P3HT Heterointerface

Article pubs.acs.org/JPCC

Strain Modulation of Band Offsets at the PCBM/P3HT Heterointerface Guido Menichetti,*,† Renato Colle,‡ and Giuseppe Grosso†,§ †

Dipartimento di Fisica, Università di Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy Dipartimento di Chimica Applicata e Scienza dei Materiali Università di Bologna, via del Lazzaretto 15/5, I-40136 Bologna, Italy § NEST, Istituto Nanoscienze-CNR, Piazza San Silvestro 12, I-56127 Pisa, Italy ‡

ABSTRACT: Improving the efficiency of organic solar cells requires atomic insight into the interface electronic band alignment of the donor and acceptor moieties composing the device. In this article, we use ab initio calculations, with inclusion of long-range (van der Waals) interactions, to address the solid-state properties of a bulk heterojunction heterointerface between a single ordered layer of PCBM molecules adsorbed on a clean P3HT crystalline polymer. The studied interface model allowed us to focus on the basic mechanisms responsible for charge polarization and migration at the interface and to refer the energies of both moieties to the same origin. After the accurate evaluation of the relative energy positions of the near-gap electronic levels in the PCBM/P3HT complex and of the optical spectra useful for determining the nature of the electronic states, we analyzed the effect of uniaxial stress on the band alignment, and we found that both the polymer band gap and the offset between the LUMO levels of the donor and the acceptor materials decrease for compressive stress. This suggests that the donor band gap can be reduced, thus increasing solar energy harvest, and that the open-circuit voltage of the system can be tuned to improve the efficiency of PCBM/P3HT-based solar cell devices.

1. INTRODUCTION The past few decades have witnessed increasing attention toward organic semiconductors for electronic applications, for molecular-level technology processes, and for the development of devices aimed at solar energy conversion. Among the reasons for this interest is the advantage such materials offer for both low-cost processing and mechanical properties.1 In particular, most promising solar cell devices with high power conversion efficiencies (PCEs) employ architectures based on heterojunctions, that is, interfaces between different organic materials, either oligomers or polymers or organic molecular crystals.2 Bulk heterojunction (BHJ) solar cells are the best-performing devices. In fact, they are designed and constructed to have multiple interfaces in the same device with regions of the constituent materials intermixed at distances on the same order of magnitude as, or lower than, the diffusion length of the electronic excitations induced in the polymer moiety of the device.2,3 Among BHJs, blends of regioregular poly(3-hexilthiophene) (rr-P3HT) and fullerene derivative [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) are the most studied,4 and for such blends, a power conversion efficiency of ≳5% was demonstrated.5 Excitons created in the π-conjugate P3HT polymer dissociate into electron−hole pairs at the interface with PCBM, and then electrons migrate into the PCBM molecular crystal, leaving holes in the P3HT polymer. Thus, P3HT acts as an electron donor, whereas PCBM acts as an electron acceptor.6 © XXXX American Chemical Society

It is evident that understanding, controlling, and optimizing BHJ PCBM/P3HT solar cells require accurate geometrical and electronic structure descriptions of the constituent materials at the atomic level, but also of the chemical and physical processes at their interface when they are in contact. For this goal, the role of the theory and computational modeling is central.3,7 From the fundamental point of view, the explanation of the initial quantum dynamics of the electron transfer process at the heterojunction interface has motivated several theoretical studies.8−11 Studies on dipole assistance to exciton dissociation,12 the rise of interfacial states,13 and criteria for energy alignments at the interfaces14−16 helped to shed light on BHJ optimization. In fact, photoinduced light absorption11,17 and light-induced electron spin resonance studies18−20 indicated that the interfacial electron transfer after exciton dissociation at the donor/acceptor heterojunction is an ultrafast process (tens or hundreds of femtoseconds)11,17 and is one of the key processes controlling the energy conversion efficiency of solar cells. The efficiency of a solar cell made with a blend of donor and acceptor moieties is strongly correlated with the alignment of their electronic bands, the band gap of the polymer, and the optical band gap of the complex system. In fact, the macroscopic parameters that control the power conversion Received: March 22, 2017 Revised: May 19, 2017 Published: May 30, 2017 A

DOI: 10.1021/acs.jpcc.7b02717 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

