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Structure-Property Relationships From Atomistic Multiscale Simulations of the Relevant Processes in Organic Solar Cells I. Thermodynamic Aspects Charlotte Brückner, Frank Würthner, Klaus Meerholz, and Bernd Engels J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06755 • Publication Date (Web): 08 Nov 2016 Downloaded from http://pubs.acs.org on November 15, 2016

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The Journal of Physical Chemistry

Structure-Property Relationships From Atomistic Multiscale Simulations of the Relevant Processes in Organic Solar Cells I. Thermodynamic Aspects Charlotte Brückner†, Frank Würthner‡, Klaus Meerholz#, Bernd Engels,†,* † Institut für Theoretische Chemie, Universität Würzburg, Emil-Fischer-Straße 42, 97074 Würzburg, Germany ‡Institut für Organische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany #

Department Chemie, Universität zu Köln, Luxemburgerstr. 116, 50939 Köln, Germany

*E-Mail: [email protected], phone number: (+49) 931 - 31 – 85394, fax number: (+49) 931 - 31 - 85331

ABSTRACT Interface structures of a variety of molecular p-type semiconductors in heterojunction with fullerene C60 were generated in molecular dynamic simulations. Using the dimer method (i.e., dimers were used as the quantum-mechanical system) along with a continuum solvation approach and macroscopic electric fields, energetic profiles of the interfaces of organic solar cells (OSCs) were calculated. Several important loss mechanisms, such as exciton trapping, charge trapping, and interfacial charge-transfer traps, were observed. Structure-property relationships were established. They reveal that apart from the molecular orientation and dipolarity, molecular size is an important parameter that influences potential loss mechanisms. Solar cells are one of the most promising devices to exploit renewable energy resources. In comparison with their inorganic counterparts, organic solar cells (OSCs) possess some major advantages such as low-cost production conditions and materials, light weight, high mechanical flexibility, and transparency.1,2 Due to the significant electron-hole binding energy in organic semiconducting layers, OSCs are usually built as donor-acceptor heterostructures with a donating hole-conducting layer and an accepting electron-conducting counterpart.3 While fullerene and its derivatives usually constitute the n-type semiconducting phase,4 both polymers5,6 and small organic molecules7,8 are used as the donors. Compared to polymers, small organic molecules take advantage from well-defined structures, tunable properties 1 ACS Paragon Plus Environment


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along with clear-cut molecular structure-property relationships, easier purification, and an improved batch-to-batch reproducibility of resulting optoelectronic devices.7,8,9,10 In OSCs, several processes take place between the absorption of sunlight and the flow of electric current. First of all, an exciton is created in one of the two semiconducting layers (Step 1: absorption). It diffuses towards the interface (Step 2: exciton diffusion) where it dissociates into a charge-transfer state across the interface (Step 3: exciton dissociation). The charges are still bound by the Coulomb attraction but via subsequent charge transport in the semiconducting layers, they are split into two separate charges (Step 4: charge separation/transport).11,12 Finally, the charges are recollected at the electrodes (Step 5: charge recollection). At this point it is important to consider that the terms “charge-transfer state” and “charge-separated state” are variably employed in the literature. For the following discussion we will consider charge-transfer states as the (bound) electron-hole pairs that immediately result from exciton dissociation at the interface. In our definition, chargeseparated states arise from these charge-transfer states as soon as the charges are sufficiently separated to escape from their mutual Coulomb binding. They are then considered as separate charges whose behavior can be described as a charge transport. For the efficiency of a device, each step is important 13,14 because the underlying processes may be hampered due to thermodynamic or kinetic reasons. Hence, insight on an atomistic scale is needed since some mechanisms, especially the formation of the charge-separated states, are still under debate.15 Moreover, energy loss channels exist for all steps, significantly restricting the device efficiencies.16 In this work, we focus on Steps 2 to 4, which include most of the prominent loss mechanisms. Although most OSCs have bulk heterojunction cell architectures,17 exciton quenching still takes place due to impurities, disorder, other quenching defects18 or exciton self-trapping.19,20,21 The responsible exciton trap states are energetically very low-lying states in the exciton energy landscapes which are populated during exciton diffusion. Their excess energy is dissipated into the environment, preventing any further migration which would thereupon be an energetic uphill process. Consequently, these excitons cannot contribute to the short-circuit current (JSC), so that such trapping processes severely limit the external quantum efficiency (EQE).13,14 Interfacial charge-transfer states can also be very low-energy states due to the significant Coulomb binding energy between the electron and the hole. As soon as their energies fall significantly below the 2 ACS Paragon Plus Environment

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energies of charge-separated states, the (in)feasibility of efficient charge separation in the cell becomes an issue. However, deep charge-transfer states do not only reduce the amount of successful charge separation from charge-transfer states. They also give rise to reduced opencircuit voltages Voc, leading to decreased cell efficiencies.22 Charges can also become trapped while migrating from the interface to the electrodes. Oxidizing agents and disorder are responsible, resulting in low-lying charge transport states which act in a similar way as exciton traps.23,24,25 In addition to energetic (thermodynamic) reasons, trapping can also result from low coupling parameters or other unfavorable kinetic constraints. In order to develop high-performing optoelectronic devices, a profound understanding of the nature of all these loss mechanisms is helpful. This is the ultimate goal of our investigations. In this objective and by using the dimer method (i.e., a dimer constitutes the basic quantummechanical system) along with an effective epsilon (i.e., folding the complex anisotropic dielectric constant into a single parameter) and macroscopic electric fields, we simulate the various processes. We use the dimer approach because excitons and charges are typically delocalized over several monomers in organic thin films. This delocalization induces both a shift and a splitting of exciton and charge energies. The splitting of these energies has an impact on exciton and charge reorganization energies and considerably modifies transport properties. Additional trapping mechanisms arise from relaxation pathways along intermolecular degrees of freedom. All of these effects are properly approximated by dimers as the quantum-mechanical systems, while the commonly employed monomer-based models with excitons and charges localized on a single molecule cannot account for them and only includes energy changes due to variations in the electrostatic potential and the polarizability of the environment. Although the inclusion of larger oligomers in the quantum-mechanical calculation would be desirable and is certainly very significant in well-ordered crystalline systems, it is much less significant for amorphous systems where environmental disorder triggers localization to a larger extent than in crystalline systems. We generated the interface structures in molecular dynamic simulations by mimicking the experimental process of evaporation or spin-coating. From the computed state energies, we could construct energetic profiles (i.e., diagrams about the relative energetic positions) of all important excitonic, charge transport and charge-transfer states around the interface that retrace the energy changes that an incident exciton undergoes upon dissociation into separate 3 ACS Paragon Plus Environment


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charges. Possible loss mechanisms such as exciton and charge traps and interfacial chargetransfer traps can easily be identified in these profiles. To increase the performance of optoelectronic devices and for a rational design of highperforming molecular semiconductors, it is important to understand the relationships between molecular properties, e.g., the molecular dipole moment, the molecular polarity or the molecular size, and supramolecular packing effects that lead to low efficiencies due to the formation of trap states. We interpreted the existence of loss mechanisms from a molecular point of view and establish some structure-property relationships on how to exclude these energy loss channels by a specific molecular design. In order to do so, for our calculations, we chose a series of p-type molecules (Figure 1) in heterojunction with fullerene C60, which is often used as the n-type semiconductor.

