Fullerene

LETTER pubs.acs.org/JPCL

Why Holes and Electrons Separate So Well in Polymer/Fullerene Photovoltaic Cells David P. McMahon, David L. Cheung, and Alessandro Troisi* Department of Chemistry and Centre of Scientific Computing, University of Warwick, CV4 7AL Coventry, U.K.

bS Supporting Information ABSTRACT: The electronic and geometric structure of a prototypical polymer/ fullerene interface used in photovoltaic cells (P3HT/PCBM) is investigated theoretically using a combination of classical and quantum simulation methods. It is shown that the electronic structure of P3HT in contact with PCBM is significantly altered compared to bulk P3HT. Due to the additional free volume of the interface, P3HT chains close to PCBM are more disordered, and consequently, they are characterized by an increased band gap. Excitons and holes are therefore repelled by the interface. This provides a possible explanation of the low recombination efficiency and supports the direct formation of “quasi-free” charge-separated species at the interface. SECTION: Energy Conversion and Storage

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rganic photovoltaic (OPV) cells have shown potential as a low-cost replacement for more conventional, higher-performing, silicon photovoltaics.1
3 The prototypical device is formed by a blend of a polymeric electron donor, the main light absorber, and an electron-acceptor material. The key process in OPV cells is the separation of an exciton close to the donor/ acceptor interface into a free hole (in the donor) and a free electron (in the acceptor). In an efficient solar cell, the majority of absorbed photons generate such hole
electron pairs.4
7 It is not clear why such a charge separation process is so efficient in some blends, for example, in the blend formed by poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM), and how one can design better OPV materials. Simple theories8,9 indicate that if a charge-transfer species with a small hole
electron separation is formed at the interface, the hole
electron Coulombic attraction is too strong for the hole
electron pair to separate before de-excitation. Several alternative explanations10,11 that have been put forward cannot be validated without a microscopic model of the interface. This can be built only by knowing the finest details of the morphology of the interface and its electronic structure, two aspects that are difficult to investigate experimentally and that have become computationally accessible only recently. In this Letter, we take a combined classical molecular dynamics (MD) and quantum chemical (QC) approach to study how the electronic structure of P3HT is modified at the interface with PCBM. Specifically, MD simulations are used to study the microstructure and morphology of a system of P3HT in contact with PCBM. The configurations from these MD simulations are used as input for the QC calculations on P3HT. The electronic density of states (DOS) is computed and the stability of the excited state assessed. This combined classical and quantum chemical approach has previously proven to be a powerful technique r 2011 American Chemical Society

for the investigation of soft electronic materials12 but has not been applied to the study of polymeric interfaces so far. An atomistic model of the P3HT/PCBM interface was built in which crystalline P3HT resides next to an amorphous phase of PCBM (schematically depicted in Figure 1a). Simple visual inspection suggests that polymer chains near the interface are more distorted than the bulk chains. Because it is expected that the electronic structure of P3HT chains is strongly affected by the distribution of the torsional angle ϕ between thiophene rings,13 we analyzed the statistical distribution of this angle (Figure 1c). This analysis indicates that, away from the interface, the polymer backbone tends to remain planar. At the interface, we observe a preference for the torsional angle to distort by approximately 20° and to assume a broader distribution of values. We shall stress that P3HT is always in the crystalline phase and that the increased “disorder” at the interface does not imply an amorphous phase. As we are interested in the relation between the local morphology and the electronic structure of the interface, we calculated the electronic DOS for P3HT chains at different distances from the interface (Figure 2) for 100 uncorrelated MD snapshots. The peaks in the P3HT DOS computed for chains not in contact with the interface are due to the finite length of the model chain and can be assigned to “quasi-band” states, with the electron relatively delocalized along the chain. To confirm this assignment, the DOS for an ideal crystalline single chain of the same length is reported in the same figure and shows a similar DOS pattern. The DOS for the chains far from the interface are similar to the idealized chain DOS but broader (because of the static disorder in the Received: September 29, 2011 Accepted: October 12, 2011 Published: October 12, 2011 2737

