Nonequilibrium site distribution governscharge-transfer electroluminescence atdisordered organic heterointerfacesArmantas Melianasa,1,2, Nikolaos Felekidisb, Yuttapoom Puttisongc, Stefan C. J. Meskersd,e, Olle Inganäsa,Weimin M. Chenc, and Martijn Kemerinkb,1

aBiomolecular and Organic Electronics, Department of Physics, Chemistry and Biology, Linköping University, 58183 Linköping, Sweden; bComplex Materialsand Devices, Department of Physics, Chemistry and Biology, Linköping University, 58183 Linköping, Sweden; cFunctional Electronic Materials, Department of Physics,Chemistry and Biology, Linköping University, 58183 Linköping, Sweden; dMolecular Materials and Nanosystems, Eindhoven University of Technology, 5600 MBEindhoven, The Netherlands; and eInstitute for Complex Molecular Systems, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands

Edited by Peter J. Rossky, Rice University, Houston, TX, and approved October 10, 2019 (received for review May 21, 2019)

The interface between electron-donating (D) and electron-accepting(A) materials in organic photovoltaic (OPV) devices is commonlyprobed by charge-transfer (CT) electroluminescence (EL) measure-ments to estimate the CT energy, which critically relates to deviceopen-circuit voltage. It is generally assumed that during CT-ELinjected charges recombine at close-to-equilibrium energies in theirrespective density of states (DOS). Here, we explicitly quantify thatCT-EL instead originates from higher-energy DOS site distributionssignificantly above DOS equilibrium energies. To demonstrate this,we have developed a quantitative and experimentally calibratedmodel for CT-EL at organic D/A heterointerfaces, which simulta-neously accounts for the charge transport physics in an energeticallydisordered DOS and the Franck–Condon broadening. The 0–0 CT-ELtransition lineshape is numerically calculated using measured ener-getic disorder values as input to 3-dimensional kinetic Monte Carlosimulations. We account for vibrational CT-EL overtones by selec-tively measuring the dominant vibrational phonon-mode energygoverning CT luminescence at the D/A interface using fluorescenceline-narrowing spectroscopy. Our model numerically reproduces themeasured CT-EL spectra and their bias dependence and reveals thehigher-lying manifold of DOS sites responsible for CT-EL. Lowest-energy CT states are situated ∼180 to 570 meV below the 0–0 CT-ELtransition, enabling photogenerated carrier thermalization to theselow-lying DOS sites when the OPV device is operated as a solar cellrather than as a light-emitting diode. Nonequilibrium site distributionrationalizes the experimentally observed weak current-density depen-dence of CT-EL and poses fundamental questions on reciprocity rela-tions relating light emission to photovoltaic action and regardingminimal attainable photovoltaic energy conversion losses in OPVdevices.

organic electronics | electroluminescence at organic interfaces | energeticdisorder | Franck–Condon vibronic progression | 3D kinetic Monte Carlo model

Organic semiconductors show great promise for use in low-cost optoelectronic devices, such as photodetectors (1) and

solar cells (2–4). In these devices the photoactive layer typicallyconsists of a disordered bulk heterojunction (BHJ) mixture of anelectron donor (D) and an electron acceptor (A). The propertiesof the D/A interface determine the overall performance of theoptoelectronic device (5) since charge carrier generation and re-combination events occur at this interface. For example, the D/Ainterface governs the open-circuit voltage (VOC) and the powerconversion efficiency of organic photovoltaic (OPV) devices (6, 7)which, despite their appealing features, remain outperformed byother photovoltaic technologies (8). Thorough understanding ofthe processes taking place at the D/A interface is critical for thedevelopment of next generations of organic optoelectronics.The D/A interface can be conveniently probed by operating the

OPV device as a light-emitting diode (LED), where the chargecarriers are injected from the electrodes and, after traversing the

photoactive layer, recombine at the D/A interface, giving rise tocharge-transfer electroluminescence (CT-EL) (9) (Fig. 1A). CT-EL measurements are particularly well suited for the study of or-ganic heterointerfaces since equipment requirements are ratherminimal and the measurements can be carried out relativelyquickly. Nevertheless, despite the ubiquitous use of CT-EL in thefield, the currently prevailing description of CT-EL is not quanti-tative and is often inconsistent with experiments as well as organicsemiconductor physics, as detailed below.The CT-EL spectrum contains valuable information regarding

the energy of the recombining carriers in their respective disorder-broadened density of states (DOS), as schematically illustrated inFigs. 1B and 2. The corresponding CT-EL peak position is com-monly used as reference to estimate the CT energy (ECT) (7, 9),which correlates with important OPV device parameters, suchas device VOC (6, 7). The CT energy is also used as a referencepoint for evaluating VOC and photovoltaic energy conversion losses(10). CT-EL is commonly assumed to originate from charge

Significance

Semiconducting polymers and small molecules have promisingapplications in organic optoelectronic devices, such as solarcells, which typically consist of a disordered mixture of donorand acceptor materials. The performance of these devices isdetermined by the properties of the donor/acceptor interface.While the donor/acceptor interface is often studied by oper-ating the solar cell device as a light-emitting diode, resulting incharge-transfer electroluminescence, the currently prevailingdescription of electroluminescence is not quantitative and isoften inconsistent with experiments. We present an experi-mentally verified and quantitative model of charge-transferelectroluminescence at donor/acceptor interfaces that recon-ciles the inconsistencies present in the literature. Our modelsimultaneously and quantitatively accounts for energetic dis-order and molecular vibrations governing charge transport andluminescence in organic semiconductors.

Author contributions: A.M., S.C.J.M., O.I., W.M.C., and M.K. designed research; A.M., N.F.,Y.P., and M.K. performed research; A.M., S.C.J.M., W.M.C., and M.K. contributed newreagents/analytic tools; A.M., N.F., Y.P., and M.K. analyzed data; and A.M. and M.K. wrotethe paper.

The authors declare no competing interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.1To whom correspondence may be addressed. Email: armantas.melianas@stanford.edu ormartijn.kemerink@liu.se.

