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Charge-Transfer States in Organic Solar Cells: Understanding the Impact of Polarization, Delocalization, and Disorder Zilong Zheng, Naga Rajesh Tummala, Yao-Tsung Fu, Veaceslav Coropceanu, and Jean-Luc Bredas ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 08 May 2017 Downloaded from http://pubs.acs.org on May 13, 2017

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ACS Applied Materials & Interfaces

Charge-Transfer States in Organic Solar Cells: Understanding the Impact of Polarization, Delocalization, and Disorder

Zilong Zheng,1 Naga Rajesh Tummala,1 Yao-Tsung Fu,1 Veaceslav Coropceanu,1,* and Jean-Luc Brédas1,2*

1School

of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States 2KAUST

Solar Center, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia

* Emails: [email protected], [email protected]

Keywords: Charge-transfer states, singlet-triplet energy splitting, electronic couplings, organic photovoltaics, range-separated hybrid functionals, pentacene-fullerene blends

ACS Paragon Plus Environment

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Abstract

We investigate the impact of electronic polarization, charge delocalization, and energetic disorder on the charge-transfer (CT) states formed at a planar C60/pentacene interface. The ability to examine large complexes containing up to seven pentacene molecules and three C60 molecules allows us to take explicitly into account the electronic polarization effects. These complexes are extracted from a bilayer architecture modeled by molecular dynamics simulations and evaluated by means of electronic-structure calculations based on long range-separated functionals (ωB97XD and BNL) with optimized range-separation parameters. The energies of the lowest charge-transfer states derived for the large complexes are in very good agreement with the experimentally reported values. The average singlet-triplet energy splittings of the lowest CT states are calculated not to exceed 10 meV. The rates of geminate recombination as well as of dissociation of the triplet excitons are also evaluated. In line with experiment, our results indicate that the pentacene triplet excitons generated through singlet fission can dissociate into separated charges on a picosecond time scale, despite the fact that their energy in C60/pentacene heterojunctions is slightly lower than the energies of the lowest CT triplet states.


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Introduction

The charge-transfer (CT) states appearing at the interface between the donor and acceptor components play a fundamental role in the operation of organic solar cells.1-4 It has been shown that the energies of the CT states correlate with the open-circuit voltage of organic photovoltaic (OPV) devices.5-7 As a result, the CT states are at the center of experimental2,

4, 6, 8-13

and

theoretical3, 14-32 studies in the OPV field. In particular, great attention is currently given to the understanding of how the extent of delocalization of the CT states affects the charge-separation and charge-recombination processes.2, 10, 16-17, 25, 31, 33-34 Thus, a better grasp of how to control the CT states can aid in the optimization of OPV materials and enhance device performance.

Although the electronic excitations on individual molecular moieties are well characterized, a comprehensive description of the CT states is still lacking. This difficulty in analyzing CT states arises from the dependence of these states on multiple factors such as the donor-acceptor interface geometry, the nature of pure and mixed donor/acceptor domains, and the crystallinity within these domains. At the electronic-structure level, all these factors can influence the electronic polarization and extent of electron delocalization and consequently have a strong influence on the energy and nature of the CT states. Using effective dielectric models can help account for the polarization energy, especially in the case of non-polar systems;24 however, studying the combined effects of electronic polarization and delocalization requires to investigate systems with large sizes.

Time-dependent density functional theory (TDDFT) calculations based on extended donoracceptor systems (beyond model systems containing just one donor site and one acceptor site) have


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been recently performed14, 16, 18, 25, 34 to investigate the effect of system size on the CT states. However, the interplay between electron delocalization and polarization effects on the nature of CT states remains to be addressed in detail. This issue is the focus of the present work, where we investigate the CT states in large C60/pentacene complexes containing up to seven pentacene molecules and three C60 molecules. In contrast to our previous work25 where calculations were performed on model systems, here, in order to account for realistic packing motifs, we use donoracceptor complexes extracted from C60/pentacene bilayer heterojunctions whose structures have been generated by means of molecular dynamics (MD) simulations. We study both the singlet and triplet lowest CT states and estimate the rates of their decay to the ground state. We also evaluate the dissociation rates of the triplet molecular excitons.

