Orientation-Dependent Electronic Structures and Optical Properties of

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Orientation-Dependent Electronic Structures and Optical Properties of the P3HT:PCBM Interface: A First-Principles GW-BSE Study Long-Hua Li,* Oleg Y. Kontsevoi, and Arthur J. Freeman Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, United States S Supporting Information *

ABSTRACT: In this work, the effect of [6,6]-phenyl-C61butyric acid methyl ester (PCBM) orientation on the electronic and optical properties of the regioregular poly(3hexylthiophene) (P3HT):PCBM blend interface was studied by means of first-principles density functional theory calculations with G0W0 approximation plus the Bethe− Salpeter equation (BSE). The band structures and photoresponse are shown to depend on the PCBM orientation. The origin of the two main optical absorption peaks is determined, and the effect of PCBM rotation on optical properties is revealed. The calculated lowest charge transfer complex state energy, exciton binding energy, and the absorption spectrum for the flat-lying model are in good agreement with the experimental values, which indicates the flat-lying structure is the predominant interface structure in the experiments. The lowestenergy configuration is also determined as the flat-lying orientation in our calculations. Our results further suggest that the dissociation of excitons and charge transfer at the interface is more efficient for the PCBM flat-lying orientation than that for the upright-standing one, which provides a possible explanation for the increased performance of the P3HT:PCBM devices after a thermal annealing treatment.

I. INTRODUCTION In the past decade, significant efforts have been made to improve the power conversion efficiency (PCE) of organic photovoltaic cells and to understand correlations between PCE and the morphology of the donor−acceptor (D−A) binary. In one of the most studied binary systems, which consists of the electron donor regioregular poly(3-hexylthiophene) (rr-P3HT) and electron acceptor [6,6]-phenyl-C61-butyric acid methyl ester (PCBM), the PCE is reported to be 5−7%.1,2 To improve PCE, it is critical to control the blend morphology.3 A number of studies have shown that the type of solvent used, donor to acceptor ratio, and thermal annealing treatment have a great impact on PCE because they could strongly affect the morphology.4−7 The correlation of nanoscale structure and device efficiency can be studied by high-resolution techniques, e.g., transmission electron microscopy (TEM)3,8 and smallangle neutron scattering (SANS); 9 however, they are insufficient to explore the relation between the morphology and local electronic properties.10 To better understand the interplay between device efficiency and nanoscale morphology, the atomistic structure of the interface and the local electronic properties should be determined. Previous studies suggested that the electronic structure of P3HT is affected by the torsion angle between thiophene rings11 which could be modified by interactions with PCBM.12 Studies on other noncovalent interfaces, such as C60:Cu(100),13 C60:PPV,14 C60:CuPc,15 and 6T:Ag(111),16 have © 2014 American Chemical Society

shown that the conductance, energy level alignment, ionization potential, and exciton absorptions are orientation dependent. This is because the changes of orientation alter intermolecular interactions, which results in changes in the charge transport properties, electron correlation, as well as dielectric screening.17 Therefore, changes in the molecular orientation should be an effective way to control the intermolecular interactions, and understanding the microstructure−photophysics relation of the organic−organic interface is of fundamental interest. However, the exact atomic structure of the P3HT/PCBM interface is not known from experiment, as of yet. The modeling of the blend interface is therefore a considerable challenge. Previous theoretical studies18−20 often simplified such a blend interface structure into one PCBM molecule upright-standing on the top of one P3HT chain, and it is not clear why only the upright-standing orientations were considered. In contrast to previous theoretical works, in this study we investigate the microstructure−property relationship at the interface by changing the orientation relation between P3HT and PCBM. We also employ the first-principles manybody perturbation theory to demonstrate the dependence of electronic and linear optical properties on the interfacial Received: February 5, 2014 Revised: April 23, 2014 Published: April 28, 2014 10263

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Figure 1. (a) Global minimal structure of P3HT:PCBM (M90). C: brown; S: yellow; H: pink; O: red. (b) Selected models with different PCBM rotation angles. (c) The dependence of the cohesive energy on the rotation angle of PCBM.

