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PUBLISHED ONLINE: 11 OCTOBER 2009 | DOI: 10.1038/NMAT
On the origin of the open-circuit voltage of
polymer–fullerene solar cells
Koen Vandewal
1
* , Kristofer Tvingstedt
2
, Abay Gadisa
1
, Olle Inganäs
2
and Jean V. Manca
1
The increasing amount of research on solution-processable, organic donor–acceptor bulk heterojunction photovoltaic systems, based on blends of conjugated polymers and fullerenes has resulted in devices with an overall power-conversion efficiency of 6%. For the best devices, absorbed photon-to-electron quantum efficiencies approaching 100% have been shown. Besides the produced current, the overall efficiency depends critically on the generated photovoltage. Therefore, understanding and optimization of the open-circuit voltage ( V oc) of organic solar cells is of high importance. Here, we demonstrate that charge-transfer absorption and emission are shown to be related to each other and V oc in accordance with the assumptions of the detailed balance and quasi-equilibrium theory. We underline the importance of the weak ground-state interaction between the polymer and the fullerene and we confirm that V oc is determined by the formation of these states. Our work further suggests alternative pathways to improve V oc of donor–acceptor devices.
T
he most successful solution-processable organic solar cells use a C 60 or C 70 fullerene derivative as an electron acceptor blended with a conjugated polymer1–3. In the field, attempts have been made to derive upper limits for the efficiency of this type of polymer–fullerene photovoltaic device, albeit with empirical arguments related to the details of the origin of the open-circuit voltage3–5^ ( V oc). However, as energy is converted from one form (radiation) to another (electrical), fundamental losses should be taken into account and it should be possible to derive an upper limit for V oc, purely on the basis of thermodynamic considerations. For single absorber materials, this fundamental question was answered in 1961 in a seminal paper by Shockley and Queisser^6. Their analysis was based on the detailed balance of absorption and emission events from the solar cell, a ‘grey’ body at the surface of the Earth, illuminated by the Sun, a black body of much higher temperature. This allowed the derivation of an expression for V oc as a function of the material’s bandgap. It was found that V oc is maximal for the ideal case in which the charges can recombine only radiatively. According to this reasoning, it is clear that the V oc of polymer– fullerene devices has not reached its thermodynamic maximal value yet. This value would be reached if the only recombination mechanism at open-circuit conditions is a radiative one^6. As a result of the severe luminescence quenching in material blends yielding a substantial charge generation, it is clear that radiative recombination is just a small fraction of the total recombination, and a reduction of the maximum obtainable V oc is expected. In fact, no correlations of V oc with the optical gap of any of the blend constituents, as predicted by Shockley and Queisser^6 , are observed. Instead, V oc is found to scale with the difference between the highest occupied molecular orbital energy of the donor and the lowest unoccupied molecular orbital energy of the fullerene acceptor4,7. This leads to the conclusion that in this type of solar cell, the V oc is determined by recombination at the donor/acceptor interface8–12. Recently, for some polymer–fullerene blends, radiative interface recombination was observed. The presence of a weak emission signal, redshifted compared to the pure components, was detected in the photoluminescence and electroluminescence spectra and
(^1) IMEC-IMOMEC, vzw, Institute for Materials Research, Hasselt University, Wetenschapspark 1, 3590 Diepenbeek, Belgium, 2 Biomolecular and Organic
Electronics, Center of Organic Electronics (COE), Department of Physics, Chemistry and Biology, Linköping University, 58183 Linköping, Sweden. *e-mail: [email protected].
