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How the Energetic Landscape in the Mixed Phase of Organic Bulk Heterojunction Solar Cells Evolves with Fullerene Content Sean Sweetnam, Rohit Prasanna, Timothy M. Burke, Jonathan A. Bartelt, and Michael D. McGehee J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00753 • Publication Date (Web): 07 Mar 2016 Downloaded from http://pubs.acs.org on March 16, 2016

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The Journal of Physical Chemistry

How the Energetic Landscape in the Mixed Phase of Organic Bulk Heterojunction Solar Cells Evolves with Fullerene Content Sean Sweetnam, Rohit Prasanna, Timothy M. Burke, Jonathan A. Bartelt, and Michael D. McGehee∗ Materials Science and Engineering Department, Stanford University, 476 Lomita Mall, Stanford, California 94305, United States E-mail: [email protected]

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Abstract Energy levels in the mixed polymer:fullerene phase of three-phase bulk heterojunction solar cells are significantly shifted from their values in the pure materials. These shifts provide an important driving force for separating charge carriers. Through cyclic voltammetry, we measure a gradual shift in the polymer HOMO and fullerene LUMO as a function of blend composition in a model BHJ system that only contains amorphous polymer. The effective band gap of the polymer:fullerene blend varies by up to 300 meV with varying blend composition. The shifts in polymer HOMO and fullerene LUMO can be quantitatively accounted for by the electrostatic potential generated by induced dipoles at the polymer:fullerene interfaces. Remarkably, however, the measured charge transfer state energy and open circuit voltage shift far less.

Introduction Organic photovoltaics are a potential technology for producing low-cost, flexible solar cells that can be rapidly manufactured at large scale. The current state-of-the-art organic solar cells are composed of blends of semiconducting polymers and fullerene derivatives in a morphology that usually includes three phases: a pure polymer phase, a pure fullerene phase, and a mixed phase. 1–4 The molecular heterojunction between polymer and fullerene acts to dissociate excitons formed upon light absorption by providing an energy offset between donor (polymer) and acceptor (fullerene). 5 After the exciton dissociates at the heterojunction, the charge carriers formed remain Coulombically bound to form an interfacial charge transfer (CT) state, with the electron residing in the LUMO of the acceptor and the hole in the HOMO of the donor. The CT state has the opportunity to dissociate and yield free carriers before recombining to the ground state. 6,7 The difference between the energies of the polymer HOMO (or local ionization potential) and fullerene LUMO (local electron affinity) sets an effective band gap for an organic solar cell (Figure 1). The CT state energy Ect is smaller than this effective band gap by the 2


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Coulombic binding energy of the electron and hole forming the CT state (Equation 1). This Ect is the energy required to directly excite an electron from the HOMO of a donor molecule to the LUMO of an acceptor molecule.

Ect = LU M OA − HOM OD − Eb

(1)

Figure 1: Schematic energy diagram of the effective band gap and the Coulombically bound charge transfer state in a three-phase bulk heterojunction solar cell

The polymer HOMO has been observed to shift by hundreds of meV upon being blended with fullerene, compared to its level in a pure polymer film. 8 In semicrystalline polymers such as regioregular Poly(3-hexylthiophene-2,5-diyl) (P3HT), a shift in the polymer HOMO might be expected due to reduced conjugation length resulting from polymer:fullerene mixing. 9 However, even polymers that do not form a crystalline phase, such as regiorandom (RRa) P3HT, exhibit significant shifts in energy levels when blended with fullerene. This indicates that within the amorphous mixed phase, there are shifts in the energy levels that are produced by intermolecular interactions between the polymer and fullerene. In this work, we investigate the origin of these energy level shifts. We perform cyclic voltammetry on a series of blends of RRa-P3HT and PCBM to measure HOMO and LUMO shifts in the amorphous 3



