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Carrier motion in as-spun and annealed P3HT:PCBM blends revealed by ultrafast optical electric field probing and Monte Carlo simulations ab c a Vytautas Abramavic ˇius,* Dimali Amarasinghe Vithanage, Andrius Devizˇis, c d d Yingyot Infahsaeng, Annalisa Bruno, Samuel Foster, Panagiotis E. Keivanidis,e b d c c Darius Abramavic ˇius, Jenny Nelson, Arkady Yartsev, Villy Sundstro ¨ m and a Vidmantas Gulbinas
Charge transport dynamics in solar cell devices based on as-spun and annealed P3HT:PCBM films are compared using ultrafast time-resolved optical probing of the electric field by means of field-induced second harmonic generation. The results show that charge carriers drift about twice as far during the first Received 31st October 2013, Accepted 5th December 2013
3 ns after photogeneration in a device where the active layer has been thermally annealed. The carrier
DOI: 10.1039/c3cp54605e
simulated drift dynamics was obtained using identical model parameters for both cells, but with different
dynamics were modelled using Monte-Carlo simulations and good agreement between experimental and average PCBM and polymer domain sizes. The calculations suggest that small domain sizes in as-spun
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samples limit the carrier separation distance disabling their escape from geminate recombination.
1. Introduction Diminishing sources of fossil fuels and the need to meet rising global demands for carbon-free energy have led to renewable sources being explored as replacements. Conjugated polymers have been investigated as alternatives to solar cells based on inorganic semiconductors1 due to their light weight, flexibility, abundance of material, low material usage and manufacturing costs. The invention of the bulk heterojunction structure (BHJ) using a donor and acceptor homogeneously mixed to produce the active material2 has aided the increase in solar cell efficiency, which is presently 9.2% for the best reported cells.3 To improve device efficiency, the charge dynamics have also been investigated and three key stages in the charge separation pathway have been identified – charge generation,4 transport5 and recombination.6 Excitons are generated when light within the absorption spectrum of the material impinges on the devices. These excitons very rapidly6 separate into positive and negative charges forming Coulombically bound electron–hole pairs (or charge transfer states (CT)). In order to separate further, the charges have to a
Center for Physical Sciences and Technology, Savanoriu 231, LT-02300 Vilnius, Lithuania b Department of Theoretical Physics, Vilnius University, Sauletekio 9-III, LT-10222 Vilnius, Lithuania. E-mail: Vytautas.Abramavicius@ff.vu.lt c Chemical Physics, Lund University, Box 124, 221 00 Lund, Sweden d Imperial College London, South Kensington Campus, London SW7 2AZ, UK e Center for Nano Science and Technology@PoliMi, Istituto Italiano di Tecnologia, Via Giovanni Pascoli, 70/3, 20133 Milano, Italy
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overcome the Columbic attraction and form mobile charges which can move towards the electrodes through a combination of diffusion and drift.7 The collection of the separated charges results in completion of the circuit and current produced by the solar cell. Here we study the polymer:fullerene combination poly(3hexylthiophene) (P3HT) and [6,6]-phenyl-C61butyric acid methyl ester (PCBM). The method of processing P3HT:PCBM devices is known to impact the active layer morphology and, as a result, the efficiency of devices, and has therefore been extensively studied. Several factors have been investigated with the aim of improving device efficiency, such as the effect of solvent, morphology, film thickness and processing conditions.8–17 Annealing was shown to have a great impact on the conversion efficiency of P3HT:PCBM solar cells, quite different from most other polymer:fullerene blends. The carrier dynamics of annealed and as-spun P3HT:PCBM films have been studied using several techniques aiming at investigating differences in mobility,5,15 morphology,14–17 EQE14 and I–V characteristics.5 Annealing to a high temperature changes the morphology and enhances the hole mobility,5,9 resulting in it being only an order of magnitude below the electron mobility.5 A similar effect was achieved with slow solvent evaporation.18 Using microsecond time scale techniques, a large spread in mobilities and their differences in as-spun and annealed samples have been reported.5,15,19 The measurements show that the two different processing methods drastically affect the mobility and charge separation time scales. Morphological studies have shown that high temperature
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results in phase separation due to crystallization of the polymer5,15,16,20 and formation of large PCBM clusters.12,14–17 There is a consensus that thermal annealing results in improved device efficiency due to enhanced phase segregation, which consequently leads to increased charge separation efficiency,21,22 improved hole conductivity and formation of optimized charge transport pathways9,15 and consequently reduced bimolecular recombination.23 The mechanism through which the thermal annealing process enables higher charge carrier mobilities is now fairly well understood. Annealing induced crystallisation of the polymer results in larger domains (thicker lamellae) of the pure polymer and at the same time expels fullerene molecules out of the crystallising polymer, thereby making more fullerene available to build a robust electron transport network.20,24–26 It is clear from such studies that the improvement in charge collection (reflected through photocurrent quantum efficiency) is associated with the growth in pure polymer and fullerene domains and resulting improvement in charge carrier mobility relative to the recombination coefficient.5,9 In this paper, we aim at unveiling how morphology affects charge transport by investigating charge mobility and charge separation at earlier timescales using electric field-induced second harmonic generation (TREFISH)7,27,28 and MC simulations. We find the morphology to influence the mobility and carrier separation on the ps to ns time scale. MC simulations show that the different carrier drift kinetics in as-spun and annealed blends may be explained by more extensive material segregation, leading to larger P3HT and PCBM domains in annealed material, enabling fast separation of carriers at larger distances and preventing their geminate recombination.
2. Experiment The experimental setup and theory have been previously described,7,27,28 so only a brief account is given here. TREF ISH is a pump–probe technique, employing a femtosecond laser pulse to excite the sample devices and generate charges, and a probe pulse that generates the SHG signal probing the dynamics of the charges. An applied electric field breaks the symmetry of the material, allowing to generate the second harmonic signal of the probe pulse. The intensity and time dependence of the second harmonic signal monitors the electric field dynamics in the sample. The excitation pulse (400 nm, 36 nJ per pulse) was obtained by frequency doubling the fundamental of the Ti:Sa laser at 800 nm; a photon density of B1012 photons per cm2 per pulse for the sample was used, which is below the onset of strong second order (non-geminate) recombination. The probing wavelength was obtained using an optical parametric amplifier (TOPAS) at 1200 nm, the second harmonic of which was within the sensitivity of the photomultiplier detector. The sample device was made using a PEDOT:PSS/ITO anode and an aluminium (Al) cathode. The PEDOT:PSS was spun to form a 40–60 nm film and the total device had an overall thickness of B115 nm. The sample cells were all prepared in a clean room environment.