Methodology

The atomic coordinates of the various complexes investigated in this study are obtained from the MD simulations of the C60/pentacene interface described in our earlier work.35 The “edge-on” morphology of the C60/pentacene bilayer was generated via deposition of the C60 molecules on top of the crystalline pentacene (001) surface. For the electronic-structure calculations, we extracted 63 clusters consisting of one C60 and one pentacene molecule (these clusters are hereafter denoted as C60/P), 21 clusters consisting of one C60 and three pentacene molecules (C60/3P), 10 clusters of 2C60/6P molecules, and 6 clusters of 3C60/7P molecules (see the structures of these clusters in Figures S1-S3 in the Supporting Information (SI)). The largest systems, 3C60/7P, contain more than 400 atoms, which means that investigations of larger clusters at the level of theory described below becomes computationally prohibitive.


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As in our earlier work,24-26 the excited states were investigated by means of time-dependent density functional theory (TDDFT) based on range-separated (RS) functionals with optimally tuned RS parameters.36-38 In a recent study,24 we indicated that the estimated CT energies of small donoracceptor complexes compare better with experiment when the RS parameter (ω) is optimized in the presence of a dielectric medium, in order to mimic the impact of the solid-state environment. However, this approach in the case of large systems where delocalization effects are present needs additional validation. In fact, our results point out that in these instances such calculations can yield unphysically small CT energies. Therefore, here, the RS parameters were optimized by minimizing J(ω), based on calculations on isolated clusters:37

J (ω) = |HOMO + IP| 2 + | LUMO+ EA| 2 (1)

where HOMO and LUMO denote the energies of the highest occupied and lowest unoccupied molecular orbitals of the system and IP and EA, the ionization potential and electron affinity. The tuned values of ω are collected in Table S1 of the SI.

The energies of the lowest excited states were obtained at the full TDDFT level with the ωB97XD39 functional as well as by means of TDDFT calculations based on the Tamm-Dancoff approximation (TDA-TDDFT) with the Baer–Neuhauser–Livshits (BNL) functional.36 All TDDFT calculations were performed with the 6-31G(d) basis set. The rates of non-radiative charge recombination were derived using Marcus semi-classical electron-transfer theory:40-41


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𝑘=

2𝜋 ℏ

|𝑉𝑒𝑙 |2

1 √4𝜋𝜆𝑘𝑏𝑇

exp⁡(−

(𝜆+∆𝐺)2 4𝜋𝜆𝑘𝑏𝑇

)

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(2)

Here, 𝑉𝑒𝑙 denotes the electronic coupling between the initial and final diabatic states; ℏ, the Planck constant; ΔG, the Gibbs free energy (driving force) and is approximated here as the energy difference between the initial and final states; 𝜆, the reorganization energy; T, the temperature; and 𝑘𝑏 , the Boltzmann constant. The radiative decay rates from the lowest CT state were obtained from the Einstein coefficient:

𝐴=

(𝐸𝐶𝑇−𝐸𝑆0 )3

|𝜇𝐶𝑇→𝑆0 |2

3𝜖0 𝜋ℏ4 𝑐 3

(3)

where 𝜇𝐶𝑇→𝑆0 is the transition dipole moment between the 1CT1 and S0 states; 𝜖0 , the vacuum permittivity; and c, the speed of light.

In order to elucidate the relative impacts of charge delocalization, electronic polarization, and energetic disorder on the frontier orbitals and CT states, we followed a tight-binding approach. The tight-binding Hamiltonian is based on the site energies of the individual pentacene and C60 molecules and on transfer integrals (tij) corresponding to hole transfer among the pentacenes and electron transfer among the C60 molecules in selected C60/pentacene clusters.

The electronic couplings (Vel) related to charge recombination were computed by means of the fragment charge difference method,42 which is based on the generalized Mulliken-Hush approach.43 The transfer integrals (tij) related to hole or electron transfer were obtained using the


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fragment orbital approach.44 The site energies of individual pentacenes and fullerenes (HOMO and LUMO energies) in a given cluster were computed by means of a combined quantum mechanical (QM)/ electrostatic model, following which the molecular orbital energies of each molecule in the cluster are computed at the QM level while the other molecules are represented by point charges (here, we take the CM5 45 charges obtained from single-point gas-phase calculations).