χ0/(1 − υχ0); and (iii) the solution that includes both υ and W, e.g., the BSE solution.27 In the case of an excitonic system, it is possible to map BSE onto the effective two-particle Schrödinger equation HexAλ = EλAλ, where Eλ and Aλ are the exciton energies and eigenvectors, respectively. The excitonic Hamiltonian Hex in the Tamm−Dancoff approximation28 is expressed as

microstructure, as well as the role of many-body effects on the optical properties of this interface. Theoretical methods to calculate the linear optical dielectric function provide a way to explore the interactions at interfaces, especially when the GW approximation21 for accurate electronic quasi-particle energies and the Bethe−Salpeter equation (BSE)22 to calculate electron−hole (e−h) interaction effects are employed for excited states. The GW-BSE-based methods were only recently applied to thin films of πconjugated polymers due to their extremely heavy computational demands.23−26 The paper is organized as follows. In Section II, the theory of optical response and the computational method are briefly introduced. In Section III, the dependence of the imaginary part of the dielectric function on the PCBM orientation is presented. The intermolecular interactions and many-body effects on the dielectric function are discussed. The conclusions are drawn in Section IV.

H ex = (εc k − εv k )δvv ′δcc ′δ kk ′ + (2υvc k, v ′ c ′ k − Wvc k, v ′ c ′ k ) ′ ′ (fc k − fv k ) (2)

where k, ν, and c are the index of the k-point, valence band, and conduction band, respectively. The εc(v)k can use DFT eigenvalues or quasiparticle energies. The first part of this Hamiltonian is analogous to the single-particle Hamiltonian, and the last two parts compose the BSE kernel. The imaginary part of the dielectric function ε″ can then be obtained25,29 ε″(ω) = lim

II. THEORY AND COMPUTATIONAL METHODS A. Optical Response. In general form, the polarizability function χ can be written as χ = χ 0 + χ 0 Kχ

q→0

8π 2 q 2V

∑ ∑ |⟨v k − q|eiqr|c k⟩A vcλ k |2 δ λ

vc k

((Ec k − q − Ev k ) − ω)

(3)

This is the function that determines the BSE optical absorption spectrum. B. Computational Methods. The electronic structure calculations and structure optimization are performed by the density functional theory (DFT) pseudopotential plane-wave method as implemented in the PWSCF code of the Quantum ESPRESSO30 package. The norm-conserving pseudopotentials are used. The kinetic energy cutoff is chosen to be 50 Ry. The sampling of the Brillouin zone is 2 × 2 × 1 according to the Monkhorst−Pack (MP) scheme. For structure relaxations, total energy LDA calculations are performed until the residual forces on atoms are less than 0.01 eV/Å.

(1)

where χ0 is the noninteracting polarizability function and K is the kernel function. The kernel function is defined as K = υ + W and contains two main parts: the bare Coulomb term υ (the local field effect, LFE) and the screened Coulomb term W. According to the above definition of χ, three different approximations of the dielectric function can be obtained: (i) the independent particle (IP) polarizability, where υ = 0 and W = 0, which leads to χIP = χ0; (ii) the random-phase approximation (RPA), where only W = 0, resulting in χRPA = 10264

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Figure 2. Quasiparticle band structures along directions y and z for (a) M0 and (b) M90. The valence band and conduction band extremes in the vertical z direction are marked in blue for P3HT and in red for PCBM. The interband transitions associated with excitons P1 and P2 are indicated by red and blue arrows, respectively. (c) Charge density of VB and CB extremes for M0 and (d) M90.

III. RESULTS AND DISCUSSIONS

To obtain a global minimum structure of the P3HT:PCBM interface, the simulated annealing method is employed. Three stages are used to simulate thermal annealing in steps of 1 ps as follows: (i) heat from 10 to 500 K within 1000 ps, (ii) keep at 500 K for 1000 ps, and (iii) slowly cool from 500 to 10 K within 5000 ps. Such a process is repeated three times to reach a solution that is close to the global minimum. Then, the plane-wave code Yambo31 is used for calculating quasiparticle (QP) energies and optical properties. The electronic structures obtained from DFT calculations are further corrected by means of the nonself-consistent G0W0 approximation. A denser k-point sampling of 6 × 6 × 2 is used to ensure the convergence of QP energies and response functions. We apply three approximations IP, RPA, and BSE in the response function as described above to explore the LF effect and e−h interactions.