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mixed phase as a function of fullerene loading. We find that the energy levels, and hence the effective band gap (defined as the acceptor LUMO minus the donor HOMO energy) varies by around 300 meV across the blends measured. In spite of the large variation in effective band gap, the charge transfer state energy varies by less than 40 meV, and the open circuit voltage tracks Ect rather than the effective band gap. We develop an electrostatic simulation of the mixed phase and show that the measured energy level shifts can be caused by dipoles at the RRa-P3HT:PCBM interfaces. These dipoles create an electrostatic potential in their vicinity that shifts the molecular energy levels. We explain why these energy level shifts do not result in commensurate shifts in the open circuit voltage and charge transfer state energy of the solar cell. Energetic disorder results in the charge transfer density of states having a low-energy tail, which is not strongly affected by the large shifts in the center of the DOS. In normal solar cell operation, this low-energy tail is what determines the measured Ect and Voc . Computational studies and Kinetic Monte Carlo simulations have shown that there are significant advantages to having energy cascades between the mixed polymer:fullerene phase and the pure polymer and fullerene domains. Energy cascades have been shown to improve geminate splitting and result in a lower threshold of local mobility and charge transfer state lifetime being required for efficient charge generation. 10,11 Microelectrostatic computations have indicated that electrostatic potential variations near the polymer:fullerene interface due to polarization effects can make it energetically favourable for a significant fraction of CT states to dissociate into free charges. 12 Energy cascades also aid in spatially separating carriers of opposite types by confining them to pure polymer and fullerene domains, and effectively suppress bimolecular recombination. 6 The positions of the polymer HOMO and fullerene LUMO levels in the mixed polymer:fullerene phase, therefore, are of great importance to the performance of organic solar cells, in setting the charge transfer state energy (and hence the open circuit voltage), in impacting charge separation, and in reducing Voc losses due to bimolecular recombination. An understanding of their origin is an important

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requirement for the elucidation of physical processes that occur in bulk heterojunction solar cells.

Energy Level Shifts in the Mixed Polymer:Fullerene Phase Cyclic voltammetry (CV) measurements were performed on a series of films of regiorandom poly(3-hexylthiophene-2,5-diyl):[6,6]-Phenyl C61 butyric acid methyl ester (RRa-P3HT:PCBM) with varying polymer:fullerene mass ratios. CV is used to measure the oxidation potential of the polymer and the reduction potential of the PCBM. Although CV does not directly measure the energy of the polymer HOMO and fullerene LUMO relative to vacuum, it does characterize the oxidation and reduction potentials of the blend film, which should have the same relative energies as the polymer HOMO and fullerene LUMO, thus providing a method to measure the effective Eg and the shifts in HOMO and LUMO produced by varying the blend composition. The polymer RRa-P3HT was chosen because it is a completely amorphous polymer and forms only a polymer:fullerene mixed phase, with no semicrystalline polymer phase, when blended with fullerenes. 2 This is helpful for our analysis as it eliminates the presence of oxidation features from pure, ordered polymer regions that are present in polymer:fullerene blends containing semicrystalline polymers like regioregular P3HT. Figure 2 shows the results of the CV measurements of the RRa-P3HT:PCBM blends with varying blend ratios. We first establish the nature of the reduction peaks observed in CV during the reduction of PCBM. The curve corresponding to pure PCBM (Figure 2a, black curve) displays two reduction peaks at -3.93 eV and -3.71 eV. PCBM often displays multiple reduction features corresponding to additional reductions of a single chemical state, 13 and these features are attributed to the first and second reduction peaks of aggregated PCBM. When RRa-P3HT is added and the PCBM content is decreased to 71%, an additional reduction feature appears at -3.82 eV, between the two reduction features observed in the pure PCBM sample (Figure

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Figure 2: Cyclic voltammetry curves of (a) reduction of PCBM and (b) oxidation of P3HT in thin film RRa-P3HT:PCBM blends with varying mass fractions of PCBM. Energy is plotted versus vacuum by using ferrocene as a reference molecule. The ferrocene formal oxidation potential occurs at -5.1 eV versus vacuum.