2Present address: Department of Materials Science and Engineering, Stanford University,Stanford, CA 94305.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1908776116/-/DCSupplemental.

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carriers recombining from the “relaxed and lowest energy” CTstate (11), where energetic disorder in the CT state is ei-ther ignored or assumed to lead to a manifold of CT states withan energy-independent optical transition matrix element (12)(see SI Appendix, Note S1 for an explanation why this as-sumption is not necessarily valid in disordered organic semi-conductors). For brevity we will refer to this scenario asrecombination from “relaxed,” “equilibrium,” or “lowest-energy”CT states in the DOS manifold as schematically shown in Fig. 2C, Left.However, adjacent equilibrium-energy DOS sites are extremely

rare—most low-energy sites are spatially separated as schemati-cally shown in Fig. 1B (dashed circles) and explicitly calculatedusing 3-dimensional (3D) kinetic Monte Carlo (kMC) forMDMO-PPV:PC61BM in Fig. 1C. In the 3D kMC simulations wehave assumed uncorrelated DOS site energies, as experimentallyconfirmed in earlier work for the systems investigated here (13),which results in most low-energy D/A sites being spatially sepa-rated by distances larger than 5 to 10 nm (see SI Appendix, Fig. S1for the radial distribution function). This renders CT-EL from“lowest-energy” CT states extremely unlikely. Having both theelectron and hole at their DOS equilibrium energy is also in-consistent with the notion that at least one of the carriers must bemobile to meet its counterpart—for CT-EL to take place at least

one of the carriers must be (thermally) excited toward thetransport level (14, 15) (Fig. 1B). However, quantitatively ac-counting for such kinetic effects while fitting CT-EL experi-ments has not yet been demonstrated.In case of equilibrium-site occupation (Fig. 2C), the CT-EL

spectrum would merely reflect a convolution of equilibriumelectron and hole populations in the DOS. In this case, the CT-EL spectra would also be expected to strongly depend on currentdensity due to the DOS state-filling prevalent in organic semi-conductors (14), but this is generally not the case—CT-ELspectra are typically only weakly (16), if at all, current-density-dependent (Fig. 1A). Instead, the absence of state-filling effectscould be rationalized by nonequilibrium DOS site occupation(Fig. 2A). Since considerably more DOS sites are accessible fortransport at higher energies, as shown in Fig. 1D, carrier-densityeffects would be significantly diminished (17), rationalizing thetypically weak current-density dependence of the CT-EL spectra(Fig. 1A). The hypothesis that CT-EL originates from higher-lying DOS sites (higher-energy CT states), as opposed to thewidespread notion that CT-EL occurs at the “relaxed and lowestenergy” CT states, was first proposed in ref. (16) on the basis ofsemiquantitative analysis of the weak current-density depen-dence of CT-EL spectra. However, this analysis relied criticallyon the assumption of an exponential DOS and does not generalize

Equilibrium energy sites where particles are

fully relaxed, immobile

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Fig. 1. CT-EL at disordered organic heterointerfaces. (A) CT-EL spectra are typically only weakly current-density J dependent, as shown for MDMO-PPV:PC61BM (1:4). (B) Schematic showing the higher-energy DOS sites sampled by the recombining carriers during the CT-EL experiment. CT-EL from adjacentlowest-energy DOS sites (dashed circles) is unlikely since such CT states are extremely rare. (C) Spatial DOS site distribution over a fraction (20 × 20 × 20 nm3) ofa simulated volume (90 × 90 × 146 nm3) obtained by 3D kMC for MDMO-PPV:PC61BM (1:4). Sites (light gray) with close-to-equilibrium energies (σ2/kT ± σbelow DOS center) are highlighted by red and blue open circles (donor HOMO and acceptor LUMO, respectively). (D) Higher-energy sites relevant for chargetransport and recombination (DOS site energies higher than σ2/kT + σ below DOS center; see the corresponding DOS schematic).

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to other DOS shapes, such as a Gaussian DOS, as describedbelow.In an exponential DOS, state-filling effects are prevalent at

all carrier densities (18), necessitating the use of higher-lyingDOS sites to rationalize the weak current-density dependence ofCT-EL spectra. In contrast, state-filling effects are absent in aGaussian DOS in the Boltzmann limit, that is, at similarly lowcarrier densities that are typically encountered in well-functioningOPV devices, as shown in SI Appendix, Fig. S2. Hence, the ex-perimentally observed weak bias dependence of CT-EL couldinstead be explained using equilibrium-site occupation in aGaussian DOS, without needing to account for higher-lying DOSsites as proposed in ref. 16 (see SI Appendix, Fig. S2 and Note S2for further explanation). As such, there currently is no consensusor general quantitative proof whether CT-EL at organic hetero-interfaces originates from lower- or higher-lying DOS sites in anyreasonable DOS shape relevant to organic semiconductors. Thisinconsistency remains unresolved and questions both the ubiqui-tous use of ECT as a reference energy as well as the interpretationof the CT-EL spectra.In addition to the ill-defined ECT, the spectral broadening of

CT-EL, which is expected to simultaneously depend on the ener-

getic disorder of the constituent materials (16) (inhomogeneousbroadening; Fig. 2 A and C, Left) and on the molecular vibrationsgoverning emission via the Franck–Condon principle (homoge-neous broadening; Fig. 2 A and C, Right) (19, 20), is not fullyunderstood. For example, CT-EL spectral broadening is material-specific and could be used to rapidly compare the D/A interface ofvarious blends, as shown in Fig. 3A. Although the energetic dis-order contribution to CT-EL spectral broadening has been sug-gested to be both negligible (20) and, recently, to be significant(21), explicit quantification of the relative contributions due toenergetic disorder versus Franck–Condon broadening remainselusive due to the absence of a quantitative CT-EL model—thereasons for the differences between CT-EL spectra as in Fig. 3Aare not entirely clear. As such, despite the widespread use ofCT-EL for OPV device characterization, the lack of a consistentframework and the resulting lack of quantitative understandinglimit its versatility.Here, we utilize current-density-dependent CT-EL experiments,

fluorescence line narrowing (FLN) spectroscopy (22, 23), andtemperature-dependent charge transport measurements in com-bination with 3D kMC simulations to demonstrate a quantita-tive model for CT-EL at disordered organic heterointerfaces.