A. Model Geometry. Due to the extremely high computational demands of GW-BSE calculations, it is very important that the size of the model used in the calculations is sufficiently small, yet it should capture all important physics of the large system. Since our focus is on the interactions of the P3HT:PCBM interface, we employ the model that contains only one PCBM molecule and ignore the interaction between PCBM. We also apply a periodic superslab geometry to avoid inclusion of vacuum space in our model which would require a large number of unoccupied states in GW calculations. The dependence of the GW quasiparticle gaps on the length of the unit cell along the nonperiodic direction was previously reported in low-dimensional structures because the images interact via the long-range part of the Coulomb potential;32 the 10265

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use of a superslab geometry allows one to avoid these GW errors. The P3HT:PCBM interface is therefore modeled by a periodic supercell consisting of one PCBM molecule and four layers of P3HT with each layer containing four thiophene rings, and the total number of atoms in the unit cell is 488. In this model there are in fact two P3HT:PCBM interfaces that are formed, with different interface geometries. However, we consider this as an advantage of the model, as it allows us to account for a degree of disorder present in the actual P3HT:PCBM system. Recent experiments9 show that the PCBM and P3HT form interpenetrating networks, and our model approximates such a morphology. The global minimum structure, obtained using the simulated annealing method, is shown in Figure 1(a); it is named the 0 degree model (M0), or flat-lying structure. Starting from this structure, we then rotate the PCBM molecule at 15° intervals and then fully relax models that are obtained after the rotations. The relaxed models with different PCBM rotation angles, denoted as M15, M30, M45, M60, M75, and M90, are shown in Figure 1(b). It can be seen that the lattice vector c increases with the decrease of the rotation angle. The strength of the intermolecular interactions is given by the cohesive energy which is defined as the energy difference between the whole system and two components calculated using the same supercell. The calculated dependence of the P3HT:PCBM cohesive energy on the rotation angle is plotted in Figure 1(c). The M0 structure is the most energetically favorable configuration, and we can therefore predict that the flat-lying structure should be the ground state of the interface. This most stable configuration is consistent with the recent coarse-grained molecular dynamics simulations.33 Although the cohesive energy decreases when the PCBM rotation angle increases and the cohesive energy of the upright-standing (M90) structure is about 0.34 eV higher than that of the M0, we cannot rule out the possibility of existence of other interfacial orientations. All of them may be observed in the experiment; it is perhaps a matter of proportion. B. Electronic Structure. The calculated G0W0 band structures of the P3HT:PCBM interface are presented in Figure 2(a) and 2(b) for the M0 and M90 models. Several important conduction bands (CB) are marked on the plot starting from the conduction band extreme (CBE), as well as a number of valence bands (VB) counting down from the valence band extreme (VBE). The band-decomposed charge densities corresponding to several main bands are shown in Figure 2(c) and 2(d). From the analysis of the charge densities the character of the bands at the interface can be summarized as follows: the first four valence bands (from VBE to VB-3) are from the π states localized on P3HT. The next two valence bands, VB-4 and VB-5, are ascribed to π states of PCBM. The first three conduction bands from CBE to CB+2 are contributed by π states of PCBM, and the next two bands, CB+3 and CB+4, are related to P3HT. (Additional charge density plots are shown in the Supporting Information, Figures S1 and S2). The conduction band and valence band extremes for P3HT are then determined as bands CB+3 and VBE; these band extremes are marked along Γ−z, i.e., the vertical z direction, by blue lines in Figures 2(a) and 2(b). The band extremities for PCBM are determined to be CBE and VB-4, which are marked in red lines. The important band offsets obtained from G0W0 calculations for interfaces with seven PCBM rotation angles are listed in Table 1. The energy offsets are defined as follows: ΔHL =