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3. Monte-Carlo simulation model The simulation model has been described in ref. 7. Briefly, charge carrier motion in the P3HT:PCBM blend was modelled by assuming a cubic lattice, characterized by a lattice constant a in all three dimensions. The lattice is divided into the donor part, where only the hole is allowed to reside and the acceptor part for the electron. The acceptor sites are defined by filling the lattice volume with ellipsoids of acceptor material (see Fig. 2) with typical average volume, which is later on used as a fitting parameter. The ellipsoids have arbitrary proportions and they are placed in arbitrary positions in the lattice and they overlap each other, thus mimicking the distribution of PCBM in the actual blend. Next, the remaining space in the lattice is filled with donor sites, which are used to create arbitrarily oriented and folded chains representing the polymer. The length of a chain is chosen randomly from the interval [L 3, L + 3], where L is the average length of chains. It should be noted, that such a blend model apparently cannot reproduce the real blend morphology, particularly of the annealed blend where a lamellar structure is suggested to be formed. The results of the calculation should rather be seen as a qualitative representation of morphology to rationalize the observed carrier dynamics. The electron and hole dynamics are controlled by site energy properties. In the presence of an external electric field the energy of an electron (hole) in the lattice consists of three parts: (1) the internal site self-energy Er, which is assumed to be a random Gaussian value; (2) the energy due to the constant external electric field F, and (3) the energy due to the Coulomb interaction between charges of opposite sign EC. The electron (hole) energy thus equals to: Ef (r) = Er 8 (Fr) + EC.
(1)
The site self-energy is distributed according to a modified Gaussian distribution, which is defined as a weighted sum of a normal Gaussian distribution with addition of longer exponential tails. The energy of the external electric field was accounted for by projecting the site position to the electric field direction. The electrostatic interaction energy is given by the shifted Coulomb potential EC ¼
q 1 4pee0 reh þ ba
(2)
Here q is the electron charge, reh is the distance between the electron and the hole, e is the mean permittivity of the material, a is the lattice constant and b is a positive dimensionless parameter, which accounts for deviation of the Coulomb potential from the point charge approximation at short distances and sets the appropriate initial electron–hole interaction energy. Both types of charges perform hopping in their respective domains of the lattice. The hopping is simulated using the Monte-Carlo algorithm as follows. As the initial configuration the hole and electron are placed on neighbouring sites in the interfacial region of the donor and acceptor domains. Only the nearest neighbour sites are taken into account for the hopping event. A charge can hop into one of six surrounding sites when it is far from the interface while hopping possibilities are fewer in the interfacial region. The hopping rates nmn for both the
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electron and the hole are calculated using the Miller–Abrahams formula:29 8 En Em < ; En 4 Em exp n mn ¼ n 0 expð2grmn Þ ; (3) kT : 1; En Em where g is a parameter which characterizes the inverse localization length of a charge density, rmn is the distance between the origin site m and the target site n, Em and En are their energies respectively. In the acceptor domain the hopping rate n0 nA is constant, while in the donor part we assume the value n0 nD1 for hopping to a target site located in a straight part of the same polymer chain as the origin site, n0 nD2 for hopping to a target site located on a folding point (the point where the orientation of the polymer chain changes) of the same polymer as the origin site and n0 nD3 for hopping to a target site located on a different polymer chain. It is assumed that a hole is less likely to hop to a site located on another polymer chain, thus the corresponding hopping rate prefactor nD3 is smaller than both nD1 and nD2. We also assume that a hole avoids folding points where holes move slower than in straight sections of the polymer chain, thus nD2 o nD1. It should be noted that a simple isotropic medium model was unable to reproduce the carrier drift kinetics during initial tens of ps therefore this more complex model, previously suggested to simulate carrier motion in the pure polymer,28 was used. When all rates of possible hopping events (including holes and electrons) have been evaluated, the rates are being translated into hopping probabilities according to: n mn pmn ¼ P ; nk
4. Experimental results Fig. 1 shows the carrier drift dynamics in as-spun and annealed samples for various applied voltages, calculated by the procedure described in ref. 19 from the experimentally measured TREFISH kinetics (not shown). Briefly, the electric field kinetics was reconstructed from the EFISH kinetics by using steady state EFISH dependence on the electric field strength. Next we assume that the electric field drop is proportional to the carrier drift distance and obtain the drift distance kinetics by normalizing the time-resolved field drop to the total field drop at long delay time when all carriers are extracted and, thus, their average drift distance equals to the half of the film thickness. The drift distances presented in Fig. 1 are averaged over electrons and holes and rapidly increase on the tens of ps time scale in both samples. At long times (>200 ps) the increase rate gradually slows down to reach a separation distance of 15–30 nm (depending on film treatment) at 2.5 ns. The drift distances are approximately proportional to the internal electric field, suggesting that the initial carrier mobility is independent of the electric field strength. Qualitatively, similar drift dynamics has been observed for neat polymers28 and
(4)
k
where the summation is performed over all calculated rates of both the hole and the electron. These probabilities are then used to determine the destination site n for either the hole or the electron, chosen by a linearly distributed random number. The charge configuration is then switched to the one that has been determined and the rates of the next hopping events are recalculated. For the simulation a 100 400 400 lattice was used. This lattice simulates the actual structure of the blend, motivating that no cyclic boundary conditions are introduced. Initially, charges were created at a random location at the interface between the donor and the acceptor regions and due to the external electric field they drifted apart in opposite directions. While charges moved through the lattice, the distance between them projected in the direction of the external electric field F, dk(t) was recorded and the result was averaged over 5000 realizations. Only one electron–hole pair was present in the lattice at a time, thus the model did not account for the nongeminate charge carrier recombination. The geminate recombination was also not accounted for assuming it to be much slower than the examined time domain.
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Fig. 1 (a) Experimental (symbols) and simulated (lines) charge drift dynamics in the as-spun (a) and annealed (b) samples at various electric fields strengths.
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attributed to carrier relaxation within a distributed density of states. The drift distances in the as-spun sample are about half of those in the annealed sample at the same applied voltages. The electron and the hole drift in opposite directions by about 2.5 nm during the initial 10 ps at 6.7 105 V cm1 electric field in the annealed sample. Thus, the electron–hole separation distance along the electric field is about 5 nm. This separation distance is around half as large in the as spun sample as in the annealed sample and is approximately proportional to the applied field.