A B

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Fig. 2. CT-EL is simultaneously governed by DOS disorder, kinetic effects, and the Franck–Condon principle. (A) Nonequilibrium case accounting for kinetic andenergetic disorder effects. (Left) Schematic shows the higher-lying DOS site distributions (shaded red) governing CT-EL at disordered D/A interfaces. The higher-lying DOS site distributions are situated above their respective DOS equilibrium energies σ2/kT (marked by the horizontal dashed line) and govern the 0–0 lineshapebroadening and 0–0 peak emission energy at ECT-EL 0–0. The central CT energy ECT centr marks jEHOMO D − ELUMOAj. (Right) The Franck–Condon principle schematic,describing the vibrational overtones m = {0, 1, . . ., M − 1} spaced by the phonon-mode energy Zwph governing CT luminescence. The blurring of the free energysurfaces illustrates the influence of the energetic disorder; the vibronic levels will broaden correspondingly (not shown for clarity). (B) Schematically shows howkinetic and energetic disorder effects (A, Left) and the Franck–Condon principle (A, Right) contribute to the final CT-EL spectrum. (C) Conventional CT-EL pictureassuming emission from equilibrium DOS sites and not accounting for kinetic effects. (Left) Schematic shows the quasi-equilibrium DOS site distributions (shadedblue) situated at σ2/kT below their respective DOS centers. In this case, which is not consistent with our experiments as described in themain text, the 0–0 lineshapeemission would occur at ECT Eq 0–0. (Right) The conventional Franck–Condon principle schematic ignoring the influence of energetic disorder. (D) Schematicallyshows the 0–0 CT-EL peak energetic position with respect to the joint electron and hole DOS (dashed black trace) in the case of thermal site distribution (blue, C)and nonthermal site distribution (red, A) governing CT-EL. Note that all of the above energy values must be corrected by the CT exciton binding energy ECT bind

following Eqs. 2 and 3.

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Our model quantitatively and simultaneously accounts for charge-transport physics in an energetically disordered DOS and Franck–Condon broadening. As input to the model we use experimentallydetermined D/A blend parameters, such as Gaussian DOS ener-getic disorder (spanning the range σ ∼60 to 100 meV), as mea-sured by temperature-dependent space-charge limited currents(SCLC) and phonon-mode energies (Zwph D/A ∼120 to 145 meV)governing CT luminescence, as selectively/directly measured byFLN spectroscopy at cryogenic temperatures (7 K). The experi-mentally calibrated model enables us to elucidate the commonlyobserved CT-EL features: emission peak position in energy, spec-tral broadening, and weak current-density dependence in terms ofmaterial DOS, which is important for the understanding of OPVdevice physics and for the definition of ECT. Complementary op-tical modeling confirms that the measured CT-EL bias de-pendence is a D/A materials property and not an optical cavityeffect. We explicitly quantify that CT-EL is governed by a non-equilibrium distribution of DOS sites which, depending on the en-ergetic disorder, are situated ∼50 to 320 meV above equilibriumdonor HOMO or acceptor LUMO DOS sites (highest occupiedmolecular orbital and lowest unoccupied molecular orbital, re-spectively), as schematically shown in Fig. 2A. For the resulting CT-EL emission, we find that the lowest-energy CT states are situated∼180 to 570 meV below the 0–0 CT-EL transition—CT-EL doesnot originate from the lowest energies in the total manifold ofavailable DOS sites.The quantitative and experimentally calibrated analysis of

CT-EL distinguishes our model from prior work (16, 21), whereenergetic disorder and vibronic progression effects were eitherdiscussed in isolation or only semiquantitatively accounted for,while kinetic effects governing charge transport to the recombi-nation sites as well as the likelihood of CT emission at thoseDOS sites during CT-EL remained unquantified. In contrast, weuse experimentally measured energetic disorder and CT phonon-mode energy values, while simultaneously accounting for kineticcharge transport/recombination effects using 3D kMC simula-tions, which is not possible using earlier employed analytical anddrift-diffusion based models. The major distinguishing feature ofour CT-EL model is not in the separate experimental validationof the above features but in the fact that our model not onlysimultaneously and quantitatively accounts for kinetic, energetic,and vibronic effects but also successfully fits bias-dependent CT-EL experiments. It is this combination that allows to provide aquantitative understanding of CT-EL.

Results and DiscussionEnergetic Disorder of D and A Materials. To estimate the energeticposition of the recombining carriers in their respective DOSduring CT-EL, the DOS energetic disorder σ of the constituentD/A materials must be known. We have performed temperature(T)-dependent SCLC transport measurements (200 to 300 K) on6 different D/A blends and have extracted their σ for both elec-trons and holes following the Gaussian disorder model (GDM)(15), which has been effectively used to explain charge motion in alarge variety of organic semiconductors in the past (13, 24) (seeSI Appendix, Figs. S3 and S4 for SCLC data). We have assumeduncorrelated Gaussian DOS site energies, as experimentallyconfirmed in earlier work (13). For the materials studied here, theextracted uncorrelated Gaussian DOS disorder values for thedonor HOMO and acceptor LUMO, σHOMOD and σLUMO A, re-spectively, span the typical range encountered in organic semi-conductors σ ∼60 to 100 meV (SI Appendix, Table S1). While theCT state disorder σCT at the D/A interface governing CT-EL maydiffer from the DOS site disorder sampled by SCLC measure-ments, σCT estimates in the literature span a comparable σCT∼60 to 100 meV range (12) and would otherwise not affect theconclusions of this work (see SI Appendix, Note S2 for details).