The ωB97XD calculations were carried out with the Gaussian 09 package46 while the calculations with the BNL functional were performed with the Q-Chem program.47

Results and Discussion

Frontier molecular orbitals. The computed HOMO and LUMO energies of all clusters considered in this study are given in Tables S2-S6, while the average HOMO and LUMO energies in the clusters along with the respective values for the isolated C60 and pentacene molecules, obtained at the tuned-BNL/6-31G(d) level, are shown in Figure 1 (the calculations using the ωB97XD functional yield very similar results, see SI). The figure illustrates that the increase in the size of the donor-acceptor clusters leads to a significant destabilization [stabilization] of the HOMO [LUMO] level by about 0.7 [0.3 eV], and thus a decrease in the LUMO-HOMO gap by about 1.0 eV (see Table S6).


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-2 Energy/ eV

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 LUMO (C ) 60

-3 -4 -5 -6

 HOMO(PEN)

Monomer C60/P C60/3P 2C60/6P 3C60/7P

Figure 1. Average energies (standard deviations are in the range of ~0.03-0.12 eV) of the frontier molecular orbitals of isolated pentacene and C60 molecules and pentacene/C60 clusters obtained at the tuned-BNL/6-31G(d) level.

We note that the energies of the frontier orbitals are the main ingredient defining the energy of the lowest CT state. In extended systems, both electronic polarization and electron delocalization affect the frontier orbital energies. In order to shed light on this matter, we show in Figure 2, as an example, the results obtained for the C60/3P #14 complex (which has the highest HOMO energy among all C60/3P complexes, see SI). The calculations indicate that the HOMO, HOMO-1, and HOMO-2 of the C60/3P complexes result from the interactions among the HOMOs of the individual pentacene molecules in the complex. When the site energies of all three pentacene molecules are identical, the total orbital energy splitting, ∆Espt= EHOMO–EHOMO-2, can be taken as a measure of the delocalization effect. A comparison of the results obtained for the C60/3P cluster and the corresponding 3P cluster shows that the interaction between the C60 and pentacene molecules results in an increase in energy by about 20 meV for all three pentacene HOMOs. This


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interaction, however, has no effect on the orbital energy splitting, which is about 520 meV in both C60/3P and 3P clusters.

The electronic couplings (transfer integrals) related to hole delocalization are shown in Figure 2b. The values are in the range of 50-100 meV and compare very well with the electronic couplings calculated previously for the pentacene single crystal.48 Calculations performed within the tightbinding model, based on the derived transfer integrals and assuming that all pentacene molecules have the same site energy, yield an energy splitting of 260 meV. This value is half the DFT ∆Espt estimate of 520 meV. This underlines that the hole delocalization effect alone cannot explain the characteristics of the cluster HOMOs and that the difference in site energies (due to site energy disorder) also contributes to the apparent splitting energy. This conclusion is also supported by the MO charge densities, which show that the HOMO, HOMO-1, and HOMO-2 are predominantly localized on just one but different pentacenes in the C60/3P and 3P clusters.

The difference in site energies is related first to the fact that the pentacene molecules in the MD simulations are somewhat geometrically different. Indeed, as seen from Figure 2a, the site energy difference due to the variations in geometry is about 70 meV, which is still not sufficient to reproduce the ∆Espt value. Importantly, another source of site energy disorder comes from electronic polarization.44, 49 Indeed, calculations based on the mixed QM/electrostatic model yield -5.34 eV, -5.29 eV, and -5.62 eV for the HOMOs of the P1, P2, and P3 monomers, respectively. Thus, the polarization-driven site-energy disorder is about 0.3 eV. Tight-binding calculations using these site energies yield -5.24 eV, -5.34 eV and -5.67 eV, for the HOMO, HOMO-1, and HOMO-


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2 energies of the complex; these orbital energies and their 430 meV splitting compare well with the DFT result for the entire system.