Figure 1: Variety of p-type molecular semiconductors, which we employed as model systems for our calculations in heterojunction with fullerene. 4 ACS Paragon Plus Environment

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The p-type semiconducting molecules were selected to cover many important classes of molecular semiconductors ranging from apolar acenes and fused aromatic systems over three-dimensional triarylamines to rather polar dyes like squaraines, diketopyrrolopyrroles, and merocyanines.26,27,28 We discuss particularities of the individual molecules in the following to explain our selection in detail. Although acenes are today rather commonly used in OFETs (organic field-effect transistors)26, we included anthracene in our model systems because it was among the first molecules where photoconductivity was observed.29,30 Moreover, the anthracene chromophore is still widely used in organic polymers31 and – in its functionalized version – as organic molecular semiconductors8,26,32,33,34 and also in dye-sensitized solar cells.35 We will primarily use anthracene to demonstrate by means of its interface energetics why device performances can be expected to be poor. As a second representative of the acene group, rubrene, a substituted tetracene with very high observed hole mobilities 36 and bright yellow fluorescence also exploited in OLEDS37, was employed. The rubrene::fullerene (PCBM) heterostructure was also experimentally investigated. 38,39,40 While high charge carrier mobilities were observed for crystalline rubrene, rubrene does not readily form crystalline films after evaporation, but rather disordered, polymorphic thin films 41,42. Also the DIP::fullerene heterojunction has been experimentally thoroughly investigated. 43,44 In contrast to rubrene, DIP readily forms crystalline films with very favorable transport properties.45 However, due to the perpendicular orientation of the transition dipole moments in deposited DIP phases,46 the amount of light absorption is significantly reduced.45 The introduction of substituents has been shown to shift the absorption maximum and to induce the formation of amorphous thin films, which improves the absorption quality in the thin film but deteriorates the transport properties.47 We comprise DIP in our model set to analyze the energetic profiles of DIP::fullerene heterostructures with different orientations with respect to each other. In contrast to the two-dimensional acenes and fused aromatics which readily crystallize, threedimensional triphenylamines are soluble48 and form amorphous films with isotropic and homogeneous properties due to the absence of grain boundaries.49,50 However, the overlap of their absorption with the solar spectrum is usually rather small.

49,50

Therefore,

triphenylamine-based molecules are often used as hole-conducting materials and in 5 ACS Paragon Plus Environment


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electroluminescent devices,50,48 but they have only recently also come to use in organic photovoltaic devices since a finetuning of their properties is possible by small structural modifications.50,51 The introduction of electron-withdrawing groups in particular shifts their absorption to longer wavelengths and ensures high oxidation potentials necessary for high open-circuit voltages while simultaneously preserving the good hole-transport properties of triphenylamines.52 These donor-acceptor triphenylamine-based compounds were shown to be promising candidates for highly efficient solar cells. 53 The inclusion of both substituted and unsubstituted triphenylamines (a triphenylamine54 without electron-withdrawing substituents, TBA, with optimized hole-transport properties as well as a triphenylamine with a conjugated aldehyde 55, TAA) in our computational chemistry case study allows us to study the influence of the introduction of accepting groups on the optoelectronic properties and on possible loss mechanisms such as charge-transfer trap states in organic thin-film solar cells. The third triphenylamine-based dye that we comprise is a donor-acceptor structure disposing a dianisylamine donor and an anthracene acceptor (TAM). It was photophysically characterized and undergoes – upon excitation – a torsional movement forming an intramolecular charge-separated state.56 However, due to the poor overlap of its absorption with the solar spectrum, an experimental characterization of its photovoltaic performance was not possible.56 This fact and the interesting excited-state properties of TAM make it an ideal candidate molecule for a computational chemistry case study. Turning to dye- and pigment-based organic semiconductors, we included a symmetric squaraine for several reasons.57 Squaraine dyes have very high absorption coefficients in the visible and NIR region.58 Like for other dyes, squaraine thin-film properties are largely determined by aggregation caused by strong intermolecular interactions, where the aggregation properties depend on substituents and fabrication conditions.59,60,58,61 Experimental investigations on the chosen symmetric squaraine revealed that the formation of J-aggregates favorably influences the photovoltaic performance of squaraine-based thin films with fullerenes.58,62,63 A better match of the redshifted absorption spectrum of the Jaggregate with the solar spectrum increases the short-circuit current. Larger hole mobilities are obtained because of larger couplings in the J-aggregate states.64 It is of interest to use computations to investigate the experimentally demonstrated close relationship between the supramolecular structure of this compound and its optoelectronic performance and to 6 ACS Paragon Plus Environment

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correlate the presence/absence of J-aggregates with the existence of computed trap states in the DOS. We comprised a diketopyrrolopyrrole65 as a representative for a compound class which has been used for high-performant pigments and inks for several decades, but has come to use in OSCs only recently.66 Also employed in low-band-gap polymers as the electron-deficient component,67 its strongly absorbing core moiety, its high mechanical and photochemical stability68 and the possibility to modify the core substituents to tailor properties69 and thinfilm morphologies70,71 led to a variety of performant photovoltaics including molecular diketopyrrolopyrroles as the donor. From a theoretical point of view, the optoelectronic properties of such a diketopyrrolopyrrole are most interesting as it constitutes a compound with a donor-acceptor-donor structure66 featuring bright intramolecular charge-transfer excitations. Finally, merocyanines are another important class of organic dyes forming dye aggregates with pronounced exciton couplings and disposing high performances in OSCs.7,72 Their high tinctorial strengths and their favorable charge-transport properties72 in combination with their structural diversity, which allows for a fine-tuning of the HOMO and LUMO levels and the absorption maxima,73 form the basis for experimentally observed high performances in photovoltaic devices.8 Due to the structural diversity of these compounds, we included two different dyes, HB19474, and MD35375, all with different donating and accepting moieties as well as different experimental cell performances, respectively. A number of theoretical investigations have addressed the organic::organic interfaces in organic photovoltaics.11,76,77 The employed methods range from high-level ab initio studies like CASPT278 and ADC(2)12 over constrained DFT and TD-DFT79 to molecular mechanics and atomistic or coarse-grained microelectrostatic models.80 The influence of the geometry of the donor-acceptor complex on the couplings, the rates, and the charge-transfer energy was thoroughly analyzed.79,81,82,83,84 The role of the electric field85 and of interface dipoles78,86 as well as their influence on charge-transfer states at the interface80 and on the mechanism of exciton transfer87 have also been investigated. The interplay of polarization and ground-state charge transfer78 and the impact of the anisotropic distribution of quadrupole moments 88 at the interface giving rise to these interface dipoles were analyzed. Various investigations focus on the adjustment of the HOMO-LUMO gap, the band offset, and the band bending in the 7 ACS Paragon Plus Environment


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vicinity of the organic::organic interfaces. 77 The band bending was shown to depend, among others, on the amount of disorder, the anisotropic epsilon, the interface dipoles, and the exact molecular conformations.77,88,89 Closely related, the mechanism of exciton transfer across the interface is addressed from a theoretical point of view. 15 In view of the absence of experimental data on atomistic structures at the interface, theoretical methods are employed to construct these interface structures.76 Molecular dynamics has been used to study the intermixing at the pentacene::fullerene interface90 and to computationally generate the organic::organic interface of a squaraine::fullerene heterojunction.91 Most of these studies focus on single donor-acceptor pairs, like e.g., on the different heterodimers at the pentacene::fullerene interface.86 In contrast, this paper analyzes trends resulting from the variations in the molecular properties. In this respect, we investigate all individual processes so that also their interplay becomes obvious. This elucidates important structure-property relationships and provides a molecular understanding for performancelimiting loss mechanisms. In addition, the application of the dimer method to organic::organic interfaces is to our knowledge unprecedented and yields information on interface energetics beyond the most often employed embedded-monomer approach. Potential loss mechanisms may result from thermodynamics (i.e., the relative energies of the involved states) or kinetics (coupling parameters). Combining both aspects with the large number of compounds in our test set is far beyond the scope of one publication. Hence, in the present paper, we focus on thermodynamic effects, while kinetic aspects are discussed in a subsequent work. This paper is organized as follows. In the section “Description of the Theoretical Approach”, we discuss the employed theoretical models to generate the interface structures on the one hand and to compute the relative energies of excitons, charges, and charge-transfer states on the other hand. In a section “Results and Discussion”, we discuss the resulting state energies, especially with respect to the relationship between molecular properties and the presence/absence of trap mechanisms and compare our results to available experimental data. Each section is subdivided to discuss special aspects in more detail. DESCRIPTION OF THE THEORETICAL APPROACH Generation of interface structures 8 ACS Paragon Plus Environment