5. MC calculation results Monte Carlo simulations by the procedure described above have been performed to model the carrier drift dynamics and to gain insight into the microscopic properties responsible for the observed differences in drift dynamics of annealed and as-spun material. The modelling of the hole motion dynamics accounts for the hole relaxation within the density of states (DOS), different hole hopping rates within a conjugated segment (nD1), between segments (nD2) and between polymer chains (nD3). The electron motion is simpler – the model accounts for the electron relaxation within the DOS and electron motion inside PCBM domains is characterised by a single electron hopping rate prefactor, nA. Both electron and hole motions are also affected by the domain structure of the blend; reaching the domain boundaries carriers are forced to search for alternative pathways to continue their motions – this process results in a domain-size dependence of carrier mobility. The drift kinetics at different voltages were simulated with the same model parameters, only varying the internal field strength. Carrier drift kinetics in as-spun and annealed samples have been modelled by using exactly the same motion parameters except for polymer and PCBM domain sizes. The best agreement was obtained with an average acceptor domain diameter of 7.5 nm for the as-spun sample and 33 nm for the annealed sample. As a result of fullerene aggregation the polymer domain dimensions were accordingly larger for annealed samples as well, but because of nonregular shapes their quantitative characterization, is more difficult. Fig. 2 illustrates the corresponding material morphologies and Fig. 1 shows the simulated carrier drift dynamics. The quite good agreement with experimental
Fig. 2 Cross section of typical simulated structures of as-spun (left) and annealed (right) samples. Dark areas denote acceptor regions (PCBM) and white areas denote donor regions (P3HT). The red line represents the length of 50 nm.
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results obtained for all curves with only one free variable, the domain size, validates the simulation results. The obtained domain dimensions of the annealed samples are somewhat larger than the B10 nm domains estimated in similar samples from experimental results.30 On the other hand, quite similar domain sizes of 10 to 30 nm were estimated by MC modelling of carrier recombination in a P3HT:PCBM blend.23 The MC simulations do not perfectly reproduce the carrier drift kinetics in annealed samples at high applied electric fields (6.7 105 V cm1) at times longer than 1 ns. This is not very surprising taking into account the relatively simple blend structure used in calculations. We proceed to infer effective charge carrier mobilities from the data for separation as a function of time. Note that these are not mobilities as usually defined, describing drift of relaxed populations of charges in the steady state, but instantaneous mobilities describing the instantaneous separation velocity of unrelaxed charge carrier populations. Since the experimental data gives us information on the sum of electron and hole drift distances, the actual electron and hole mobilities remain undisclosed, the ratio between electron and hole hopping rates being a free parameter. We have chosen the electron hopping rate on the basis of additional available information on the ultrafast time-resolved electron mobility and on the basis of the best agreement between experimental and calculated carrier drift kinetics. By means of time-resolved microwave conductivity, Savenije et al.31 obtained the electron mobility inside PCBM nanocrystals of 8 102 cm2 V1 s1 and a similar mobility of about 0.1 cm2 V1 s1 was also obtained on a subpicosecondseveral ps time-scale in PCBM film by dynamic Stark effect measurements.32 Thus, we have chosen an electron hopping rate prefactor nA to give an electron mobility of 0.1 cm2 V1 s1 at 0.3 ps, while its subsequent evolution was obtained from the best fitting with experimental data. Similar information on the initial hole mobility in P3HT is not available and therefore it was obtained from the modelling of the carrier drift kinetics. The best agreement was obtained with about ten times lower hole mobility than that of electrons. The simulation parameters used to obtain the best agreement between calculated and measured drift kinetics (see Fig. 1) are presented in Table 1. A lower initial hole mobility in comparison with the electron mobility was also concluded for a polyfluorene/fullerene blend.33 On the other hand, mobilities obtained from time resolved THz measurements on another polyfluorene low-bandgap polymer/ fullerene blend (APFO3/PCBM) show that picosecond time scale hole mobility is higher than the electron mobility by approximately a factor of five.34 The reason for this difference in the relative mobility of holes and electrons is probably a result of different sensitivity to intra- and inter-chain hole transport of the experimental methods. Fitting of the simulation and experimental results allows significant freedom of correlated variation of hopping rates of electrons and holes in different directions, thus the distinction of electron and hole mobilities is not reliable. Therefore we present, in Fig. 3, the carrier mobility averaged over electrons and holes, obtained directly from the experimental data. The short time carrier mobility is almost two times larger for the annealed sample. Carrier mobilities
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Paper Numerical values of the parameters of the model
Lattice dimension in the x direction (nm)
Lattice dimension in the y direction (nm)
Lattice dimension in the z direction (nm)
Lattice constant a (nm)
Average size of the acceptor ellipsoid M (nm)
100
400
400
1
As-spun: 220 annealed: 19 800
Average length of the donor chain (nm)
Hopping rate prefactor in the acceptor nA (s1)
Hopping rate prefactor in the donor nD1 (s1)
Hopping rate prefactor in the donor nD2 (s1)
Hopping rate prefactor in the donor nD3 (s1)
6
2.8 1016
2 1015
1 1015
5 1014
Parameter g (nm1)
Disorder in the acceptor sA (meV)
Disorder in the donor sD (meV)
Temperature T (K)
Mean dielectric permittivity e
5
70
80
293
3
Correction parameter b of the initial electron–hole interaction energy
Fraction of exponential distribution exp(E/s) in the modified Gaussian distribution
2
0.19
Fig. 3 Carrier mobility averaged over electrons and holes for as spun (closed circles) and annealed (open circles) samples at 4.7 105 V cm1 field strength.
in both samples drop down several tens of times during 1 ns. The TREFISH mobilities at t > 1 ns approach literature data for steady state mobility,5,18,19 indicating that carrier populations have almost relaxed into trap states during this time. Qualitatively similar mobility dynamics was observed in pure polymer films,27,28 showing that both inherent polymer and PCBM properties, as well as nanostructured blend morphology, are responsible for the mobility dynamics. Our experimental data give information on the carrier drift distance, while the absolute carrier separation distance is determined by carrier diffusion as well as drift. These two processes are interrelated through the Einstein relation D = mkBT/q, where D is the diffusion coefficient, m is the carrier mobility, kB is the Boltzmann coefficient, T is the temperature and q is the electron charge. In our previous paper we have shown that the diffusion distance on a ps time scale significantly exceeds the drift distance at low fields and is responsible for the weakly field dependent carrier separation yield.7 MC simulation is a convenient approach to obtain average absolute carrier separation distances caused by both carrier
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Fig. 4 Calculated absolute charge carrier separation distances in as spun (dotted lines) and annealed (solid lines) samples at different electric field strengths obtained by Monte Carlo simulation using a model fitted to the drift distance data in Fig. 1. The curves at higher electric field strengths are vertically shifted.
