Band Gap Enhancement by Covalent Interactions in P3HT/PCBM Photovoltaic Heterojunction

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1 Journal of the Korean Physical Society, Vol. 57, No. 1, July 2010, pp Band Gap Enhancement by Covalent Interactions in P3HT/PCBM Photovoltaic Heterojunction Xiaoyin Xie, Heongkyu Ju and Eun-Cheol Lee College of Bio-Nano Technology, Kyungwon University, Gyeonggi , and Gachon Bio-Nano Research Institute, Gyeonggi (Received 4 May 2010, in final form 31 May 2010) First-principles calculations report that the poly-3-hexylthiophene (P3HT) band gap is increased by covalent linkings of P3HT and [6,6]-phenyl-C 61 butyric acid methyl ester (PCBM) in a heterojunction with charge overlap between P3HT and PCBM enhanced, which may lead to efficient exciton dissociation. The covalent reaction occurs between the two different carbon double bonds on the P3HT and the PCBM molecules, forming a four-membered ring between the molecules and requiring a reaction energy of 2.2 ev. The possibility of band gap engineering of P3HT through this covalent interaction is discussed. PACS numbers: f, Bc, Cd, Wp Keywords: Polymer solar cell, Band gap engineering, P3HT/PCBM interface, Density-functional theory DOI: /jkps I. INTRODUCTION Polymer-based solar cells have recently attracted much attention because of their advantages, such as low production cost, mechanical flexibility, and environmentfriendliness. Bulk heterojunctions with the composites of poly-3-hexylthiophene (P3HT) and [6,6]-phenyl-C 61 butyric acid methyl ester (PCBM) are the most dominant material system for polymer solar cells [1 3] because of their having the best power conversion efficiency, above 5% [4]. Many technologies achieving higher efficiency are under development for P3HT/PCBM-based solar cells; for example, the efficiency can be increased above 6% by using the tandem cell architecture [5]. Understanding of P3HT/PCBM bulk heterojunctions on an atomic scale is very important for devising a new technology that can improve the efficiency. Recently, Kanai and Grossman theoretically showed that, although P3HT and PCBM are noncovalently interacting, charge transfer between P3HT and PCBM possibly occurs through the lowest-excited state with significant charge overlap between P3HT and PCBM [6]. However, in most inorganic solar cells with higher efficiencies, donor and acceptor materials are covalently bonded. Exciton dissociation might be more efficient at the interface of covalently bonded P3HT and PCBM due to the strong electron overlap at the interface. Thus, it is important to examine the usefulness of covalently-bonded states of P3HT and PCBM for enhancing the device performance. Corresponding Author: eclee@kyungwon.ac.kr; Fax: In this paper, we present an atomic model for a covalently bonded P3HT/PCBM interface based on firstprinciples density-functional calculations. We found that the reaction between parallel double bonds (C=C bonds) on the P3HT and PCBM molecules leads to the formation of a four-membered ring linking of P3HT and PCBM, similar to the dimerization in solid C 60 films [7, 8]. In contrast to the noncovalent state, the lowest unoccupied molecular orbital (LUMO) of P3HT for the covalent configuration has a significant charge distribution across the interface in the ground state, which may lead to efficient exciton dissociation even under lowexciton-density conditions. The covalent interaction also increases the P3HT band gap, leading to a lowering of the energy of the highest occupied molecular orbital (HOMO) of P3HT. The P3HT band gap can be continuously enhanced by using the degree of covalent interactions. The energy barrier for forming the covalent bonding is calculated to be 2.2 ev. We discuss the possibility that these covalent complexes may be used to improve the power conversion efficiencies of P3HT/PCBM-based solar cells. II. COMPUTATIONAL METHOD Calculations are performed using density-functional theory (DFT) within the generalized gradient approximation [9] and ultrasoft pseudopotentials [10]. The wave functions and charge densities are expanded in plane waves with kinetic energy cutoffs of 30 and 240 Ry, respectively. We simulate the P3HT/PCBM interface by -144-