was assigned to the emission of interface electron–hole pairs or charge-transfer excitons13–17. The signature of this emitting state is also present in the absorption spectrum as a new, weak subgap absorption band in several polymer–fullerene blends used for photovoltaic applications18–20. Such absorption bands are typical for the formation of a ground-state charge-transfer complex (CTC) between the polymer and the fullerene. Furthermore, good correlations between the open-circuit voltage and the spectral position of the charge-transfer absorption^20 , photoluminescence^15 or electroluminescence^17 could be made. Here, we show that the electroluminescence and photovoltaic external quantum efficiency spectra in the low-energy, charge- transfer region are related to each other as predicted by the detailed balance approach. Furthermore, it is shown that at V oc, the photocurrent generated by the absorption of sunlight balances with the recombination current, resulting in emission of photons by the excited CTCs. This confirms previous suggestions10,15,20, that V oc is determined by the CTC formation between the polymer and the fullerene. To validate the generality of the detailed balance treatment for polymer–fullerene solar cells, blends of five different donor polymers and two fullerene derivatives, that is, [6,6]-phenyl C61 butyric acid methyl ester (PC 61 BM) and [6,6]-phenyl C butyric acid methyl ester (PC 71 BM), were investigated. The polymers belong to different conjugated polymer material families, comprising different conjugated backbones. These conjugated polymers are representative of the donor polymers used in polymer–fullerene solar cells explored in the community at present. Their chemical structures are shown in Fig. 1. Devices based on poly[2-methoxy-5-(30,70-dimethyloctyloxy)- 1,4-phenylene vinylene] (MDMO-PPV) and poly[2,7-(9-di-octyl- fluorene)-alt-5,5-(4′, 7 ′-di-2-thienyl-2′, 1 ′, 3 ′^ benzothiadiazole)] (APFO3) were prepared using different polymer/fullerene sto- ichiometries. Optimal devices were obtained using a 1:4 poly- mer/fullerene weight ratio, resulting in a power conversion efficiency of ∼2% and ∼ 2 .5% respectively. At a lower fullerene content, the photogenerated current becomes lower and the
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ARTICLES NATURE MATERIALS^ DOI: 10.1038/NMAT
S
N N
S
S S NS N
N N
S S
OC 8 H 17
S (^) *
OC 10 H 21
H 3 CO
C 6 H 13
C 6 H 13
H 9 C 4 O
OC 4 H 9
H 17 C 8 O
H 17 C 8 C 8 H 17
C 4 H 9 C 4 H 9
C 2 H 5 C^2 H^5
a
d e
b c
Figure 1 | The chemical structures of the donor polymers used. a , MDMO-PPV. b , P3HT. c , PCPDTBT. d , LBPP5. e , APFO3.
Table 1 | Measured J sc , V oc and calculated J 0 for all of the devices studied in this work.
Material J sc (A m^2 ) V oc (V) J 0 (A m −^2 )
P3HT–PC 61 BM (1:1) annealed 81 (±8) 0.62 (± 0 .01) 1.3 (± 0 .9) E- as prepared 35 (±8) 0.76 (± 0 .03) 5.6 (± 3 .0) E- PCPDTBT–PC 61 BM (1:2) with octyldithiols 100 (±5) 0.64 (± 0 .01) 1.9 (± 1 .1) E- without octyldithiols 66 (±7) 0.67 (± 0 .01) 6.7 (± 5 .3) E- LBPP5–PC 71 BM (1:3) 45 (±9) 0.73 (± 0 .015) 5.4 (± 2 .1) E- MDMO-PPV–PC 61 BM 1:4 34 (±7) 0.83 (± 0 .02) 2.2 (± 0 .8) E- 1:1 14 (±2) 0.88 (± 0 .01) 1.1 (± 0 .4) E- 4:1 3 (± 0 .6) 0.92 (± 0 .02) 3.8 (± 2 .2) E- APFO3–PC 61 BM 1:4 45 (±5) 1.02 (± 0 .01) 1.6 (± 0 .6) E- 1:1 28 (±4) 1.08 (± 0 .015) 2.7 (± 1 .0) E- 4:1 10 (±1) 1.16 (± 0 .01) 1.3 (± 0 .8) E- APFO3–PC 71 BM 1:4 35 (±5) 0.98 (± 0 .01) 1.5 (± 0 .3) E- 1:1 30 (±3) 1.00 (± 0 .01) 1.0 (± 0 .2) E- 4:1 10 (±2) 1.13 (± 0 .01) 6.6 (± 4 .4) E-
J 0 was calculated using the EQE PV( E ) and EQE EL( E ) spectra by means of equation (3). The errors on J sc and V oc are experimental errors obtained by measuring different devices. For the errors on J 0 , the variation of J 0 over the spectral range of the CTC was taken into account as well as the experimental error on EQE EL.