2a, purple curve). This new reduction feature is due to the presence of fullerene in the mixed polymer:fullerene phase, as it is known that amorphous P3HT and PCBM mix, 2,14 and that the reduction potential of PCBM is decreased in the disordered phase because the PCBM is no longer able to aggregate. 15 We assign this middle peak, which appears only in blends and is absent from the CV scan of pure PCBM, to the LUMO of PCBM in the mixed polymerfullerene phase, and track its evolution across the blend compositions. As P3HT content is further increased, the reduction feature at -3.93 eV associated with pure, aggregated PCBM vanishes, and is no longer apparent in samples with less than 48% PCBM. As shown by recently reported Grazing Incidence X-ray Diffraction measurements, PCBM aggregates are observed only for RRa-P3HT:PCBM blends with PCBM content of 50% or higher. 16 The disappearance of the aggregated PCBM peak at low PCBM content, therefore, is due to the miscibility of PCBM in the amorphous P3HT: as the PCBM content drops below the miscibility limit of PCBM in amorphous P3HT, it no longer forms aggregated domains, so the remaining reduction features are due only to the PCBM in the mixed polymer:fullerene phase. In the curves corresponding to blends with 38% and 29% PCBM, only a single peak is visible, which we assign to the LUMO of mixed phase PCBM. Because the effective Eg 6


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Figure 3: Experimentally determined (markers) and simulated (lines) values of the polymer HOMO (ionization potential), fullerene LUMO (electron affinity), and effective bandgap Eg as functions of fullerene content. Experimentally determined values are from cyclic voltammetry, while simulated values are determined by our electrostatic model. The dotted lines are the polymer HOMO (orange) and fullerene LUMO (blue) for the pure materials.

is the difference of the polymer HOMO and PCBM LUMO in the mixed polymer:fullerene phase, our analysis tracks the change in the reduction peak associated with the PCBM in the mixed polymer:fullerene phase. As the PCBM content is reduced, the mixed PCBM peak shifts towards vacuum, from a value of -3.82 eV in the blend with 71% PCBM to an energy of -3.60 eV at 29% PCBM blend. This corresponds to a total change in the reduction potential (or LUMO level) of PCBM of 220 meV. We next consider the impact of blend ratio on the RRa-P3HT oxidation potential as shown in Figure 2b. RRa-P3HT displays a relatively sharp oxidation onset and in most samples also displays an oxidation peak near the onset of oxidation. There are additional oxidation features in several of the RRa-P3HT CV curves beyond the first oxidation peak that we do not discuss here in detail, as they do not relate to the measurement of the effective Eg of the mixed phase. These features are most likely due to additional oxidations of the RRaP3HT, or a second morphological fraction of RRa-P3HT with a shorter conjugation length 7



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(and thus larger bandgap, and deeper HOMO) than the morphological phase associated with the first oxidation process. The pure RRa-P3HT oxidation potential lies at -5.52 eV. As the PCBM content is increased, the oxidation potential of the polymer shifts away from vacuum monotonically as the PCBM fraction is increased, reaching a value of -6.13 eV at a PCBM content of 71%, for a total change of 610 meV. The overall trend is that as the PCBM content in the blend film increases, both the polymer oxidation peak and the fullerene reduction peak are shifted away from vacuum. The shifts to polymer HOMO (ionization potential) and fullerene LUMO (electron affinity) energies relative to their values in neat films as determined from CV peaks are shown in Figure 3. We also determine the effective Eg for each blend composition by measuring the onset-to-onset separation of the RRa-P3HT oxidation potential and PCBM reduction potential (Figure 4). Overall, the effective gap of the polymer:fullerene blend increases by 300 meV as the PCBM content is increased from 29% to 71%.