2 Band Gap Enhancement by Covalent Interactions in P3HT/PCBM Photovoltaic Heterojunction Xiaoyin Xie et al Table 1. Total energies (in units of ev) of P3HT-PCBM complexes for different reaction sites on P3HT and PCBM. Reaction site on P3HT Reaction site on PCBM C=C bond C-C bond C=C bond 0 a 1.09 C-C bond C-S bond 0.47 a The total energy of this complex is set as the zero reference energy. Table 2. Amount ( E) of energy evolution of the HOMO and the LUMO levels of P3HT and PCBM after the covalent reaction. Fig. 1. (Color online) Atomic structures of (a) noncovalently- and (b) covalently-interacting PCBM and P3HT molecules. Charge density contours, with a contour spacing of 0.06 a.u., for the interacting C double bonds on P3HT and PCBM are also plotted for the (c) noncovalent and (d) covalent states. using an orthorhombic supercell with lateral dimensions of Å Å 23.4 Å. The supercell contains 188 atoms of a PCBM monomer and four regioregular thiophene units aligned along the z direction, and a P3HT chain is well separated from others by vacuum in the x and the y directions to avoid interactions between the chains. The PCBM: P3HT mass ratio of this structure is 1:1.37 while the mass ratios between 1:1 and 1:2 are widely used in experiments. The Γ point is used for the summation of charge densities over the Brillouin zone. The atomic coordinates are fully relaxed until the residual forces are less than 0.02 ev/å. III. RESULTS AND DISCUSSION First, we examine the atomic and the electronic structures of the P3HT/PCBM interface. We find that P3HT and PCBM molecules are interacting noncovalently in the most stable configuration, as shown in Fig. 1(a). The distance between P3HT and PCBM is about 3.5 Å in the perpendicular direction to the polymer chain, which is characteristic of π-π stacked systems [11], in good agreement with previous calculations. The charge density analysis in Fig. 1(b) clearly shows that there is no covalent bonding between P3HT and PCBM and that the charge overlap between P3HT and PCBM is negligible as compared with the charge distribution around C=C bonds in Fig. 1(b). In addition, the HOMO-LUMO P3HT PCBM HOMO LUMO HOMO LUMO E (ev) gaps of P3HT and PCBM, i.e., 1.13 ev and 1.46 ev, respectively, are found to remain unchanged when compared with those for the isolated molecules. Thus, in the ground state, such weak charge overlap may not lead to efficient charge transfer and exciton dissociation, but the overlap is significantly enhanced in the excited state [6]. In contrast to the noncovalently-linked interface, the covalently-linked interface shows strong charge overlap between P3HT and PCBM. We optimize the atomic structures by taking the C-C, C-S, and C=C bonds as possible reaction sites on the thiophene ring and the C-C and C=C bonds as those on PCBM. As shown in Table 1, we find that the reaction between C=C bonds on P3HT and PCBM molecules results in the lowest-energy configuration. In this structure, P3HT and PCBM is covalently linked by a four-membered ring, as shown in Fig. 1(c), similar to dimerized C 60 molecules [7,8]. Comparison of the charge densities indicates that some charges in the C=C bonds in the noncovalent state are transferred to two newly-created C-C bonds in the covalent state [see Figs. 1(c) and 1(d)]. Thus, after the chemical reaction, the two C=C bonds are broken into single C-C bonds, and the C atoms involved in the chemical reaction are displaced from their ideal positions, with sp 3 hybridizations enhanced, as compared to other C atoms. The bond lengths of the newly-formed C-C bonds are 1.61 Å while those of the single and the double bonds in the C 60 part of PCBM are 1.45 and 1.40 Å, respectively. It is evident that the charge distribution across the interface is significantly enhanced by the chemical bonding, as shown in Fig. 1(d). The strong coupling between P3HT and PCBM in the covalent state increases the P3HT band gap while that of PCBM remains almost unchanged. This band gap enhancement mainly originates from the π-electron inter-