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Molecular dynamics (MD) was shown to be the most suitable computational tool to generate disordered interface structures.90,77,89 A problem of MD, however, are the high barriers between the conformations at the interface. This increases the importance of the MD starting point since a complete sampling of the conformational space is not feasible. 92,93,77 Many computational investigations of interfaces start with the donor and acceptor crystal structures, which are aligned and thermally equilibrated in a subsequent MDs. 77,94,88 We modify this approach to mimic experimental layer deposition techniques to obtain disordered organic phases.95 In order to do so, successive MDs are conducted. The process is visualized in Figure 2. In a first step, a single monolayer is taken from the experimental crystal structure. Vacancies are created to enhance the flexibility of the system (approximately 30%). A short dynamic simulation is performed. Assuming a kinetically controlled process, the last frame is chosen, which does not necessarily correspond to a completely equilibrated configuration. The meanwhile disordered molecules are then frozen. In the next step, a second crystal slice with vacancies is placed several angstroms above the frozen molecules. A harmonic potential is applied to mimic adhesion forces between the newly added molecules (of the second slice) and the deposited film, i.e., the frozen slice. The molecules of the second slice are then accelerated towards the frozen slice in a second MD simulation. Thereupon, all positions of the newly deposited molecules are frozen again. This cycle is repeated for the p-type semiconducting molecules four to five times. In a similar procedure, the fullerene layers are deposited on top of the generated film of p-type semiconducting molecules using the same iterative procedure. In order to ensure a more complete sampling of the conformational space, the procedure is conducted for slices taken from the three basic crystallographic planes of the p-type semiconductor crystal structure ( (001), (010), (100) ). These slices are identical in the cubic face-centered crystal structure of fullerene. 96 The horizontal extensions of the crystal slices are determined as the least common multiple of the unit cell dimensions of the p-type semiconductor and the fullerene, respectively. This should allow for a more complete sampling of the conformational space as well. Finally, we obtain three different interface structures for each investigated p-type semiconducting molecule (Figure 2).

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Figure 2: Visualization of the chosen approach to generate interface structures with a differing degree of disorder. The starting point is a single crystal slice: It is viewed from above in the first panel and from the side in the second panel. Successive MD simulations are conducted to construct the final structure of the interface. For more information see text. Theoretical approaches to characterize the processes To calculate the energies of relevant exciton, polaron, and charge-transfer states in the vicinity of the interface, a large number of calculations have to be performed. Furthermore, the amorphous environment needs to be taken into account because it critically influences especially the energies of polaron and charge-transfer states.84,77 In view of this considerable computational demand, dimers are used as the quantum-mechanical systems, which are embedded into a dielectric continuum to model the thin-film environment. This approach neglects the polarization of the environment.


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It is usually assumed that charge carriers and excitons in disordered organic semiconductors are delocalized over a few monomers.97 However, most atomistic computational approaches to simulate processes in large amorphous systems rely on monomer-based calculations, and only a limited number of investigations focus on larger aggregates (see for example 19,21,98,99,100

). In this work, we use the dimer approach because in contrast to monomer-based

approaches, taking dimers as the quantum-mechanical system has the advantage of including intermolecular interactions on a quantum-mechanical level. Moreover, it allows for the delocalization of excitonic or charged states over two monomer units so that trapping effects induced by motions of the monomers with respect to each other are taken into account. Furthermore, in large systems, dimer computations are computationally feasible as opposed to the treatment of larger aggregates.21,101 For the interfaces, three types of nonequivalent dimers can be distinguished as visualized in Figure 3: dimers composed of two p-type semiconducting molecules, dimers composed of two fullerenes, and heterodimers composed of one p-type semiconducting molecule and one fullerene. While singlets excitons and charge transport energies are calculated with the homodimers composed of either fullerenes or p-type semiconducting molecules, heterodimers are used to calculate charge-transfer states and interfacial excitations, i.e., excited donors directly located at the interface next to a ground-state fullerene or vice versa. All next-neighbor dimers are cut out from the generated interface structures based on a distance criterion relying on the centers of mass because particularly Dexter-type delocalization in charge-transfer and charge-transport states is extremely distancedependent.102 Distances are provided in the Supporting Information (Table S1). Ground-state monomer geometries optimized with high-level ab initio methods are superimposed onto the dimer geometries obtained from the dynamic simulations described above. For intramolecular polaron or exciton relaxations, the optimized excited-state or open-shell monomer geometries for the dimers were used. The procedure of superimposing ab initio monomer geometries on dimers in arrangements that are determined with force-field based dynamic simulations is necessary because force-field monomer geometries, especially those of compounds like merocyanines or triphenylamines with very complex electronic structures,103 are often too inaccurate for subsequent ab initio single-point calculations of excitation energies and coupling parameters. This superposition approach neglects the influence of intermolecular interactions on monomer geometries. 11 ACS Paragon Plus Environment


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All state energies are referenced to the neutral singlet ground state of the interface (i.e., the monomer ground-state reorganization energy is added if excited- or charged-state geometries are used in the superposition) (Figure 3).

Figure 3: QM system of the dimer method applied to the generated interfaces. A singlet exciton may form a charge-transfer state at the interface (Step 3, exciton dissociation, see above), i.e., an initially bound geminate electron-hole pair. The energy of such a charge-transfer state is approximately calculated from the ionization potential of the underlying heterodimer 𝐼𝑃𝑝−𝑡𝑦𝑝𝑒 (ℎ𝑒𝑡𝑒𝑟𝑜𝑑𝑖𝑚𝑒𝑟) and the electron affinity of the same heterodimer 𝐸𝐴𝑛−𝑡𝑦𝑝𝑒 (ℎ𝑒𝑡𝑒𝑟𝑜𝑑𝑖𝑚𝑒𝑟). Furthermore, the Coulomb attraction

𝑒2 4𝜋𝜀0 𝜀|𝑟⃗|

of the

geminate electron-hole pair is included, which is computed assuming that the electron is fully localized on the fullerene while the hole is entirely situated on the donor moiety. The distance |𝑟⃗| is the distance between the centers of mass of the fullerene and the p-type semiconductor.

This approximate scheme to calculate interfacial charge-transfer is further described and evaluated in the Supporting Information by means of constrained density functional theory (c-DFT).104 𝑒2

𝐸 𝑐ℎ𝑎𝑟𝑔𝑒 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 = 𝐼𝑃𝑝−𝑡𝑦𝑝𝑒 (ℎ𝑒𝑡𝑒𝑟𝑜𝑑𝑖𝑚𝑒𝑟) − 𝐸𝐴𝑛−𝑡𝑦𝑝𝑒 (ℎ𝑒𝑡𝑒𝑟𝑜𝑑𝑖𝑚𝑒𝑟) − 4𝜋𝜀

0 𝜀|𝑟⃗|

(1)

The interfacial charge-transfer state may eventually dissociate into an independent electron and a hole (Step 4, charge separation, see above). The energies of the charge-transport states for the hole and the electron are significantly influenced by their mutual Coulomb binding energy, which has to be included in the calculations. 97,77,14 Therefore, in contrast to the energy 12 ACS Paragon Plus Environment

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calculations of excitons and charge-transfer states, for which dimers are the basis entities, a pair of dimers (Figure 4, black circles on the left-hand side; the black crosses mark the positions of the charges) is used to calculate the charge transport energies of geminate electron-hole pairs moving away from the interface. For an electron-hole pair situated on a pair of dimers with the negative charge located on a fullerene dimer and the positive charge localized on a dimer of p-type semiconducting molecules (Figure 4), the energy 𝐸 𝑐ℎ𝑎𝑟𝑔𝑒 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 can be calculated from the electron affinity of the fullerene dimer 𝐸𝐴𝑛−𝑡𝑦𝑝𝑒 (𝑓𝑢𝑙𝑙𝑒𝑟𝑒𝑛𝑒 𝑑𝑖𝑚𝑒𝑟), the ionization potential of p-type molecular dimer 𝐼𝑃𝑝−𝑡𝑦𝑝𝑒 (𝑝 − 𝑡𝑦𝑝𝑒 𝑑𝑖𝑚𝑒𝑟), and the Coulomb binding energy between them

𝑒2 4𝜋𝜀0𝜀|𝑟⃗|

. The distance |𝑟⃗| entering into the Coulomb binding

energy is approximated by the distance between the centers of mass of the two dimers. 𝑒2

𝐸 𝑐ℎ𝑎𝑟𝑔𝑒 𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡 = 𝐼𝑃𝑝−𝑡𝑦𝑝𝑒 (𝑝 − 𝑡𝑦𝑝𝑒 𝑑𝑖𝑚𝑒𝑟) − 𝐸𝐴𝑛−𝑡𝑦𝑝𝑒 (𝑓𝑢𝑙𝑙𝑒𝑟𝑒𝑛𝑒 𝑑𝑖𝑚𝑒𝑟) − 4𝜋𝜀

0 𝜀|𝑟⃗|

(2)

Please note that due to the large number of dark states of fullerene C60, the charge-transfer state cannot be directly computed in an excited-state calculation. For a pairwise selection of the dimers, further approximations had to be introduced. This is shown in Figure 4. Firstly, we considered only those geminate electron-hole pairs where the distances of the electron and the hole to their joint origin at the interface (i.e., the heterodimer where the charge transfer took place) are approximately equal. Secondly, we are mostly interested in charge carrier diffusion in the direction perpendicular to the interface. Therefore, we select only those pairs in which both dimers have similar perpendicular displacements from the interface (e.g., dimers situated in the two equally colored regions in Figure 4, left-hand side). The interface is defined as the center plane between the center of mass of all fullerenes and the center of mass of all p-type semiconducting molecules.