Ect and Voc do not track energy level shifts The open circuit voltage of the solar cell has been shown to correlate strongly with Ect , which is in turn related to the effective band gap as shown in Equation 1. 7 Modeling of the quasi-equilibrium that exists between CT states and free carriers at open circuit has shown that the open circuit voltage of the solar cell is given by 6

qVoc = Ect − kT log(

qf N0 L ) τct Jsc

(2)

where Ect is the charge transfer energy measured by fitting the sub band gap absorption spectrum to an expression from Marcus theory of non-adiabatic electron transfer, 7 N0 is the spatial density of interfacial states, Jsc is the short circuit current density, τct is the charge transfer state lifetime, f is the volume fraction of the mixed phase in the active layer, L is 8


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the thickness of the active layer, k is Boltzmann’s constant, and T is temperature. Empirical data from a wide range of organic solar cells has shown that the Voc is almost always about 0.6 eV lower than the experimentally measured Ect . 17,18 Figure 4: Changes in effective band gap (Eg), charge transfer state energy (Ect ), and open circuit voltage (Voc ) with blend composition.

Equations 1 and 2 suggest that varying the effective band gap by moving the donor HOMO and acceptor LUMO levels should result in corresponding variations in the Ect and Voc . We measure Ect for all the blend compositions by fitting the sub band gap absorption spectrum using the procedure outlined by Vandewal et al. 7 As Figure 4 shows, however, the effective band gap changes by around 300 meV across the blends, but the measured Ect shifts by no more than 40 meV, and Voc follows no discernible trend. It is remarkable that Ect and Voc are not significantly affected by large changes in the fullerene content of the blend. An important implication of this finding is that the driving force for pushing charge carriers out of the mixed phase and into the pure phases of three-phase bulk heterojunctions might have very little dependence on the miscibility of fullerenes in the mixed phase. This observation 9



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also highlights that Ect in a donor-acceptor blend cannot be estimated by simply measuring the effective band gap. It must be measured by fitting the sub bandgap absorption spectrum of the blend, which corresponds to absorption at the donor-acceptor interfaces to directly create charge transfer states. 7 The problem with subtracting two energy level measurements to estimate Ect is that there is no guarantee that the energy levels being measured are from neighboring donor and acceptor molecules. In a film with a complex energetic landscape, it is essential to know the energy levels of neighboring molecules. In the rest of this manuscript, we develop a model to understand why the energy of the charge transfer state does not depend on the fullerene content, even though the effective band gap does.

Modeling Energy Level Shifts with Interfacial Dipoles Computational modeling studies using classical microelectrostatics have suggested that electrostatic interactions give rise to dipoles at the molecular heterointerface between polymer and fullerene. 12,19,20 We hypothesize that the electrostatic potential created by these dipoles acts to shift the energy levels of individual molecules in the blend. Interfacial dipoles can be mutually induced at the polymer-fullerene interface, for example, polarization of PCBM by the quadrupole moment of P3HT. 21 Molecular dynamics studies can provide insight into what the origin of interfacial dipoles might look like in P3HT:PCBM. 22 These models have shown that C60 packs preferentially on the molecular face of pentacene, resulting in the C60 approaching the out-of-plane π-orbitals of the pentacene. The π-orbitals polarize the C60 , pushing electron density away from the molecular interface. This results in an induced dipole on the fullerene, which points toward the interface (in a convention where dipole moment points from negative to positive charge). The dipole on C60 in turn induces a dipole on the pentacene with the same orientation. Dipoles oriented in this fashion would stabilize electrons on the donor (since it is near the positive end of a dipole), pushing the donor HOMO level away from vacuum, and destabilize electrons

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on the acceptor, pushing the LUMO level towards vacuum. Figure 5 shows a schematic of this configuration. Separately, density functional theory studies have reported large dipoles at the interface of PCBM and an oligomer of P3HT, which are found to be produced by polarization of the electron cloud of P3HT by the permanent dipole moment of PCBM. 23 While the specific molecular arrangement will vary for systems other than the picture presented here for pentacene and C60 , a similar process of dipoles being mutually induced will still hold true. Figure 5: Schematic diagram describing change in energy levels of P3HT (orange squares/lines) and PCBM (blue circles/lines) in the mixed phase as PCBM content increases. The change in energy levels is attributed to the electrostatic potential created by mutually induced dipoles on the molecules at the interface, whose direction is indicated in this schematic by arrows that point from negative to positive charge.