Table 1. Characteristics of the Band Structure Offsets for Selected Models from M0 to M90a system

ΔHL (eV)

ΔHH (eV)

ΔLL (eV)

ΔE(P3HT)

ΔE(PCBM)

M0 M15 M30 M45 M60 M75 M90 Exp.b

1.04 1.04 1.00 1.30 1.28 1.19 1.48 1.40

−1.42 −1.45 −1.47 −1.32 −1.42 −1.48 −1.37 −0.90

0.96 1.05 1.03 0.84 0.65 1.01 0.93 0.70

1.99 2.08 2.03 2.14 1.94 2.21 2.41 2.10

2.46 2.49 2.46 2.62 2.70 2.67 2.85 2.30

The band offsets include: ΔHL − the offsets of the valence band extreme (VBE) for P3HT and conduction band extreme (CBE) for PCBM; ΔHH − the offsets of the CBE for PCBM and P3HT; and ΔLL − the offsets of the VBE for P3HT and PCBM. ΔE is the offset between VBE and CBE for P3HT and PCBM. bFrom ref 10. a

Ec(PCBM) − Ev(P3HT); ΔHH = Ev(PCBM) − Ev(P3HT); ΔLL = Ec(P3HT) − Ec(PCBM); ΔE(P3HT) = Ec(P3HT) − Ev(P3HT); ΔE(PCBM) = Ec(PCBM) − Ev(PCBM), where Ec and Ev are the CBE and VBE for the corresponding phases at the interfaces. ΔLL and ΔHL are important energy offsets which are related to the dissociation of excitons and opencircuit voltage (Voc); ΔLL acts as a driving force for exciton dissociation; ΔHL is equal to Voc in the ideal conditions, assuming that the work function of the anode matches ideally the donor HOMO (CBE), while the work function of the cathode matches the acceptor LUMO (VBE) (see refs 33 and 34 for more discussion). The opposite sign of ΔHH and ΔLL indicates that the band alignment belongs to the type-II heterojunction. The PCBM rotation does not alter the type of band alignment but could change the interfacial gap ΔHH, as can be seen from Table 1. The change of ΔHH does not exhibit a single relation to the PCBM rotation angle because the PCBM orientation affects the electronic bands of two P3HT:PCBM interfaces. The influence of PCBM orientation on the interfacial electronic structure is indicated by the charge density plots in Figure 2(c) and Figure 2(d) as well as in Figures S1 and S2 (Supporting Information), where the charge distributions are significantly different between M0 and M90. However, some trends can still be observed. The change in ΔHH between different orientations is less than 0.1 eV, as well as the difference in ΔLL, except for M45 and M60. As a result, the interface gap ΔHL follows almost the same changes as the changes of the band gaps ΔE for P3HT and PCBM: the ΔHL and ΔE tend to blue-shift as the PCBM rotation angle increases. The calculated band offsets for M0 are in reasonably good agreement with recently measured experimental values.10 The notable difference is for ΔHL, which in the most stable configuration is still smaller than the experimental ΔHL value by 0.36 eV. The agreement with experiment is much better for the band gaps, ΔE, for the two individual components at the interface, which are only 0.11 eV smaller than the experimental value for P3HT and 0.16 eV larger for PCBM. It can be therefore concluded that the underestimation of ΔHL in M0 is not the result of band gap underestimation for the two components but is likely due to the overscreening at the interface. The bands that associate with P3HT should have large QP correction because the π bands (pz) of P3HT are less screened, especially for the first layer of P3HT that is near the 10266