drift and diffusion from the carrier drift kinetics. Fig. 4 shows a comparison of the absolute carrier separation distances in as-spun and annealed samples at different electric field strengths. At zero electric field, only the diffusion drives the carrier motion, thus curves at zero field represent diffusion driven charge separation dynamics. At 0 and 1.7 105 V cm1 electric fields the separation distances on a tens of ps time scale are almost independent of the sample annealing. The difference appears on a ns time scale, when electrons approach the boundaries of small PCBM domains in the as-spun sample, while in the annealed sample with larger PCBM domains, they continue an unrestricted motion. At higher electric field, when the carrier drift contributes more to their motion, charge
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6. Conclusions
Fig. 5 Calculated time dependence of the absolute carrier separation distance at zero electric field and at various initial separation distances.
carriers move faster and reach domain boundaries in the as spun sample already on a ps time scale, thus the difference in separation distances appears already during tens of ps. Strongly restricted carrier motion in the as-spun sample with smaller PCBM and polymer domains prevents carrier escape from the Coulomb attraction. In devices such restricted carrier motion leads to enhanced charge carrier recombination, which is apparently one of the major factors limiting the carrier generation yield and performance efficiency of non-annealed P3HT/ PCBM solar cells.23 Our MC simulations have been performed assuming that only nearest neighbor e–h pairs are created by exciton splitting at the donor–acceptor interface as was suggested in ref. 7 and 33. However, there are publications35–37 arguing that charge carrier separation at much longer distances takes place on a femtosecond time scale and it helps for final separation of e–h pairs into free charges. Since this is still an open question, which could be also related to the blend annealing, we have also performed additional calculations directed towards evaluation of the role of the initial carrier separation distance in the charge separation process. Fig. 5 shows the calculated absolute charge carrier separation distances at zero applied field with the model parameters obtained from the above described simulations. Diffusion driven separation at long times is large with larger initial separation, but the influence of the initial separation gradually decreases with time and after several ns the separation distance is almost independent of the initial ultrafast separation if this separation is significantly smaller than 8 nm. Thus, initial carrier separation only weakly influences the final carrier separation process (at several ns when charges have reached a distance where the electrostatic attraction energy is similar to kT), unless the initial separation is comparable with the Coulomb capture radius. On the other hand, as we have discussed in ref. 7, the large distance carrier separation is hardly compatible with our experimental carrier drift data showing no quasi-instantaneous carrier drift component.
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In conclusion, our experimental investigations of the initial carrier motion in as-spun and annealed P3HT:PCBM blends together with Monte Carlo simulations of the carrier drift dynamics suggest a mechanism for the improved performance of annealed solar cells. The initial carrier drift rates, on a subnanosecond–nanosecond time scale are about two times larger in annealed samples. Monte Carlo simulations of the motion dynamics suggest that the increase in the carrier separation rate caused by blend annealing is related to the increased polymer and PCBM domain sizes enabling longer distance carrier separation on a ps time scale, which reduces the probability of their geminate recombination and thus increases the free charge carrier generation yield in annealed samples. On the other hand, the role of other material properties such as the presence of energy traps, or formation of semicrystalline polymer domains, which change as a result of annealing, cannot be completely ruled out. Additional MC simulations directed towards evaluation of the role of the initial carrier separation distance showed that the more efficient carrier separation in annealed samples can be hardly related to increased initial carrier separation distance. The initial separation distance only weakly influences the carrier separation efficiency at times and distances where free charges are formed if it is shorter than about 8 nm, while longer distance separation is non-compatible with our experimental data.
Acknowledgements This research was funded by the European Social Fund under the Global Grant measure, by the Swedish and European Research Councils (ERC 226136-VISCHEM), by the Swedish Energy Agency and the Knut & Alice Wallenberg Foundation and by Laser Lab Europe (project ID LLC001578, framework of the Initiative of Infrastructures Programme), by the UK Engineering and Physical Sciences Research Council via the Supergen programme and by the Royal Society.
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23 R. Hamilton, C. G. Shuttle, B. O’Regan, T. C. Hammant, J. Nelson and J. R. Durrant, J. Phys. Chem. Lett., 2010, 1, 1432–1436. 24 T. G. J. van der Hofstad, D. Di Nuzzo, M. van den Berg, R. A. J. Jensses and S. C. J. Meskens, Adv. Energy Mater., 2012, 2, 1095–1099. ¨ller, T. A. M. Ferenczi, M. Campoy-Quiles, J. M. Frost, 25 C. Mu D. D. C. Bradley, P. Smith, N. Stingelin-Stutzmann and J. Nelson, Adv. Mater., 2008, 18, 3510–3515. 26 T. Agostinelli, S. Lilliu, J. G. Labram, M. Campoy-Quiles, M. Hampton, E. Pires, J. Rawle, O. Bikondoa, D. D. C. Bradley, T. D. Anthopoulos, J. Nelson and J. E. Macdonald, Adv. Funct. Mater., 2011, 21, 1701–1708. 27 A. Devizis, A. Serbenta, K. Meerholz, D. Hertel and V. Gulbinas, Phys. Rev. Lett., 2009, 103, 027404. 28 A. Devizis, K. Meerholz, D. Hertel and V. Gulbinas, Chem. Phys. Lett., 2010, 498, 302–306. 29 A. Miller and E. Abrahams, Phys. Rev., 1960, 120, 745–755. 30 W. L. Ma, C. Y. Yang and A. J. Heeger, Adv. Mater., 2007, 19, 1387–1390. 31 T. J. Savenije, J. E. Kroeze, M. M. Wienk, J. M. Kroon and J. M. Warman, Phys. Rev. B: Condens. Matter Mater. Phys., 2004, 69, 155205. 32 J. Cabanillas-Gonzalez, T. Virgili, A. Gambetta, G. Lanzani, T. Anthopoulos and D. De Leeuw, Phys. Rev. Lett., 2006, 96, 106601. 33 D. Veldman, O. Ipek, S. C. J. Meskers, J. Sweelssen, M. M. Koetse, S. C. van Bavel, J. Loos and R. A. J. Janssen, J. Am. Chem. Soc., 2008, 130, 7721–7735. 34 C. S. Ponseca, H. Nemec, N. Vukmirovic, S. Fusco, E. Wang, M. R. Andersson, P. Chabera, A. Yartsev and V. Sundstrom, J. Phys. Chem. Lett., 2012, 3, 2442–2446. 35 A. A. Bakulin, A. Rao, V. G. Pavelyev, P. H. M. van. Loosdrecht, M. S. Pshenichnikov, D. Niedzialek, J. Cornil, D. Beljonne and R. H. Friend, Science, 2012, 335, 1340–1344. 36 I. A. Howard, R. Mauer, M. Meister and F. Laquai, J. Am. Chem. Soc., 2010, 132, 14866–14876. 37 C. Deibel, T. Storbel and V. Dyakonov, Phys. Rev. Lett., 2009, 103, 036402.