3 -146- Journal of the Korean Physical Society, Vol. 57, No. 1, July 2010 Fig. 2. (Color online) Energy level evolution from isolated P3HT and PCBM molecules to the covalent P3HT-PCBM complex. The empty region between the shaded areas indicates the HOMO-LUMO gap of P3HT or PCBM. For the covalent complex, the energy levels are shifted in the horizontal direction to indicate if the P3HT (left) or the PCBM (right) character is more dominant in the corresponding states. Fig. 3. (Color online) Charge densities for the (a) HOMO and the (b) LUMO of P3HT of the noncovalent P3HT-PCBM complex are shown in the upper panel, and those for the (c) HOMO and the (d) LUMO of P3HT of the covalent P3HT- PCBM complex are shown in the lower panel for an isosurface of a.u. actions between P3HT and PCBM. When the distance between P3HT and PCBM becomes smaller, the π electrons of P3HT start to interact with those of PCBM, forming the bonding and antibonding states. The energy level splitting is also affected by the lattice distortion in the covalent reaction and by the charge overlap between the molecules. As shown in Fig. 2, the bonding-antibonding splitting is prominent for the interaction of the HOMO of an isolated P3HT chain (at 0 ev) and the level of an isolated PCBM molecule at 0.37 ev. Since the bonding level moves down to ev, the level at ev becomes the HOMO of P3HT for the covalent complex. This level is the antibonding state of the levels at and ev of isolated P3HT and PCBM molecules, respectively. The new HOMO has an extended charge distribution along the P3HT chain, similar to the original P3HT HOMO [see Figs. 3(a) and 3(c)]. By contrast, the LUMO of P3HT for the covalent complex evolves from the original LUMO of an isolated P3HT chain, through a weak bonding combination with the level of an isolated PCBM molecule at 1.22 ev. For the HOMO and the LUMO of PCBM, their interactions with P3HT are neglected in Fig. 2 because they are found to be very weak through a charge density analysis. The changes in the HOMO and the LUMO of P3HT and PCBM are summarized in Table 2. The HOMO- LUMO gap of P3HT is increased by 0.60 ev while that of PCBM is decreased slightly by 0.07 ev. Here, our calculations correspond to an extreme case where all PCBM molecules are covalently bonded to P3HT because one PCBM monomer, chemisorbed on P3HT, represents all PCBM monomers in the entire sample in our supercell approach. Thus, in real experiments, the shift in the band gap of P3HT is expected to be between 0 and 0.60 ev, depending on the degree of covalent bonding. In other words, a continuous band gap enhancement of P3HT is possible by controlling the concentration of the covalently-bonded sites. Since the amount of band gap enhancement is determined by the energy level splitting by the chemical bonding, it may not be affected by errors in the energies of unoccupied levels in the DFT calculations. However, to confirm this expectation, further studies using hybrid methods are required. Despite the great interests in low band gap donor polymers, high band gap donor polymers are also under investigation [12,13] for efficient absorption of short-wavelength visible light in the photovoltaic devices. Especially, application of high band gap polymers to tandem or folded reflective tandem cells, which allow for the use of multiple band gap materials, can lead to improvements in the efficiency and the charge mobility [14]. Our results indicate that, by inducing covalent reactions, P3HT might behave as a high band gap polymer, with the band gap finely tuned to efficiently absorb short-wavelength visible light in the nm region. As shown in Fig. 3(d), there is a significant hybridization of the PCBM charges in the LUMO of P3HT for the covalent complex, which leads to significant charge transfer from P3HT to PCBM whereas it is negligible for the noncovalent complex [see Fig. 3(b)]. These findings may be valid for low-carrier-density conditions such as the short-circuit condition because these ground-state calculations correspond to extreme cases with no elec-