PCBM molecules on the P3HT surface, but also because it employs a different model for the geometry and contents of the cell, in particular, the arrangements of the two superimposed and shifted P3HT polymer chains characteristic of the P3HT crystal, which allows for the close interpretation of X-ray absorption measurements.26 Moreover, we have taken into account long-range van der Waals interactions, as required by the closed-shell electronic structures of P3HT and PCBM, and we have performed the geometrical optimization processes starting from different initial orientations in the simulation cell of the PCBM molecule on the P3HT surface. Starting from the evaluated morphology and electronic structure of the PCBM/P3HT interface, we then addressed the effects of applied uniaxial stresses, both tensile and compressive, on the fine-tuning of the band gap and the alignment of the near-gap electronic levels of the system considered. The effects of various experimental deposition parameters, including the choice of solvents and external conditions such as temperature and surface contamination, that influence the performance of organic solar cells are not considered in the present article. Our aim is to show the effects of strain on the alignment of the neargap energy levels of the considered donor/acceptor system. In section 2, we discuss the geometrical model and numerical details employed for studying the PCBM/P3HT interface. In section 3, electronic band structure and band alignment in the complex system are discussed and compared with those of an isolated P3HT crystal. The optical spectra evaluated from the electronic band structure are described to further highlight the role of the PCBM/P3HT interface. In section 4, we report the study of the stress dependence of the energy levels that are important for the determination of the power conversion efficiency of the device, and we demonstrate that uniaxial compressive stress favors the efficiency of the solar cell. Section 5 contains the conclusions.

efficiency of the solar cell device are directly or indirectly related to the relative positions of the energy levels of the device,7,16,21−23 which are a result of the evaluated electronic structure, as discussed in section 4 below. First-principles theoretical contributions have often been applied to the study of the PCBM/P3HT interface using simplified supramolecular models composed of one strand of n thiophene units with one C60 fullerene molecule superimposed on top.9−15,24,25 In effect, the real system is more complicated because the symmetry of the C60 molecule is lost in the case of PCBM, because of the attached side chain. Moreover, it is wellknown that the sequence of the thiophene units in the P3HT polymer is distorted by the attached alkyl chains, interdigitated with the alkyl chains of the adjacent polymers.26 It is thus relevant to consider the mutual orientations of the P3HT chains and PCBM molecules. In fact, the frequently used “upright-standing” structure of the side chain of the PCBM molecule when deposited on P3HT does not lead to the lowest-energy configuration of the system.28 Moreover, as shown in the case of one PCBM molecule deposited on one strand of P3HT, van der Waals interactions also play a significant role in the energy optimization process of the global supramolecular structure.24 Improving on the supramolecular models, the quantum mechanical description of the PCBM/P3HT three-dimensional system requires the determination of the minimum-energy geometrical structures of the constituents while also taking the environmental interactions into account. A first-principles calculation exploiting the periodicity of the P3HT polymer with adsorbed PCBM molecules was proposed by Kanai et al.27 They modeled the interface in terms of a repeating tetragonal unit cell, along the polymer backbone direction, containing one strand of P3HT polymer composed of four thiophene rings with attached alkyl chains and one PCBM molecule with an upright-standing side chain. The cell chosen was separated by vacuum regions from the adjacent units in the other two directions, thus simulating a rod-type structure. More recently, Li et al.28 studied the effects of the orientation of the side chain of PCBM on the electronic and optical properties of the PCBM/P3HT crystalline system. They considered a supercell geometry made of the periodic repetition, along the z direction, of a single layer of PCBM molecules intercalated between two upper and two lower layers of P3HT polymer. The simulation cell contained one PCBM molecule and four strands of the P3HT polymer (with each strand composed of four thiophene rings with attached alkyl chains) in a sandwich-type arrangement. For such a system, the quasiparticle GW electronic band structure, with the excitonic states obtained using the Bethe−Salpeter equation, was reported.28 Periodic boundary conditions were also employed by Falke et al.8 with a simulation cell containing four thiophene rings and one C60 molecule. To contribute to a sound understanding of the PCBM/ P3HT interface at the atomic level, we present in this article a first-principles study of the adsorption of a single infinite layer of PCBM molecules on the surface of a P3HT crystal. The analysis of the interface electronic interactions and the alignment of the electronic states is the main object of our investigation. Our model differs from those used in refs 8, 27, and 28 not only because it describes the adsorption of a single layer of

