Non-Radiative Recombination of Triplet Charge-Transfer State as the Key of Limiting Eciency Mediates the Positive Relevance of JSC and VOC

Non-fullerene organic solar cells (NF OSCs) with A-D-A acceptors have realized the positive relevance of short-circuit current density ( J SC ) and open-circuit voltage ( V OC ), because of the restricted energy loss. However, non-radiative energy loss remains unclear, resulting in the positive relevance could not maximize power conversion efficiency (PCE). Here, the impact of non-radiative recombination directly related to the singlet- and triplet-charge-transfer ( 1 CT and 3 CT) states on the positive relevance is explored. It establishes the essential connection between 3 CT-state non-radiation and positive relevance, points out the former mainly hinders PCE. The root reason is that decisive factors of decay rates in two pathways are completely different, but hard to adjust coordinately. Especially, another trade-off is still detected in NF OSCs, causing a bottleneck in PCE. To the end, we propose the defects of A-D-A molecular design by revealing 3 CT-state non-radiation mediates the positive relevance. formal


Introduction
As a promising technology, the power conversion efficiency (PCE) of state-of-the-art organic solar cells (OSCs) with donor: acceptor bulk heterojunction structure has surpassed 18%. [1][2][3] High-efficiency charge separation is achieved at almost negligible energy offset in OSCs based on non-fullerene acceptors (NFAs) with A-D-A structure. [4][5][6] The trade-off inherent in fullerene-OSCs between short-circuit current density (JSC) and open-circuit voltage (VOC) that affects PCE, is addressed. 7,8 Furthermore, the realization of positive relevance could simultaneously increase JSC and VOC among the NFA systems with A-D-A structure. 7,9 However, such phenomenon has not yield the highest PCE. Meanwhile, PCE is still limited by energy loss mediated by charge-transfer (CT) state. 10,11 It is crucial to understand the impact of energy loss on the positive relevance of JSC and VOC.
Compared with significant driving force produced by fullerene systems with weak absorption and weak emission properties, non-radiative energy loss (ΔE3) is the main cause of energy loss in NFA systems with high-efficient charge separation at low driving force. 12 The generation of ΔE3 is shown in Fig. 1(a), singlet-CT ( 1 CT) state is allowed to decay to the ground state (GS) ( 1 CT→GS) or convert to the triplet-CT ( 3 CT) state ( 1 CT→ 3 CT) in geminate recombination process. 13 The previous studies almost tend to focus on 1 CT-state non-radiation and improve this mechanism, which can effectively avoid non-radiative loss by promoting 1 CT state luminescence. 14 But ΔE3 is still insurmountable and further restricts VOC because of they ignore the potential effect of the 3 CT non-radiation, where the complicated processes of 3 CT state decay to GS ( 3 CT→GS) or convert into triplet local exciton ( 3 LE) states of either donor or acceptor ( 3 CT→ 3 LE). 15,16 The previous studies almost tend to focus on the 1 CT-state non-radiation, but ignore the influence of the 3 CT non-radiation. As a result, the potential effect of 3 CT-state recombination on ΔE3 remains unclear.
In this study, the fundamental mechanism of ΔE3 on positive correlation of JSC and VOC, are explored by a multi-scale method, along with the 1 CT→GS and 3 CT→ 3 LE pathways. The results demonstrate that the decay rates tracing the two pathways are respectively controlled by different factors. 3 CT→ 3 LE pathway mainly determines the ΔE3, and thus affects the positive relevance.
Importantly, we prove that the root reason is potential existence of trade-off, which makes it difficult to obtain the maximum PCE for positive correlation in NF OSCs. Our research establishes the internal connection between the ΔE3 mediated by 3 CT state and the positive relevance of JSC and VOC, and finally proposes the drawback in the molecular design of A-D-A structure from the perspective of energy loss.

Models
IT-4F, IOM-4F, and IM-4F with A-DD'D-A structure were select as research objects, which JSC and VOC of the three NFA-based blends presented a gradient change of positive relevance ( Fig. 1(b) and Supplementary Table 1). 8 The differences of structures were reflected on the D' unit of the A-DD'D-A structure, where the hydrogen atom of IT-4F on D' unit is replaced by methoxy group for IOM-4F and methyl group for IM-4F severally. 8 For purposes of comparison, fullerene derivative PC71BM was used as reference with a negative relevance of JSC and VOC in fullerene-based blend. 17 All systems were based on the same donor copolymer PM6, which was simplified as four units because the good convergence of the HOMO energy levels (see Supplementary Fig. 1).

