POLYMER DESIGN FOR ORGANIC SOLAR CELLS: A COMPUTER SIMULATION APPROACH

Jean Frédéric Laprade and Michel Côté

Département de physique et Regroupement québécois sur les matériaux de pointe Université de Montréal, C.P. 6128, Succ. centre-ville, Montréal (Québec), H3C 3J7, Canada

ABSTRACT Organic materials, particularly polymers, are a promising alternative to traditional semiconductors as the active material for solar cells. In this article, we review the physical concepts behind the conversion of light into electricity in organic materials and discuss the actual limitations to the organic solar cell efficiency. To understand the performance of those devices, the polymers electronic properties are determined by quantum mechanical numerical calculations based on the density functional theory (DFT). We show how the polymers electronic properties can be related to the parameters that influence the photovoltaic efficiency. On this basis, it is possible to identify new polymers that could improve the performance of organic solar cells.

INTRODUCTION The energy crisis that we are nowadays facing is certainly not the first one of human history, but it could be the first for which the energetic challenge is not only limited to the availability of the resources but also to the sustainability of the production methods. Conversion of solar energy into electricity is probably the best way to tackle this problem considering that the 2004 worldwide energy consumption amounts to 5 x 1020 J and that the sun irradiates 3.8 x 1024 J per year on Earth (Energy Information Administration, U.S. Department of Energy, 2006). Moreover, installation of solar panels can be done on existing structures limiting the controversies arising from the integration of production plants in inhabited regions such as the recent controversies surrounding windfarms. Despite these facts, only 0.04% of the world energy production was delivered by photovoltaic cells in 2003 (OECD, IEA, 2007). The origin of this limited place on the market stems from the production price that must be reduced in order to compete with other production methods. The large majority of the solar panels manufactured today are made of silicon, either mono or polycrystalline. These panels show good power conversion efficiency (the power output over the incident light intensity) but since silicon is an indirect

gap semiconductor, the amount of material necessary to absorb the incoming light is important. About half the cost of the silicon-based devices comes from the Si wafer. It is thus complicated to reduce the prices, especially with the pressure that the increased demand puts on the silicon production which has even led recently to shortages. Other materials can be used: amorphous silicon, III-V semiconductors such as GaAs and InP or also CdTe, but in all cases the efficiency-cost balance has not yet met expectations. Carbon-based, or organic, materials can be an alternative to classical semiconductors (Malliaras et al., 2005). The interest for organics comes from the fact that molecules and polymers are abundant and affordable. Furthermore, the fabrication of devices based on such materials can be done by a simple roll-to-roll printing process, an industrial technique that is cheap and does not require any high-tech facilities. Another interesting feature of organic materials is the possibility to make flexible devices that could be easily incorporated to architectural design. However, the photophysics of organic solar cells differs from the one of cells made of conventional semiconductors and a good understanding of these systems is essential in order to improve their efficiency. In this article, we will first discuss the underlying physical processes that influence the conversion of photons into free charges and their collection at the electrodes in the context of organic solar cells. Special attention will be paid to the electronic properties of the active material (where light is absorbed) and how these properties affect the different parameters that determine the efficiency. We will then describe how theoretical calculations can be of great help in understanding these parameters and how their results can be used to improve the physical characteristics of the active material. We rely on the density functional theory to perform such investigation and we will briefly describe this method. Finally, we will present some results and discuss their significance for the improvement of organic solar cells power conversion efficiency.

