated intense interest due to the potential for light, flexible, coloured or semi-transparent solar cells that can be manufactured cheaply, and for the appealing prospect of controlling device properties via molecular design. However, photovoltaic devices based on organic materials often suffer much larger non-radiative voltage losses (0.2-0.5 V) compared to the state-of-the-art silicon-based devices (<0.2 V), therefore limiting the power conversion efficiency (PCE). A recent theoretical study by Benduhn and co-workers demonstrated that the vibronic coupling between the ground state (GS) and charge transfer (CT) state determines the non-radiative voltage loss of organic photovoltaic devices (OPVs), and that the non-radiative voltage loss decreases with increasing CT state energy, following the Energy Gap Law that relates the rate of non-radiative transitions to the free energy difference between GS and CT state (Nat. Energy 2, 17053 (2017)). This work was an important step towards understanding the fundamental limits of open-circuit voltage (VOC) in OPVs. Inspired by Benduhn’s work, we recently extended his model to account for additional properties of the CT state, including oscillator strength, reorganization energies, and the electronic coupling between local excited state and CT state (hybridization) (Phys. Rev. X 8, 31055 (2018) and J. Am. Chem. Soc. 141, 6362–6374 (2019)). However, the effect of CT state energy variation (static disorder) on voltage loss was not investigated in any of those models. Static disorder is a common and important feature of organic heterojunctions that results from the considerable morphological and structural disorder present in such soft, multi-component materials.
The impact of static disorder on the absorption and luminescence from CT state was previously addressed by Kahle et al (Mater. Horizons 5, 837–848 (2018)) using a modified Marcus–Levich–Jortner (MLJ) model with a gaussian type static disorder implemented in the same way as the low-frequency reorganization energy. Similar methods of implementing static disorder have been used by different groups (J. Phys. Chem. C 121, 22739–22752 (2017), Adv. Energy Mater. 9, 1–7 (2019), J. Phys. Chem. Lett. 11, 3563–3570 (2020), and Phys. Rev. Appl. 13, 024061 (2020)); however, the principle of detailed balance between photon absorption and emission- an important prerequisite and observation- has been overlooked in the above-mentioned models. There are also several recent studies (Panhans et al. Nat. Commun. 11, 1–10 (2020); Tvingstedt et al. Mater. Horiz., 2020,7, 1888; and Göhler et al. Phys. Rev. Applied 15, 064009, 2021) that report that static disorder plays a less important role in dilute blends although dilute blends are seldom used in high efficiency devices. Those studies justify using a single-state mode to analyse experimental data on devices (Phys. Rev. B 81, 125204, 2010), which has been widely used to determine the energy of CT state. However, in more typical OPV blends, the energy and energetic distribution of CT are very sensitive to the phase behaviour, structural order, and interfacial orientation (Adv. Energy Mater. 8, 1702816 (2018)). Those observations highlight the importance and urgent need to understand the role of static disorder in CT state decay, CT state absorption and in voltage loss.
In our recent paper published in Nature Communications (https://www.nature.com/articles/s41467-021-23975-3) we introduce a modelling framework, following prior models of voltage loss (Phys. Rev. X 8, 31055 (2018) and J. Am. Chem. Soc. 141, 6362–6374 (2019)) to implement a general distribution of electronic CT state energies (DoS-CT) as the static disorder of CT states. The model satisfies the principle of detailed balance regardless of the shape of DoS-CT. We show that with significant amount of static disorder an analysis based on a single-state model can lead to misinterpretation of the energy of CT state and the associated reorganization energies, and eventually overestimate the values of voltage loss. We also demonstrate that static disorder can be seriously detrimental to the voltage and efficiency.
We test our model via a systematic study of emission, absorption and voltage losses as a function of blend composition in two P3HT: nonfullerene acceptor blends, i.e. P3HT:O-IDTBR and P3HT:O-IDFBR, where we have seen contrasting phase behaviour upon varying composition in a recent study (Chem. Mater. 2020, 32, 8294−8305). Using injection-current dependent electroluminescence (EL) experiments, we observe distinct CT features in both blends, indicating significant amount of static disorder, which is further confirmed using temperature-dependent external quantum efficiency (EQE) and electroluminescence (EL) experiments. Interestingly, only in the blend of O-IDFBR, we observe the change of DoS-CT while changing the composition, and DoS-CT maintains in the blend of O-IDTBR. Moreover, using the proposed model with two CT features, we are able to reproduce the trends in CT-state emission, CT-state absorption and voltage loss of the devices with different compositions.
Our study demonstrates the importance of accounting for CT-state energy disorder in analysing the voltage losses in OPV devices. Ultimately, approaching the limits to performance will require such static disorder be minimised. In polymer:molecule blends, this will mean reducing the disorder that arises from the conformational phase space of polymers, from aggregation and from molecular anisotropy. At the same time, good electronic and excitonic transport must be maintained.