The local energetic environment in the polymer-fullerene blend will, therefore, be influenced by the local distribution of interfacial dipoles, and the electrostatic potential that they create. In the RRa-P3HT:PCBM blends measured by CV, as the fullerene content increases from a low value, a P3HT molecule will tend to have a higher density of nearby PCBM molecules, and hence, more nearby interfacial dipoles. Thus, as PCBM content increases, the polymer HOMO level is expected to move further from vacuum. Conversely, because the 11



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electrostatic dipole on the P3HT shifts the PCBM LUMO towards vacuum, as the PCBM density increases and the density of P3HT molecules near a given PCBM decreases, the PCBM LUMO will shift away from vacuum. Both of these predictions are consistent with the observed CV trends in Figure 2. We design a simple model to compute the effects of interfacial dipoles on energy levels of the polymer and fullerene. We model the polymer-fullerene mixed phase as a cubic lattice that is randomly occupied by donor or acceptor molecules. Each lattice site is divided into a 3x3x3 sub-lattice. Interfacial dipoles are created by moving fractional charges within the sub-lattice. Dipoles are created on donor sites that have acceptor nearest neighbors, and on acceptor sites that have donor nearest neighbors, in the direction described above in the example with pentacene and C60 . The relative sizes of dipoles on polymer and fullerene are chosen to be in the ratio of the polarizability of P3HT and PCBM (more details in the Experimental section). The polymer-fullerene morphology is created by randomly occupying lattice sites with polymer or fullerene molecules in the overall ratio of a range of polymer-fullerene blend compositions, to model random mixing in the mixed phase (Figure 6a). For fullerene concentrations above the miscibility threshold (set to be a fullerene mass fraction of 0.6), spherical aggregates of pure fullerene are created to ensure that the fullerene concentration in the mixed phase remains at the miscibility limit. After the lattice is populated and dipoles are created at all polymer-fullerene interfaces, the electrostatic potential at each point due to the assembly of all interfacial dipoles is calculated by solving the Poisson equation. The potential at each lattice site produces a shift in the energy levels of the molecule at that lattice site. The resulting shift in the energy level of the molecule at each site is shown as a colormap in Figure 6(panels b and c). By plotting a histogram of the potentials at all polymer sites, a density of states for the polymer HOMO is created, relative to a hypothetical isolated molecule DOS, which is a delta function centered at 0.0 eV. Similarly, a density of states for the fullerene LUMO is

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plotted as a histogram of potentials at all fullerene sites. These histograms represent both the broadening and relative shifts to the energy levels produced by the potential created by interfacial dipoles. The densities of states thus generated are plotted in Figure 7 for a range of blend ratios. The shifts in the centers of the polymer HOMO and fullerene LUMO densities of states are qualitatively consistent with the shifts measured by cyclic voltammetry (Figure 2). A quantitative correspondence of simulation to experiment is obtained by fitting the predicted shifts of the centers of the HOMO and LUMO DOS to the shifts experimentally measured by CV, using the magnitude of the interfacial dipoles as the only fit parameter. The model reproduces the CV-measured energy level shifts well (Figure 3), showing that the potential created by dipoles at the polymer-fullerene interface can correctly account for the energy level shifts observed in blends. The size of dipole required to account for observed shifts is sensitively dependent on the distance between the dipole and the molecule whose energy level it is shifting. Computational studies optimizing the structure of the P3HT-PCBM interface 23 have found that the distance between monomer unit and PCBM is 0.4 nm. In a lattice with this intermolecular separation, dipoles of realistic magnitude can quantitatively account for the energy level shifts measured. The fit values for the dipole magnitude so obtained are 5.1 D and 2.6 D on fullerene and polymer respectively, which is close to the known permanent dipole moment of PCBM, 5.0 Debye. 23 A determination of exact dipole magnitudes present in the mixed phase is beyond the scope of this study however, our modeling shows that interfacial dipoles of realistic magnitude can fully account for the experimentally measured trend of energy level shifts with blend composition.