2. MODELING OF THE PCBM/P3HT INTERFACE AND COMPUTATIONAL DETAILS To investigate the interface between P3HT and PCBM, we studied a model crystal made of a single layer of PCBM molecules adsorbed on the crystalline P3HT polymer surface. The problem of the regioregular-head-to-tail (rr-HT)-P3HT structure has been debated in the literature mainly regarding the arrangement of the alkyl side chains of the polymer. The lamellar packing of P3HT obtained from X-ray diffraction experiments29−39 and electron diffraction40−42 was theoretically interpreted26 including van der Waals interactions. It was demonstrated26 that the energetically favored crystalline structure corresponds to polythiophene chains with slightly rotated (∼16°) non-coplanar rings and a fishbone arrangement of interdigitated tilted alkyl side chains, in full agreement with the measured X-ray spectra. Moreover, it was shown that the primitive cell of the isolated P3HT polymer crystal contains two polymer chain strands one on top of the other, with each one composed of two thiophene rings mutually shifted (by one thiophene ring and one C−C bond) along their backbones and decorated by an alkyl side chain; see Figure 1a,b. The best fitting to the measured X-ray spectra was obtained using an almost orthorhombic primitive cell with parameters a = 16.76 Å, b = 7.52 Å, c = 7.94 Å, α = 90.1°, β = 89.9°, and γ = 90.2°. The c cell edge is along the backbone polymeric axis, the a edge is along the alkyl side-chain direction, and the b edge is along the stacking direction of the polymeric chains. As shown in ref 26, one chain strand in the primitive cell lies on the b = 0 plane, B


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It is worth noticing that the van der Waals contribution to the cohesive energy was found to be ∼23.7 eV per cell, which amounts to 0.06% of the total energy per cell. The contribution of the van der Waals interaction is significant for the overall equilibrium arrangement of the system. In fact, the distance between the center of the fullerene ball and the topmost P3HT chain was found to be 3.44 Å with the van der Waals contribution compared to 3.63 Å without it. Moreover, the average distance between the P3HT chains was also affected, as demonstrated by the distance between the fullerene center and the mean value of the polymer chains, which was found to be 4.12 Å with the van der Waals interaction versus 4.46 Å without it. To test the stability of the obtained geometry, we repeated the optimization procedure using the Quantum ESPRESSO code51 with an energy cutoff of 100 Ry on the plane-wave basis set and the same choice of MP k-point grid, arriving at the same geometry as obtained using the CRYSTAL code. To further check the stability of the obtained optimized geometrical structure, we randomized and then relaxed the atomic positions following the Car−Parrinello molecular dynamics approach at T = 0 with a fictitious electron mass of μ = 400 me. We thus obtained the minimum-energy conformation reported in Figure 2, which is almost indistinguishable from the one obtained using the CRYSTAL code.

Figure 1. (a) Schematic arrangements of rr-HT-P3HT polymer chains. a, b, and c are the edges of the primitive cell (in light blue) containing two strands of P3HT chains stacked along the b edge and mutually shifted along the c edge. For the PCBM/P3HT system, the P3HT cell (in light red) used in this work has dimensions a′ = a, b′ = b, and c′ = 2c. (b) Side view of the PCBM/P3HT system.