efficiency drops. However, V oc increases as the fullerene content is decreased (see Supplementary Information). APFO3-based devices were prepared with both PC 61 BM and PC 71 BM. For the poly[3- hexylthiophene] (P3HT)–PC 61 BM blends, ordering of the polymer phase, for example, induced by annealing, has been proven to have a major influence on the device performance^21. Therefore, in this study, as-prepared and annealed devices were characterized. For this material system, typical conversion efficiencies of 3.5% were reached. However, higher efficiencies for P3HT–PC 61 BM devices of up to 5% have been reported^22. A polymer of particular interest is poly[2,6-(4,4-bis-(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b′]- dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT), as it has a low optical gap, close to the optimum as predicted by Shockley and Queisser^6. It was shown that the addition of thiols in a PCPDTBT–fullerene solution improves the device performance^23. We obtained for PCPDTBT–PC 61 BM devices typically a power conversion efficiency of 3%. Efficiencies of 5.5% were reported for
0 0
EQE
PV
EQE
PV
0.5 1.0 1.5 2.0 2.5 3. E (eV)
0.5 1.0 1.5 2.0 2.5 3. E (eV)
100
10 ¬
10 ¬
10 ¬
10 ¬
10 ¬
10 ¬
106
107
105
104
103
102
101 100
5
4
3
2
1
Number of photons (eV
¬ s – m^
)
Number of photons (x
(^21) eV ¬ s (^) – m
)
P3HT–PC 61 BM
APFO3–PC 61 BM
PCPDTBT–PC 61 BM
MDMO-PPV–PC 61 BM
LBPP5–PC 71 BM
a
b
Figure 2 | The EQE PV spectra of polymer–fullerene devices. The devices comprise active layers: P3HT–PC 61 BM (1:1) (annealed), PCPDTBT–PC 61 BM (1:2), LBPP5–PC 71 BM (1:3), MDMO-PPV–PC 61 BM (1:4) and APFO3–PC 61 BM (1:4). a , The spectra on a linear scale. The standard AM1.5 G spectrum is shown on the right axis. b , The spectra on a logarithmic scale, to make the weak contribution of the low oscillator strength CTC visible. A charge-transfer band is clearly visible for all five material blends. Depending on the donor polymer, the spectral position of the charge-transfer band varies. On the right axis of b , the emission spectrum of a black body at room temperature is shown.
PCPDTBT–PC 71 BM devices^23. As in this article, there is particular interest in the V oc of the devices; note that the obtained V oc values correspond to what is found in the literature for similar devices. An overview of the devices studied in this work and the measured short-circuit current ( J sc) and V oc values are listed in Table 1. In Fig. 2a, photovoltaic external quantum efficiency ( EQE PV) spectra are shown on a linear scale for five devices using the
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ARTICLES NATURE MATERIALS^ DOI: 10.1038/NMAT
10 ¬
10 ¬
10 ¬
10 ¬
10 ¬
10 ¬
10 ¬
EQE
EL
(eV
¬ )
10 ¬
10 ¬
10 ¬
10 ¬
10 ¬
10 ¬
10 ¬
qEQE PV (^) BB 0 IJ (^) (eV ¬ )
φ
qEQE
PV
BB
/ EQE
EL (A m
¬
)
φ
1.0 1.2 1.4 1.6 1.8 2. E (eV)
1.0 1.2 1.4 1.6 1.8 2. E (eV)
10 ¬
10 ¬
10 ¬
10 ¬
10 ¬
10 ¬
10 ¬
P3HT PCPDTBT LBPP MDMO-PPV APFO
a
b
Figure 4 | Comparison of the measured EQE EL with the product of the EQE PV spectrum with the black-body spectrum at room temperature. a , Left axis: The EQE EL spectra devices based on the material blends P3HT–PC 61 BM (1:1) (annealed), PCPDTBT–PC 61 BM (1:2), LBPP5–PC 71 BM (1:3), MDMO-PPV–PC 61 BM (1:4) and APFO3–PC 61 BM (1:4). These EQE EL were obtained using injection currents in the range (1–10) times J sc. Right axis: EQE EL spectra, proportional to the product of the EQE PV spectrum with the black-body spectrum at room temperature. b , The ratio of the EQE PV and EQE EL multiplied by the black-body spectrum at room temperature. This value is fairly constant over the low-energy spectral region and equals J 0.