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Figure 4: Description how the dimers are selected (left-hand side) and examples (right-hand side). Please note that the coordinates were rotated compared to Figure 3. For more information see text. Even for polar substances, interactions in amorphous organic thin films can be very efficiently and accurately taken into account by continuum solvation approaches using effective epsilon values.77,105,106,107 It should be, however, emphasized that such continuum solvation approaches do not include any polarization of the environment. In the case of the interfaces, three different regions exist with different molecular polarizabilities and (supposedly) different effective epsilon values: the bulk phase of the p-type organic semiconductor, the bulk fullerene phase, and the adjacencies of the interface. We use measured permittivities of fullerene108 and molecular organic semiconductors. Unknown values are approximated by the permittivities of known, very similar substances. The values employed to approximate the isotropic bulk interactions among the p-type semiconducting molecules can be found in the Supporting Information (Table S2). In contrast to the two bulk phases, the direct adjacencies of the interface are characterized by variations in the epsilon value due to the presence of molecules with different polarizability77 and the less dense packing,94 making an adequate description by a single permittivity value impossible. Meanwhile, the energy of the interfacial charge-transfer states can be very sensitive to the choice of the epsilon value.77,109 In order to include the varying environment while maintaining the computational efficiency of a continuum solvation approach, we use a two-fold procedure demonstrated in Figure 5. In a first step, we employ the average value of the effective epsilons of the two adjacent bulk phases. Interactions across the interface and from outside of the electric double layer, such 14 ACS Paragon Plus Environment

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as the Coulomb binding energy of geminate electron-hole pairs in particular, are calculated using the average epsilon value as well. Please note, however, that whenever the electron and the hole are located on adjacent dimers, this epsilon value is decreased because no shielding takes place. In a second step, we furthermore include missing effects like ground-state charge transfer, differing degrees of polarization in the adjacent phases, and the anisotropic distributions of molecular multipole moments by a mean electric field perpendicular to the interfacial plane. The value for the electric field is calculated starting from an electrostatic potential fit (ESP fit) of a heterodimer situated at the interface. This yields the dipole moment from which, via classical electrochemical considerations110 (see Supporting Information, Table S3 – Table S4), a reasonable estimation of the electric field strength can be obtained. The influence of the electric field on the interfacial excitation energies is analyzed for representative examples in the Supporting Information (Tables S8-S11). Among others, Volpi et al. emphasized the influence of a static electric field on charge transport in disordered organic semiconductors and on charge separation in the anthracene::C60 model system.111,85,112 The electric mean field strength employed in the present work completely ignores the considerable variations of the interfacial electric fields, which were shown to sometimes inverse their directions86 and critically depend on the morphology as analyzed by Castet and Cornil et al. 113,114 In combination with the averaged permittivity, however, the approach constitutes a computationally very efficient and intuitive route to model the influence of the varying environment at the interface. The electric field is only employed to calculate the interfacial excitation energies, but it is neglected when computing the polaronic and the interfacial charge-transfer states. For the polaronic states, this seems to be justified because the dipole moment of the polaronic electron-hole pair is considerably larger than the interfacial electric dipole moment. This difference results from both larger charges of the electron-hole dipole moment compared with the interfacial dipole moment, and from a larger distance between these charges. We furthermore neglect the interfacial electric field when calculating the interfacial chargetransfer states using Eq. (1) because the effects resulting in the interfacial dipole moments and hence in the electric field are already partially included in the underlying heterodimer computations. 15 ACS Paragon Plus Environment


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Figure 5: Illustration of the approach to describe the dielectric situation at the interface. Computational Details All molecular dynamic simulations for the construction of the interfaces were performed with the Tinker program package115 using a revised version of the OPLS-AA force field (see Supporting Information, Figure S1, Table S5 – Table S7).116,117 An NPT-ensemble was used with a pressure of 1 bar. No periodic boundary conditions were employed. The time step was set to 1.0 fs and the simulations were run for 0.1 ns at 500K. To speed up calculations, a van-derWaals cutoff of 12 Å and an electrostatic cutoff of 16 Å were used. All monomer ground and excited states were optimized at the SCS-CC2118,119/cc-pVDZ120 level of theory. The anionic and cationic monomer geometries were optimized with ωB97X-D121/ccpVDZ. Both methods were beforehand carefully benchmarked. 103 Electron correlation phenomena that are decisive for correct structures of many of the compounds in Fig. 1 are best reproduced by SCS-CC2.103 Moreover, SCS-CC2 is also most suitable for excited-state geometries, most notably for the excited-state inversion of the conjugation pattern in merocyanines and for the excited-state twisting in triphenylamine-based compounds.122 Due to the considerable spin contamination of the HF reference, SCS-CC2 cannot, however, be used for open-shell systems. Further benchmark calculations on cationic systems revealed that ωB97X-D yields rather accurate open-shell geometries,123 which is therefore used in the following. 16 ACS Paragon Plus Environment

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Ab initio ground-state geometries are used to calculate all vertical excitonic, charge-transfer, and polaronic states. Optimized excited-state geometries are employed in calculations on relaxed excitonic states. The merocyanine MD353 was predicted to undergo an excited-state torsion disabled by steric strain in the thin film. 107 Therefore, instead of using the optimized twisted gas-phase excited-state geometry, an artificially untwisted but otherwise unchanged SCS-CC2 excited-state geometry is employed to calculate relaxed excitonic energies. Optimized charged geometries are used to compute relaxed charge-transfer and polaronic states (see also Table 1). Excitation energies were obtained with ZINDO,124,125,126 which was demonstrated to be very reliable for neutral excitations.103 Ground-state charge-transfer states of the heterodimers (Eq. 1) and the charge transport energies for geminate electron-hole pairs (Eq. 2) were obtained using RI-BLYP-D3127,128, 129,130,131/cc-pVDZ along with the MARIJ approximation132 to make the calculations computationally affordable and to eliminate the effects of spin contamination. Please note that the fullerene possesses a threefold degenerate LUMO so that the negatively charged fullerene dimer as an open-shell species is very prone to spin contamination. Moreover, since electron affinities and ionization potentials are calculated from energy differences between differently charged states of the dimers and not from orbital energies, the underestimation of these quantities by BLYP should be less pronounced.123 All SCS-CC2 and RI-BLYP calculations were conducted using the Turbomole program package.133 All ωB97X-D and ZINDO calculations were performed using the Gaussian program package.134 Depending on the program package, either the COSMO135 or the IEFPCM continuum solvation model136 was used. RESULTS AND DISCUSSION In this section, we present our results and discuss resulting structure-property relationships as well as a comparison of the dimer- and the monomer-based approach. After a short outline of the general features of the calculated state energies, the discussion is organized according to the types of loss mechanisms. After addressing exciton traps in a first step, we turn to charge traps. Subsequently, we focus on interfacial trap states and investigate the influence of molecular orientation, molecular size, and polarity on energies of these states. For the