and the other lies on the parallel plane at b/2 separated by ∼3.8 Å from the first; see Figure 1a. The alkyl side chains attached to the thiophene rings do not lie on the polymer layer (a−c plane), as can be seen in the schematic presented in Figure 1a, and are only slightly interdigitated. In the present calculations, we employed a model semiinfinite crystal whose repeated simulation cell, with edges a′ = a = 16.76 Å along the alkyl side chains, c′ = 2c = 15.88 Å along the thiophene backbones, and γ = 90.2°, contained one PCBM molecule and two mutually shifted strands of P3HT polymer disposed along the b edge. The a−c cell parameters were dictated by the P3HT crystal lattice, and the b′ cell parameter, orthogonal to the interface, was chosen to be large enough to avoid interaction with the adjacent cells along the stacking direction. We then allowed the complete system composed of PCBM and P3HT (with 200 atoms belonging to the P3HT slab and 88 atoms to the PCBM molecule) to relax freely at fixed cell parameters to obtain the minimum-energy configuration of the global system. Several positions of the PCBM molecule on the P3HT layer were tested as initial conditions for the geometrical optimization process. These positions were chosen following the hypothesis, suggested by chemical considerations, that each PCBM molecule preferentially anchors in the bay region of the polythiophene chains on the a′−c′ surface (see Figure 1) where the thiophene rings are located. Several starting orientations of the PCBM molecule were tested with differing orientations of the side chain. The total interaction energy per cell between the two moieties in the lowest-energy configuration, evaluated as Einter = EPCBM/P3HT − EPCBM − EP3HT, was found to be −0.6 eV. We verified that other orientations of the PCBM side chain led to higher interaction energies: For example, the upright-standing configuration of the PCBM side chain gave Einter = −0.4 eV. The total electronic energy was evaluated in the Kohn−Sham density functional theory (KS-DFT) scheme43,44 with added van der Waals long-range interactions calculated using Grimme’s method.45 These calculations were performed using the CRYSTAL14 code,46 a periodic ab initio program based on atom-centered (Gaussian) basis sets, with the PBEsol exchangecorrelation functional47 with the TVPQ basis set.48 For the kpoint mesh, we used a (6 × 6) Monkhorst−Pack (MP) grid49 and a (12 × 12) Gilat grid.50

Figure 2. Optimized geometrical structure of the primitive cell of the PCBM molecular layer on the P3HT surface. Two surface primitive cells are reproduced along the direction of the alkyl side chains to indicate the bay region of the polymer crystal where PCBM molecules are anchored. Yellow, cyan, magenta, and red balls represent carbon, hydrogen, sulfur, and oxygen atoms, respectively. The side chain of the PCBM molecule is schematically shown in orange.

It is worth noticing that, to simulate the P3HT substrate, it is sufficient to consider only a single slab made of two shifted chains of P3HT in the primitive cell, as shown in Figure 2. In fact, we verified that the electronic band structure of P3HT did not change significantly when we used two slabs with four polymer chains per cell. In this case, the number of bands was doubled, but the correction of the energy gap was less than 0.1 eV and did not modify the overall profile of the near-gap band structure.

3. ELECTRONIC AND OPTICAL SPECTRA OF THE PCBM/P3HT SYSTEM We present in this section the KS-DFT electronic band structure of the P3HT crystal surface with a single layer of adsorbed PCBM molecules. For these calculations, we employed the B3LYP exchangecorrelation functional,52−55 which includes both gradient C


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Figure 3. (a) KS-DFT energy band structure of the optimized system composed of a single layer of PCBM molecules adsorbed on a P3HT crystalline slab. The red (black) energy curves correspond to the PCBM (P3HT) states of the complex system. The energy zero is on top of the PCBM P3HT PCBM valence band. (b) Pictorial representation of the main band alignments: ΔLL = |EP3HT LUMO − ELUMO| = 0.56 eV, ΔHH = |EHOMO − EHOMO| = 1.28 eV, and PCBM P3HT ΔHL = |ELUMO − EHOMO| = 1.44 eV. (Note: LUMO, lowest unoccupied molecular orbital; HOMO, highest occupied molecular orbital.)

