N.
Felekidis
a,
E.
Wang
*b and
M.
Kemerink
*ac
aComplex Materials and Devices, Department of Physics, Chemistry and Biology (IFM), Linköping University, SE-581 83 Linköping, Sweden. E-mail: martijn.kemerink@liu.se
bDepartment of Chemistry and Chemical Engineering, Chalmers University of Technology, SE-412 96 Göteborg, Sweden. E-mail: ergang@chalmers.se
cDepartment of Applied Physics, Eindhoven University of Technology, PO Box 513, NL-5600 MB Eindhoven, The Netherlands
First published on 19th November 2015
Organic bulk heterojunction solar cells based on ternary blends of two donor absorbers and one acceptor are investigated by experiments and modeling. The commonly observed continuous tunability of the open circuit voltage VOC with the donor1:donor2 ratio can quantitatively be explained as quasi-Fermi level splitting due to photocreated charges filling a joint density of states that is broadened by Gaussian disorder. On this basis, a predictive model for the power conversion efficiency that accounts for the composition-dependent absorption and the shape of the current–voltage characteristic curve is developed. When all other parameters, most notably the fill factor, are constant, we find that for state-of-the-art absorbers, having a broad and strong absorption spectrum, ternary blends offer no advantage over binary ones. For absorbers with a more narrow absorption spectrum ternary blends of donors with complementary absorption spectra, offer modest improvements over binary ones. In contrast, when, upon blending, transport and/or recombination kinetics are improved, leading to an increased fill factor, ternaries may offer significant advantages over binaries.
Broader contextSolar cells based on blends of organic semiconductors almost routinely achieve power conversion efficiencies (PCEs) in the 10% range. One of the strategies that has been proposed to push this limit further upward is the use of so-called ternary blends in which two absorbing donor materials instead of one are blended with the electron acceptor. Systematic improvement of PCE by ternary blending has been reported. Despite the experimental success, the current understanding of both the PCE enhancement and the underlying puzzling tunability of the open circuit voltage VOC is limited and essentially qualitative. In this contribution, we develop and validate a quantitative and predictive framework for both the VOC and PCE of ternary organic solar cells, which allows us to propose design rules. In contrast to current wisdom, we demonstrate that PCE enhancement in ternary blends hardly results from optimizing the overlap with the solar spectrum but predominantly from synergetic improvement of the charge transport and recombination kinetics. The model can be easily extended to include more details and will allow other researchers to upfront evaluate the photovoltaic potential of ‘any’ ternary material combination. |
The reason for the continuously tunable VOC remains somewhat in the dark. Recently, Yang et al. proposed a ‘parallel junction’ model to phenomenologically describe this behavior.10 On the same basis, Savoie et al. proposed an empirical expression for VOC as a current-weighted average of the two sub-systems and used this to estimate the maximal theoretical PCE (13%) for varying donor bandgaps.11 Apart from lacking a formal basis, there are two problems with the parallel junction picture. First, it relies on a specific morphology in the active layer that allows different regions to act as independent binary cells that are electrically decoupled. Even if a fortunate morphology would lead to the presence of two (hole-) percolating networks that are electrically isolated from each other, the presence of metal contacts does unavoidably enforce equal quasi-Fermi levels in the subcells. The subcells cannot be treated independently. This problem becomes evident while considering the equivalent circuit of two parallel photodiodes. When biased beyond the lowest VOC, i.e. in the regime where the high-VOC subcell is supposed to boost VOC, the low-VOC subcell is in fact biased in its forward direction and will short the system. Alternatively, Street proposed a model for the formation of organic alloys in ternary blends based on two fullerene acceptors and a single donor.12 For this model to apply the charge wavefunction must be delocalized over many sites; for example for a 1:9 acceptor ratio, delocalization over more than 10 acceptor units is required to ‘feel’ on average at least one instance of each acceptor type. Although this may be conceivable for well-packed fullerenes, this intuitively seems to be rather unlikely for mixtures of heterogeneous polymers. Nevertheless, Khlyabich et al. recently argued for such an alloying effect in polymers, although no explicit calculations of VOC were presented.4
Hence for a quantitative assessment of the (im)possibilities of ternary bulk heterojunction solar cells there is need for a somewhat more rigorous model. Here, we implement a simple physical model based on state filling in a disordered Gaussian density of states. By first assuming a constant occupation the experimentally observed gradual dependence of VOC on the donor1:donor2 (D1:D2) ratio is explained. The assumption of constant occupation for all different polymer fractions is then expanded to include absorption and transport allowing a quantitative analysis of the achievable short circuit current (jSC) and power conversion efficiency in ternary blends. In agreement with experiments, it is predicted that for materials with a wide and strong absorption spectrum no improvement can be expected going from binary to ternary devices when all other parameters, like the fill factor, are unaffected by the blending. On the other hand, a moderate improvement is expected for ternary over binary blends for more narrow-spectrum absorbers. In contrast, we demonstrate that when the transport and/or recombination dynamics are simultaneously improved, ternary blends may offer significant advantages over binaries.