Upper Limit for Inhomogeneous 0–0 Lineshape Broadening. To showthat the energetic disorder of the constituent materials does notsuffice to explain the CT-EL spectral broadening, we quantify theupper limit for inhomogeneous CT-EL broadening via the con-volution of the hole and electron Gaussian DOS, which equals thegeometric mean of the experimentally determined σHOMOD andσLUMO A. Fig. 3B shows that the experimentally observed CT-ELbroadening σCT-EL, obtained by Gaussian fitting to CT-EL mea-surements in Fig. 3A, is larger than CT-EL broadening estimatedby DOS convolution σSCLC 0–0 (Fig. 3B, open circles). The lackof correlation between experimental CT-EL spectral broadeningand DOS energetic disorder becomes apparent when comparingmaterials with overall similar energetic disorder but different CT-EL broadening, for example rr-P3HT:PC61BM and MDMO-PPV:PC61BM in Fig. 3B.The actual disorder contribution to CT-EL broadening is even

less than estimated above, since the distribution of spatiallyneighboring donor HOMO and acceptor LUMO DOS sitescontributing to CT emission is much narrower than assumed byDOS convolution. This is due to kinetic effects governing thelikelihood of charge carriers meeting at specific DOS sites, aswell as the likelihood of CT emission at those DOS sites. To ex-plicitly account for such kinetic effects, we have performed numerical

BA

Fig. 3. CT-EL spectral broadening. (A) CT-EL peak broadening σCT-EL is material-dependent. The spectra have been centered at 1.2 eV for comparison and arecompared at a current density of J = 200 mA cm−2. (B) Comparison of experimental CT-EL peak broadening (filled squares) and 0–0 transition lineshape broadeningestimated by DOS convolution σSCLC 0–0 (open circles) for different donor polymers blended with either PC61BM or PC71BM. The actual DOS-induced broadening ofthe 0–0 transition is σ3D kMC 0–0 ∼70 to 80 meV (filled circles), as calculated by 3D kMC using energetic disorder values measured by T-dependent SCLC.

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3D kMC simulations of the 0–0 lineshape, which are described indetail below. These simulations confirm that the resulting 0–0 line-shape broadening (Fig. 3B, filled circles) is indeed less thanobtained by DOS convolution (Fig. 3B, open circles).

Three-Dimensional kMC Simulations of the 0–0 Lineshape. We ex-plicitly calculate the energetic position of the recombining carriersin their respective DOS during the CT-EL experiment by nu-merical OPV device simulations using 3D kMC based on the ex-tended GDM (25), which describes nearest-neighbor chargehopping in an energetically disordered Gaussian DOS (we alsoconsider an exponential DOS; see SI Appendix, Fig. S5). It is anextension of a previously described model, shown to successfullydescribe photoinduced charge separation (26) and transient pi-cosecond–microsecond carrier dynamics for polymer:fullerene(27–30), polymer:polymer (30), and small-molecule:fullerene (31)blends in illuminated OPV devices, now used to model OPV de-vices operating as LEDs.Briefly, our model accounts for charge injection/extraction

at ohmic contacts, charge transport, electric field, and state-fillingeffects, all Coulomb interactions including the contribution of the∼220-meV CT binding energy on CT-EL spectra, image charges in

metal electrodes, and electron–hole recombination. The ∼220-meVCT binding energy estimate corresponds to an intersite D/Adistance of 1.8 nm where CT recombination occurs, but theelectron–hole interaction is distance-dependent as numericallycalculated by the model. Charges forming a CT complex do notnecessarily recombine and can meet/separate multiple times duringtheir lifetime under favorable conditions. This implicitly accountsfor the experimentally observed CT state diffusion by correlatedelectron and hole hopping motion (32). While extending ourmodel to quantitatively account for the quantum yield of CT lu-minescence is also possible and important for understanding en-ergy losses in optoelectronic devices, this is beyond the scope ofthis work.As in our previous work, we use the simplest treatment with

uncorrelated electron/hole Gaussian DOS sites, which was in-dependently confirmed for the investigated D/A blends by T-dependent SCLC measurements in earlier work (13). To dem-onstrate model generality, we have also performed 3D kMCsimulations assuming an exponential DOS. See SI Appendix, Fig.S5 and Note S3 for a discussion of possible alternatives, such asaccounting for reorganization effects (found to be insignificant),DOS site correlations, and an exponential DOS, all showing that

ħw = 143 meV

LUMOA

HOMOD

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σ kTHOMO D

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Fig. 4. Three-dimensional kMC simulations of the 0–0 lineshape reveal nonequilibrium DOS site distributions governing CT-EL and enable CT-EL modelfitting to experiments. (A) Bias-dependent 0–0 lineshape simulations using 3D kMC for materials with σHOMO D = 50 meV and σLUMO A = 60 meV (black) andσHOMO D = 100 meV and σLUMO A = 120 meV (blue). (Inset) The calculated spectra for different active layer thicknesses, confirming that the calculatedspectra are a thickness-independent D/A materials property and not an artifact present only in devices with a thin active layer. (B) Energy-resolved HOMO(red) and LUMO (blue) site energies leading to CT-EL obtained by 3D kMC for σHOMO D = 100 meV and σLUMO A = 120 meV, at an applied bias of 1 V (filledarea) and 5 V (shaded area). The horizontal colored lines mark the equilibrium σ2/kT energy in a Gaussian DOS (lightly shaded gray area, not to scale). (C )Global model fit (blue dashed lines) to experimental CT-EL spectra (red lines) for MDMO-PPV:PC61BM (1:4) at the indicated current-densities. The 0–0 peak(shaded gray) is obtained by 3D kMC, whereas the lower energy 0–1 and 0–2 vibrational peaks (lighter shade of gray) are generated using Eq. 1. (D) PLspectra following 1.39 eV (890 nm) excitation of MDMO-PPV:PC61BM (1:4) (red) and pristine MDMO-PPV (black) measured by FLN spectroscopy at 7 K.These measurements confirm the characteristic vibrational energy Zwph D/A = 137 meV, independently obtained by model fits to CT-EL spectra in C, whereZwph fit = 143 meV.