4 Band Gap Enhancement by Covalent Interactions in P3HT/PCBM Photovoltaic Heterojunction Xiaoyin Xie et al Fig. 4. Total energies as a function of the configuration coordinate of the P3HT-PCBM complex along the covalent reaction path. trons excited to the LUMO of P3HT. On the other hand, a previous study showed that there is significant charge transfer even in the noncovalent complex when one electron is excited to the LUMO of P3HT in the supercell containing four thiophene units [6]. This case can be regarded as a high-carrier-concentration condition because the concentration of the excited electrons is estimated to be about cm 3, which is similar to the carrieraccumulated open-circuit condition. To further compare the charge transfer efficiencies in the above-mentioned high-carrier-density condition, we also calculate, as in a previous study [6], the charge transfer in spin-triplet excited states. We find that the charge transfer ( 0.60 e) in the covalent complex is still more significant than that ( 0.47 e) in the noncovalent complex. Thus, the charge transfer is more efficient in the covalent complex than in the noncovalent complex under both high- and low-carrier-density conditions. Comparison of the total energies indicates that the covalent complex is found to be 1.54 ev less stable than the noncovalent complex, indicating that the concentration of the covalent complex may not be high under thermodynamic equilibrium. Thus, it is difficult to detect the covalent complexes in experimental samples near thermodynamic equilibrium conditions. The reaction energy path for transforming the noncovalent into the covalent complex is also optimized using a climbing image nudged elastic band method, which effectively drives the highest energy image to the saddle point [15]. As shown in Fig. 4, the energy barrier for this reaction is found to be 2.2 ev. Since the reverse transformation from the covalent to the noncovalent complex is also kinetically hindered by an energy barrier of 0.65 ev, the concentration of the covalent complex may be significantly enhanced in nonequilibrium states. We expect that such states are possibly driven by various excitation techniques as in other experiments; for example, irradiation with UV light or an electron beam is widely used for inducing covalent dimerization in solid C 60 films, where a four-membered ring is also formed between two parallel C=C bonds, similar to our covalent complex. Since the thermal scission rate of covalent bonds between molecules might be proportional to the Boltzmann factor, the life time (τ) of the covalent bond is roughly estimated to be exp(e a /k B T), where E a is the activation energy barrier, i.e., 0.65 ev and τ is calculated to be s at T = 25 C. Such nonequilibrium excitations may be effective after the thermal annealing processes, which are usually performed during the fabrication of P3HT/PCBM solar cells [1 3], while the thermal annealing drives the system toward equilibrium. Our results show that the P3HT band gap and the charge transfer efficiency are simultaneously enhanced by inducing covalent bondings at the P3HT/PCBM interface. Further studies are required to develop techniques achieving our simulation conditions in experiments and to confirm that the formation of the covalent complexes is experimentally feasible. IV. CONCLUSIONS In conclusion, based on first-principles calculations, we have found that the P3HT band gap is increased by fourmembered-ring-mediated covalent linking of P3HT and PCBM. The covalent bonding also improves the charge transfer efficiency across the P3HT/PCBM interface under both low and high exciton density conditions. Since the band gap enhancement depends on the degree of the covalent reactions, the P3HT band gap may be continuously enhanced. The activation energy for the covalent reaction is calculated to be 2.2 ev. We discussed the possibility of achieving our simulation conditions in experiments. ACKNOWLEDGMENTS This research was supported by the GRRC program of Gyeonggi province and by the Kyungwon Universtity Research Fund in Calculations in this work were done using the QUANTUM-ESPRESSO package [17], and some figures were generated by using the XCRYS- DEN program [18]. REFERENCES [1] Y. Kim, S. Cook, S. M. Tuladhar, S. A. Choulis, J. Nelson, J. R. Durrant, D. D. C. Bradley, M. Giles, I. Mc- Culloch, C-S. Ha and M. Ree, Nat. Mater. 5, 197 (2006). [2] G. Li, V. Shrotriya, J. Huang, Y. Yao, T. Moriarty, K. Emery and Y. Yang, Nat. Mater. 4, 864 (2005). [3] X. Yang, J. Loos, S. C. Veenstra, W. J. H. Verhees, M. M. Wienk, J. M. Kroon, M. A. J. Michels and R. A. J. Janssen, Nano Lett. 5, 579 (2005). [4] W. Ma, C. Yang, X. Gong, K. Lee and A. J. Heeger, Adv. Funct. Mater. 15, 1617 (2005).

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