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Figure 6: (a) A representative plane of a cubic lattice randomly populated with polymer (orange) and fullerene (blue) sites, used to model a mixed polymer:fullerene phase. (b) and (c) show maps of the electrostatic potential of the PCBM and polymer sites respectively for the slice shown in panel (a). This potential is that created by dipoles at polymer-fullerene interfaces. X and Y positions are given in number of lattice sites.

Disorder-Induced Broadening Creates a Low-Energy Tail in the CT DOS that Determines Ect and Voc We now turn to the question of why the measured Ect and Voc do not change proportionally to the changes in the effective band gap. If the HOMO and LUMO levels are broadened by energetic disorder in the bulk heterojunction, the CT density of states will have a low-energy tail. Under typical operating conditions of one sun light intensity, the carrier density in the solar cell is on the order of 1016 cm−3 . 24 This implies that only the low energy tail of the CT DOS is occupied, and hence it is the low-energy tail of the CT DOS that in practice sets the measured Voc . Further, in the measurement of the CT state energy (as described in reference 7 ), it is only the low energy tail of the CT DOS that is fit to an expression for nonadiabatic charge transfer, since the center of the CT DOS is usually hidden under the singlet absorption of the polymer. The cyclic voltammetry measurements presented above show that variations in blend 14


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Figure 7: Simulated shifts in the density of states of the polymer HOMO (left) and fullerene LUMO (right) produced by the potential created by interfacial dipoles, for fullerene fractions from 30% to 70%.

composition produce large changes (on the order of hundreds of meV) in the centers of the HOMO and LUMO densities of states. However, if energetic disorder ensures that there are enough CT states of low energy to accommodate typical carrier densities under solar cell operation, these states will effectively determine measured Voc and Ect despite changes in the positions of the centers of the densities of states across blends, in line with what is observed. To investigate this possibility, we generate the CT density of states using our electrostatic model, in the same way as we generated the HOMO and LUMO densities of states. We do this by considering all polymer:fullerene neighbor pairs and taking the difference in their electrostatic potentials to be the shift in their CT energy. The simulated CT DOS is shown in Figure 8a. Zooming in on the low energy tail of the CT DOS reveals that it indeed has a low-energy tail that is not strongly affected by blend composition. At the typical charge density found at one sun illumination at open circuit (1016 cm−3 ), 24 indicated by the horizontal line in Figure 8b, the maximum difference in CT density of states across different blends is 100 meV, about the same extent to which Voc varies across the blends. This relative invariance of the low energy tail of the CT DOS explains the experimental observation that measured Ect and Voc do not track the large shifts in effective band gap.

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The important difference between measuring effective band gap through cyclic voltammetry and measuring Ect by fitting the sub band gap absorption is that while sub band gap absorption explicitly fits the low-energy tail of the CT DOS, CV almost certainly misses this part of the density of states. Since the peaks in a CV trace are broad and overlapping, the low-energy tails of the HOMO and LUMO peaks are hidden underneath adjacent peaks. Thus, while CV measures the shifts in the centers of the polymer HOMO and fullerene LUMO densities of states, it provides no direct information about the low-energy tails, which are in practice what determine measured Ect and Voc . Figure 8: (a) CT density of states relative to an unshifted delta function DOS centerd at 0.0 eV. (b) Zoomed-in view of the low-energy tails of the CT densities of states. The horizontal line indicates typical carrier densities in organic solar cells at one sun illumination at open circuit.