We now consider the factors contributing to the modification of the HOMO energy in the C60/3P system with respect to the HOMO of the isolated pentacene molecules. Taking the P2 molecule as a reference (as it has the highest HOMO level in the system), we find that the overall increase in energy is about 270 meV, see Figure 2. Since ca. 20 meV result from the interaction between C60 and the 3P cluster, 250 meV are due to the combined effect of electronic polarization (within the pentacene cluster) and electron delocalization. Our results show that, if all three pentacene molecules were identical, the maximum increase (destabilization) in energy could reach 380 meV. That the actual energy of 250 meV is smaller than this maximum value is due to the dual role played by electronic polarization. On the one hand, it contributes to the increase of the site energies while, on the other hand, it also contributes to the site energy disorder. As a result, the effect of delocalization is diminished and the HOMO, HOMO-1, and HOMO-2 in the C60/3P and 3P complexes show a tendency to localize on a single pentacene molecule.

Turning to the LUMO energies in the selected 3C60/7P systems, the calculations indicate that the decrease in energy is mostly due to electronic polarization, while the contribution from electron delocalization is very small. This is in the line with the results for the transfer integrals, which show that the electronic couplings are smaller for electrons than for holes. We note that, here, we only considered charge delocalization parallel to the donor-acceptor interface. Due to a more isotropic nature of the C60 domains (and resulting electronic couplings), delocalization


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perpendicular to the C60/P interface can be expected to be larger for electrons than for holes, as was suggested for other fullerene containing systems.50-51

Figure 2. Electronic structure of a representative C60/3P complex #14 and the corresponding 3P complex (see Figure S1): (a) HOMO energies of the individual pentacene (P1, P2 and P3) molecules; (b) transfer integrals; illustration of the HOMO, HOMO-1, and HOMO-2 for the (c) C60/3P and (d) 3P complexes. All calculations are performed at the 𝜔B97XD/6-31G(d) level with 𝜔=0.147 bohr-1.52

Charge transfer singlet states. We now turn to the discussion of the CT states. The energies of the lowest singlet CT states averaged over each set of clusters of the same size are given in Figure 3 and Table 1. The calculations using the BNL and ωB97XD functionals again yield very similar


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results, therefore only the BNL results are discussed hereafter (the results derived with the ωB97XD functional can be found in the SI). In a way similar to the trends for the frontier orbitals and the HOMO-LUMO gap, an increase in cluster size from C60/P to 3C60/7P leads to a decrease in the average energy of the lowest CT state, from ca. 2.2 eV to about 1.3 eV. We note that, as in the case of previous calculations,25-26 the lowest CT state in C60/P is located above the lowest pentacene-based “local” state; depending on the system geometry, CT1 in C60/P is found to correspond to an excited state located between S7 and S13. As the system size grows, the CT1 state is increasingly found to correspond to the first excited state (S1) of the cluster: S1 has a CT character in ca. 80% of the C60/3P systems and 90% of the 2C60/6P systems; in the 3C60/7P clusters, S1 is always a CT state. The calculated average value of the vertical CT1 energy for the 3C60/7P complexes is 1.25 eV. Recent external quantum efficiency (EQE) measurements indicate that the lowest CT band in a planar heterojunction made of nano-crystalline pentacene and C60 is characterized by an adiabatic transition energy of about 1.0 eV and a reorganization energy (𝜆) of about 0.3 eV.11 Using the TDDFT estimate of the vertical CT1 energy and the experimental 𝜆 value, we derive a value of 0.95 eV for the average adiabatic CT1 energy in the 3C60/7P complexes, which is fully consistent with the experiment value.


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2.0 1.5

1

Energy of CT1 (eV)

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1.0 0.5 0.0 C60/P (63 conf.)

C60/3P 2C60/6P 3C60/7P (21 conf.)

(10 conf.)

(6 conf.)

Figure 3. Average energies and standard deviations of the lowest vertical CT state as a function of the P/C60 complex size, as obtained at the tuned-BNL/6-31G(d) level.