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discussion we use selected examples, while all other results (further molecules and/or crystallographic planes) are given in the Supporting Information (Figure S2 – Figure S24). General description of the energetic profiles, Comparison dimer vs. monomer approach To discuss the general features of the calculated energetic profiles, i.e., of the relative energetic positions of the states, we begin with the anthracene::fullerene interface because it is simpler than the other systems. For this interface, we briefly discuss the mechanism of exciton breakup, the importance of triplet states for the energy landscapes, and compare results from our dimer approach with those obtained from the monomer approach. The energetic profile, i.e., the relative energetic positions of exciton, charge, and chargetransfer states, for the anthracene::fullerene interface (generated using the b-ccrystallographic plane of the anthracene crystal structure) is shown in Figure 6 (upper panel). The lower panel gives the corresponding values obtained with a monomer approach. The horizontal axis displays the perpendicular displacement from the interface. The interfacial plane is situated at about -7 Å. The simulated cell has a thickness of approximately 50 Å, which is in the order of typical exciton diffusion lengths in molecular organic semiconductors. 137 Its horizontal dimensions depend on the system (see Supporting Information, Table S8). For this system the size is 45 Å times 45 Å. Therefore, the simulation cells are sufficiently large to include all important processes. The vertical axis yields the state energies in eV. All symbols are explained in Table 1. Please note that we employ the expressions “exciton” (“polaron”) to designate both vertical and relaxed excitations (charges) in the semiconducting layers although vertical excitation (ionization) is not accompanied by a considerably lattice relaxation (in contrast to what these expressions might suggest). Table 1: Symbols used to designate different states in the following figures. If not mentioned otherwise, the symbols refer to states of the p-type semiconducting molecules. For a State

Symbol

bulk excitations bulk exciton (vertical) bulk exciton (relaxed) interfacial excitations 18 ACS Paragon Plus Environment

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interfacial exciton (vertical) interfacial exciton (=donor) (relaxed) interfacial excited fullerene polarons polaron (vertical) polaron (relaxed) interfacial charge transfer charge-transfer state (vertical) charge-transfer state (relaxed)

An incident exciton created by photon absorption in the anthracene layer diffuses towards the interface (right-hand side, Figure 6, upper panel). Vertical singlet excitation energies are shown as dark red circles (“bulk exciton (vertical)”, Table 1). Please note that the x-coordinates of the points correspond to the positions of the centers of mass of dimers. According to Marcus theory, the amount of reorganization taking place after excitation strongly influences the efficiency of exciton transport. In the framework of the dimer approach, three different relaxation mechanisms exist for an exciton. First of all, intramolecular relaxation, which arises from the deformation of the single monomers, leads to an energy loss of ~ 0.1 eV (red circles, Figure 6, “bulk exciton (relaxed)”, upper panel, see also Table 1). This relaxation is also taken into account in the monomer approach (Figure 6, red circles, lower panel). Secondly, the dimer approach includes the relaxation of an exciton from the upper to the lower Frenkel state. This amount of relaxation is given by the Davydov splitting, represented by the vertical red bars on all excitonic state energies. Thirdly, while excitonic states obtained from a monomer-based model correspond to two flat lines (dark red/red points, Figure 6, lower panel, see also Table 1) separated by the reorganization energy, relaxed excitonic state energies of the lowest Frenkel state calculated with the dimer approach cover a range of ~0.15 eV depending on the dimer structure (Figure 6, upper panel). Taking into account the variations in the second Frenkel state, this energy range approximately doubles (~0.30 eV). These energy variations result from different orientations of the monomers in different dimers. The low-lying states represent trap states because the endothermic hopping process from a low-lying excitonic state to an adjacent higher-lying excitonic state is hardly possible. Hence, the energetic 19 ACS Paragon Plus Environment


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disorder of exciton hopping sites induces a further energetic relaxation of diffusing excitons inexistent in monomer-based approaches as discussed by Bässler et al.97 Upon arriving at the interface, the exciton begins to sense the neighboring fullerenes. Excitonic state energies slightly change (red and dark red bars, Figure 6, “interfacial exciton (vertical)”, “interfacial exciton (relaxed)”, see also Table 1). More importantly, the excitonic state energies spread across a larger energy range (2.80 eV to 3.40 eV). This type of band bending at organic::organic interfaces is in line with the findings of Yost et al., who analyzed the effects of disorder and vacancies on the bands in adjacent organic semiconductors. 84,77 Please note that the monomer approach cannot include band bending (Figure 6, lower panel, red and dark red bars, see also Table 1) apart from the effects of varying electrostatic contributions, which are very weak. Several possible pathways for the incident exciton exist at the interface. On the one hand, the excitation could undergo Förster transfer to the fullerene (grey bars, Figure 6, “excited interfacial fullerene”, see also Table 1). The final state of such an excitation energy transfer process corresponds to an excited fullerene next to a ground-state anthracene. On the other hand, the exciton could dissociate into an interfacial charge transfer state being localized on an anthracene (+) and a fullerene (-) (white bars, Figure 6, “charge-transfer state (vertical)”, see also Table 1). These states also relax leading to the “charge transfer states (relaxed)” (black bars, Figure 6, see also Table 1). For solar cells, it is important that populating the charge-transfer states is efficient, since this is a prerequisite for later-on charge separation. From the thermodynamic point of view,14 this efficiency depends on the relative energies of the various states. In Figure 6, the chargetransfers state are energetically lower than the state resulting from the excitation energy transfer process (white bars compared to grey bars, Figure 6, both panels). This is important to obtain exciton dissociation. Even if the excitation energy transfer step is kinetically favored as observed for instance for an oligophenylenevinylene::fullerene-derivative dyad, 138 it would eventually end in a charge-transfer state via hole back transfer from the fullerene to the anthracene phase as long as this charge-transfer state is energetically lowest.138 If, however, the charge-transfer state is energetically higher than the excitation energy transfer process, exciton dissociation cannot occur to a high extent.139 20 ACS Paragon Plus Environment

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In contrast to the results obtained with dimers, charge-transfer states in monomer-based calculations include only the varying Coulomb attraction determined by the distance between the electron located on a fullerene and the hole located on an anthracene molecule. Thus, monomer-derived interfacial charge-transfer states feature an exact r-1 dependence (Figure 6, lower panel, black and white bars). The energetic distribution of charge-transfer states obtained from calculations on dimers leads to a considerably higher energetic disorder at the organic interface (Figure 6, upper panel, black and white bars). This demonstrates the significance of the inclusion of delocalization effects.



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DIMER

MONOMER

Figure 6: Energetic profile for the anthracene::fullerene interface (b-c-plane). Upper panel: results with the dimer method, i.e., a dimer is the basic system. Lower panel: results with a monomer-based approach. Solid lines serve as a guide to the eye. For an explanation of the symbols see Table 1. Please note that the charge-transfer states in the monomer approach were calculated from the ionization potential of a single anthracene, the electron affinity of a 22 ACS Paragon Plus Environment

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single fullerene, and a continuously varying Coulomb attraction according to Eq. 1. This leads to artificially high binding energies for hypothetically small electron-hole separations. Potentially, the interfacial charge-transfer state dissociates and charges – an electron and a hole – populate the charge transport states. Vertically ionized states are shown as black circles in Figure 6 (“polaron(+/-)-vertical”, see Table 1) while relaxed ionized states are depicted as black squares in Figure 6 (“polaron(+/-)-relaxed”, see Table 1). The two types of ionized states are separated by the amount of charge reorganization energy. In the vicinity of the interface, the polarons still feel their mutual Coulomb binding energy, which reduces with an r -1dependence when the polarons diffuse away from the interface. The polaronic states (Figure 6, upper panel, black circles and squares) take on a similar r-1-shape and become a flat line for large distances from the interface. It represents the limit where both charges start to escape from one another. After this, the polarons diffuse to the electrodes and charge recollection will eventually complete the light-to-electricity conversion. The energetic disorder of the polaron levels arising from variations of the ionization potentials and electron affinities as functions of the mutual orientation of the monomers in the dimer can be compared to the straight lines of the monomer-based approach (Figure 6, lower panel). This disorder again hampers the transport because a transfer from a lower-lying to a higher-lying state is strongly suppressed. As discussed above, exciton, charge, and interfacial charge-transfer states with low energies lead to significantly decreased solar cell performances because they act as trap states. It is obvious from Figure 6 that no such trap states exist around the anthracene::fullerene interface. In comparison to other compounds (see below), exciton and polaron bands are rather narrow and also interfacial charge-transfer states cover only a rather small energy range. The fact that anthracene::fullerene solar cells are nowadays inexistent must be due to other reasons such as the poor overlap of the anthracene absorption with the solar spectrum or the high reactivity of photoexcited anthracenes to give cycloaddition products.140 To get more insight, the mechanism of charge generation and the importance of triplet states are discussed. Charge generation in OSC can occur either via a cold or a hot exciton breakup mechanism. In the cold mechanism, relaxed (=cold) charge-transfer excitons dissociate into separate charges. According to the hot exciton dissociation mechanism, a vibrationally/electronically excited 23 ACS Paragon Plus Environment