From the evaluation of the density of states projected onto the atoms of the primitive cell, we obtained the contributions to the valence and conduction bands from the moieties forming the complex. We thus noticed that the topmost (π) valence bands, VB and VB − 1, were generated by the pz orbitals of the thiophene rings belonging to both polymer chains in the cell, but with higher contributions from those in the lower chain, whereas VB − 2 and VB − 3 (presented in red in Figure 3) originated only from the p orbitals on the fullerene balls; in fact, the energy levels corresponding to the orbitals of the atoms belonging to the PCBM side chain were found to be far from the near-gap energy region. Regarding the conduction bands, we observed that the CB, CB + 1, and CB + 2 bands were generated by the p orbitals of the fullerene part of PCBM, whereas the CB + 3 and CB + 4 bands were due to the antibonding (π*) states of the thiophene chains. These results are presented in panels a and b of Figure 4, where the colored isosurfaces highlight the spatial distributions of the contributions to the charge density from the near-gap valence and conduction bands, respectively. To obtain information on the charge transfer between the P3HT crystal surface and the adsorbed PCBM molecules, we performed a topological analysis of the electron density by means of the Bader procedure67,68 as implemented in the TOPOND1469 and CRITIC270,71 codes. A comparison of the electron-density topology of the total PCBM/P3HT system with those of its isolated components makes evident the electron charge redistribution upon adsorption and allows for a description of the interface region.25 This analysis showed that the adsorption of PCBM molecules on a P3HT substrate produces a charge transfer from the topmost polymer chain of P3HT to the PCBM molecule that amounts to 0.07 electrons per cell, a result that is in qualitative agreement with similar calculations for supramolecular PCBM/P3HT complexes.24 The z component of the total electric dipole moment due to the rearrangement of the charges of the two moieties and to the charge migration between them, evaluated with the CRYSTAL code, is 3.15 D and is directed from PCBM to P3HT. We also observed that the shortest intermolecular distance at the interface between PCBM and the P3HT surface was about

corrections and a tunable fraction of the Hartree−Fock exchange, a bonus used to tune the energy band gap to the experimental accepted band gap of pristine P3HT crystal (1.9 eV).56−64 To obtain this value, a 28% fraction of exchange was sufficient. The map of the evaluated electronic band structure for the PCBM/P3HT system is reported in Figure 3. The zero of energy was set on the topmost valence band. The fundamental band gap of the system was found to be direct and to occur at the Γ point. Its value was calculated as 1.44 eV, which is lower than the band gap of the isolate pristine P3HT crystal (1.9 eV). We noticed that the bands originating from the PCBM molecule were flat over all of the BZ cell, whereas the bands of P3HT were flat along the K → J′ line of the BZ, which corresponds in real space to the alkyl side-chain directions (see Figure 1a). Conversely, the largest band dispersion was along the thiophene-backbone direction, which corresponds to the Γ → J′ and the K → J lines in k space. The doubled band structure shown in black in Figure 3 confirms the presence of two stacked weakly interacting P3HT chains in the primitive cell. A further result, also shown in Figure 3, is that, once the PCBM layer was adsorbed on the P3HT, the energy band gap of P3HT increased to 2 eV, a value higher than the optical band gap of the pristine P3HT crystal.57−62,64 Moreover, the HOMO−LUMO separation for the PCBM molecular layer on P3HT was found to be 2.7 eV, whereas the same calculation for the isolated PCBM layer gave 2.76 eV. The above results, summarized in the band alignment sequence presented in Figure 3b, are in good agreement with the experimental results,65,66 which indicate a blue shift of the pristine P3HT band gap when the PCBM/P3HT system is formed. The band alignments of the bottom conduction and top valence band structures of the moieties forming the BHJ are the most important quantities for designing high-efficiency solar cells. For the determination of these quantities, quantum mechanical calculations on the complete system are required. In fact, simple knowledge of the band structures of the two separate components is not sufficient because of the ill-defined choice of the origin of energy for the separate band-structure calculations. D


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2.35 Å and occurred between a H atom of P3HT and a C atom of the PCBM side chain, whereas the longest one, between a H atom of P3HT and a C atom of fullerene, was 3.1 Å. Moreover, at the bond critical point between PCBM and P3HT, the charge density was less than 10−2, which confirmed the absence of covalent bonds between PCBM and P3HT. To provide further insight into the role of the PCBM/P3HT interface, we investigated the relationship between the electronic band structure and the optical properties of the PCBM monolayer adsorbed on P3HT. We calculated the optical properties of the complex system using the yambo package72 with the PBEsol functional, which required a scissor operator of 1.1 eV to reproduce the electronic band structure of Figure 3. The calculations were performed in the independentparticle random phase approximation. In this approach, the KS electronic orbitals and energies are used in the expression for the macroscopic transverse dielectric function whose imaginary part, ε2, enters the definition of the optical absorption spectrum, α = ωε2/nc, where n is the ordinary refraction index.73 The spectra shown in Figure 5 were obtained after convergence tests on the points used to represent the wave functions and on the number of bands (380 bands for the P3HT crystal and 530 for the PCBM/P3HT system). As expected from previous experimental and numerical results on the P3HT/PCBM blend, the absorption coefficient of the full system (see Figure 5, red line) bears the fingerprints of the isolated constituents: The features mainly related to the π → π* transitions of pristine films of P3HT polymeric crystals are in the low-energy region (less than 3 eV), whereas those due to transitions involving the PCBM molecules are at higher energies. In particular, we found a large feature of radiation absorption occurring at ∼850 nm that should involve transitions from VB and VB − 1 to CB and CB + 1. In the evaluated absorption spectrum, after the onset, we found a shoulder at ∼580 nm and two stronger peaks at 518 and 492 nm, which correspond to the transitions VB − 1 → CB + 3, VB → CB + 4, and VB − 1 → CB + 4, respectively (see Figure 3). These features essentially correspond to the π → π* transitions in the P3HT polymer. We also noticed that the adsorption of the PCBM monolayer on P3HT led to a blue shift of ∼100