Table 1. Average charges (QCT/e) and energy (ECT/eV) of the two lowest singlet CT states, and their energy difference, calculated at the tuned-BNL/6-31G(d) level. See Tables S7-S14 for the individual CT state energies of all the configurations. C60/P C60/3P 2C60/6P 3C60/7P

QCT1 0.89 0.94 0.92 0.88

ECT1 2.18 1.54 1.45 1.25

QCT2 0.85 0.93 0.90 0.89

ECT2 2.30 1.65 1.53 1.34

ECT2 - ECT1 0.12 0.11 0.08 0.09

In general, in the larger clusters, there can appear several singlet CT states below the lowest strongly absorbing local (i.e., intra-molecular) excited state. The energetics and density of these states are important to understand exciton dissociation, geminate recombination, and the formation of free carriers. Higher-energy CT states along with CT1 also contribute to the lowenergy part of the absorption spectrum and EQE. As seen from Table 1, the energy difference between CT2 and CT1 is on the order of 0.1 eV, irrespective of system size. It is computationally


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very time consuming to evaluate all the excited states of interest in the 2C60/6P and 3C60/7P complexes. However, the calculations for the C 60/3P complexes indicate that even in such relatively small-size systems, there could be more than 20 pentacene-to-C60 or pentacene-topentacene intermolecular CT states below the bright pentacene local state at 2.2 eV.

The calculations also indicate that higher-energy CT states can originate from what can be considered as excited states of the charged donor (cation) or acceptor (anion). As an example, we show in Figure 4 the natural transition orbitals (NTOs) describing the lowest three CT states of the 2C60/6P complex #6 (see SI). The hole-NTO in each case represents a linear combination of pentacene HOMOs. However, the electron-NTO of the second CT state is very different from that of the first and third excited CT states and actually corresponds to an excited configuration of the fullerene anion. As a result, the relaxation from CT3 to CT2 represents a complex combination of hole transfer within the pentacene subsystem and internal conversion within the radical-anion states of C60; on the other hand, the transition from CT2 to CT1 represents a simple intra-molecular conversion process that should therefore be much faster than the CT3 →CT2 transition.


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1

CT3 

1.56 eV

1

CT2 

1.49 eV

1

CT1 

1.38 eV

Figure 4. Natural transition orbitals and energies of the lowest three singlet CT states for the 2C60/6P complex # 6.


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As we underlined above, the natures of the CT states depend on electron delocalization, electronic polarization, and disorder. All these factors are strongly dependent on the geometry (morphology) of the systems. Figure 5 illustrates the NTOs describing the CT1 states in the six investigated 3C60/7P complexes. Complex #4 has the lowest CT1 energy and also shows the largest delocalization of both hole and electron. However, CT1 in complex #1, despite its extensive delocalization, has a higher energy than CT1 in complex #6 where both hole and electron are largely localized on a single donor unit and acceptor unit, respectively. As in the case of the frontier orbitals, the electronic polarization is found to have the largest impact on the energy of the CT states in these systems.


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Figure 5. Natural transition orbitals and energies of the lowest singlet 1CT1 states for the six 3C60/7P clusters (#1-#6, see Figure S3 in the SI).


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Charge transfer triplet states. We also investigated the lowest-energy triplet CT states. We note that the lowest triplet CT state is located above the singlet CT states in 32% and 14% of the C60/P and C60/3P clusters, respectively; in the case of the 2C60/6P and 3C60/7P systems, all the lowest CT states are triplets. This evolution might be related to the fact that, as the energy of CT states decreases with the increase in system size, the interactions among diabatic local and CT triplet states become larger than in the case of singlet states. However, further investigations are clearly required to pinpoint more definitely the origin of the results.

The absolute triplet-singlet splitting energies (∆|𝐸 s-t |), averaged over each set of systems of the same size, are given in Table 2. The calculations indicate that the average singlet-triplet energy splitting does not exceed 10 meV. However, as result of disorder these energies show a significant standard deviation. As seen we note that experimental measurements locate the lowest triplet CT state ca. 5 to 50 meV below the singlet CT state in several donor-acceptor blends.53-55 While in general the average ∆|𝐸 s-t| energy decreases in going from C60/P to C60/3P and then to 2C60/6P, this energy increases somewhat in the case of 3C60/7P systems (we note, however, that in these 3C60/7P systems the calculations for the triplet states converged only in the case of two of the clusters).