Molecular dynamics simulation details
Molecular dynamics (MD) simulation were performed using the GROMACS 2018.4 software package. 18 Atom types and intra-and inter-molecular interaction parameters of PM6 and acceptors were built from the general AMBER force field (GAFF) 19 and charges were obtained by the restricted electrostatic potential (RESP) fitting method. 20 The simulations were carried out under three-dimensional periodic boundary conditions by means of the leap-frog integrator. A spherical cut-off of 1.0 nm for summation of Van de Waals interactions and the Particle-Mesh-Ewald (PME) method for long-range Coulomb interactions were employed throughout. 21 All equilibration processes were as follows: (i) Randomly placing 200 molecules in the periodic box size of 100 Å × 100 Å × 100 Å for PM6/acceptors to generate an initial geometry; (ii) 2 fs of NVT ensemble and 1 ns of NPT ensemble to make molecules close together. In the NPT ensemble, pressure and temperature were hold at constant 1 bar and 300 K adopted Parrinello-Rahman barostat 22 and the velocity rescaling thermostat, 23 respectively. (iii) 150 ns of equilibration were conducted at NPT ensemble to obtain better equilibrium conformations.

Quantum chemical calculation
The radiative recombination rate (kr) of 1 CT state is obtained from the Einstein coefficient relation: 24 (1) where µtr is the transition dipole moment; ε0 is the vacuum permittivity; h is the Planck constant; and c is the speed of light in vacuum. In classical Marcus electrons hopping model, 25 non-radiative recombination rate (knr) of 1 CT and 3 CT state is defined as: 26,27 Ef k µ ε πhc (2) where Vel denotes the electronic coupling between initial and final states; σ is the static energy disorder; and λ is the reorganization energy. Three-state model was applied to account for the electronic couplings and reorganization energy between the GS, CT and LE states, and the calculation details were given in the Supporting Information. Three-state model was applied to account for the electronic couplings, reorganization energy, and other parameters in the decay rate. For monomers, the PM6 was simplified into two repeated units and the side chains were substituted based on extracted molecular clusters, because of the HOMO and LUMO mainly delocalized on two repeat units. 28 Donor PM6 and all acceptors were optimized at the PBE0/6-31G(d) levels, because of PBE0 method could provide an accurate evaluation of geometric and electronic structures for thiophene derivatives. 29,30 The lowest 3 LE-state energies were evaluated at TD-PBE0/6-31G(d) levels. For PM6/acceptor blends, the simulation results include a variety of packing modes, among which the face-on orientation is favorable for exciton dissociation. Through the statistics of face-on configuration, the typical PM6/acceptor molecular clusters and blending morphologies were extracted from the final 5 ns ( Fig. 2 and Supplementary ( ) Fig. 2). The lowest 1 CT-and 3 CT-state energies and decay rates were calculated at the TD-CAM-B3LYP/6-31G(d) levels. 31 1 CT and 3 CT state were identified by the natural transition orbital (NTO) method described by Multiwfn 3.7, that is, the electron is located on the acceptor, the hole is located on the donor (Supplementary Fig. 3). 32 All the above-mentioned calculations were performed in the Gaussian 09 D.01 software package. 33

Results and discussion
Radiative and non-radiative recombination originated from 1 CT→GS pathway 1 CT→GS pathway suffers losses via radiative and non-radiative recombination. 34 Table 1 and 2). Therefore, we speculate modifying the D' unit according to the electron-donating/withdrawing character, may achieve the simultaneous increase of JSC and VOC.
In terms of the decay rate of 1 CT state, for a fullerene system with weak luminescence and weak absorption, it is difficult to reduce the energy loss even if k r 1 CT is higher than k nr 1 CT in PM6/PC71BM. However, NFA with strong absorption and strong emission could lead to large EQEEL values, since EQEEL affected kr and knr, is in an inverse relationship with ΔE3 (detailed equation (1) and (2)  in k nr 1 CT is still originated from the increase in exponential terms. However, the fact is just the opposite, the positive relevance of JSC and VOC still appears. Furthermore, the three orders of magnitude decline in the value of k r 1 CT is significantly less than the eleven orders of magnitude decline of k nr 1 CT , which likewise leads to decreased ΔE3. In two cases, although the trends of k r 1 CT and k nr 1 CT are different, both lead to a decrease in ΔE3, and further achieve simultaneous increase of JSC and VOC. Meanwhile, it laterally reflects that remaining the A-DD'D-A backbone structure of NFAs unchanged, and increasing 1 CT-state energy could indeed reduce the loss of 1 CT→GS pathway to achieve positive relevance. To comprehensively consider the impact of non-radiative recombination, another 3 CT→ 3 LE loss pathway is worth further exploration.

Non-radiative recombination originated from 3 CT→ 3 LE pathway
Compared with 1 CT→GS pathway, 3 CT→GS is almost ignored because of forbidden transition, 3 CT→ 3 LE route is more complicated. 35 Experimentally, it is intricate to detect 3 CT signal directly, and further to distinguish the 1 CT-and 3 CT-state energies, but is realizable for theoretical study. 36 As depicted in Fig. 4(a) and Supplementary  To complement the results of 3 CT→ 3 LE pathway based on energy alignments, the decay rates of 3 CT state are calculated, where the higher value of rate determine the trend of pathway possibly.