Figure 4. Isosurfaces highlighting (in red) the contributions to the charge density from the near-gap (a) valence and (b) conduction bands, evaluated at the Γ point.

Figure 5. Calculated optical absorption spectrum of one monolayer of PCBM adsorbed on P3HT (blue) and of a pristine P3HT crystal (red). The main absorption frequencies and the absorption edge are indicated by arrows. In panel a, the polarization direction of the incident radiation is along the thiophene chains; the inset shows the experimental data for a 1:1 P3HT/PCBM blend film extrapolated from ref 19. In panel b, the polarization direction is parallel to the direction of the alkyl side chains. For comparison, the experimental absorption spectrum76 of a pristine PCBM film is presented in the inset. E


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The Journal of Physical Chemistry C meV of the spectrum of pristine P3HT and a reduction of ∼20 meV of the distance between VB and VB − 1. For the absorption spectra, shown in Figure 5, only interband electronic transitions were considered without resolving them into vibronic bands. In effect, as discussed in ref 74, chain aggregation could also contribute to the optical absorption of systems composed of conjugated polymers, but in the solidstate phase, engineering of the electronic states to tune the absorption coefficient is the main way to improve the performance of solar cell devices.75 The optical absorption spectrum of PCBM/P3HT, evaluated for incident light polarized along the c′ axis of the simulation cell, is reported in Figure 5a and compared with the corresponding experimental spectrum.19 The quantitative agreement between the calculated and measured spectra is evident from the positions of the main spectral features and further confirms the reliability of the geometrical structure obtained for the crystalline PCBM/P3HT complex, in particular, the doubled band structure of P3HT with two superimposed and shifted chains of P3HT in the cell and the orientation of the side chains attached to the fullerene molecules. Figure 5b reports the evaluation of the PCBM/ P3HT optical absorption for incident radiation polarized along the alkyl-side-chain axis of the simulation cell; for comparison, the experimental absorption spectrum76 of the pristine PCBM film is reported in the inset. Comparison of panels a and b of Figure 5 shows the strong anisotropy of ε∥2 in the low-energy region ℏω < 3 eV, where mainly optical π → π* transitions involving P3HT orbitals of the thiophene chains contribute. In fact, in the case of ε∥2 , the electric field of the incident radiation is directed along the thiophene backbone of the polymer. Conversely, in the higher-energy region, the difference between ε∥2 and ε⊥2 is reduced because the optical transitions mainly involve the states of the fullerene part of PCBM, which is spatially isotropic.