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The Journal of Physical Chemistry Letters chain) and with a slightly larger band gap (another effect of static disorder), exactly as expected for the crystalline phase of such a polymer. Because of the increased disorder of the polymer chains near the interface, the DOS of P3HT chains closer to the interface is broader and the band gap larger, with a marked decrease of the valence band edge energy (∼150 meV) and a more modest increase of the conduction band edge energy (∼10 meV).14 This energy landscape is “static”, that is, it is not modified along the computed trajectory by dynamic disorder. The results above indicate that an electron hole in P3HT is repelled by the P3HT/PCBM interface. To verify that, as suggested by the DOS, also the exciton on P3HT is repelled by the interface, we performed ZINDO excited-state calculations on individual chains at different distances from the interface for the same configurations used to compute the DOS. The lowest

Figure 1. (a) Schematic of the simulated system containing a region of amorphous PCBM, denoted in gray, and a crystalline P3HT region, with the individual polymer chains denoted in blue. Periodic boundary conditions are applied in all directions, and shadings indicate chains that are equidistant from the interface (there are therefore two interfaces in the model). (b) Top view of the PCBM interface where only the first P3HT layer is represented. (c) Probability distribution of the thiophene
thiophene torsional angle (ϕ) for chains in the first, second, and third layers from the interface.

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excitation energy is 2.30 ( 0.09 eV for the P3HT chains in contact with PCBM and decreases to 2.17 ( 0.08 and 2.14 ( 0.07 eV as the distance from the interface increases (the indicated error is the standard deviation in the results). From the determined increased disorder at the interface, the effect on the electronic states is certainly not unexpected considering the experimental data on absorption and photoemission spectra of P3HT with different regioregularity and/or crystalline order.15,16 Moreover, these calculations including all valence electrons incorporate the largest part of the dielectric screening effect, confirming that the one electron DOS of Figure 2 is unlikely to be altered by the effect of electron
electron interactions. While the conclusions of this paper are not affected by the exact positioning of the computed valence and conduction band edge, both electronic structure methods used here underestimate the band gap by 0.4
0.6 eV.17,18 The fundamental process in organic photovoltaics based on P3HT/PCBM is the generation of a separated electron
hole pair from the exciton formed by incident light in P3HT. For charge separation to occur, the generated exciton must diffuse to the interface where it separates to yield an unbound electron and hole. The separated hole remains in the valence band of the P3HT, while the electron is subsequently transferred to the LUMO of the PCBM. It is often assumed that the exciton is split at the interface, giving a charge-transfer state where the hole and electron are Coulombically bound. The efficient separation of this hole
electron pair cannot be understood on the basis of classical Onsanger
Braun theory,8 which would predict it to occur in microseconds, while it must occur in nanoseconds to explain the observed yield of free charge formation. In the absence of a microscopic model of the interface like the one proposed here, there are two possible explanations for the efficient free charge generation. The first hypothesis is that the charge- transfer state remains hot, that is, with high vibrational energy, long enough to allow the formation of free charges before vibrational relaxation kicks in.9,11 A second hypothesis is that the exciton leads directly to relatively delocalized charge carriers (still not free charges) before thermal relaxation.10,19 Computational studies of the bulk have shown a distribution of localized and delocalized charges in P3HT13 and PCBM20 in agreement with classical localization theories.21 These studies also show that it is not expected that the charge is localized much by polaronic effects, that is, by the nuclear relaxation following the generation of free charges, because of the large conjugation and the very low dielectric constant. The previous studies in conjunction with the present one predict a scenario for the charge

Figure 2. (left) DOS (states monomer
1 eV
1) of P3HT for layers at different distances from the interface with PCBM. The plots are offset for clarity. This panel also illustrates that the increased band gap near the interface is mostly due to a reduction of the valence band edge energy. The black curve is the (rescaled) DOS for an idealized isolated chain with no disorder. (center) A schematic of the interface with increased chain disorder near the interface. (right) A snapshot from the simulation showing that for the two P3HT/PCBM interfaces per snapshot, the P3HT chains are more disordered near the interface. 2738

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Figure 3. (left) A schematic of the energy levels emerging from the simulation with the exciton and hole repelled by the interface and electron transfer likely involving a chain not in contact with the interface. (right) Modification of the ground and excited potential energy surfaces when the charge separation leads to a relatively delocalized hole
electron pair in comparison with the case of the formation of a localized charge-transfer state.17 States with larger delocalization of hole and electron are higher in energy and have smaller polaronic effects (shallower potential energy minima). While there is a barrier for the formation of a charge-transfer state, this barrier is reduced or disappears for the formation of delocalized hole
electron pairs.