The relationship of 1 CT→GS and 3 CT→ 3 LE non-radiative rate affecting ΔE3
Based on the previous analysis, many differences are found between 1 CT→GS and 3 CT→ 3 LE non-radiative pathway, mainly in energy and the factors that affect the decay rate. Compared to 1 CT→GS pathway, a larger value of k nr 3 CT of 3 CT→ 3 LE pathway is obtained in the three PM6/NFAs blends ( Fig. 5 and Supplementary Fig. 4). For instance in PM6/IM-4F blend, the order of magnitude of k nr 3 CT (1.16×10 13 s -1 and 1.48×10 10 s -1 ) is larger than k nr 1 CT (1.15×10 -11 s -1 ).
Under each pathway, the decisive factor of knr and consequences are different. For 1 CT→GS pathway, k nr 1 CT is dominated by energy level. Because the ground state is definite, the raised 1 CT-state energy is generated by small changes in the structure of NFAs. Compared to the product term (Vel) with a smaller change, the exponential term (λ-ECT) has a greater impact. For 3 CT→ 3 LE pathway, the actual existence of the two pathways to 3 LE state of donor or acceptor complicates the impact of the interfacial triplet loss. We think k nr 3 CT is mainly affected by Vel. Relative to the smaller difference in exponential terms, Vel with very large fluctuation has the greatest impact, which seems to be uncontrollable. It further causes the losses of two pathways cannot be controlled together through simple structural modifications. Even if the influencing factors are different, the dominant role of 3 CT→ 3 LE pathway is confirmed in the non-radiative recombination process, whether from the energy offset or the decay rate. Furthermore, the 3 CT→ 3 LE pathway has a major impact on the positive relevance of JSC and VOC. However, previous studies were tended to reduce the ΔE3 in the perspective of 1 CT, while ignoring the role of 3 CT. Based on this knowledge, we found that the realization of positive relevance leads to a slight increase in PCE (from 13.80% to 14.17% in Supplementary Table 1).
It seems PCE is still restricted and low than 18%. And it is unclear whether the problem arises in the interfacial triplet loss has not been suppressed.

A trade-off in NF-OSCs?
Based on above A-DD'D-A structure of NFAs, the realization of positive relevance is not equivalent to the maximum efficiency. According to the conclusions of the former sections, it is speculated that the reason is the interfacial triplet loss. Where is the bottleneck? Is it a specific state or a problem from fundamental A-DD'D-A structure?
To analyze the reasons for limiting PCE, the relative increase amplitude ΔJSC and ΔVOC were investigated ( Fig. 6(a)). We found that there is still a trade-off in the non-fullerene systems, limiting the PCE! Specifically, although both ΔJSC and ΔVOC are greater than 0, the increased ΔJSC is unexpectedly accompanied by decreased ΔVOC. Is it a specific state or a problem from fundamental A-DD'D-A structure? To avoid data contingency, we further summarize five groups of NFA with the positive relevance of JSC and VOC reported ( Fig. 6(b) and Supplementary Table   6). This feature is observed by calculating the slope (k) of the functions, where k < 0 in all blends ( Fig. 6(c)). It most likely comes from the 3 CT-state loss, but the root cause may be in its own structure. trade-off consists in both fullerene and NFA systems and is difficult to be counteracted. It is reasonable to suspect that the A-DD'D-A structure of NFAs has two sides, not only brings the advantages of positive relevance, but also hides a certain degree of loss. Maybe a more rigid structure is required to achieve weak phosphorescent emission from 3 CT state to GS, to ameliorate some problems.

Conclusions
Considering the effect of non-radiative recombination loss mediated by CT state on positive relevance of JSC and VOC and thus the influence on PCE, a series of NFA systems with A-DD'D-A structure were studied. This work clarifies the leading role of the 3  Regardless of experiment or theory, our common appeal is a clear mechanism to improve PCE.
The key point is the molecular design strategy. Based on our research, it is speculated that the effects of A-DD'D-A structure have two-sidedness. On the one hand, the modification on D' unit could obtain high-efficiency NFA. On the other hand, it also caused the loss of 3 CT state and further restricted PCE. This defect may be compensated by modifying the alkyl chain on the D unit in the A-DA'D-A structure to reduce the driving force and ΔE3, which is currently under study.
Another effective method is suppressing the 3 CT-state loss by promoting charge separation rate is higher than intersystem crossing rate (kCS >> kISC). Although the phenomenon of positive relevance is not promoted, efforts of improving photovoltaic parameters are currently and always underway.   Experimental JSC and VOC and theoretical radiative and non-radiative recombination rates "k" _"r" ^"1CT" and "k" _"nr" ^"1CT" of 1CTGS pathway (from Ref. 8). Figure 4 (a) Schematic diagram of 3LE-states, interfacial 1CT-and 3CT-states energies (eV) for PM6/acceptors blends. (b) The change curve of "k" _"nr" ^"3CT" (s-1), corresponding to decay from 3CT states to 3LE state of donor and acceptors.

Figure 5
Schematic diagram of non-radiative recombination rates of 1CTGS and 3CT3LE pathway in PM6/IM4F blend. The top is the 3CT state decay to 3LE state of donor, and the bottom is decay to 3LE state of acceptor.