Here, φEL( E , V ) is the excess electroluminescence spectral photon flux and φBB( E ) is the black-body spectrum at 300 K, integrated over all possible incidence angles. The φBB( E ) spectrum is shown on the right axis of Fig. 2b. Note that this is an exponentially decreasing function with increasing photon energy, making only the low-energy part of EQE PV( E ) important in the evaluation of equation (1). For a low-mobility organic metal–insulator–metal, it was recently shown that relation (1) becomes only approximately valid^33. However, the deviations are expected to be within one order of magnitude. A simple relationship between EQE EL( E ) and EQE PV( E ) can be deduced if the ideal diode equation is used to describe the injected current J inj( V ):
J inj( V ) = J 0
exp
qV kT
Here, J 0 is the dark saturation current. We can deduce the following relationship between the EQE PV and EQE EL spectra:
J 0 EQE EL ( E ) = qEQE PV ( E )φBB ( E ) (3)
Here, J 0 is assumed to be implicitly voltage dependent, to maintain the generality of equation (2) for the description of dark I – V curves of polymer–fullerene devices. Typically, J 0 is determined
Calculated
V oc
(V)
Measured V oc (V)
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.
P3HT LBPP MDMO-PPV APFO
PCPDTBT
Figure 5 | The V oc obtained by means of the detailed balance approach versus the measured V oc. The different colours indicate devices based on different donor polymers: P3HT–PC 61 BM (1:1), PCPDTBT–PC 61 BM (1:2), LBPP5–PC 71 BM (1:3), MDMO-PPV–PC 61 BM, APFO3–PC 61 BM and APFO3–PC 71 BM. Measured and calculated V oc values were obtained for freshly prepared and annealed P3HT-based devices. For MDMO-PPV–PC 61 BM, APFO3–PC 61 BM and APFO3–PC 71 BM, the stochiometry was changed (4:1, 1:1, 1:4). PCPDTBT–PC 61 BM (1:2) was studied with and without the addition of octyldithiols in the solution. The grey line is a one-to-one correspondence. Experimental errors on the measured V oc were obtained by measuring different samples. Error bars on the V oc calculated by means of detailed balance were obtained by using the errors on the calculated J 0 and the absolute value of the measured EQE EL.
by injection and recombination mechanisms of the free carriers^34. For polymer–fullerene blends, diode equations with ideality factors between one and two are often used^35. In the notation used here, J 0 is in that case exponentially dependent on voltage. See the Supplementary Information for further details regarding J 0 and the ideality factor. Equation (3) relates the shape of the EQE PV( E ) spectrum to the shape of the EQE EL( E ) spectrum. The validity of this simple relation for polymer–fullerene solar cells is shown in Fig. 3a. It can be seen that multiplying EQE PV( E ) by the ambient black-body spectrum φBB( E ), the charge-transfer-dominated EQE EL( E ) of all photovoltaic devices comprising our five different donor polymers is obtained within acceptable limits. Note that these relations are valid also for large Stokes shifts between the charge-transfer absorption and emission. Furthermore, using equation (3), a value for J 0 can be deduced, by taking the ratio between qEQE PV( E )φBB( E ) and EQE EL( E ). Here, EQE EL is measured under injection conditions equivalent to 1–10 suns, whereas EQE PV( E ) was measured under short-circuit conditions. Note that J 0 obtained in this way is fairly constant over the range of overlapping EQE PV( E ) and EQE EL( E ). Only a slight decrease of J 0 with increasing photon energy is observed. This is at least partly due to the fact that during the EQE EL measurements, current is injected into the device, causing the effective temperature of the devices to increase as compared with room temperature. This heating slightly broadens the emission bands and causes the observed small slope. Further experimental errors on J 0 originate from the experimental errors on the absolute EQE EL. The obtained J 0 values for all investigated photovoltaic devices with their experimental errors are listed in Table 1. Integrating equation (3) yields the following expression for J 0 :
J 0 =
q EQE EL
EQE PV ( E )φBB ( E )d E (4)
Here, EQE EL is the overall electroluminescence external quantum efficiency, obtained by integrating EQE EL( E ) over all photon
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energies. The essential contribution of EQE PV( E ) to the integral in equation (4) is in fact only the low-energy charge-transfer part, as φBB is exponentially decreasing with increasing photon energy. This is in correspondence with the suggestion made by Potscavage et al.^10 that the dark current originates from thermal excitations of ground- state charge-transfer complexes. At open circuit, the injected current J inj( V ) causing the low- quantum-efficiency charge-transfer emission equals J sc; hence, by reforming equation (2), we obtain a commonly used equation for V oc:
V oc =
kT q
ln
J sc J 0