ORGANIC SOLAR CELLS It has been known for about fifty years that organic materials can be used for charge transport. The early works dealt with charge transfer between molecules such as perylene and anthracene. A major step was realized in the sixties and seventies with the pioneering works done by Weiss et al. on conducting polymers such as polypyrrole and polyacetylene. Alan Heeger, Alan MacDiarmid and Hideki Shirakawa were finally awarded the 2000 Nobel Prize in Chemistry for “The discovery and development of conductive polymers”. The charge transport property of carbon-based materials is restricted to conjugated molecules and polymers for which carbon atoms bond through sp2 orbitals. These orbitals are characterized by three in-plane σ orbitals that form the polymer backbone while the remaining pz orbital sticks out of the polymer plane. The resulting conjugated polymer is composed of alternating single and double bonds and its electronic properties are described by a valence and a conduction bands formed by bonding π and anti-bonding π* orbitals respectively. The bandgap range from 1 to 5 electron-volts depending on the polymer. These π orbitals form the channel for charge transport under chemical doping, charge injection or photo-excitation, being therefore the basic element of organic electronics. Nowadays, organic light-emitting diodes (Gross et al., 2000) are commercially available while organic field-effect transistors (Dimitrakopoulos et al., 2002) and organic solar cells (Peet et al., 2007) are the object of intense research. Indeed, many reviews on the photophysics of organic solar cells have been published in recent years (Brabec et al., 2001 ; Rand et al., 2007 ; Hoppe et al., 2004). The major differences between the underlying physics of organic solar cells compared to their inorganic relatives come from the low mobility (between 1 to 10-5 cm2/Vs) of the charge carriers as well as the low dielectric constant that results in strong Coulomb interaction between electron and hole after photo-excitation (Jaiswal et al., 2006). On the other hand, the absorption of the organics is usually very good with coefficients higher than 105 cm-1 (Rand et al., 2007). These properties constitute a great challenge in understanding the mechanisms influencing the efficiency of devices and they make organic photovoltaics a field of research in itself. With an exciton binding energy of the order of hundreds of meV, an applied field of 106 V/cm (Rand et al., 2007) is necessary to dissociate the bounded charges, making the metal-insulator-metal (MIM) of a single organic semiconductor a non-efficient architecture. It is therefore necessary to look at the heterojunction device in which an electron-donor and an electron-acceptor share an interface where the exciton dissociation takes place (Figure 1). The

process of charge collection is realized in four steps: (i) photoexcitation and formation of the bond electron-hole pair, (ii) exciton migration to the interface, (iii) electron transfer from the donor to the acceptor and (iv) transport of the free charges to the electrodes. Each of the steps mentioned above has a direct influence on the overall external quantum efficiency (EQE) and it is well worth looking at them individually.

Figure 1 : Bulk heterojunction solar cell structure with the constraints that apply on the energy levels of the constituents. The photo-excitation consists of the absorption of a photon by an electron of the donor molecule thus creating the bound electron-hole pair. Figure 2 shows the total irradiance as a function of wavelength for the air mass 1.5 global spectrum which is the standard terrestrial solar spectrum. Since half the photons have a wavelength below 1000 nm (1.24 eV), it is essential to have a low bandgap material with a high absorption coefficient in order to maximize the exciton formation. However, strict constraints (Figure 1) apply on the energy levels of the donor since i) the donor lowest unoccupied molecular orbital (LUMO) must be sufficiently above the LUMO level of the acceptor in order to have an efficient charge transfer and ii) the donor highest occupied molecular orbital (HOMO) energy, or equivalently the ionization potential, must be smaller than -5.3 eV in order to be air stable. The exact energy difference between the LUMO of the donor and acceptor will depend on the binding energy of the exciton. This value is still debated in the scientific community, but it is commonly accepted that a value of 0.3 eV is necessary (Scharber et al., 2006). In the case of solar cells that use a fullerene derivative (PCBM) as the electron acceptor, a 1.3 eV lower bound is imposed on the bandgap. The best case scenario consists therefore in a contribution to the external quantum

efficiency from only half the photons of the spectrum, but experimental measurements show that only a fraction of the photons with wavelengths appropriate to the absorption peak effectively promote an electron to the conduction band. By increasing the thickness of the layer, it is possible to improve the absorption, but this does not necessarily turn into a greater short-circuit current since the diffusion length of excitons in organics is generally in the range of 20-50 nm and the mobility of the free charge carriers is low. This means that optimum devices consist of thin-film layers of active organic materials that are usually 100 to 300 nm thick.