the absorption of radiation up to charge collection at the electrodes. Moreover, the donor−acceptor synthesis process, the solvents used, and the thermal annealing and chemical processes also play a role in the final value of the PCE of a BHJ solar cell. Optimization of the efficiency of a BHJ solar cell thus involves optimization of the efficiencies of absorbing solar energy, dissociating excitons at the donor/acceptor heterointerface, transfering charge to the electrodes, and eventually collecting charge at the electrodes. The energy band alignment of the moieties composing the BHJ system is expected to be of relevance mainly in the processes of radiation absorption and exciton dissociation. In fact, the ability of the donor to absorb P3HT P3HT solar energy is related to its band gap: EP3HT Gap = |ELUMO − EHOMO |. The main driving force for exciton dissociation at the donor/ acceptor interface (thus contributing to the short-circuit current Jsc) is the LUMO offset, that is, the interface potential, which is related to the difference between the lowest conduction bands PCBM of the complex system: ΔLL = |EP3HT LUMO − ELUMO|. Conversely, the open-circuit voltage Voc, which is a measure of the maximum voltage that a solar cell can provide to an external circuit, is related to the band gap of the complex system, with P3HT an upper limit given by the difference ΔHL = |EPCBM LUMO − EHOMO |. From the above considerations, it is evident that a good strategy is to reduce the polymer band gap so that the highest part of the solar spectrum can be absorbed,7,21 and to simultaneously increase the open-circuit voltage, namely, the ΔLL energy interval.16,22 Increasing Voc can be obtained chemically by raising the LUMO level of the acceptor by appropriate substituents in PCBM23 or by electron irradiation.78 For the PCBM/P3HT system considered here, we show that the energy band profiles can be engineered with an applied constant strain, to optimize the two photovoltaic parameters that govern high harvesting of the solar energy spectrum and high dissociation of the created excitons into free carriers in the ideal case of the absence of impurities and defects at the donor/ acceptor interface. The effects of mechanical strain on the electronic properties of organic semiconductors are receiving increasing attention both in the field of organic electronics and in photovoltaic applications.79,80 In particular, it was found that applying hydrostatic pressure to a polymer material is an efficient method of controlling the planarity of its backbone configuration81 and an easy procedure for continuously modulating Voc and the energy gap parameter in OPV cells.82 Moreover, changes in the LUMO offset and band gap with applied hydrostatic pressure on a PCBM/P3HT blend were experimentally measured by variation of photoluminescence and absorption spectra82 and interpreted in terms of polymer planarization and the consequent variation of the conjugation length along the polymer backbone.81 We evaluated the effects of applying uniaxial stress, both tensile and compressive, on the electronic structure of the PCBM/P3HT interface analyzed in the previous section. Before performing numerical calculations, we noticed that, for the donor/acceptor organic light-harvesting materials most often used in solar cells, the optical band gap is in the range of 1.7−2.1 eV and Voc is generally less than 1 eV. Moreover, it was shown83 that, for a large number of organic BHJs, the relationship eVoc = ΔHL − 0.3 eV holds, where the empirical factor 0.3 eV summarizes different energy loss mechanisms at work. In addition, to favor exciton dissociation, it is necessary

4. TUNING THE BHJ SOLAR CELL BAND STRUCTURE USING STRESS The microscopic description of the interface between the P3HT crystalline polymer and the adsorbed PCBM molecular layer allows for the exploration of a strategy to modify the neargap energy levels of the complex system to enhance its efficiency as an active material for organic photovoltaic (OPV) cells. The power conversion efficiency (PCE) of an organic solar cell is defined as the ratio between the output energy provided by the cell and the incident solar energy. Two important photovoltaic parameters contributing to the cell PCE are the open-circuit voltage, Voc, and the short-circuit current, Jsc. Voc is essentially related to the band gap of the complex system, whereas Jsc mainly contributes to the interface potential, which is responsible for dissociation into long-lived electron and hole charges without previous recombination77 of excitons reaching the donor/acceptor interface. In effect, a variety of processes occur in the functioning of an organic BHJ and in conditioning its PCE. After the absorption of solar radiation, many-body excitations in the polymer system are generated, which are often schematized as electron−hole bound neutral pairs. Afterward, the excitons that reach the polymer/ acceptor interface within their typical diffusion length (∼10 nm) might dissociate, leaving holes in the donor material and electrons in the acceptor material. The free charges then undergo diffusion to the electrodes. In all of these steps, loss mechanisms due to different causes are present, starting from F