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Table 2. Average charges (QCT/e-) and energy of the lowest triplet CT states as well as average CT singlet-triplet splitting energy (∆Es-t) and their standard deviations (σ), obtained at tunedBNL/6-31G(d) level. Q (3CT1) E(3CT1)/eV ∆|𝐸 s-t|/meV AVE. AVE. σ AVE. σ C60/P 0.95 2.18 0.08 8.2 21.5 C60/3P 0.85 1.54 0.09 3.6 14.5 2C60/6P* 0.92 1.39 1.3 3C60/7P* 0.88 1.13 4.0 *These averages are computed from fewer configurations than those used for singlet CT states (see SI). See Figures S8-S10 and Tables S15-S18 for the individual triplet CT state energies.

Radiative and non-radiative charge recombination rates. Singlet CT states can decay to the ground state via both radiative and non-radiative electron transfer. Charge recombination can also occur via local donor and acceptor triplet states. 15 The averaged electronic couplings related to these two recombination channels are given in Table 3. The electronic couplings are calculated to be very similar irrespective of the system size; this can be understood on the basis that, due to site-energy disorder, the CT states on average are localized on a just few donor and acceptor sites. The electronic couplings between local pentacene triplet states and triplet CT states show the same trend and are only slightly smaller than those involving singlet states.

Table 3. Average S0-1CT1 and T1-3CT1 electronic couplings and their standard deviations (σ) [in meV] derived at the tuned-BNL/6-31G(d) level. S0-1CT1 T1-3CT1 AVE. σ AVE. σ C60/Pen 12 14 10 13 C60/3Pen 13 13 8 9 2C60/6Pen 11 11 10 3C60/7Pen 13 8 7 -


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The rates computed for the non-radiative 1CT1S0 and 3CT1T1 recombination pathways along with the radiative constants for the 1CT1S0 transition are summarized in Table 4 (see also Figure S11). In these calculations, we used the 0.3 eV value for the reorganization energy (𝜆 ) estimated from the EQE measurements;11 we also took the experimental value of 0.86 eV for the energy of the lowest triplet exciton state in pentacene, 56-57 which puts this state by about 0.1 eV below the 1CT 1

state. In agreement with previous work,16 the radiative rate constant for the transition from

the lowest singlet CT state to the ground state is found to be about 105 s-1, irrespective of system size. Due to the lowering of the 1CT1 energy, the nonradiative recombination rate from this state to the ground state increases with an increase in cluster size and reaches an average value of 1.1x108 s-1 in 3C60/7P. This value is, however, about four orders of magnitude smaller than the average rate for the 3CT1T1 electron transfer pathway.

Table 4. Radiative (Ar) and non-radiative (knr) rates for the 1CT S and 3CT T decay processes. 1 0 1 1 1CT S 3CT T 1 0 1 1 radiative non-radiative non-radiative Ar rate (s -1) knr rate (s-1) knr rate (s-1) C60/P 7.0×105 5.4×10-14 1.5 × 108 5 3 C60/3P 2.2×10 2.8×10 3.4 × 1012 2C60/6P 1.1×105 1.8×105 4.6 × 1012 4 8 3C60/7P 9.6×10 1.1×10 0.2 × 1012

Triplet exciton dissociation rate. It was recently shown that the EQE could exceed 100% in pentacene/C60 solar cells.58 The reason is that the pentacene singlet exciton can split (via a singlet fission process) within 80 fs into a pair of triplet excitons,59 which can then dissociate at the