Figure 2 : Standard spectral irradiance distribution (Myers et al., 2003) Once the bond electron-hole pair is formed, it must diffuse to the interface without recombination. Since the exciton mobility in polymers is very low, their diffusion length is limited to a few tenths of nanometers. The concept of bulk-heterojunction (BHJ) has been introduced in order to shorten the distance to the interface that excitons have to cover without reducing the layer thickness that would result in a lower absorption. By spin-casting a solution of the donor-acceptor blend or by co-deposition, an interpenetrating network is obtained in which the interface is dispersed through the bulk (Figure 1). The morphology of these films, i.e., a fine phase separation as well as connected domains, is crucial for the performance of the device and it has been proved that the nature of the solvent used has a major influence on morphology and consequently on power conversion efficiency (Ma et al., 2007 ; Peet et al., 2007). Nowadays, the best power-conversion efficiencies have been obtained by bulk-heterojunction solar cells and can now reach more than 5%. With an appropriate alignment of the donor and acceptor LUMO levels, the exciton dissociation at the interface takes place in about 45 fs (Brabec et al., 2001) with a yield that approaches 100%. The physically

separated charges are however bounded by a Coulombic force in what is called a geminate pair. Despite the strong interaction, the generation of free charge carriers is a process that shows high efficiency. It has been suggested (Peumans et al., 2004) that the reason for this comes from the presence of an interface that limits the volume available for recombination and aligns the dipole moment in a direction that favors dissociation.

Figure 3 : Typical IV curve showing the short-circuit current (Jsc), the open-circuit voltage (Voc) and the current and voltage at maximum power point (JMPP, JMPP) As mentioned before, a major drawback of organic materials is the low mobility of the charge carriers. Highly ordered molecular crystals have shown charge-carrier mobilities greater than 0.1 cm2/Vs (van de Craats et al., 1999), which is of the order of amorphous silicon, but in the context of bulk-heterojunction solar cells where conjugated polymers are used for holes transport and C60 for electrons transport, the recorded mobilities vary from 10-3 to 10-5 cm2/Vs. These systems are highly disordered and the charge transport is therefore described by a hopping process where the electron and hole are strongly localized on molecules. Indeed, different groups have demonstrated the enhancement of BHJ cells performances under annealing and/or when the polymers structure favors a highly organized packing (Kim et al., 2006). A promising avenue is the development of organized photoactive materials either by using molecular self-assembly or 1D nanostructures such as nanorods (Somani et al., 2007) or carbon nanotubes (Sun et al., 2006).

ORGANIC SOLAR CELLS PERFORMANCES Even if power-conversion efficiencies above 5% (Green et al., 2008 ; Wang et al., 2008 ; Peet et al., 2007) have been demonstrated, this power-conversion has to be doubled in order to make organic solar cells

economically attractive. The power output at the maximum power point (MPP) is given by the product of the voltage and the current : Pout = VMPP · JMPP. A convenient way to express the power output is with the fill factor FF = (VMPP · JMPP)/( Voc · Jsc) where Voc and Jsc are respectively the open-circuit voltage and the short-circuit current, the power output being therefore Pout = (FF · Voc · Jsc). The factor ( Voc · Jsc) represents the maximum power that could be delivered by a cell where only radiative recombination would take place, assuming that the emitted photons are reabsorbed by other electrons after recombination. FF is therefore a ratio of the ability to collect free charges at the electrodes as a function of electron-hole pair generation. This value will increase with reduced serial resistance and augmented parallel resistance of the device. Figure 3 shows a typical IV curve. The origin of the Voc in bulk-heterojunction diodes still remains unclear, but there is evidence that it depends strongly on the difference between ionization potential of the donor and the electron affinity of the acceptor (Brabec et al., 2001). It is also known that the short-circuit current is intimately related to the film morphology as well as the absorption coefficient of the materials. It is therefore essential to have a good understanding of the donor and acceptor electronic properties in the effort to improve the performance of organic solar cells. Ab initio quantum mechanical calculations, which do not depend on external parameters, are of great help in this regard since they can predict the structure, the energy levels as well as the optical transition strength of compounds before their synthesis.