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Carrier motion in as-spun and annealed P3HT:PCBM blends revealed by ultrafast optical electric field probing and Monte Carlo simulations ab c a Vytautas Abramavic ˇius,* Dimali Amarasinghe Vithanage, Andrius Devizˇis, c d d Yingyot Infahsaeng, Annalisa Bruno, Samuel Foster, Panagiotis E. Keivanidis,e b d c c Darius Abramavic ˇius, Jenny Nelson, Arkady Yartsev, Villy Sundstro ¨ m and a Vidmantas Gulbinas
Charge transport dynamics in solar cell devices based on as-spun and annealed P3HT:PCBM films are compared using ultrafast time-resolved optical probing of the electric field by means of field-induced second harmonic generation. The results show that charge carriers drift about twice as far during the first Received 31st October 2013, Accepted 5th December 2013
3 ns after photogeneration in a device where the active layer has been thermally annealed. The carrier
DOI: 10.1039/c3cp54605e
simulated drift dynamics was obtained using identical model parameters for both cells, but with different
dynamics were modelled using Monte-Carlo simulations and good agreement between experimental and average PCBM and polymer domain sizes. The calculations suggest that small domain sizes in as-spun
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samples limit the carrier separation distance disabling their escape from geminate recombination.
1. Introduction Diminishing sources of fossil fuels and the need to meet rising global demands for carbon-free energy have led to renewable sources being explored as replacements. Conjugated polymers have been investigated as alternatives to solar cells based on inorganic semiconductors1 due to their light weight, flexibility, abundance of material, low material usage and manufacturing costs. The invention of the bulk heterojunction structure (BHJ) using a donor and acceptor homogeneously mixed to produce the active material2 has aided the increase in solar cell efficiency, which is presently 9.2% for the best reported cells.3 To improve device efficiency, the charge dynamics have also been investigated and three key stages in the charge separation pathway have been identified – charge generation,4 transport5 and recombination.6 Excitons are generated when light within the absorption spectrum of the material impinges on the devices. These excitons very rapidly6 separate into positive and negative charges forming Coulombically bound electron–hole pairs (or charge transfer states (CT)). In order to separate further, the charges have to a
Center for Physical Sciences and Technology, Savanoriu 231, LT-02300 Vilnius, Lithuania b Department of Theoretical Physics, Vilnius University, Sauletekio 9-III, LT-10222 Vilnius, Lithuania. E-mail: Vytautas.Abramavicius@ff.vu.lt c Chemical Physics, Lund University, Box 124, 221 00 Lund, Sweden d Imperial College London, South Kensington Campus, London SW7 2AZ, UK e Center for Nano Science and Technology@PoliMi, Istituto Italiano di Tecnologia, Via Giovanni Pascoli, 70/3, 20133 Milano, Italy
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overcome the Columbic attraction and form mobile charges which can move towards the electrodes through a combination of diffusion and drift.7 The collection of the separated charges results in completion of the circuit and current produced by the solar cell. Here we study the polymer:fullerene combination poly(3hexylthiophene) (P3HT) and [6,6]-phenyl-C61butyric acid methyl ester (PCBM). The method of processing P3HT:PCBM devices is known to impact the active layer morphology and, as a result, the efficiency of devices, and has therefore been extensively studied. Several factors have been investigated with the aim of improving device efficiency, such as the effect of solvent, morphology, film thickness and processing conditions.8–17 Annealing was shown to have a great impact on the conversion efficiency of P3HT:PCBM solar cells, quite different from most other polymer:fullerene blends. The carrier dynamics of annealed and as-spun P3HT:PCBM films have been studied using several techniques aiming at investigating differences in mobility,5,15 morphology,14–17 EQE14 and I–V characteristics.5 Annealing to a high temperature changes the morphology and enhances the hole mobility,5,9 resulting in it being only an order of magnitude below the electron mobility.5 A similar effect was achieved with slow solvent evaporation.18 Using microsecond time scale techniques, a large spread in mobilities and their differences in as-spun and annealed samples have been reported.5,15,19 The measurements show that the two different processing methods drastically affect the mobility and charge separation time scales. Morphological studies have shown that high temperature
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results in phase separation due to crystallization of the polymer5,15,16,20 and formation of large PCBM clusters.12,14–17 There is a consensus that thermal annealing results in improved device efficiency due to enhanced phase segregation, which consequently leads to increased charge separation efficiency,21,22 improved hole conductivity and formation of optimized charge transport pathways9,15 and consequently reduced bimolecular recombination.23 The mechanism through which the thermal annealing process enables higher charge carrier mobilities is now fairly well understood. Annealing induced crystallisation of the polymer results in larger domains (thicker lamellae) of the pure polymer and at the same time expels fullerene molecules out of the crystallising polymer, thereby making more fullerene available to build a robust electron transport network.20,24–26 It is clear from such studies that the improvement in charge collection (reflected through photocurrent quantum efficiency) is associated with the growth in pure polymer and fullerene domains and resulting improvement in charge carrier mobility relative to the recombination coefficient.5,9 In this paper, we aim at unveiling how morphology affects charge transport by investigating charge mobility and charge separation at earlier timescales using electric field-induced second harmonic generation (TREFISH)7,27,28 and MC simulations. We find the morphology to influence the mobility and carrier separation on the ps to ns time scale. MC simulations show that the different carrier drift kinetics in as-spun and annealed blends may be explained by more extensive material segregation, leading to larger P3HT and PCBM domains in annealed material, enabling fast separation of carriers at larger distances and preventing their geminate recombination.