separation process that is both new and simple (Figure 3). The exciton does not reach the interface, where its energy would increase; instead, it is split through an ultrafast process, leaving an electron hole a few layers away from the interface and an electron in one of the partially delocalized states in PCBM. The hole is repelled by the interface, explaining the unlikelihood of geminate (and nongeminate) recombination in these blends. The formation of more separated holes and electrons upon exciton splitting has been indirectly suggested by other data. Veldmann et al. found that if PCBM does not form sufficiently large domains (sustaining more delocalized states), the hole and electron recombine more easily.22 If the charge separation is studied in a very localized fashion on a model system containing only a short P3HT oligomer and a PCBM molecule,23 the ultrafast charge separation and the absence of a temperature dependence in this process7 cannot be explained, even within the error of the computational modeling, which predicts the existence of a barrier for the separation process. On the other hand, the formation of relatively delocalized electron
hole pairs, with higher energies of the charge-separated species and therefore a reduced barrier, can become ultrafast (Figure 3b). Importantly PCBM can accept electrons on its LUMO+1 and LUMO+2 orbital, creating a large energy window of about 0.3 eV for the ultrafast electron transfer.24 The proposed mechanism is only acceptable if the donor
acceptor electronic coupling does not vanish when the donor states are farther away from the interface. When donor and acceptors are not in contact but coupled through other “bridge” states (in this case, provided by spectator polymer chains), the effective electronic coupling between them is described by superexchange theory.25 The charge-transfer rate between the donor and acceptor decreases by a factor of exp(
βR), where R is the distance between the donor and acceptor and β is an attenuation factor. β can be estimated through the Gamow model of electron tunneling through a one-dimensional barrier, which gives β = 0.31 Å1 for a barrier of Δ = 0.09 eV (evaluated from the conduction band DOS peaks shown in Figure 2(left)). Virtually the same result is obtained using the McConnell formula,26 β = 2/L ln |Δ/V|, where the interchain coupling V is

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computed to be 0.05 eV, that is, one-fourth of the band dispersion in the direction perpendicular to the chains in a crystal.27 With such an attenuation factor, the CS rate of an exciton in the third layer would only be 10 times smaller that the CS rate of an exciton in contact with PCBM (the interchain distance L is 3.8 Å, and the rate at contact2 is about ∼20 ps
1). Such a rate would still be faster or comparable to the rate of excitons approaching the interface by hopping (of the order of 0.1 ps
1),28 the appropriate term for comparison in this case. Moreover, the model that we presented assumes that the vibrational relaxation of the exciton (at least the relaxation of the dihedral angles between monomers) is slower than the charge separation event. This is certainly true for the CS rate in the range of 2
20 ps
1. The exciton may also be delocalized in the direction perpendicular to the interface depending on the strength of the exciton
exciton interaction (not considered here), but this would further increase the tendency of forming a CS state with larger hole
electron separation and would not modify fundamentally the mechanism proposed here. The energy-level landscape emerging from the atomistic model is expected to be rather general in blends where at least one component tends to form crystalline phases. It is well-known from polymer physics that the boundaries between crystalline domains in polymers are more disordered because of an increased free volume.29 At the interface between immiscible soft materials, present in any eligible OPV blends, it is only expected that the free volume, and therefore the disorder, is larger. This effect is maximized when a crystalline domain can be formed close to the phase boundary and minimized when the two materials form very diffuse interfaces, in agreement with the rule of thumb that the more crystalline the polymer, the better the solar cell. The interface is expected to be more diffuse between donor and acceptor materials made by polymers with similar solubilizing alkylic chains, and this may explain why polymer
fullerene solar cells are more efficient than polymer
polymer cells. The proposed mechanism is consistent with the findings of Guo et al.,28 who proved that in regioregular (crystalline) and regiorandom (noncrystalline) P3HT, most excitons can dissociate at the interface, but only in the regioregular P3HT do the majority of excitons lead to free carriers (in regiorandom P3HT, this happens only one-third of the time). For the development of additives for photovoltaic blends,30 this study suggests that they should be aimed at preserving the local crystallinity of at least one of the two phases. It was certainly not unexpected that the efficiency of bulk heterojunction solar cells depended intimately on the microscopic structure of the interface, but in the absence of appropriate modeling, too many possible interpretations could be given to the spectroscopic data, especially those concerning ultrafast processes. In this Letter, we have used a large-scale atomistic model of the most studied bulk heterojunction to show that electron holes and excitons formed in the electron donor are repelled by the interface, providing for the first time a realistic picture of the interface morphology and electronic structure that is consistent with all of the observations and may help explain why some donor
acceptor pair combinations lead to extremely high quantum yields of free charges. Of all the processes and interface types that can be tackled by the approach presented here, we have shown what we believe is of most immediate relevance for the experimental community, but once a model of the morphology is available, many additional opportunities arise. For example, it should be possible to investigate the direct excitation of 2739