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PCBM. On the side of PCBM, the π orbitals are almost symmetrically localized on C60, and electronic screening is instead significant. Therefore, the QP correction should have a much smaller impact on PCBM-related bands than that of P3HT. Overscreening at the interface could be related to the underestimation of distance between P3HT and PCBM after relaxations with LDA. One may try to apply the van der Waals functional to correct LDA overbinding, but it is beyond our scope in this paper. C. Optical Properties. To get a first insight into the impact of PCBM orientation on the photoresponse of the P3HT:PCBM interface, the imaginary part of the dielectric function (ε″) is calculated at the IP level for seven selected models. Only the largest transitions along the yy polarization direction are compared in Figure 3(a). First of all, noticeable

due to the small optical transition matrix element between VBs of P3HT and CBs of PCBM caused by the flat CBs of PCBM. Interestingly, although the second predominated peak is related to the bright absorption of the P3HT component, its line shape and position are also modified by the PCBM orientation. However, as we will show later, such modifications can be become significantly less pronounced if e−h interactions are included in the calculations. The BSE optical calculations with LF effects and e−h interactions are then performed to explore the excitonic properties for two distinct structures: flat-lying (M0) and upright-standing (M90) interfaces. First, the LF and e−h effects on the absorption spectra are analyzed. Figures 3(b) and 3(c) show ε″ with a different level of approximation, as described in Section II. The imaginary part of the dielectric function of P3HT:PCBM interfaces is highly anisotropic. The spectrum is dominated by transitions in the yy polarization direction, which is parallel to the backbones of P3HT. The xx polarization is parallel to the lamella direction of P3HT, and the zz polarization direction is perpendicular to the interface. Since wave function overlaps along the x and z directions are weak, the transitions with polarization along these two directions are therefore small in the low-energy region. Beyond the IP picture, a remarkable line shape modification in a relative high-energy region is found in the RPA picture due to the LF effects, namely, at energies higher than 5 eV in the upright-standing interface and higher than 4 eV in the flat-lying interface. Except for that, the IP and RPA pictures are similar to each other. Therefore, the importance of the LF effects on the optical spectrum is limited in this case. The excitonic effects (blue lines in Figures 3(b) and 3(c)) on the optical properties of the P3HT:PCBM interface are evident from comparing the RPA and the BSE results. The e−h interactions cause a remarkable red-shift and oscillator strength redistribution of spectra in all three polarization directions. Moreover, the e−h interactions not only enhance the strength of the P1 and P2 peaks but also decrease the energy offset between P1 and P2. The energy difference in the RPA between P1 and P2 is 0.81 eV for the M0 structure and 1.25 eV for M90, while they decrease to 0.13 and 0.62 eV for M0 and M90, respectively, after including the e−h interactions. We now discuss the main difference of optical excitations between M0 and M90. The first two excitons are located at P1 (1.56 eV) and P2 (2.18 eV) for the flat-lying structure (M0). Comparing with M0, the first peak P1 shows a significant 0.6 eV blue-shift in M90. However, the second peak, P2, shows a relatively small blue-shift of only 0.1 eVfrom 2.18 eV in M0 to 2.28 eV in M90. The reason for the discrepancy could be explained as follows. From the analysis of matrix elements of the optical transitions, P1 is determined by the interband transitions between VBs of P3HT and CBs of PCBM (marked by red arrows in Figure 2(a,b)) which are affected significantly by the intermolecular coupling at the interface. However, P2 is associated with the transitions from VBs to CBs of P3HT only (blue arrows in Figure 2(a,b)). Since intermolecular interactions have limited impacts on the intrinsic quality of P3HT, the difference of P2 between M0 and M90 is smaller than that of P1. To further confirm our analysis, in Figure 4 we plot the e−h charge density calculated with the hole position fixed at the first layer of P3HT since P3HT acts as a donor at the interface. In both M0 and M90 configurations, the lowest singlet exciton P1 is characterized by the hole and electron at different

Figure 3. Calculated imaginary part of the dielectric function. (a) The dependence of optical absorption on PCBM rotation; dashed line tracks a blue shift of P1 from M0 to M90. (b) Three different approximations (IP, RPA, and BSE) of dielectric function for flat-lying (M0) and (c) upright-standing (M90) structure in three optical polarization directions.