METHOD The formalism used to study the electronic properties of the polymers is the density functional theory (DFT) (Hohenberg et al., 1964 ; Kohn et al., 1965) for which the energy of a system is described as a functional of the electronic density. The density that uniquely minimizes that functional determines the system ground state. The important aspect of this method is that it does not rely on any fitting parameter to model the interactions: the input is limited to the atom types and their positions and the only approximation comes from the exchange-correlation functional (Exc) that tends to recast the many-body problem into a simpler independent-particle scheme. We use the code GAUSSIAN 03 (Frisch et al., 2004) to run our calculations with the Becke (Becke, 1993), three-parameter, Lee-Yang-Parr (Lee et al., 1988) (B3LYP) exchange-correlation functional. It has been shown that this functional gives an accurate description of carbon-based materials. The GAUSSIAN 03 code uses molecular orbitals as basis set to construct the wave function of the system. In order to obtain an accurate description of the physical system, we used the large 6-

311G* basis set for first to third row atoms and the LANL2DZ for the rest. Structural optimization was done without any constraints.

RESULTS AND DISCUSSION Figure 4 shows the energy levels of the HOMO and LUMO orbitals of different polymers for which the best power conversion efficiencies have been obtained when they are integrated as the active material in photovoltaic cells (see Table 1). For clarity, the polymers are named after their chemical structure acronym: PCPDTBT stands for poly [2,6-(4,4-bis-(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b’]-dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] ; PCDTBT for poly[N-9′-heptadecanyl-2,7-carbazole-alt-5,5-(4′,7′-di-2-thienyl-2′,1′,3′-benzothiadiazole)] ; PFDTBT for poly [9,9-didecanefluorene-alt- bis-thienylene benzothiadiazole] ; P3HT for poly 3-hexylthiophene. The energy levels of PCBM (1- 3-methoxycarbonyl -propyl-1-phenyl- 6,6 C61) are shown for reference. This figure compares the theoretical values to those measured experimentally by cyclic voltammetry. The overall overestimation of the energy levels is expected from the B3LYP functional. The principal parameters that determine the efficiency of the cells are listed in Table 1. For PFDTBT and PCDTBT, the difference between their HOMO energy (respectively -5.4 eV and -5.5 eV) and the LUMO energy of PCBM (-4.3 eV) is consistent with the high measured Voc (respectively 1.0 V and 0.9 V). P3HT, with a HOMO energy of -4.9 eV is also consistent with the Voc value of 0.6 V. The only discrepancy between experimental values comes from the HOMO level of PCPDTBT (-5.3 eV) which should lead to an open-circuit voltage higher than the 0.62 V measured. We can understand this conflict by looking at the theoretical HOMO energy values for which PCPDTBT has a relatively higher energy (-4.57 eV), in fact quite close to P3HT (-4.38 eV). B3LYP calculations give therefore a good insight of the Voc that can be expected from a bulk-heterojunction solar cell on the basis of the difference between the donor HOMO and acceptor LUMO. Figure 5 shows the four polymers band structures. We see that copolymers, namely, PCPDTBT, PCDTBT and PFDTBT, are characterized by narrow bands that can limit the exciton and hole mobilities. At the opposite, P3HT bands are highly dispersive. This is inherent to copolymers since what we want is precisely an electronic structure whose HOMO level comes from the electron-rich unit and the LUMO level from the electron-deficient unit in order to obtain low bandgap materials. As a result, the wave functions are typically localized on one of the polymer co-units.

PCPDTBT PCDTBT PFDTBT P3HT Eg (eV) 1.5 1.9 1.9 1.9 Efficiency 5.5% 5.3% 4.2% 4.9% Voc (V) 0.62 0.9 1.0 0.6 Isc (mA/cm2) 16.2 12.21 7.7 11.1 HOMO (eV) -5.3 -5.5 -5.37 -4.9