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The Journal of Physical Chemistry Letters charge-transfer states or to verify whether the partially delocalized state described here can be identified with the CT states discussed by most spectroscopists. The same modeling strategy could also be adopted for the study of charge recombination or triplet formation and, more generally, to explore microstructure
photophysics relations in heterojunctions. A possible limitation of this or other bottom-up approaches is the difficulties of achieving a general view on a particular process if not after an extensive set of similar investigations. Other donor
acceptor pairs have respectable device characteristics, and because they are formed by less structurally characterized materials, they are more difficult to study. For this reason, the generality of our results must be assessed by exploring alternative material combinations.

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deviation, 0.037 eV, due to the variability of the structure along the trajectory.

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional details on the classical simulation setup, the calculation of the electronic structure, and the excited state calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ METHODOLOGY OUTLINE MD simulations consisted of 160 PCBM molecules forming a side-on interface with a crystalline phase of type-I P3HT (Figure 1) containing 24 chains, with 20 thiophene rings each, arranged into 4 layers of 6 chains. The initial configuration of PCBM was taken from ref 31. For P3HT, starting crystal structure parameters were adapted from the experimental crystal structure of poly(3-butylthiophene),32 with side chains fully extended and noninterdigitated to give the most stable polymorph of the polyalkylthiophenes.33 An all-atom force field of the OPLS (optimized potentials for liquid simulations) form was used to describe the PCBM intra- and intermolecular interactions.34,35 The P3HT interactions were described using the force field of Moreno et al.36 Initial systems of P3HT and PCBM were equilibrated separately by 1 ns of a NVT simulation at 100 K, followed by a 1 ns NPT run at both 100 and 300 K. The equilibrated PCBM system was taken and resized to obtain a crosssectional area identical to that of the P3HT system. The two systems were combined while leaving a gap of 3
4 Å between the P3HT and PCBM, and the energy was minimized followed by a 1 ns NVT run at 100 K and a 1 ns NPT run at 100 K. Constant NPT MD simulations were performed at 300 K with a pressure of 1 atm. Simulations consisted of 5 ns of equilibration and 10 ns of data gathering. Data for quantities averaged over the entire simulation were gathered every 5 ps. LAMMPS was used for all MD simulations.37 The DOS was computed for 100 MD snapshots, uniformly sampled along the trajectory, using the previously developed and validated localized molecular orbital method (LMOM),38 and then averaged. Alkyl side-chains were substituted with methyl groups (resulting in a systematic positive shift of the frontier orbital energy of less than 30 meV), and a few frontier orbitals of the monomer units (from HOMO
1 to LUMO) were taken as a basis set to represent the orbitals relevant to the system. The LMOM divides the polymer into fragments from which the polymer orbitals and orbital energies are obtained by diagonalization of an approximate Fock matrix built from computations, at the DFT//B3LYP/6-31G* level of theory, containing only pairs of spatially close fragments. The model did not consider long-range electrostatic interactions that may further modify the energy levels of the hole states, as found in other systems.39 To provide a crude estimate of the microelectostatic effect at the interface, we computed the electrostatic potential experienced by the polymer chains in direct contact with the interface and polymer chains in the third layer.40 The difference between the two electrostatic potentials was just 0.014 eV (the electrostatic potential is higher on the chains in the third layer away from the interface) with a substantial standard

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