2. Experiment The experimental setup and theory have been previously described,7,27,28 so only a brief account is given here. TREF ISH is a pump–probe technique, employing a femtosecond laser pulse to excite the sample devices and generate charges, and a probe pulse that generates the SHG signal probing the dynamics of the charges. An applied electric field breaks the symmetry of the material, allowing to generate the second harmonic signal of the probe pulse. The intensity and time dependence of the second harmonic signal monitors the electric field dynamics in the sample. The excitation pulse (400 nm, 36 nJ per pulse) was obtained by frequency doubling the fundamental of the Ti:Sa laser at 800 nm; a photon density of B1012 photons per cm2 per pulse for the sample was used, which is below the onset of strong second order (non-geminate) recombination. The probing wavelength was obtained using an optical parametric amplifier (TOPAS) at 1200 nm, the second harmonic of which was within the sensitivity of the photomultiplier detector. The sample device was made using a PEDOT:PSS/ITO anode and an aluminium (Al) cathode. The PEDOT:PSS was spun to form a 40–60 nm film and the total device had an overall thickness of B115 nm. The sample cells were all prepared in a clean room environment.
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3. Monte-Carlo simulation model The simulation model has been described in ref. 7. Briefly, charge carrier motion in the P3HT:PCBM blend was modelled by assuming a cubic lattice, characterized by a lattice constant a in all three dimensions. The lattice is divided into the donor part, where only the hole is allowed to reside and the acceptor part for the electron. The acceptor sites are defined by filling the lattice volume with ellipsoids of acceptor material (see Fig. 2) with typical average volume, which is later on used as a fitting parameter. The ellipsoids have arbitrary proportions and they are placed in arbitrary positions in the lattice and they overlap each other, thus mimicking the distribution of PCBM in the actual blend. Next, the remaining space in the lattice is filled with donor sites, which are used to create arbitrarily oriented and folded chains representing the polymer. The length of a chain is chosen randomly from the interval [L 3, L + 3], where L is the average length of chains. It should be noted, that such a blend model apparently cannot reproduce the real blend morphology, particularly of the annealed blend where a lamellar structure is suggested to be formed. The results of the calculation should rather be seen as a qualitative representation of morphology to rationalize the observed carrier dynamics. The electron and hole dynamics are controlled by site energy properties. In the presence of an external electric field the energy of an electron (hole) in the lattice consists of three parts: (1) the internal site self-energy Er, which is assumed to be a random Gaussian value; (2) the energy due to the constant external electric field F, and (3) the energy due to the Coulomb interaction between charges of opposite sign EC. The electron (hole) energy thus equals to: Ef (r) = Er 8 (Fr) + EC.
(1)
The site self-energy is distributed according to a modified Gaussian distribution, which is defined as a weighted sum of a normal Gaussian distribution with addition of longer exponential tails. The energy of the external electric field was accounted for by projecting the site position to the electric field direction. The electrostatic interaction energy is given by the shifted Coulomb potential EC ¼
q 1 4pee0 reh þ ba
(2)
Here q is the electron charge, reh is the distance between the electron and the hole, e is the mean permittivity of the material, a is the lattice constant and b is a positive dimensionless parameter, which accounts for deviation of the Coulomb potential from the point charge approximation at short distances and sets the appropriate initial electron–hole interaction energy. Both types of charges perform hopping in their respective domains of the lattice. The hopping is simulated using the Monte-Carlo algorithm as follows. As the initial configuration the hole and electron are placed on neighbouring sites in the interfacial region of the donor and acceptor domains. Only the nearest neighbour sites are taken into account for the hopping event. A charge can hop into one of six surrounding sites when it is far from the interface while hopping possibilities are fewer in the interfacial region. The hopping rates nmn for both the
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electron and the hole are calculated using the Miller–Abrahams formula:29 8 En Em < ; En 4 Em exp n mn ¼ n 0 expð2grmn Þ ; (3) kT : 1; En Em where g is a parameter which characterizes the inverse localization length of a charge density, rmn is the distance between the origin site m and the target site n, Em and En are their energies respectively. In the acceptor domain the hopping rate n0 nA is constant, while in the donor part we assume the value n0 nD1 for hopping to a target site located in a straight part of the same polymer chain as the origin site, n0 nD2 for hopping to a target site located on a folding point (the point where the orientation of the polymer chain changes) of the same polymer as the origin site and n0 nD3 for hopping to a target site located on a different polymer chain. It is assumed that a hole is less likely to hop to a site located on another polymer chain, thus the corresponding hopping rate prefactor nD3 is smaller than both nD1 and nD2. We also assume that a hole avoids folding points where holes move slower than in straight sections of the polymer chain, thus nD2 o nD1. It should be noted that a simple isotropic medium model was unable to reproduce the carrier drift kinetics during initial tens of ps therefore this more complex model, previously suggested to simulate carrier motion in the pure polymer,28 was used. When all rates of possible hopping events (including holes and electrons) have been evaluated, the rates are being translated into hopping probabilities according to: n mn pmn ¼ P ; nk
4. Experimental results Fig. 1 shows the carrier drift dynamics in as-spun and annealed samples for various applied voltages, calculated by the procedure described in ref. 19 from the experimentally measured TREFISH kinetics (not shown). Briefly, the electric field kinetics was reconstructed from the EFISH kinetics by using steady state EFISH dependence on the electric field strength. Next we assume that the electric field drop is proportional to the carrier drift distance and obtain the drift distance kinetics by normalizing the time-resolved field drop to the total field drop at long delay time when all carriers are extracted and, thus, their average drift distance equals to the half of the film thickness. The drift distances presented in Fig. 1 are averaged over electrons and holes and rapidly increase on the tens of ps time scale in both samples. At long times (>200 ps) the increase rate gradually slows down to reach a separation distance of 15–30 nm (depending on film treatment) at 2.5 ns. The drift distances are approximately proportional to the internal electric field, suggesting that the initial carrier mobility is independent of the electric field strength. Qualitatively, similar drift dynamics has been observed for neat polymers28 and
(4)
k
where the summation is performed over all calculated rates of both the hole and the electron. These probabilities are then used to determine the destination site n for either the hole or the electron, chosen by a linearly distributed random number. The charge configuration is then switched to the one that has been determined and the rates of the next hopping events are recalculated. For the simulation a 100 400 400 lattice was used. This lattice simulates the actual structure of the blend, motivating that no cyclic boundary conditions are introduced. Initially, charges were created at a random location at the interface between the donor and the acceptor regions and due to the external electric field they drifted apart in opposite directions. While charges moved through the lattice, the distance between them projected in the direction of the external electric field F, dk(t) was recorded and the result was averaged over 5000 realizations. Only one electron–hole pair was present in the lattice at a time, thus the model did not account for the nongeminate charge carrier recombination. The geminate recombination was also not accounted for assuming it to be much slower than the examined time domain.