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and potentially very delocalized charge transfer exciton with excess energy dissociates.77,14 Many experimental and theoretical investigations were dedicated to this subject. 141,142,143 From the energetic profiles, we can analyze whether cold exciton transfer is in principle feasible. Figure 6 shows that for the anthracene::fullerene system, the relaxed charge-transfer states (black bars) are energetically rather stable due to the significant Coulomb binding energy, which is screened only to a small extent because of the low dielectric constant of the organic medium. The strong Coulomb binding energy also results because the molecular structure of anthracene leads to an average distance of only about 7 Å between the electron and the hole. This value is in coincidence with experimental values ranging from 5 Å to 10 Å. 14 Consequently, the interfacial charge-transfer states at the anthracene::fullerene interface (black bars, see Table 1) are lower in energy than the charge-separated states (polaron states, black circles and squares, see Table 1) by an average value of 0.2 eV to 0.5 eV. This largely exceeds the available thermal energy so that a relaxed interfacial charge-transfer exciton could not overcome this barrier. Hence, according to our computations, the cold exciton transfer mechanism cannot lead to charge separation for the anthracene-fullerene system. The light-to-electrical-power-conversion in OSC must be an energetic down-hill process. This means that the charge-separated state must be lower in energy than the singlet excitons in the anthracene and/or the fullerene phase, but also lower than the corresponding triplet states, which represent other traps.14 The triplet energy of fullerene amounts to 1.6 eV. 144 From Figure 6, it is obvious that the charge-separated states are considerably higher in energy due to the high ionization potential of anthracene 26. Hence, fullerene triplet formation in the acceptor phase should be another thermodynamic sink of the anthracene::fullerene system. The combined effects of possible triplet formation and the strong Coulomb binding energy in combination with the experimentally characterized poor overlap of the anthracene absorption with the solar spectrum (see above) along with other aspects might explain why no efficient anthracene-based OSCs are known. A comparison between the energetic profiles of the anthracene::fullerene system and the related rubrene::fullerene system (see Supporting Information, Figure S13 – Figure S15) offers an explanation why rubrene::fullerene OSCs show significantly improved performances.39 Mainly, this could result from the better overlap of the absorption spectrum of rubrene with the solar spectrum. Additionally, two supplementary effects favor the rubrene-fullerene 24 ACS Paragon Plus Environment

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system. (1) The ionization potential of rubrene is considerably lower. Charge-separated states are lower than the fullerene triplet state so that fullerene triplet states do not constitute trap states. (2) Rubrene is larger than anthracene and possesses bulky phenyl substituents. This increases the separation of electrons and holes in an interfacial charge-transfer state reducing the Coulomb binding energy. Due to the resulting higher energies of interfacial charge-transfer states, they can dissociate more easily and even a cold exciton breakup becomes possible. Such effects of side chains on the open-circuit voltage, possibly via the position of interfacial charge-transfer states, have been experimentally found by You et al.145 Furthermore, it was found that the energetic positions of the charge-transfer states at the rubrene::fullerene interface depend on the crystallographic orientation of the rubrene phase with respect to the fullerene surface (see Supporting Information, Figure S13 – Figure S15). Exciton traps in the p-type semiconducting layer A special exciton trapping mechanism, i.e., exciton self-trapping, arises in DIP layers. DIP::fullerene OSCs have shown high efficiencies but only if the DIP layer is crystalline.45 This can be traced back to surprisingly long exciton diffusion lengths which exceed 60-70nm in DIP crystals.146,21 In contrast, in PTCDA crystals (perylenetetracarboxylic dianhydride), the exciton diffusion lengths are considerably shorter (22nm) although both molecules are very similar in terms of size and electronic properties.21 In contrast the corresponding computations for DIP agree quite nicely with the experimental data. 21 A monomer-based computation of the exciton diffusion lengths in PTCDA strongly overestimates the exciton diffusion, indicating that some effects are missing.21 The underlying reason for the differences between DIP and PTCDA is the orientation of the molecules in the crystal structure. In the dimer approach, the orientation in PTCDA allows for a relaxation of the exciton from the initially populated upper Frenkel state to the lower Frenkel state. For DIP, this relaxation channel is suppressed due to the steric effects of the crystal structure. In view of this study, the strong decrease of the exciton diffusion length in amorphous DIP 146 could result because a less dense packing permits the dimer relaxation taking place in PTCDA but being disabled in DIP due to the crystal packing. However, Figure 7 shows that trap states already arise because in amorphous materials, the individual molecules of the dimer adopt various orientations. This leads to pronounced variations in the energetic positions of the excited states because ground-state energies and excitation energies strongly vary as a 25 ACS Paragon Plus Environment


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function of the dimer geometry. When hopping to such a trap state, the exciton relaxes by about 0.3 eV in energy (low-lying light red circles in Figure 7 compared to the average of the states, light red line). The exact value depends on the structure of the dimer, but it is considerably larger than the available thermal energy. Therefore, the exciton self-trapping constitutes a potential loss mechanism in amorphous DIP phases. Please note that as discussed above for anthracene, the intramolecular relaxation (dark red circles, light red circles in Figure 7) and the relaxation from the upper to the lower Frenkel state constitute additional relaxation channels in DIP thin films.

Figure 7: Energetic profile along the DIP::fullerene interface (a-c-crystallographic plane). The DIP molecules are orientated almost flat and face-on on top of the fullerene phase – a lying conformation. Please note that the Davydov splitting is depicted as small bars. For an explanation of the symbols see Table 1.


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Apart from exciton-self-trapping, other exciton trapping mechanisms exist in triphenylaminebased semiconductors. We already mentioned the considerations leading to the development of different triphenylamine-based compounds for OSCs. To investigate the efficiencydetermining processes for them in more detail, we discuss them for two model compounds, TBA and TAM, in the following. While TBA represents a triphenylamine-based dye containing only conjugating phenyl substituents, TAM, a methoxy-substituted triarylamine, possesses electron-donating anisyl substituents. A considerable number of exciton traps is also found in the bulk phase of the TAM, an intramolecular charge-transfer compound (see energetically low-lying red circles in Figure 8). Our calculations suggest that these exciton traps are formed by intermolecular charge-transfer states. These intermolecular charge-transfer states can arise in rather large molecules where the donating and the accepting moieties are sufficiently separated. Then, in a thin film, distances between donating and accepting groups located on different molecules might become smaller than the intramolecular distances between the donor and the acceptor. In such a case, the intermolecular charge-transfer complex (excimer) can drop energetically below the intramolecular charge-transfer state. The relationship between intramolecular charge-transfer emission and excimer emission has been experimentally observed and investigated in different donor-acceptor dyes (see for example 147,148

). Please note that the formation of such excimers in the bulk phase of TAM is further

enhanced by the photoinduced intramolecular twisting, a special characteristic of this molecule. The relaxed excited-state geometry of the substituted triphenylamine compound was experimentally and computationally shown to be highly twisted (see Introduction). As can be seen from Figure 8, more exciton traps exist for relaxed exciton states (light red circles) with the highly twisted monomer geometry than for the vertical exciton states (dark red circles). This indicates that the photoinduced twisting favors excimer formation.