In our simplified model, the only source of energetic disorder is the assembly of randomly oriented electrostatic dipoles. In addition to their short-range effects that shift energy levels, these dipoles, which are macroscopically oriented at random, generate a non-uniform electrostatic background that broadens the energy levels of all sites in the lattice. This randomly varying electrostatic background creates a low energy tail in the DOS in all blends. In the actual solar cell blend, in addition to the disorder created by the randomly varying electrostatic background of the dipoles, there will likely be other sources of disorder - such as local variations in intermolecular packing and in conjugation length. 16


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To test for the presence of energetic disorder in the solar cells measured, we perform temperature-dependent Fourier Transform Photocurrent Spectroscopy on the solar cells of all blend compositions. This technique, described elsewhere, 6 measures the width of the CT density of states, modelled as a Gaussian, by measuring the experimental Ect at a variety of temperatures (details in the Experimental section). In all the solar cells measured, approximately 100 meV of CT energetic disorder was found (Table 1), confirming that the CT density of states is not a single sharp value but rather a broadened Gaussian with a low energy tail. As our simulations show, this low-energy tail is present in all the blends despite large changes in the center of the CT DOS with blend composition. As a result, the measured Ect and Voc do not track shifts in the centers of the DOS.

Conclusion In this work, we have shown that the energy levels of both the polymer and fullerenes shift considerably as the fullerene content is varied and have attributed the effect to the formation of dipoles at the polymer-fullerene interface. Although these dipoles dramatically affect the energetic landscape of the film, they have little effect on the energy of the lowest energy charge transfer states. Since it is the energy of these charge transfer states that determines the voltage of a solar cell, the open circuit voltage does not have a strong dependence on the fullerene content. It is fortunate that the open circuit voltage of organic solar cells is not highly sensitive to the miscibility of fullerenes in the mixed phase.

Experimental Cyclic Voltammetry Substrates used were ITO-coated glass (Xinyan Technologies). Substrates were immersed in a detergent solution of 1:9 extran:deionized water solution and scrubbed with a brush.

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Samples were then sonicated in the detergent solution, rinsed with deionized water, sonicated in acetone, sonicated in isopropanol, and blown dry with nitrogen. Substrates were stored in an oven held at 115 C. Immediately before depositing films onto substrates, substrates were exposed to a UV-ozone plasma for 15 minutes. PC60 BM was purchased from Solenne BV. RRa-P3HT was obtained from Rieke. Stock solutions of RRa-P3HT and PCBM (separately) were prepared at concentrations of 20 mg/ml solids in chloroform (CF) and stirred overnight at 60 C. RRa-P3HT:PCBM blend solutions were prepared by mixing the appropriate volume ratio of the RRa-P3HT and PCBM stock solutions, and then diluting with pure CF to obtain a polymer concentration of 4 mg/ml. All films were deposited in a nitrogen filled glovebox (H2 O and O2 levels typically below 10 ppm) onto prepared substrates via spin-coating at 1000 RPM for 45 seconds with a ramp speed of 500 RPM/sec. Cyclic voltammetry (CV) measurements were performed on a Bio-logic VMP3 potentiostat. The electrolyte used was 0.02M tetrabutylammonium hexafluorophosphate (TBA HFP) (Fluka) in acetonitrile. A platinum wire was used as a counter electrode and a Ag/AgCl wire was used as a quasireference electrode. Nitrogen was bubbled through the electrolyte before each measurement to remove oxygen. All electrochemical measurements were performed at a scan rate of 10 mV/s. Ferrocene was used as a reference molecule. After electrochemical measurement of a sample was performed, ferrocene was added to the electrolyte without removing the sample, and several CV curves of the sample were taken again in the ferrocene containing electrolyte. The formal potential of the ferrocene was determined from the CV curve containing both the ferrocene redox process and the sample redox process. Only the first electrochemical cycle was considered for analysis because RRa-P3HT samples display degraded electrochemical and optical properties on subsequent cycles.

Solar cells and FTPS measurements RRa-P3HT:PCBM solar cells preparation: Cleaned and UV-ozone exposed ITO glass (per the substrate cleaning methodology outlined above) was coated with a thin layer of PE18