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Fig. 1 (a) Experimental (symbols) and simulated (lines) charge drift dynamics in the as-spun (a) and annealed (b) samples at various electric fields strengths.
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attributed to carrier relaxation within a distributed density of states. The drift distances in the as-spun sample are about half of those in the annealed sample at the same applied voltages. The electron and the hole drift in opposite directions by about 2.5 nm during the initial 10 ps at 6.7 105 V cm1 electric field in the annealed sample. Thus, the electron–hole separation distance along the electric field is about 5 nm. This separation distance is around half as large in the as spun sample as in the annealed sample and is approximately proportional to the applied field.
5. MC calculation results Monte Carlo simulations by the procedure described above have been performed to model the carrier drift dynamics and to gain insight into the microscopic properties responsible for the observed differences in drift dynamics of annealed and as-spun material. The modelling of the hole motion dynamics accounts for the hole relaxation within the density of states (DOS), different hole hopping rates within a conjugated segment (nD1), between segments (nD2) and between polymer chains (nD3). The electron motion is simpler – the model accounts for the electron relaxation within the DOS and electron motion inside PCBM domains is characterised by a single electron hopping rate prefactor, nA. Both electron and hole motions are also affected by the domain structure of the blend; reaching the domain boundaries carriers are forced to search for alternative pathways to continue their motions – this process results in a domain-size dependence of carrier mobility. The drift kinetics at different voltages were simulated with the same model parameters, only varying the internal field strength. Carrier drift kinetics in as-spun and annealed samples have been modelled by using exactly the same motion parameters except for polymer and PCBM domain sizes. The best agreement was obtained with an average acceptor domain diameter of 7.5 nm for the as-spun sample and 33 nm for the annealed sample. As a result of fullerene aggregation the polymer domain dimensions were accordingly larger for annealed samples as well, but because of nonregular shapes their quantitative characterization, is more difficult. Fig. 2 illustrates the corresponding material morphologies and Fig. 1 shows the simulated carrier drift dynamics. The quite good agreement with experimental
Fig. 2 Cross section of typical simulated structures of as-spun (left) and annealed (right) samples. Dark areas denote acceptor regions (PCBM) and white areas denote donor regions (P3HT). The red line represents the length of 50 nm.
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results obtained for all curves with only one free variable, the domain size, validates the simulation results. The obtained domain dimensions of the annealed samples are somewhat larger than the B10 nm domains estimated in similar samples from experimental results.30 On the other hand, quite similar domain sizes of 10 to 30 nm were estimated by MC modelling of carrier recombination in a P3HT:PCBM blend.23 The MC simulations do not perfectly reproduce the carrier drift kinetics in annealed samples at high applied electric fields (6.7 105 V cm1) at times longer than 1 ns. This is not very surprising taking into account the relatively simple blend structure used in calculations. We proceed to infer effective charge carrier mobilities from the data for separation as a function of time. Note that these are not mobilities as usually defined, describing drift of relaxed populations of charges in the steady state, but instantaneous mobilities describing the instantaneous separation velocity of unrelaxed charge carrier populations. Since the experimental data gives us information on the sum of electron and hole drift distances, the actual electron and hole mobilities remain undisclosed, the ratio between electron and hole hopping rates being a free parameter. We have chosen the electron hopping rate on the basis of additional available information on the ultrafast time-resolved electron mobility and on the basis of the best agreement between experimental and calculated carrier drift kinetics. By means of time-resolved microwave conductivity, Savenije et al.31 obtained the electron mobility inside PCBM nanocrystals of 8 102 cm2 V1 s1 and a similar mobility of about 0.1 cm2 V1 s1 was also obtained on a subpicosecondseveral ps time-scale in PCBM film by dynamic Stark effect measurements.32 Thus, we have chosen an electron hopping rate prefactor nA to give an electron mobility of 0.1 cm2 V1 s1 at 0.3 ps, while its subsequent evolution was obtained from the best fitting with experimental data. Similar information on the initial hole mobility in P3HT is not available and therefore it was obtained from the modelling of the carrier drift kinetics. The best agreement was obtained with about ten times lower hole mobility than that of electrons. The simulation parameters used to obtain the best agreement between calculated and measured drift kinetics (see Fig. 1) are presented in Table 1. A lower initial hole mobility in comparison with the electron mobility was also concluded for a polyfluorene/fullerene blend.33 On the other hand, mobilities obtained from time resolved THz measurements on another polyfluorene low-bandgap polymer/ fullerene blend (APFO3/PCBM) show that picosecond time scale hole mobility is higher than the electron mobility by approximately a factor of five.34 The reason for this difference in the relative mobility of holes and electrons is probably a result of different sensitivity to intra- and inter-chain hole transport of the experimental methods. Fitting of the simulation and experimental results allows significant freedom of correlated variation of hopping rates of electrons and holes in different directions, thus the distinction of electron and hole mobilities is not reliable. Therefore we present, in Fig. 3, the carrier mobility averaged over electrons and holes, obtained directly from the experimental data. The short time carrier mobility is almost two times larger for the annealed sample. Carrier mobilities
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Paper Numerical values of the parameters of the model
Lattice dimension in the x direction (nm)
Lattice dimension in the y direction (nm)
Lattice dimension in the z direction (nm)
Lattice constant a (nm)
Average size of the acceptor ellipsoid M (nm)
100
400
400
1
As-spun: 220 annealed: 19 800
Average length of the donor chain (nm)
Hopping rate prefactor in the acceptor nA (s1)
Hopping rate prefactor in the donor nD1 (s1)
Hopping rate prefactor in the donor nD2 (s1)
Hopping rate prefactor in the donor nD3 (s1)
6
2.8 1016
2 1015
1 1015
5 1014
Parameter g (nm1)
Disorder in the acceptor sA (meV)
Disorder in the donor sD (meV)
Temperature T (K)
Mean dielectric permittivity e
5
70
80
293
3
Correction parameter b of the initial electron–hole interaction energy
Fraction of exponential distribution exp(E/s) in the modified Gaussian distribution
2
0.19
Fig. 3 Carrier mobility averaged over electrons and holes for as spun (closed circles) and annealed (open circles) samples at 4.7 105 V cm1 field strength.