Note that this formula for V oc does not contain a parameter related explicitly to any optical gap. Spectral band positions are present in the equation implicitly in the term J 0 through equation (3). Note that, as both J 0 and J sc are proportional to respectively φBB( E ) and the AM1.5 spectrum integrated over EQE PV( E ), their ratio is determined by the spectral shape of EQE PV( E ) alone, which was measured at short circuit in this work. Furthermore, this formula is expected to be valid if the injected current is diode- like, as it is for the devices investigated in this work at voltages comparable to V oc (Fig. 3). To check the validity of equation (5), J 0 is obtained as described above. J sc is obtained by integrating the EQE PV spectrum over the solar spectrum or by measuring it directly under solar illumination. Experimental errors on J sc were obtained by comparing the calcu- lated data with the measured data of several devices on different solar simulators. The used J sc values with their experimental errors of all the devices studied in this work are listed in Table 1. The V oc values calculated by means of detailed balance versus the measured V oc values are shown in Fig. 5 for all studied devices comprising the five investigated polymers, using different preparation conditions. An overview of all preparation conditions is shown in the Supplementary Information. Excellent correspondence of the measured V oc with the calculated V oc is observed and differences in V oc on changing preparation conditions, such as stoichiometry alterations and annealing, are accurately reproduced. These differences in V oc are interpreted as being mainly caused by the spectral shifts of the charge-transfer bands on changing the preparation conditions13,18. The obtained new insights reveal pathways to increase the V oc of polymer–fullerene devices. From equation (4) it is clear that, because of the exponential nature of φBB( E ) a blueshift of the charge-transfer band results in an exponential decrease of J 0 through the term EQE PV( E )φBB( E ). Owing to the logarithmic dependence of V oc on J 0 (equation (5)), V oc depends linearly on the spectral position of the charge-transfer band. This results in the good correlations of V oc with the onset of the charge-transfer band^20 or the peak of charge-transfer emission15,17. The spectral position of the charge-transfer band is mainly determined by the energetic difference between the highest occupied molecular orbital of the donor polymer to the lowest unoccupied molecular orbital of the electron acceptor36–38. The presented theoretical approach explains the widely observed correlation between V oc and this energy level difference. However, there are other factors influencing the spectral position of the charge-transfer band, such as the binding energy of the charge- transfer exciton and its electrostatic environment36–38. Up to now, increasing the lowest unoccupied molecular orbital level of the fullerene39,40^ or using donor polymers with optimized energetic levels^41 , have been the most followed pathways for increasing the V oc of polymer–fullerene solar cells. From equation (5) however, other pathways for increasing V oc become apparent. Reducing the electronic coupling between the polymer
and the fullerene will suppress the charge-transfer band oscillator strength and will reduce J 0 , and thus increase V oc. The fact that V oc can also depend on the coupling between donor and acceptor material, was recently shown by Perez and colleagues^42. In the devices studied here, the recombination rate exceeds many times the charge-transfer emission rate, hence the low EQE EL in the studied devices. At solar illumination conditions, values of EQE EL are of the order of 10−^6 or 10−^9. Increasing EQE EL, by eliminating the extra non-radiative pathways and thus improving the carrier lifetime, will result in a decrease of J 0 (formula (5)) and therefore an increase in V oc. The theoretical maximum V oc will be obtained at EQE EL equals unity. This means that all non-radiative pathways are eliminated, resulting in a maximum charge-carrier lifetime, only determined by radiative recombination. Note that even in this case V oc does not necessarily equal the optical gap of the material blend, as fundamental thermodynamic losses owing to entropy creation will always cause the potential of the device to be lower than the energy of the relaxed charge-transfer exciton. From equations (4) and (5), we can deduce that, increasing EQE EL by a factor of 10 will result in an increase in V oc of ∼58 mV at room-temperature conditions. This means that for polymer–fullerene solar cells, for which EQE EL ∼ 10 −^9 –10−^6 , 0 .5–0.3 V is still to be gained, by eliminating the non- radiative recombination pathways, if this is possible. Therefore, to improve V oc, the exact origin of these non-radiative recombination pathways should be investigated in future works.