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The Journal of Physical Chemistry C that ΔLL be greater than the typical exciton binding energy Eb, which is on the order of 0.3−0.5 eV for conjugated polymers, and to prevent electron−hole recombination in the donor material, it is preferable to have ΔHH > Eb. For stress applied along a given direction, in the linear approximation regime, the Poisson ratio ν = −ξ⊥/ξ∥ relates the strains perpendicular and parallel to the stress direction. We evaluated the Poisson ratio for uniaxial stress on the P3HT slab with adsorbed one layer of PCBM molecules, changing the lattice parameter of the simulation cell along the thiophene-chain direction as ξ∥ = (c − c0)/c0, where c and c0 are the strained and equilibrium lattice parameters, respectively, while applying stress-free boundary conditions in the transverse a direction. For each value of the strained cell, we calculated the Poisson ratio after full relaxation both of the simulation cell parameters and of the coordinates of all atoms in the cell. We found that, for small percentage strains (between −3% and 3%), the Poisson ratio is almost constant with a value of about 0.30, which is near the experimental value of 0.3584 for blends of P3HT with PCBM. We calculated the Poisson ratio only for stresses parallel to the c edge of the cell because the carbon atoms of the thiophene backbone provide the most important contribution to the electron energy bands near the band gap. Using the evaluated Poisson ratio, the values for the c and a cell edges were deduced from the expressions c′ = c(1 + ξ∥) and a′ = a(1 − νξ∥). For each strained and relaxed configuration, we calculated the electronic band structure and the band alignments. The numerical results reported in Figure 6 and

Table 1. Band Structure Offsets ΔHL, ΔLL, and ΔHH and PCBM Energy Gaps EP3HT as Functions of the Uniaxial Gap and EGap Strain along the c Crystal Axisa strain

ΔHL (eV)

ΔLL (eV)

ΔHH (eV)

EP3HT Gap (eV)

EPCBM (eV) Gap

−3 −2 −1 0 1 2 3 exptb

1.23 1.29 1.37 1.44 1.52 1.59 1.66 1.40

0.63 0.62 0.58 0.56 0.53 0.52 0.49 0.70

1.49 1.42 1.35 1.28 1.2 1.13 1.05 0.90

1.86 1.91 1.95 2 2.05 2.11 2.15 2.10

2.71 2.71 2.72 2.72 2.72 2.72 2.72 2.30

a

See Figure 3 for definitions of symbols. bExperimental values for unstrained P3HT/PCBM (1:1) melt.66

5. CONCLUSIONS We have shown that continuous tuning of the alignment of the electronic band edges of the complex made of a layer of PCBM molecules adsorbed on the surface of the crystalline P3HT polymer can be used to enhance the power conversion efficiency of a BHJ solar cell, being able to influence its macroscopic photovoltaic parameters. It is worth noticing that the determination of the energy level alignment of the two moieties forming the BHJ cannot be done from the knowledge of the separate band structures of the moieties: The alignment of energies must be deduced from the band structure obtained for the complex system. For this purpose, we first addressed by ab initio methods the energy optimization of the geometrical structure of the system and then evaluated its electronic band structure and the spatial and atomistic nature of the states involved in the near-gap region. After evaluation of the Poisson ratio, for each strained structure, we determined the full relaxed geometry of the cell and the atoms in the cell and the electronic band structure of the complex strained system. We thus determined that a compressive uniaxial stress can reduce the energy band gap of the donor material, thereby increasing the harvest of solar energy, and increase the LUMO offset, thereby enhancing the exciton dissociation into free charges.

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Figure 6. Band offsets as a function of uniaxial strain. The ΔLL energy offsets and donor polymer band gap in the complex system are presented in red and blue, respectively. The band gap of the complex system is presented in black. Lines are drawn as guides to the eye.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Guido Menichetti: 0000-0002-9588-5002 Notes

Table 1 show that the application of a uniaxial pressure along the direction of the polymer backbone produces a reduction of the energy gap of the donor material (with a consequent increase in the solar energy absorption and, thus, in the shortcircuit current) and also a less pronounced increase of the LUMO offsets (with a consequent increase of exciton dissociation at the donor/acceptor interface). We also observed a reduction of the energy gap of the complex system, ΔHL, between the LUMO level of the donor and the HOMO level of the acceptor (which conversely reduces the open-circuit voltage), in agreement with the results of ref 85. We can thus conclude that a uniaxial compressive strain should favor the efficiency of the solar cell with an appropriate compromise among the rates of modification of the alignment of the energy levels under stress.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the “IT center” of the University of Pisa for computational support. We also acknowledge the allocation of computer resources from CINECA through ISCRA C Projects HP10C6H6O1 and HP10CAI9PV.

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