modifications of the shape and the amplitude of the first peak P1 (around 2 eV) are found due to changes in the orientation of PCBM. The P1 peak is large for M0, while it becomes smaller in other orientation models and almost disappears in M75 and M90. Moreover, a blue-shift of this first peak is found with the increase of PCBM rotation angle. Our calculations demonstrate that the change of PCBM orientation is an effective way to modify the interfacial optical absorption. The blue-shift of the first peak is caused by the transitions at the interface from VBs of P3HT to CBs of PCBM, which will be discussed later. Furthermore, the oscillator strength of the first peak is much smaller than that of the second peak P2. This is 10267

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Figure 4. Response charge density |ψ(rh − re)|2 of P1 and P2 (arrows in Figure 3(b) and (c)) for (a, b) flat-lying and (c, d) upright-standing models with an isosurface value of 0.02 e/Å3. The hole position is fixed at the top of the P3HT layer and is marked by a black square.

The influence of PCBM orientation on the predominant P2 exciton is clearly exhibited in Figure 4(b) and Figure 4(d). The electrons are localized on the P3HT chains that are close to the interface in M0, while they are localized on P3HT chains that are away from the interface in M90. The remarkable difference of P2 e−h distribution between M0 and M90 is due to the different optical transitions (shown by blue arrows in the band structures in Figure 2(a, b)), which again are associated with the change of intermolecular interaction caused by the orientation of PCBM. In the flat-lying structure (M0), the P2 is formed by a mixture of the transitions between VB-1 and CB +4 and transitions between VB-2 and CB+3. For the uprightstanding structure (M90), the P2 is dominated by the transitions from VB-1 only to CB+3 and CB+4. When comparing the optical absorption of M0 with experiment, it should be noted that there are two features in our BSE calculated spectra that are different from the measured absorption spectra. One is that the absorption peak P1 around 2 eV is revealed in our calculations, but it is not observed in the measured linear optical spectra.35,36 P1 is deep below the optical gap of the material constituents.14,34 It is hardly detected by linear absorption measurements but can be observed by EA34 spectroscopy. Our calculated charge transfer complex state, P1, has an onset at 1.5 eV for M0, which is close to the recent EA experimental value of 1.2 eV. Another difference is that the absorption higher than 3 eV is not evident in our calculations but is shown in experiments. This difference may be associated with the concentration of PCBM (or, more precisely, attributed to intermolecular interactions among PCBM). The marked absorption above 3 eV which is related to the PCBM states is only seen in experiment for concentration of PCBM higher than 20 wt %.35 In our calculation model a single layer of PCBM is used, which is insufficient to reveal significant PCBM-associated optical transitions. Thereby, the absorption at energies higher than 3 eV is not evident. Except for that, the BSE predicts absorption of P3HT between 1.89 and 2.87 eV, which agrees well with the experiment of 1.85−2.7 eV.35,36 In addition, the calculated EB of P3HT is 0.78 eV, which is consistent with the recently measured experimental value of 0.7 eV.37 In summary, our calculations show that the flat-lying orientation of PCBM at the interface has a better charge

constituents of the interface, which is the charge transfer complex (CTX) state.14,34 The exciton P2 is also the charge transfer (CT) state where the e−h pairs are localized on different P3HT chains. Although P1 and P2 are CT-type excitons for both M0 and M90 configurations, the details are different. First of all, the electrons of P1 are much more delocalized on PCBM in M0 than that in M90, as seen from comparison of Figure 4(a) and Figure 4(c). This suggests that the e−h interaction at the interface is stronger for M90 compared with M0. Second, the hole is surrounded by some electrons in M90, which means that the P1 of M90 is the mixture of Frenkel (FR) and CT-type excitons. However, in M0 the hole and electron are separated on P3HT and PCBM, respectively; therefore, it is a pure CT exciton. It is known that the e−h interaction of a FR exciton is stronger than that of a CT exciton. On the basis of the above analyses, we could deduce that the exciton dissociation at the interface is faster in M0 than that in M90. This conclusion can also be drawn from the comparison of exciton binding energies (EB). Small binding energy yields fast charge separation. In principle, the EB is evaluated from the energy difference between the onset energy of the corresponding interband transition in the RPA picture and the excited energy in BSE. The EB values of P1 and P2 for M0 and M90 are listed in Table 2. The EB of P3HT is the same Table 2. Exciton Binding Energy EB (eV) of M0 and M90, Which Is Defined As the Energy Difference of the Onset Energies of Peaks P1 and P2 in RPA (ERPA) and BSE (EBSE) Pictures system