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the conclusions of our work are expected to be general to anyorganic semiconductor.The model accounts for equilibrium as well as nonequilibrium

phenomena (carrier populations characterized by a temperatureequal to the lattice temperature or an effective temperature higherthan the lattice temperature, respectively). For brevity, the terms“nonequilibrium,” “nonthermal,” or “nonrelaxed” are used inter-changeably and refer to charges at DOS sites with significantlyhigher energy than DOS equilibrium site energies.While the investigated D/A blends in this work have moderate

energetic offsets for charge separation [with the exception ofAPFOgreen9:PC71BM, which was deliberately chosen due to itslow energetic driving force (33)], the CT-EL mechanism outlinedin this work also applies to state-of-the-art systems with smallenergetic offsets (34). As long as the materials do not havestrong DOS site energy correlations or anticorrelations, neitherCT-S0 nor S1-S0 emission is likely to occur from sites that haveboth a low hole energy and a low electron energy. The influenceof spatial correlations is insignificant, as shown previously (35).Even in the limit of negligible energy offsets at the D/A interface,resulting in charge transfer and subsequent luminescence from thepristine D or A components, the model conclusions remain valid,but the model would have to be adapted to accommodatespecific details.

The 0–0 Lineshape Broadening. We simulate the 0–0 lineshapebroadening for the materials shown in Fig. 3 using experimentallydetermined σHOMOD and σLUMO A, and applied bias corre-sponding to J = 200 mA cm−2 (2 to 3 V across devices to ensure asufficient signal-to-noise ratio for D/A blend comparison). Fig. 3Bshows that the resulting inhomogeneous 0–0 lineshape broaden-ing obtained by 3D kMC is σ3D kMC 0–0 ∼70 to 80 meV acrossdifferent D/A combinations and depends only weakly on theDOS disorder of the constituent materials, spanning the range σ∼60 to 100 meV for the investigated D/A blends.To highlight the weak dependence of the 0–0 CT-EL lineshape

broadening on DOS disorder, we simulate a hypothetical low-disorder case σHOMO D = 50 meV and σLUMO A = 60 meV,resulting in 62-meV inhomogeneous 0–0 lineshape broadening,whereas a high-disorder case σHOMO D = 100 meV and σLUMO A =120 meV leads to 85 meV (Fig. 4A shows the corresponding 0–0 CT-EL spectra, 0–0 broadening was estimated at 2 V). We proposethat the weak 0–0 lineshape broadening dependence (σ0–0 ∼60 to85 meV) on D/A energetic disorder (σ ∼50 to 120 meV) is ageneral feature of D/A organic semiconductor blends with aGaussian DOS. As a result, the experimental CT-EL spectralbroadening cannot be explained by the 0–0 transition broadeningas the latter is almost invariant on D/A combination (Fig. 3B,filled circles). From a practical standpoint, this means that CT-EL broadening is mostly indicative of Franck–Condon broad-ening (19, 20) but is a poor indicator of the energetic disorderpresent in the BHJ mixture.

Energetic Position of the Recombining Carriers in Their DOS. Fig. 4Bshows the simulated energetic position of the recombining carriersin their respective Gaussian DOS for a material with σHOMO D =100 meV and σLUMO A = 120 meV. Clearly, most CT-EL photonsoriginate from carriers recombining at sites ∼180 meV and∼330 meV (holes and electrons, respectively) above their DOSequilibrium energy σ2/kT.To rule out the influence of charges residing at artificially high-

lying DOS sites following injection from the contacts, we havecarried out reference simulations of OPV devices with differentactive layer thicknesses (Fig. 4 A, Inset). These reference simu-lations confirm that the simulated nonequilibrium DOS sitedistribution governing CT-EL (Fig. 4B) is indeed a thickness-independent D/A materials property and is not an artifactpresent only in devices with a thin active layer. Complementary

transfer matrix model (TMM) simulations (36), accounting foroptical interference effects in the device stack during CT-EL(37) and the possible bias dependence of the emission zoneposition in the active layer, reveal that cavity effects also can-not explain the experimentally observed and simulated CT-ELbias dependence (see SI Appendix, Fig. S6 for details). Both ofthese results confirm that the observed and simulated CT-ELbias dependence as well as the simulated nonequilibrium DOSsite distribution in Fig. 4B are a D/A materials property.The gap between the sites contributing to CT emission and the

equilibrium energy sites decreases with decreasing energeticdisorder and tends to zero for low disorder. Indeed, our modelpredicts that for σHOMOD = 50 meV and σLUMO A = 60 meV thehole recombination energies center around σ2/kT, whereas thenonequilibrium gap for electrons decreases to ∼20 meV. However,to the best of our knowledge, a combination of such low D/Adisorder values is rare for OPV materials, and the gap remainssignificant for typically encountered disorder values (13, 30, 31) (seeSI Appendix, Note S2 for further discussion regarding disorder val-ues). For example, CT-EL in a device with modest disorder valuesσHOMOD = 81 meV and σLUMOA = 73 meV, as found in the T-dependent SCLC analysis of MDMO-PPV:PC61BM, is governed bynonequilibrium gaps of ∼80 meV and ∼60 meV, respectively, with atotal difference of ∼140 meV compared to an equilibrium picture(Fig. 2C)—a significant number for a photovoltaic device.The observed disorder dependence highlights that the CT-EL

peak position only in part depends on the donor HOMO andacceptor LUMO levels—D/A disorder also governs the 0–0 CT-EL peak position. For example, materials with identical donorHOMO and acceptor LUMO levels but different disorder valueswill have their 0–0 CT-EL peaks situated at different energies.This renders the commonly employed ECT assignment on basis ofGaussian fitting of the high-energy CT-EL tail and the low-energy tail of subgap external quantum efficiency (EQE) spec-tra (38) ambiguous, as will be shown below.Most importantly, our model also reproduces the weak bias or

current-density dependence of CT-EL (Fig. 4A), which origi-nates due to the nonequilibrium DOS site distribution in Fig. 4B.SI Appendix, Fig. S5 shows that the same conclusion holds truewhen accounting for reorganization effects (found to be insig-nificant), DOS site correlations, and an exponential DOS, mean-ing that the conclusions of our work are expected to be general toany organic semiconductor. As such, these results resolve the in-consistencies present in the literature regarding which DOS sitesgovern CT-EL and show that CT-EL originates from considerablyhigher than equilibrium energy DOS site distributions (Fig. 2A), incontrast to the widespread equilibrium picture (Fig. 2C).