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Figure 8: TAM::Fullerene interface (a-b-crystallographic plane). Please note the existence of some energetically low-lying relaxed singlet excitons. For an explanation of the symbols see Table 1. An advantage of TAM is the rather narrow energy range covered by the polaron states (Figure 8, black squares and circles). Their small energetic spread becomes especially evident upon comparison with the polaronic states in DIP (Figure 7). The spread of the polaronic states is even smaller for TBA suggesting very efficient charge transport (black circles and squares, Figure 9). Also for this compound, exciton traps from intermolecular charge-transfer states presumably limit the efficiency of exciton diffusion (red circles, Figure 9). This is well in line with the fact that few OSCs based on triphenylamines exist52 and that triphenylamine-based molecules are widely used as hole conductors.49,50 It is of interest to note that these features seem to be independent of the crystallographic orientation (see Supporting Information for additional crystallographic planes, Figure S21 – Figure S24). This is in accordance with a large variety of experimental findings that thin films composed of triphenylamine-based compounds possess isotropic and homogeneous properties.49,50


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Figure 9: TBA::fullerene interface (a-c-crystallographic plane). For an explanation of the symbols see Table 1. High excitation energies leading to a small overlap with the solar spectrum and low-lying charge-transfer interfacial states (black bars, Figure 8 and 9) resulting in small open-circuit voltages149 are drawbacks of triphenylamine-based OSCs. To get materials with improved properties, electron-withdrawing groups were attached to the triphenylamine moiety. This should induce bathochromic shifts in the absorption spectra and increase the ionization potential. The latter should give rise to higher-lying interfacial charge-transfer states because their energetic position correlates with the ionization potential of the p-type semiconductor (see anthracene::fullerene system and Eq. 1). A comparison of Figures 8 and 9 to the energetic profile of TAA (Supporting Information, Figure S18 – Figure S20), an aldehyde-substituted triarylamine, delivers a theoretical foundation for this experimental guideline. In comparison to TBA, the energy of the charge-transfer states for the TAA compound increases by about 0.5 eV although the compound is smaller. The smaller size primarily decreases the charge-transfer state energy due to an increased Coulomb binding energy. However, this decrease is apparently overcompensated by the increase of the ionization potential. Except for this difference, the overall energy landscape of the TAA::fullerene interface qualitatively agrees with those of the other triphenylamine-based compounds.



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Figure 10: Squaraine::fullerene interface (a-b-crystallographic plane). Please note that a singlet exciton in the squaraine bulk phase is energetically below a fullerene singlet exciton. For an explanation of the symbols see Table 1. Polaron traps in the p-type semiconducting layer The energetics of the squaraine::fullerene system is summarized in Figure 10. The exciton bands in the squaraine are extremely narrow (red circles, Figure 10). This means that the exciton diffusion is only insignificantly affected by traps. All dimer configurations are almost equal so that little energetic disorder exists for excitons. Barely any intramolecular relaxation occurs. This results because the rigid electron-rich squaraine core is responsible for the excitations (see Introduction).58 Hence the photoinduced reorganization is small. Our results are in accordance with experimentally measured narrow and redshifted absorption bands due to compact J-aggregate formation in thin films.62,64 Moreover, it was experimentally found that the squaraine bulk phase is ideally suited for exciton transport, in line with the results of our computations.62 In contrast to the exciton transport levels of the squaraine, the corresponding polaronic states (black squares and circles) are energetically broader. This suggests poor hole mobilities, which have indeed been experimentally detected.57,64 In our calculations, the large energy range covered by the polaronic states arises from electrostatic interactions between the ionized molecules and the partial charges localized on adjacent squaraic acid cores. Small 30 ACS Paragon Plus Environment

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displacements of the squaraine molecules in the J-aggregate with respect to each other, occurring in the MDs and barely affecting excitation energies, can lead to both favorable and unfavorable electrostatic interactions of a later-on ionized molecule with its environment. Interfacial charge transfer traps The relationship between the energetic positions of the interfacial charge-transfer states and the

open-circuit

voltage

has

thoroughly

been

discussed

in

a

number

of

investigations.149,150,22,151,152 The influence of individual molecular properties like the polarity or the orientation on the interfacial charge-transfer states has been previously investigated.77,84 However, to the best of our knowledge, no comprehensive study exists taking into account their combination and interplay. We investigate the influence of molecular orientation, molecular polarity and molecular size on the overall properties at the interface to obtain a clear understanding of the factors influencing the positions of the interfacial chargetransfer states.

Figure 11: Energetic profile along the DIP::fullerene interface (a-b-crystallographic plane). DIP molecules stand on top of the fullerene phase. Please note the existence of exciton selftrapping sites in the bulk DIP phase. For an explanation of the symbols see Table 1. Experimental studies of – among others – Brütting et al.,153 of Barrena et al.,154 and of Chen et al.155 have focused on the influence of a standing/lying DIP orientation at organic::organic 31 ACS Paragon Plus Environment


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interfaces on the charge-transfer rates and energies. Although a lying orientation allows for larger couplings and rates according to Brédas et al. for the pentacene::fullerene interface,80 the open-circuit voltage was found to be higher for a standing orientation. Figure 11 shows the energetic profile for the standing orientation of DIP on fullerene, which can be compared to the lying orientation in Figure 7. The energies of the lowest interfacial charge-transfer states amount to about 1.4 eV (black bars, Figure 11). For the lying orientation of the DIP molecules on top of the fullerene phase (Figure 7), a value of approximately 1.2 eV was computed. The decrease of 0.2 eV of the charge-transfer states is in line with the decrease of the open-circuit voltage by a similar amount (~ 0.2 eV) as observed by Brütting et al.153 From a theoretical point of view, the stabilization of the interfacial charge-transfer state when going from the standing to the lying orientation of the DIP molecule is due to (1) an increased ground-state charge transfer contribution due to larger couplings and (2) to an increased Coulomb binding energy of the geminate electron-hole pair due to a smaller distance between the electron situated on the fullerene and the hole located on the DIP molecule lying on top of the fullerene. The distances between the charges in the initially formed interfacial charge-transfer states depend on the molecular size. A larger molecular size will lead to larger distances between the charges, which reduces the Coulomb binding energy and results in higher charge-transfer energies (see Eq. 1). The influence of molecular size was already demonstrated in Figure 10 because the large linear squaraine molecules ensure significant electron-hole distances in the charge-transfer states. Despite the rather low ionization potential of the squaraine molecule, the charge-transfer energies (black bars) amount to approximately 1 eV, i.e., higher compared to the triphenylamine-based compounds (TBA: 0.9 eV, TAM: 0.6 eV), which are smaller due to their bulky structure. Moreover, the charge-transfer states of the squaraines are not systematically lower than the polaronic states (black squares and circles), which means that cold exciton dissociation could be possible.


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Figure 12: Energetic profile of the diketopyrrolopyrrole::fullerene interface (a-bcrystallographic plane). For an explanation of the symbols see Table 1. Similar effects are demonstrated for the diketopyrrolopyrrole::fullerene interface in Figure 12. It can be seen that an almost isoenergetic electron-transfer process from the interfacial charge-transfer state (black bars) to the charge-separated state (black circles and squares) is possible. This results because the electron-hole separation on the

interfacial

diketopyrrolopyrrole-fullerene heterodimer already amounts to an average value of 14 Å. In comparison to the anthracene::fullerene interface with a considerably shorter average distance of 7 Å, this reduces the Coulomb binding energy by 50%. Moreover, for the diketopyrrolopyrrole, both exciton (red circles) and polaron levels (black circles and squares) are narrow, owing to little structural disorder between the rigid diketopyrrolopyrrole core moieties. Molecular polarity significantly influences the energies of the interfacial charge-transfer states as well. Although the highly polar merocyanines’ structures differ significantly from traditional molecular semiconductors used in OSCs and although the Bässler model predicts low conductivities for polar substances, OSCs based on merocyanines are surprisingly efficient.75,74 This behavior is attributed to the fact that dipolar merocyanines self-assemble already in solution into tightly bound centrosymmetric dimers 156 that also prevail in the majority of known crystal structures.10 Accordingly, the dipolarity vanishes on the supramolecular level of



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a dimer unit. Our calculations highlight another aspect with respect to the efficiencies of merocyanines in OSCs. Vandewal, McGehee, and Neher et al.157 showed that for very well-performing OSCs, the process of charge separation from an interfacial charge-transfer state to separate polarons should be almost isoenergetic. This can occur only if the energies of the interfacial chargetransfer states are high, while the Coulomb attraction within the polaron pair does not change much upon charge separation. Then, these weakly bound charge-transfer states at the interface readily dissociate into separate charges.157 One way to reduce the energetic barrier to a charge-separated state is to reduce the Coulomb binding energy of the electron-hole pair via a high effective epsilon, which efficiently screens the charges. According to Seki et al., this process is further favored if a high effective epsilon in the bulk phase is accompanied by a low effective epsilon at the interface. This favors the separation process because a low epsilon at the interface destabilizes the charge-transfer states representing the starting points of the charge separation process,158 while a high bulk epsilon stabilizes the polaron states compared to the charge-transfer states. Our computations predict both a high dielectric constant ε for the bulk phase and a reduced ε at the interface for merocyanines. In the bulk phase of merocyanines, the effective epsilon was already predicted to be quite high107 and also the polarizable fullerene phase possesses a significant epsilon.108,159 The reduction of ε at the interface is caused by the less dense packing which results from the different shapes of fullerenes in comparison to the p-type semiconductors.