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pentacene/C60 interface.58 Transient absorption spectroscopy measurements on devices based on 150 nm-thick pentacene films found that the decay of triplet excitons and charge generation occur within 2-10 ns after photoexcitation.60 However, the time-resolved two-photon photoemission spectroscopy (TR-2PPE) data obtained for devices based on very thin pentacene films, where excitons are formed directly at the pentacene/C60 interface (and thus where the exciton dissociation time is not limited by any diffusion process), indicate that the triplet exciton dissociation rate is about 2×1011 s-1.61 In order to assess whether the energy levels and the electronic couplings obtained with our methodology are consistent with these experimental findings, we computed the rate of triplet exciton dissociation (see Table 5). The calculations show that the dissociation rate of triplet excitons in 3C60/7P clusters is about 1.3×1011 s-1, which is in good agreement with the TR2PPE estimate. Our results, taken together with the fact that triplet excitons in pentacene are long lived (5 ns in polycrystalline films and about two orders of magnitude longer in the single crystal) 60, 62

and assuming that the transition from the triplet CT states to free charges is fast enough, explain

why triplet excitons can split very efficiently in pentacene/C60 heterojunctions even though the molecular triplet states are slightly lower in energy than the CT triplet states. Based on the same arguments, we can also conclude that the non-radiative decay of CT triplet states is controlled by the lifetime of the local triplet states; as a result, the decay kinetics of triplet and singlet CT states to the ground state are comparable.

Table 5. Average triplet exciton, T1  3CT1, dissociation rates (s-1). C60/P 7.7×10-6 C60/3P 3.7×107 2C60/6P 8.0×109 3C60/7P 1.3×1011


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Conclusions

We have investigated the nature of the singlet and triplet CT states at realistic planar interfaces between pentacene and C60, as derived from molecular dynamics simulations. In particular, we were interested in examining the impact of charge delocalization, electronic polarization, and energetic disorder on the frontier orbitals and CT states. Our calculations indicate that, when increasing the size of C60/pentacene clusters from C60/P to 3C60/7P, the LUMO-HOMO gap decreases by 1.2 eV, which leads to a decrease of the lowest CT state energy by 1 eV. This decrease in energy is due to both electron delocalization and electronic polarization effects. The electronic polarization is seen to play a dual role as it also contributes to the energetic disorder that acts to limit the impact of charge delocalization on the frontier orbitals and CT states.

Given the more complex energetic landscape displayed by these more realistic interfaces (with respect to model systems with just a single donor and a single acceptor), other salient results of our work are: •

The adiabatic energy of the lowest charge transfer state in 3C 60/7P clusters is about 0.95 eV, which is in close agreement with the results of recent EQE measurements, with the next CT state located about 0.1 eV above CT1.

•

The average singlet-triplet splitting energy of the lowest CT states does not exceed 10 meV. In all larger 2C60/6P and 3C60/7P systems, the lowest CT state is a triplet.

•

In the large pentacene/C60 clusters, the transition rates from the triplet CT state to the local triplet state are up to four orders of magnitude faster than the transition rate from


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the singlet CT states to the ground state. However, in agreement with experimental data, the reverse up-conversion from the local triplet states to the CT triplet states is also fast, in the picosecond regime, which is several orders of magnitude faster than the decay rate of the local excitons to the ground state. This explains why pentacene triplet excitons generated through singlet fission can efficiently split at pentacene/C60 heterojunctions. •

The overall decay kinetics of triplet CT states in pentacene/C60 heterojunctions is controlled by the lifetime of the local triplet excitons and, in these systems, is comparable with those of the singlet CT states.

Finally, we note that further investigations are needed, in particular regarding the estimation of intersystem crossing rates among CT states, in order to get a better understanding of the spindependent charge-recombination processes in pentacene/C60 and other donor/acceptor heterojunctions.

Supporting Information The configurations, natural transition orbitals, HOMO/LUMO energies, CT state energies and electronic couplings are given for all the investigated complexes. This material is available free of charge via the Internet at http://pubs.acs.org.


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Acknowledgments We acknowledge the financial support of this work at the Georgia Institute of Technology by the Department of the Navy, Office of Naval Research, under the MURI “Center for Advanced Organic Photovoltaics” (Awards Nos. N00014-14-1-0580 and N00014-16-1-2520) and by King Abdullah University of Science and Technology (V.C.). A KAUST competitive research funding and the Office of Naval Research – Global (Award No. N62909-15-1-2003) supported the work at King Abdullah University of Science and Technology.


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Charge-Transfer States in Organic Solar Cells ... - ACS Publications

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