Methods
The devices were manufactured by spin-coating the active-layer blend solutions on top of electronic-grade poly(3,4-ethylenedioxythiophene) poly(styrenesulphonate) (Clevios P VP Al 4083) coated indium tin oxide/glass slides. For the P3HT-, PCPDTBT- and MDMO-PPV-based devices, chlorobenzene solutions were used. For the APFO3 and LBPP5 devices, chloroform was used as a solvent. All devices are finalized by thermal sublimation of 0.7 nm LiF or 20 nm of Ca, finalized by a 70 nm Al top electrode. The active areas of the cells range from 0.25 to 1 cm^2 and thicknesses are between 80 and 150 nm. P3HT was obtained from Merck, MDMO-PPV from Aldrich, PCPDTBT from Konarka and PC 61 BM and PC 71 BM from Solenne. APFO3 and LBPP5 were synthesised at Chalmers University. 1,8-octanedithiol, used for the PCPDTBT-based devices, was obtained from Aldrich. Device annealing of P3HT–PC 61 BM devices was carried out after electrode deposition. Photovoltaic devices were characterized by measurement of the I – V curve under solar illumination. J sc and V oc were extracted from these measurements. Error bars were obtained by measuring several different devices with two different solar simulators. V oc is typically very stable (± 0 .01 V). For J sc however, considerable deviations can be observed. Values for all devices are listed in Table 1. For the electroluminescence measurements, an Oriel optical liquid light guide was located as close to the biased cell as possible and connected to the entrance slit of the spectrometer. A Newton electron-multiplying CCD (charge-coupled device) Si array detector cooled to − 60 ◦^ C in conjunction with a Shamrock sr 303i spectro- graph from Andor Technology served as the emission-detection system. The system was wavelength-calibrated by an argon lamp to a resolution better than 0.5 nm. The transmission of the entire fibre-monochromator–CDD system was further radiometrically calibrated by an Optronic OL245M standard spectral irradiance lamp. The CCD detector is ‘back illuminated’, which increases the sensitivity but unfortunately also gives rise to some interference effects at wavelengths between 850 and 1,000 nm. Absolute values of the EQE EL spectrum could be obtained by mea- suring the total number of emitted photons in the 300–1,100 nm wavelength range with a homebuilt system using a large-area calibrated Si photodiode from Oriel. For the FTPS measurements, the modulated illumination beam of a Thermo Electron Nicolet 8700 FTIR with an external detector option was used. For the scaling to absolute EQE PV , a calibrated silicon photodiode was used as a reference detector.
Received 4 June 2009; accepted 15 September 2009; published online 11 October 2009
References
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- Park, S. H. et al. Bulk heterojunction solar cells with internal quantum efficiency approaching 100%. Nature Photon. 3, 297–302 (2009).
- Dennler, G., Scharber, M. C. & Brabec, C. J. Polymer-fullerene bulk-heterojunction solar cells. Adv. Mater. 13, 1323–1338 (2009).
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