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Figure 13: Energy profiles of the interfaces of two different merocyanines (a-b-crystallographic planes; first panel: HB194, second panel: MD353). As a consequence, for the two merocyanines, the transfer from the charge-transfer state at the interface to the charge-separated state is essentially isoenergetic (black bars vs. black circles and squares in Figure 13) and the polaronic states (black circles and squares in Figure 13) barely show any r-1 dependence. Thus, according to our computations, the charge separation should be very efficient. Moreover, few (MD353) or no (HB194) interfacial chargetransfer states (black bars, Figure 13) are found below the polaron levels (the black circles and 35 ACS Paragon Plus Environment


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squares), i.e., we predict increasing efficiencies for MD353 and HB194. This correlates nicely with the experimentally determined power conversion efficiencies of 0.87% for MD35375 and 2.49% for HB194.9 The charge transport levels (black circles and squares, Figure 13) in the bulk merocyanine phases possess trap states, as it was the case for the squaraine (see above). This is completely in line with the Bässler model on the impact of dipolar disorder for charge migration in disordered organic semiconductors which predicts the existence of charge traps in polar media.97 CONCLUSION In this article, we investigated structure-property relationships of molecular p-type semiconductors in heterojunction with fullerene C 60 employing atomistic simulations of the important processes within OSCs. The simulation includes a model of the solar cell and comprises exciton diffusion, charge-transfer across the interface, charge separation and migration, i.e., all processes except for exciton generation and charge recollection at the electrodes. To elucidate structure-property relationships we include eleven different p-type semiconductors which vary in structural (size, shape) and electronic (polarity, photoinduced behavior, excitation energies, ionization potentials, electron affinities) properties. To keep the amount of data manageable, we focused on thermodynamic properties in this paper while kinetic parameters will be discussed in a subsequent paper. The underlying interface systems used to simulate the processes in OSCs containing amorphous materials are generated in a multistep approach which mimics the coevaporation or spincoating process used experimentally for the generation of OSCs. In contrast to most previous investigations, we apply a dimer approach for the characterization of the various processes. It describes the next-neighbor interaction correctly and includes intra- and – in contrast to the monomer approach – also intermonomer relaxation processes. The underlying quantum-chemical approach seems to be sufficiently accurate because our study is in agreement with known experimental findings, e.g., the phenomenon of exciton self-trapping found in perylene-based dyes,21 high hole conductivities in triphenylamine-based compounds,49,50 efficient exciton transport in squaraines along with a redshifted and narrow absorption,58 excimer formation in donor-acceptor compounds like 36 ACS Paragon Plus Environment

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in acceptor-substituted triphenylamines,147,148 and the dependence of the open-circuit voltage on morphological properties in DIP thin films 153 or on substituents of diketopyrrolopyrroles.160 Table 2: Summary of the importance of the investigated trap mechanisms for the analyzed p-type semiconductors (green bars: no trap states; yellow crosses-bars: few existing trap states; red crosses: considerable amount of deep trap states). compound class

polarity

model compound

aromatic hydrocarbons

no local/no net dipole moments

anthracene DIP

rubrene

triphenylamines/ D-A-D compounds

low polarity no net but local dipole moments

TBA

TAM

TAA intermediate polarity squaraine

diketopyrrolopyrrole

merocyanines

large net dipole moments

HB194

high polarity

MD353

trap states particularities exciton interfacial polaron traps chargetraps transfer traps no functional OSC exciton self-trapping − + − interfacial traps depend on morphology influence of bulky − − − substituents (vs. anthracene) excimer formation: + − − exciton traps isotropic efficient polaron transport excimer formation: + − − exciton traps isotropic efficient polaron transport higher interfacial + − + charge-transfer states due to accepting groups polaron traps in − − + aggregates very efficient exciton transport polaron traps in − − + aggregates isoenergetic charge separation (large size) polaron traps in − − + aggregates isoenergetic charge separation (polarity) polaron traps in − − + aggregates few interfacial trap states (close contact)



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Our study underlines the importance of several loss mechanisms in OSCs and indicates basic structure-property relationships. An overview is given in Table 2. The loss mechanisms can originate from exciton traps in the bulk phase of the p-type semiconductors, from loss processes during the charge separation process at the interface or from trap states in the polaron states during charge transport in the bulk phases. With respect to exciton traps, our calculations indicate that energy losses arising from the intermonomer effects, which are only included in the dimer approach, hamper exciton diffusion more strongly than those resulting from intramonomer effects already included in the monomer-based approaches. It is important to note that in amorphous materials such trap states already result from different orientations of the monomers with respect to each other. Dynamic processes such as excitedstate reorganization, which could be impeded by steric strain, are not necessary for exciton self-trapping in amorphous thin films. Additional traps result from excimer formation in the bulk phases of triphenylamine-based compounds. According to our computations, such traps should limit the efficiencies of OSCs based on molecules with structural motifs similar to the TBA or the TAM compound. They are on the other hand less relevant for dyes forming tight and stacked aggregates, e.g., merocyanines and squaraines. For such molecules, however, polaron traps become an important loss channel because migrating charges are surrounded by a densely-packed stack composed of molecules with large partial charges. For these molecules, mutual Coulomb attraction and repulsion lead to a broad energy distribution of polaron states including deep trap states. Further important loss channels result from interface processes. Only if the interfacial chargetransfer states, created upon exciton dissociation at the interface, are higher in energy than the polaron states, no barrier for charge separation exists. In such cases, both hot and cold exciton breakup can occur. If, however, energetically low-lying charge-transfer states exist at the interface, the efficiency of charge separation should be significantly reduced. Therefore, interfacial charge-transfer states should be high in energy while the polaron states in the vicinity of the interface should be energetically low irrespective of their orientation relative to the interface. The energies of the interfacial charge-transfer states depend on the dielectric properties at the interface, the molecular size, and the morphology. A reduced epsilon at the interface compared to the bulk phase destabilizes the interfacial charge-transfer states. Similarly, large 38 ACS Paragon Plus Environment

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molecules like rubrene or diketopyrrolopyrroles or distinct morphologies like the edge-on orientation of DIP molecules on top of fullerenes lead to increased distances of the electron and the hole initially formed at the interface, reducing the Coulomb binding energy and raising the energy of the charge-transfer states. In contrast to this, small molecules like anthracene or compact bulky triarylamines give rise to small electron-hole separations and consequently strongly bound interfacial charge-transfer states. If in addition to high-lying interfacial charge-transfer states the energies of the polaronic states do not depend on their vertical distance to the interface, charge separation becomes very efficient because it is almost isoenergetic. This is the case for polar and polarizable compounds like merocyanines or diketopyrrolopyrroles where the high effective epsilon of the bulk phases efficiently screens the Coulomb attraction between the electron and the hole. In contrast, in traditional acenes like anthracene or in DIP, the polarons are strongly bound by their mutual Coulomb attraction even if they are already separated by several molecular layers. The resulting strong increase in the energies of the polaron states hampers an efficient charge separation process. Supporting Information Available: threshold values for dimer selection, effective epsilon values of environment, further energetic profiles, details on the interfacial electric fields, constrained DFT calculations, dimensions of the model systems, further computational details, densities of the model systems. This material is available free of charge via the Internet at http://pubs.acs.org

ACKNOWLEDGMENTS We thank the DFG for funding in the framework of the FOR1809, the SPP1355, and the GRK2112. CB thanks the Gaussian technical support for technical assistance.



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