Table 1 : Efficiency parameters of cells made of different donor polymers : PCPDTBT (Muhlbacher et al., 2006 ; Peet et al., 2007) ; PCDTBT (Blouin et al., 2007 ; private communication) ; PFDTBT (Slooff et al., 2007) ; P3HT (Reyes-Reyes et al., 2005) We can use the predicting power of DFT calculations to sample polymer structure variations that could lead either to higher orbital delocalization, to better optical absorption or to smaller bandgap. Figure 6 (a) pictures the interplay between the co-units of benzothiadiazole (BT) based copolymers. The first column shows the valence and conduction band of a polymer whose repeating unit is DTBT. On the right are shown the valence and conduction bands for polymers made of respectively fluorene (carbon), carbazole (nitrogen), dibenzosilole (silicon) and borafluorene (boron). Are also shown the resulting valence and conduction bands of the copolymers. In the first three cases, these polymers have been integrated to photovoltaic devices (see Table 1 and Boudreault et al., 2007). We can see that their LUMO level lies high above the DTBT LUMO. Consequently, the copolymers LUMO orbitals are strongly localized on the BT unit as can be seen in Figure 6 (b) for the fluorene case. At the opposite, borafluorene LUMO level lies close to DTBT conduction band and the LUMO orbital of the copolymer is delocalized over the backbone (Figure 6 (c)). The synthesis of this polymer has not been done yet but a chemical route for the synthesis of borafluorene (Chen et al., 2006) has recently been published, opening the way to the integration of borafluorene in solar cells active material. This unit is promising since a delocalized orbital could result in shallower energy traps for the exciton migration.

CONCLUSION Organic solar cells could lead to a significant production price reduction. Their power conversion

efficiency above 5% is promising, but it must be increased in order to be competitive. The open-circuit voltage, the short-circuit current and the fill factor are the device parameters that determine the efficiency. Polymer electronic properties such as the orbital energy levels and orbital delocalization directly influence those parameters. Density functional theory has been used in order to compute the electronic properties of four polymers for which good power-conversion efficiencies have been measured. We find good agreement with experimental parameters, in particular the open-circuit voltage that we can evaluate from the difference between the polymers HOMO and PCBM LUMO. The fill factor and the short-circuit current are strongly dependant on the charge carrier mobility which is limited for copolymers that form highly disordered films. We find that by using borafluorene as the electron-rich unit, the LUMO orbital of the copolymer is delocalized over the polymer backbone and this could result in a better exciton mobility.

ACKNOWLEDGMENTS This work was supported by grants from NSERC and FQRNT. The computational resources were provided by the Réseau québécois de calcul de haute performance (RQCHP). The authors would like to thank Mario Leclerc, Nicolas Blouin and Carlos Silva for helpful discussions.

REFERENCES Becke, A. D. (1993). "Density-Functional

Thermochemistry .3. The Role of Exact Exchange." Journal of Chemical Physics 98(7) 5648

Blouin, N., A. Michaud, et al. (2007). "A low-bandgap poly(2,7-carbazole) derivative for use in high-performance solar cells." Advanced Materials 19(17) 2295

Boudreault, P. L. T., A. Michaud, et al. (2007). "A new poly(2,7-dibenzosilole) derivative in polymer solar cells." Macromolecular Rapid Communications 28(22) 2176

Figure 4 : Theoretical and experimental energy levels of different high efficiency polymers.

Figure 5 : Band diagrams of different high efficiency polymers. PCPDTBT, PFDTBT and PCDTBT are copolymers.

Figure 6 : (a) Energy levels of the co-units in their polymerized form and the resulting copolymers. (b) PFDTBT LUMO orbital localized on the BT unit. (c) PBFDTBT (borafluorene electron-rich unit) LUMO orbital delocalized over the polymer backbone.

Brabec, C. J., G. Zerza, et al. (2001). "Tracing photoinduced electron transfer process in conjugated polymer/fullerene bulk heterojunctions in real time." Chemical Physics Letters 340(3-4) 232

Brabec, C. J., N. S. Sariciftci, et al. (2001). "Plastic solar cells." Advanced Functional Materials 11(1) 15

Chen, R. F., Q. L. Fan, et al. (2006). "A general strategy for the facile synthesis of 2,7-dibromo-9-heterofluorenes." Organic Letters 8(2) 203

Dimitrakopoulos, C. D. and P. R. L. Malenfant (2002). "Organic thin film transistors for large area electronics." Advanced Materials 14(2) 99

Energy Information Administration, U.S. Department of Energy. (2006). "World Consumption of Primary Energy by Energy Type and Selected Country Groups, 1980-2004."