Three-Dimensional kMC Model Accounting for Energetic Disorder,Kinetic Effects, and the Franck–Condon Principle. To demonstratethe full consistency of our newly proposed model, we develop, as anext step, a framework that quantitatively and simultaneouslycombines the 3D kMC model (accounting for kinetic chargetransport/recombination physics in an energetically disorderedDOS; Fig. 2 A, Left) together with the Franck–Condon progression(accounting for the vibronic replicas of the 0–0 emission; Fig. 2 A,Right). To avoid ambiguous fits to the experimental CT-ELcurrent-density dependence, we describe the full CT-EL spec-trum with the least number of experimentally unknown parametersfollowing ref. 19. by

ICT−ELðZωÞ= ½nðZωÞZω�3 ·XM − 1

m= 0

e−SSm

m!·Γ

�Zω−

�Zω0−0 −mZωph

��,

[1]

where n(Zw) is the refractive index at photon energy Zw, S is theHuang–Rhys factor,m = {0, 1, . . .,M − 1} denotes the vibrational

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energy level and M the total number of vibronic peaks, Zw0–0 isthe 0–0 transition energy (lowest D+/A− excited state to D/Aground state), and Zwph is the effective phonon-mode energygoverning CT luminescence (see Fig. 2 schematic). We accountonly for emission from the lowest-energy D+/A− excited state tothe vibrational D/A ground state manifold (Fig. 2 A, Right); sinceon-site thermalization is considerably faster (<1 ps) (39, 40) thanintersite thermalization in the DOS, the latter may take as long as1 μs to complete (29). The model can be extended to account forthe D+/A− excited state manifold but this is outside the scope ofthis work.The first term [n(Zw)Zw]3 accounts for the influence of the

photon DOS (in the medium surrounding the emitter) to theemission spectrum. Since n(Zw) of D/A blends is typically onlyweakly energy-dependent at CT-EL emission energies, as con-firmed by spectroscopic ellipsometry for the blends in this work (SIAppendix, Fig. S7), the energy dependence of n(Zw) has only aminor effect on the overall shape of the CT-EL emission spectrum.Differences in the CT-EL emission spectra between the D/Ablends mainly originate from the remaining terms in Eq. 1.The last term Γ(Zw – (Zw0–0 – mZwph)) describes the 0-m

transition lineshape, which is red-shifted by m × Zwph with re-spect to the 0–0 transition. To limit the number of unknown pa-rameters, the 0-m and 0–0 lineshapes are assumed to beidentical. The 0–0 lineshape is calculated by 3D kMC simulationsas shown in Fig. 4A, using experimentally determined disordervalues σHOMO D/LUMO A whenever appropriate (see SI Appendix,Note S2 for details) and using the experimental set of bias orcurrent-density conditions. The experimental CT-EL bias orcurrent-density dependence is then fully captured by the simulatedbias dependence of the 0–0 transition (Fig. 4A), accounting for thenonequilibrium DOS distribution governing CT-EL (Fig. 4B). Wesimulate a volume of 90 × 90 × d nm3, where d is the measuredOPV device thickness, spanning the range 80 to 220 nm for theinvestigated D/A blends, optimized for photovoltaic performance.We incorporate the Franck–Condon progression (19) (second

term in Eq. 1) by simultaneously fitting the entire set of experi-mental current-density- or bias-dependent CT-EL spectra, severelyconstraining the model and ensuring reliable fits. All current-density conditions in Fig. 4C are globally fitted by a single pa-rameter set, resulting in a 3-parameter fit (Zwph fit, S, and M). Fig.4C shows excellent fits to the experimental CT-EL current-densitydependence of MDMO-PPV:PC61BM, whereas SI Appendix, Fig.S8 shows equally good fits for the other D/A blends.Model fits for MDMO-PPV:PC61BM suggest that the vibra-

tional energy responsible for CT-EL is Zwph fit = 143 meV(1,150 cm−1), which is characteristic for C–C skeletal vibration.Note that the typical vibrational energy governing Sn-S0 transi-tions is not necessarily dominant in the CTn-S0 case discussedhere due to the different geometry and coupling involved (intra-versus intermolecular transition). Indeed, using FLN spectros-copy (22, 23) we found that the phonon-mode energy Zwph D/Agoverning CT luminescence differs from the phonon mode thatgoverns the S1-S0 transition (see the next section and SI Ap-pendix, Figs. S9 and S10 for details).

Measurements of the Phonon-Mode Energy Governing CT Luminescence.To ensure our framework is fully consistent with experiments, weindependently confirm the number of vibronic peaks M and thecharacteristic phonon-mode energy Zwph governing CT lumines-cence using FLN spectroscopy (22, 23). Briefly, we rely on D/Ablend photoexcitation using low-energy photons (1.39 eV forMDMO-PPV:PC61BM and 1.49 eV for most of the other blends)to predominantly excite the low-energy part of the CT mani-fold, leading to line narrowing such that the 0–0 and 0-m tran-sitions can be clearly resolved. We record D/A blend filmphotoluminescence (PL) at cryogenic (7 K) temperatures to fur-ther suppress inhomogeneous broadening, which allows us to re-

veal the underlying vibronic progression at the D/A interfacegoverning CT luminescence. The resulting spectra are shown inFig. 4D for MDMO-PPV:PC61BM and in SI Appendix, Fig. S9 forthe other blends. Comparison to pristine MDMO-PPV spectraclearly shows that the blend FLN spectra correspond to CTemission (Fig. 4D). This is the case for all except one of the otherblends, APFOgreen9:PC71BM, which has a low energetic drivingforce for charge separation (33). While the strong overlap withpristine D luminescence in the case of APFOgreen9:PC71BM hasprevented us to unambiguously assign the blend FLN spectra toCT luminescence, we were able to extract the characteristic vi-brational energy governing CT-PL in all of the other blends, asshown in SI Appendix, Fig. S9.To estimate the characteristic vibrational energy governing