ERPA(P1)

EBSE(P1)

EB(P1)

ERPA(P2)

EBSE(P2)

EB(P2)

M0 M90

1.87 2.68

1.49 2.05

0.38 0.63

2.96 3.06

2.18 2.28

0.78 0.78

for M0 and M90, which indicates that the intrinsic exciton binding energy of P3HT is not influenced by the PCBM orientation. The much smaller EB of P1 than that of P2 is likely to be one of the reasons why the hole and electron separation is efficient at the P3HT:PCBM interface. Our results show that the flat-lying orientation of PCBM at the interface has a better charge separation than the upright-standing orientation. 10268

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separation than the upright-standing orientation, which suggests that the enhancement of the separation of electron− hole pairs at the blend interface can be achieved by applying experimental techniques that could improve bulk and interface ordering of the P3HT:PCBM blend, such as thermal annealing. In fact, recent experimental works8,10 demonstrate that annealing causes a significant increase of power conversion efficiency of OPV devices, compared with the nonannealed samples. Our results suggest one possible explanation for the mechanism of such an improvement: the annealing causes P3HT and PCBM to self-order at the interface to form a flatlying PCBM configuration because such a configuration has the lowest total energy, as our calculations demonstrate. Additionally, annealing increases ordering and crystallinity of P3HT, and a more face-on orientation of the P3HT chain packing is observed in the postannealed sample, as opposed to the nonannealed film that has more edge-on orientations.8 Face-on P3HT orientations at the interface lead to better separation of electron−hole pairs at the blend interface because they allow for the direct interaction of PCBM with the π states of the P3HT thiophene rings, in contrast to edge-on orientations, in which PCBM would directly interact only with P3HT side chains.

Article

ASSOCIATED CONTENT

S Supporting Information *

Charge density of VB-5 to CB+4 bands along Γ-Z for M0 and M90 structures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Argonne-Northwestern Solar Energy Research (ANSER) Center, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, and Office of Basic Energy Sciences under Award Number DE-SC0001059.

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REFERENCES

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IV. CONCLUSIONS In this work, the structure, electronic, and optical properties of the P3HT:PCBM interface were studied by means of firstprinciples calculations with G0W0 approximation and the Bethe−Salpeter equation, and the effect of PCBM orientation on these properties was investigated. It was determined that the ground state of the interface has a flat-lying orientation of PCBM molecules relative to the P3HT layers. Thus, a significant number of flat-lying structures can be expected in the P3HT:PBCM bulk heterojunction. The calculated band structures and band offsets for the flat-lying configuration are in good agreement with experimental values and confirm that the band alignment belongs to the type-II heterojunction. The calculated optical properties of the interface are characterized by two main peaks in the imaginary part of the dielectric function: P1, originating from interband transitions between VBs of P3HT and CBs of PCBM, and P2, associated with the transitions from VBs to CBs of P3HT alone. Our calculations demonstrate that the interfacial optical absorption can be changed by the PCBM rotation, and the orientation effects are summarized as follows: (i) the PCBM orientation directly affects the PCBM-associated transitions, such as P1, the charge transfer complex state. A blue-shift of this first peak is found with the increase of PCBM rotation angle. (ii) The origin of the bright absorption peak P2 for the P3HT constituent changes slightly. (iii) The exciton binding energy is higher for the upright-standing structure than that of the flat-lying one. These differences of optical properties between the PCBM flat-lying and upright-standing structures imply that the flat-lying structure is better for e−h separation and charge transfer than the upright-standing model in previous researches. Finally, our results show that the e−h interactions are important to predict the optical absorption at the P3HT:PCBM interface. The calculated exciton binding energy and the charge transfer complex state onset energy for the PCBM flat-lying orientation structure agree with the available experimental data, as well as the absorption spectrum, which are essential to understanding of the experimental results. 10269

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