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DOT:PSS (Clevios) by spin coating at 4000 RPM for 30 seconds in air. The substrates were then annealed at 140 C for 10 minutes to drive out any residual air. RRa-P3HT:PCBM films were then spin cast in a dry nitrogen glovebox using the same solution concentrations, blend ratios, and spincasting conditions as outlined above for the RRa-P3HT:PCBM samples used in CV. A top electrode of 7 nm Ca and 250 nm Al (Plasmaterials and K. J. Lesker, respectively) was thermally evaporated at pressures of below 10−6 torr. Solar cell characteristics were measured using a Keithley 2400 source meter and a solar simulator calibrated to 1 sun, AM1.5 G, with a NREL certified KG-5 filtered silicon photodiode. FTPS measurements were performed using a Nicolet iS50R FT-IR spectrometer, with signal amplified using a Stanford Research Systems Model SR570 Low-Noise Current PreAmplifier. Samples were mounted on the cold finger of a Janis Research Company ST-100H cryostat. Thermal paste was used to maintain good thermal contact between the cold finger and the sample. Sample temperature was controlled using a LakeShore 331 Temperature Controller. The sample was measured at several temperatures from 82K to 300K. Before each measurement, the sample temperature was set to the desired value and then allowed to stabilize until less than 0.05K variation in temperature was observed on the temperature controller. The photocurrent spectra was then recorded with no band pass filter, and with two bandpass filters which blocked all light transmission above approximately 13800 cm−1 and 12088 cm−1 . The three resulting spectra were stitched together, prioritizing the spectra generated with the lowest wavenumber filter, to create a photocurrent spectrum for the sample. Ect and reorganization energy were determined as outlined by Vandewal et al. 7

Electrostatic Simulations Electrostatic simulations were carried out using the Numpy package with the Python programming language. A cubic lattice with cubic sites was filled with sites representing either polymer or fullerene. The sites were randomly occupied, with the probability of occupation by a fullerene site equal to the fullerene fraction. All simulations used a lattice with 19



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Table 1: Effective Eg , Voc , and temperature dependent CT state absorption fit parameters E0ct , λ0 , and σ for RRa-P3HT:PCBM solar cells with varying PCBM content. PCBM content 71 59 48 38 29

Effective Eg (eV) Voc (V) 2.12 0.83 2 0.88 1.91 0.82 1.96 0.57 (0.84) 1.81 0.93

Ect0 (eV) Lambda0 (eV) Sigma0 (eV) 1.66 0.06 0.1 1.64 0.08 0.1 1.65 0.09 0.09 1.63 0.12 0.09 1.67 0.09 0.1

100x100x100 sites. Induced dipoles in fullerene sites with polymer nearest neighbors were modeled by creating a vector for each polymer nearest neighbor which points directly away from the polymer nearest neighbor, and then summing these vectors and normalizing the resulting vector. The fullerene site was then broken into 27 smaller cubes of equal volume, and a partial positive and negative charge were distributed in these cubes such that a vector pointing from the positive to negative charge had the same direction as the vector which points away from the polymer nearest neighbors. A similar process was used to create dipoles on polymer sites. The magnitude of the charge placed on the sites was used as the only fit parameter, and the data was fit to the experimentally measured band gap. DFT calculations reported for sexithiophene 12 have calculated the polarizability of T6 as 53.2 Å3 along the lamellar packing direction and 24.1 Å3 in the out-of-plane direction. The presence of sidechains is likely to increase the polarizability: the same report calculated an isotropic polarizability of 1.66 Å3 per -CH2 - unit in the alkyl chain. The DFT-calculated polarizability of PCBM is 102 Å3 . For our simplified model, therefore, we assume the ratio of polymer to fullerene polarizability is 1:2. The dielectric constant used was 3.5. The Poisson equation is solved for the generated charge distribution using fast Fourier transforms to obtain the electrostatic potential at every lattice site. The polymer and fullerene DOSs are determined by taking a histogram of all the polymer and fullerene sites. A CT site is defined to be one polymer:fullerene nearest neighbor pair, and the CT DOS is determined by obtaining a histogram of all these CT pairs.

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Acknowledgement This work was supported by the Department of the Navy, Office of Naval Research Award No. N00014-14-1-0580. We thank William R. Mateker for useful discussions.

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Graphical TOC Entry

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How the Energetic Landscape in the Mixed Phase ... - ACS Publications

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