CT-PL in MDMO-PPV:PC61BM we use multipeak Gaussian fit-ting (Fig. 4D, dashed black lines). To minimize the number ofexperimentally unknown fit parameters, we allow the 0-m line-shape broadening to increase for the lower-energy 0-m transitions,which we tentatively attribute to the presence of more than onevibrational frequency (41) or dispersion in molecular vibrations;both warrant further study but are outside the scope of this work. Thecharacteristic energy obtained from the fits (Zwph D/A = 137 meV)and the number of clearly visible vibronic peaks (M = 3) arein good agreement with the model fits to CT-EL in Fig. 4C,confirming the validity of our proposed CT-EL model by inde-pendent experiments. SI Appendix, Figs. S8 and S9 and Table S2show equally good agreement for the other blends. This is a se-lective and direct measurement of the characteristic phonon-modeenergy Zwph D/A governing CT luminescence in organic semicon-ductors, without being overshadowed by the otherwise dominantpristine D and/or A luminescence.

CT-EL Recombination Mechanism. To gain further insight, we haveinvestigated whether charges residing at higher-lying DOS sites,which could be considered “more mobile,” perform the last hop torecombine with charges residing at lower-energy DOS sites, whichcould be considered as temporarily “immobile/trapped.” Thismechanism would be consistent with multiple-trapping-and-release type models often used to describe charge carrier recom-bination in OPV devices. To the contrary, as detailed in SI Appendix,Fig. S11, our 3D kMC simulations indicate that CT-EL is insteadgoverned by events in which the charge carrier that makes the lasthop resides at a lower-energy DOS site to recombine with a chargecarrier residing at a higher-lying DOS site. A similar recombina-tion mechanism was proposed earlier in the context of chargeseparation of photogenerated charge pairs (42).

Relation to Subgap Absorption Measurements and the CT Energy.Having developed a fully consistent framework for CT-EL, wenow demonstrate the importance of CT emission occurring froma nonequilibrium DOS site distribution (Fig. 2A) in relation tosubgap absorption and EQE measurements. For comparison, wedetermine the conventionally defined CT energy ECT conv fol-lowing the procedure outlined by Vandewal et al. (38), whichrelies on Gaussian fitting of appropriately-normalized reducedEQE and CT-EL spectra, as shown in SI Appendix, Fig. S12. Thefollowing analysis indicates that there are many available DOSsites for charge generation, transport, and recombination belowthe conventionally defined CT energy. The energy definitionsused in subsequent analysis are schematically shown in Fig. 2.Fig. 5 shows the experimental and modeled CT-EL spectra

together with subgap EQE spectra measured by Fourier-transformphotocurrent spectroscopy (FTPS). The remaining discrepancy be-tween the measured and modeled CT-EL spectra (red and bluetraces in Fig. 5, respectively) likely originates due to the materialDOS not being exactly Gaussian, and possibly due to S1-S0 emissionfrom the pristine D and/or A at higher energies, which is notaccounted for by the model. Nevertheless, model fitting at low

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energies is already superior to the conventional approach (see alsoSI Appendix, Fig. S12) and sufficiently accurate for subsequentanalysis. Since the position of the recombining carriers in their re-spective DOS is known from our model (Fig. 4B), Fig. 5 enables usto estimate the position of ECT conv in relation to the joint DOS ofthe D/A blend (Fig. 2D).The importance of high-energy DOS sites governing CT-EL

becomes apparent when comparing ECT conv and CT states withequilibrium DOS site energies ECT eq across different D/Acombinations, calculated for an electron and hole pair forming aCT state at DOS equilibrium sites as

ECT  eq =���EHOMO D

�� − σ2HOMO D

kT

�

−���ELUMO A

�� − σ2LUMO A

kT

�− ECT  bind,

[2]

where EHOMO D and ELUMO A are the donor HOMO and accep-tor LUMO energies, respectively, and ECT bind is the CT excitonbinding energy ∼220 meV, corresponding to an intersite D/Adistance of 1.8 nm as used in 3D kMC. Fig. 5 shows that ECT eqis situated significantly below the conventionally defined CT en-

ergy. The ECT conv − ECT eq difference is substantial and spansthe range ∼290 to 800 meV for the investigated D/A blends (see SIAppendix, Table S3 for values and SI Appendix, Note S4 regardingEHOMOD/LUMO A determination). This implies that there are manyavailable DOS sites for charge generation, transport, and recom-bination below the conventionally defined CT energy. Fig. 5 alsoillustrates that the conventionally determined ECT conv is not a goodmeasure of the central CT energy ECT centr, corresponding to thedifference between the donor HOMO and acceptor LUMOlevels corrected by the CT binding energy, determined as

ECT  centr = jEHOMO D − ELUMO Aj − ECT  bind. [3]

The main purpose of Fig. 5 is not to redefine ECT but tohighlight that CT-EL originates from considerably higher-lyingDOS sites than previously thought, as depicted schematically inFig. 2. The many available DOS sites below ECT conv also ratio-nalizes the experimentally observed photogenerated carrierthermalization to these low-lying DOS sites (29), even followingphotoexcitation at ECT conv (31), when the OPV device is oper-ated as a solar cell rather than as an LED.Generally speaking, blend DOS describes all hopping sites,

whereas the manifold probed in CT emission corresponds to a

0.8 1.2 1.6 2.010-3

10-2

10-1

100

101

CT-

EL

(arb

.)

APFOgreen9:PC71BM 1:3

EQ

E-F

TPS

(%)

Energy (eV)

EQE-FTPSCT-EL

CT-EL model0-00-10-2

0.8 1.2 1.6 2.010-6

10-4

10-2

100

CT-

EL

(arb

.)