in both samples drop down several tens of times during 1 ns. The TREFISH mobilities at t > 1 ns approach literature data for steady state mobility,5,18,19 indicating that carrier populations have almost relaxed into trap states during this time. Qualitatively similar mobility dynamics was observed in pure polymer films,27,28 showing that both inherent polymer and PCBM properties, as well as nanostructured blend morphology, are responsible for the mobility dynamics. Our experimental data give information on the carrier drift distance, while the absolute carrier separation distance is determined by carrier diffusion as well as drift. These two processes are interrelated through the Einstein relation D = mkBT/q, where D is the diffusion coefficient, m is the carrier mobility, kB is the Boltzmann coefficient, T is the temperature and q is the electron charge. In our previous paper we have shown that the diffusion distance on a ps time scale significantly exceeds the drift distance at low fields and is responsible for the weakly field dependent carrier separation yield.7 MC simulation is a convenient approach to obtain average absolute carrier separation distances caused by both carrier
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Fig. 4 Calculated absolute charge carrier separation distances in as spun (dotted lines) and annealed (solid lines) samples at different electric field strengths obtained by Monte Carlo simulation using a model fitted to the drift distance data in Fig. 1. The curves at higher electric field strengths are vertically shifted.
drift and diffusion from the carrier drift kinetics. Fig. 4 shows a comparison of the absolute carrier separation distances in as-spun and annealed samples at different electric field strengths. At zero electric field, only the diffusion drives the carrier motion, thus curves at zero field represent diffusion driven charge separation dynamics. At 0 and 1.7 105 V cm1 electric fields the separation distances on a tens of ps time scale are almost independent of the sample annealing. The difference appears on a ns time scale, when electrons approach the boundaries of small PCBM domains in the as-spun sample, while in the annealed sample with larger PCBM domains, they continue an unrestricted motion. At higher electric field, when the carrier drift contributes more to their motion, charge
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6. Conclusions
Fig. 5 Calculated time dependence of the absolute carrier separation distance at zero electric field and at various initial separation distances.
carriers move faster and reach domain boundaries in the as spun sample already on a ps time scale, thus the difference in separation distances appears already during tens of ps. Strongly restricted carrier motion in the as-spun sample with smaller PCBM and polymer domains prevents carrier escape from the Coulomb attraction. In devices such restricted carrier motion leads to enhanced charge carrier recombination, which is apparently one of the major factors limiting the carrier generation yield and performance efficiency of non-annealed P3HT/ PCBM solar cells.23 Our MC simulations have been performed assuming that only nearest neighbor e–h pairs are created by exciton splitting at the donor–acceptor interface as was suggested in ref. 7 and 33. However, there are publications35–37 arguing that charge carrier separation at much longer distances takes place on a femtosecond time scale and it helps for final separation of e–h pairs into free charges. Since this is still an open question, which could be also related to the blend annealing, we have also performed additional calculations directed towards evaluation of the role of the initial carrier separation distance in the charge separation process. Fig. 5 shows the calculated absolute charge carrier separation distances at zero applied field with the model parameters obtained from the above described simulations. Diffusion driven separation at long times is large with larger initial separation, but the influence of the initial separation gradually decreases with time and after several ns the separation distance is almost independent of the initial ultrafast separation if this separation is significantly smaller than 8 nm. Thus, initial carrier separation only weakly influences the final carrier separation process (at several ns when charges have reached a distance where the electrostatic attraction energy is similar to kT), unless the initial separation is comparable with the Coulomb capture radius. On the other hand, as we have discussed in ref. 7, the large distance carrier separation is hardly compatible with our experimental carrier drift data showing no quasi-instantaneous carrier drift component.
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In conclusion, our experimental investigations of the initial carrier motion in as-spun and annealed P3HT:PCBM blends together with Monte Carlo simulations of the carrier drift dynamics suggest a mechanism for the improved performance of annealed solar cells. The initial carrier drift rates, on a subnanosecond–nanosecond time scale are about two times larger in annealed samples. Monte Carlo simulations of the motion dynamics suggest that the increase in the carrier separation rate caused by blend annealing is related to the increased polymer and PCBM domain sizes enabling longer distance carrier separation on a ps time scale, which reduces the probability of their geminate recombination and thus increases the free charge carrier generation yield in annealed samples. On the other hand, the role of other material properties such as the presence of energy traps, or formation of semicrystalline polymer domains, which change as a result of annealing, cannot be completely ruled out. Additional MC simulations directed towards evaluation of the role of the initial carrier separation distance showed that the more efficient carrier separation in annealed samples can be hardly related to increased initial carrier separation distance. The initial separation distance only weakly influences the carrier separation efficiency at times and distances where free charges are formed if it is shorter than about 8 nm, while longer distance separation is non-compatible with our experimental data.
Acknowledgements This research was funded by the European Social Fund under the Global Grant measure, by the Swedish and European Research Councils (ERC 226136-VISCHEM), by the Swedish Energy Agency and the Knut & Alice Wallenberg Foundation and by Laser Lab Europe (project ID LLC001578, framework of the Initiative of Infrastructures Programme), by the UK Engineering and Physical Sciences Research Council via the Supergen programme and by the Royal Society.
Notes and references 1 J. Nelson, Curr. Opin. Solid State Mater. Sci., 2002, 6, 87–95. 2 G. Yu, J. Gao, J. C. Hummelen, F. Wudl and A. J. Heeger, Science, 1995, 270, 1789–1791. 3 Z. He, C. Zhong, S. Su, M. Xu, H. Wu and Y. Cao, Nat. Photonics, 2012, 6, 591–595. 4 J. Guo, H. Ohkita, H. Benten and S. Ito, J. Am. Chem. Soc., 2010, 132, 6154–6164. 5 V. D. Mihailetchi, H. Xie, B. de Boer, L. Jan Anton Koster and P. W. M. Blom, Adv. Funct. Mater., 2006, 16, 699–708. 6 S. De, T. Pascher, M. Maiti, K. G. Jespersen, T. Kesti, ¨s, A. Yartsev and V. Sundstro ¨m, J. Am. F. Zhang, O. Ingana Chem. Soc., 2007, 129, 8466–8472. 7 D. Amarasinghe Vithanage, A. Devizˇis, V. Abramavicˇius, Y. Infahsaeng, D. Abramavicˇius, R. C. I. MacKenzie, P. E. Keivanidis, A. Yartsev, D. Hertel, J. Nelson, ¨m and V. Gulbinas, Nat. Commun., 2013, 4, 2334. V. Sundstro
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