Frisch, M. J., et al. (2004). "Gaussian 03, Revision C.02" Gaussian, Inc., Wallingford CT

Green, M. A., K. Emery, et al. (2008). "Solar cell efficiency tables (version 31)." Progress in Photovoltaics 16(1) 61

Gross, M., D. C. Muller, et al. (2000). "Improving the performance of doped pi-conjugated polymers for use in organic light-emitting diodes." Nature 405(6787) 661

Hohenberg, P.; W. Kohn. (1964) "Inhomogeneous Electron Gas" Physical Review 136(3B), B864

Hoppe, H. and N. S. Sariciftci (2004). "Organic solar cells: An overview." Journal of Materials Research 19(7) 1924

Jaiswal, M. and R. Menon (2006). "Polymer electronic materials: a review of charge transport." Polymer International 55(12) 1371

Kim, Y., S. Cook, et al. (2006). "A strong regioregularity effect in self-organizing conjugated polymer films and high-efficiency polythiophene: fullerene solar cells." Nature Materials 5(3) 197

Kohn, W.; L. J. Sham. (1965). "Self-Consistent Equations Including Exchange and Correlation Effects." Physical Review 140(4A), A1133

Lee, C. T., W. T. Yang, et al. (1988). "Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron-Density." Physical Review B 37(2) 785

Ma, W., J. Y. Kim, et al. (2007). "Effect of the molecular weight of poly(3-hexylthiophene) on the morphology and performance of polymer bulk heterojunction solar cells." Macromolecular Rapid Communications 28(17) 1776

Malliaras, G. and R. Friend (2005). "An organic electronics primer." Physics Today 58(5) 53

Muhlbacher, D., M. Scharber, et al. (2006). "High photovoltaic performance of a low-bandgap polymer." Advanced Materials 18(21) 2884

Myers, D. R., A. Andreas, et al. (2003). "NREL Spectral standards development and broadband radiometric calibrations." NREL Conference Paper

OECD, IEA (2007). "Renewables In Global Energy Supply - An IEA Fact Sheet."

Peet, J., J. Y. Kim, et al. (2007). "Efficiency enhancement in low-bandgap polymer solar cells by processing with alkane dithiols." Nature Materials 6(7) 497

Peumans, P. and S. R. Forrest (2004). "Separation of geminate charge-pairs at donor-acceptor interfaces in disordered solids." Chemical Physics Letters 398(1-3) 27

Rand, B. P., J. Genoe, et al. (2007). "Solar cells utilizing small molecular weight organic semiconductors." Progress in Photovoltaics 15(8) 659

Reyes-Reyes, M., K. Kim, et al. (2005). "High-efficiency photovoltaic devices based on annealed poly(3-hexylthiophene) and 1-(3-methoxycarbonyl)-propyl-1-phenyl-(6,6)C-61 blends." Applied Physics Letters 87(8) 083506

Scharber, M. C., D. Wuhlbacher, et al. (2006). "Design rules for donors in bulk-heterojunction solar cells - Towards 10 % energy-conversion efficiency." Advanced Materials 18(6) 789

Slooff, L. H., S. C. Veenstra, et al. (2007). "Determining the internal quantum efficiency of highly efficient polymer solar cells through optical modeling." Applied Physics Letters 90(14) 143506

Somani, P. R., S. P. Somani, et al. (2007). "Toward organic thick film solar cells: Three dimensional bulk heterojunction organic thick film solar cell using fullerene single crystal nanorods." Applied Physics Letters 91(17) 173503

Sun, J. L., J. Wei, et al. (2006). "Photoinduced currents in carbon nanotube/metal heterojunctions." Applied Physics Letters 88(13) 131107

van de Craats, A. M., J. M. Warman, et al. (1999). "Record charge carrier mobility in a room-temperature discotic liquid-crystalline derivative

of hexabenzocoronene." Advanced Materials 11(17) 1469

Wang, E. G., L. Wang, et al. (2008). "High-performance polymer heterojunction solar cells of a polysilafluorene derivative." Applied Physics Letters 92(3) 033307