MDMO-PPV:PC61BM 1:4

EQ

E-F

TPS

(%)

Energy (eV)

ECT conv

ECT eq 0-0

0.8 1.2 1.6 2.010-5

10-3

10-1

101

CT-

EL

(arb

.)

APFO3:PC61BM 1:4

EQ

E-F

TPS

(%)

Energy (eV)

0.8 1.2 1.6 2.010-3

10-2

10-1

100

101

102

CT-

EL

(arb

.)

TQ1:PC71BM 1:2.5

EQ

E-F

TPS

(%)

Energy (eV)

ECT centr

ECT conv

ECT eq 0-0

ECT centr

ECT conv

ECT eq 0-0

ECT centr

ECT conv

ECT eq 0-0

ECT centr

A

C D

B

Fig. 5. Relation between nonequilibrium DOS sites governing CT-EL and subgap EQE measurements and the definition of ECT. Comparison of CT stateswith DOS equilibrium site energy ECT eq (black dashed lines, Eq. 2) to the conventionally defined ECT conv (38) reveals a substantial ECT conv − ECT eq ∼290- to800-meV difference depending on the D/A blend, highlighting the importance of the high-energy DOS site distributions governing CT-EL. Here, theexperimental CT-EL spectra (red lines), the CT-EL model fit (blue dashed line), and the corresponding vibronic progression are scaled by a constant, suchthat the experimental EQE-FTPS spectra (open circles) and the CT-EL spectra would coincide at ECT conv, which was independently determined followingthe definition proposed by Vandewal et al. (38) (see SI Appendix, Fig. S12). ECT centr marks the central CT energy jEHOMO D − ELUMO Aj corrected by the CTexciton binding energy ECT bind ∼220 meV following Eq. 3. (A) MDMO-PPV:PC61BM (1:4), (B) APFO3:PC61BM (1:4), (C ) TQ1:PC71BM (1:2.5), and (D)APFOgreen9:PC71BM (1:3).

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subset of the total DOS sites forming a D/A interface, weightedby the probability of an electron and a hole meeting and recom-bining. Although the D/A interface can be probed by spectroscopictools such as CT-EL and EQE-FTPS, the relation of the probedsites to the total DOS, relevant for carrier transport and ther-malization, is typically elusive in such measurements. Figs. 4 and 5reveal how DOS sites relevant to subgap photovoltaic action andCT-EL relate to the total DOS.

Relation to Device Open-Circuit Voltage and Energy Losses. In viewof the higher-energy DOS subset sampled during CT-EL, it isnot evident why the conventionally defined ECT conv has beenso effective in quantitatively describing VOC (6, 7) and photo-voltaic energy conversion losses in OPV devices, since modelsbased on ECT conv generally assume that equilibrium DOS siteoccupation governs CT-EL. While the results presented heredo not invalidate established ECT to VOC relations, the non-equilibrium DOS site distribution governing CT-EL adds alayer of previously overlooked complexity.Comparing the measured EQE-FTPS spectra to the EQE

spectra derived from CT-EL measurements, we find that thecommonly employed reciprocity analysis (6, 7) also applies tothe investigated systems, as detailed in SI Appendix, Fig. S13;nevertheless, detailed understanding of how charge transport/recombination kinetics and energetic disorder affect reciprocityrelations requires further investigation. Analysis accountingfor these factors, while outside the scope of this work, is expectedto deepen the insight into the underlying photophysics, especially inthe origins of energy losses in OPV devices. In addition, extendedtreatment of photogenerated charge energetics could reveal novelroutes to improved VOC. As such, these results pose fundamentalquestions, particularly regarding the meaning of reciprocity rela-tions relating light emission to photovoltaic action, and could serveas motivation for the continued pursuit of fully understanding VOCand energy losses in organic optoelectronic devices.

Materials and MethodsFull material names, photovoltaic device fabrication and characterizationusing CT-EL, FLN and EQE-FTPS measurements are described in SI Appendix,Materials and Methods.

Material Choice. To accurately model experimental CT-EL spectra, materialcombinations showing only CT emission and no pristine material emission (overthe investigated current-density range) were selected. The APFOgreen9 basedBHJ system was deliberately chosen due to its low energetic driving force forcharge separation (33).

Three-Dimensional kMC Simulations. The most comprehensive model de-scription can be found in ref. 29. TheMiller–Abrahams formalism was used toquantify with the least number of unknown parameters the nearest-neighborhopping rate of a charge carrier in a cubic lattice with an uncorrelatedGaussian DOS (an exponential DOS was also considered; see SI Appendix, Fig.S5). The BHJ active layer was treated as an effective medium, meaning that theused hopping parameters represent average values over the entire BHJ film—

local variations in the physical properties of the nanoscale morphology are notexplicitly accounted for. The experimentally measured BHJ active layer thick-ness was used in the simulations. Additionally, ohmic contacts were included asquasi-infinite reservoirs for charge injection and extraction. The correspondingMiller–Abrahams rates were calculated with respect to the contact Fermi level;site energies in the semiconductor were corrected for the image potential. Thenumber of particles in 3D kMC simulations of the 0–0 lineshape in Fig. 4Aspans the range of 113× to 303× particles for the 1 V and the highest voltagesimulations, respectively, corresponding to a reasonable carrier densityrange of 1.5 × 1017 cm−3 to 4.4 × 1017 cm−3.

Data Availability. All data are provided in the main text and SI Appendix.

ACKNOWLEDGMENTS. We thank René A. J. Janssen, Alberto Salleo, andAnna Köhler for feedback on the manuscript; Luis Ever Aguirre for perform-ing spectroscopic ellipsometry measurements; and Jonas Bergqvist for helpwith the TMM simulations. We gratefully acknowledge support from theKnut and Alice Wallenberg Foundation for Grant KAW 2016.0494 to A.M.for postdoctoral research at Stanford University, Grant KAW 2014.0041 toW.M.C., and a Wallenberg Scholar grant to O.I.

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