In the present work, we focus on donor1:donor2:acceptor BHJ OPVs but the concept should be equally applicable to donor:acceptor1:acceptor2 devices. It is unimportant if the constituent donor(s) and acceptor(s) are polymers, oligomers or small molecules. Moreover, for transparency we shall refer to the central energy of the disorder-broadened HOMO and LUMO levels as the HOMO or LUMO energy, which differs from what is probed by common electrochemical methods like cyclic voltammetry. Also the optical bandgap, when taken to be the absorption onset, is substantially smaller than the HOMO–LUMO gap due to (a) broadening and (b) excitonic effects. Because of the large uncertainties associated with both the absorption onset and the exciton binding energy we refrain from attempts to convert HOMO–LUMO gaps to optical gaps. This has no effect on the conclusions of this work.
Fig. 2 Experimental (symbols) and simulation (lines) data of VOCvs. composition for TQm6:TQm12:PC71BM (black) and TQp6:TQm12:PC71BM (blue) DDA ternary blends. The x-axis is the ratio of the concentration of the first polymer to the total polymer concentration. The estimated standard deviation in VOC as determined from several devices on multiple substrates did not exceed 10 meV (plotted error bar) for any of the VOC measurements. The parameter values used for the simulations are listed in Table S1 in the ESI.† The inset shows the same data normalized to the values at x = 0 and x = 1. |
The open circuit voltage of ternary systems based on TQm6:TQm12 (black symbols in Fig. 2) and TQp6:TQm12 (blue symbols) shows smooth and near-monotonous composition dependence. The two outlying VOC data points of the TQm6:TQm12 at 0.5 and 0.6 polymer ratios were investigated by AFM but no systematic (deviations in) phase separation was observed (Fig. S2 in ESI†); neither did any of the other performance indicators indicate specific problems for these two devices. Irrespective of the particular functional shape, all ternary systems are consistent with previous reports that VOC is continuously tunable via the D1:D2 ratio. Moreover, they strongly suggest an increasing bowing of the trend line with increasing difference between the VOCs of the binary extremes. This is better visible in the inset to Fig. 2 where the normalized VOC shifts are plotted.
In order to rationalize these observations, we apply a simple state filling model where the disordered Gaussian density of states for the two donor polymers and the acceptor are defined according to
(1) |
Geff = fD1·GD1 + (1 − fD1)·GD2 | (2) |
(3) |
(4) |
VOC = EF,el − EF,hole | (5) |
As a further confirmation we used the same model to successfully describe experimental VOC data for three optimized D1:D2:A ternary systems reported in the literature.4,5 The fitting results and used parameter values are shown in the ESI,† as Fig. S5–S7 and Tables S2–S4, respectively. These fitting results confirm the conclusion from Fig. 2 and 3 above, that larger differences in VOCs between the binary extremes lead to a more pronounced curvature of the VOCvs. composition curve. Importantly, it does so without invoking any structural or alloying effects.4,12
Having established a simple, but physically consistent model to describe the composition dependence of VOC in ternary blends, the question arises if the ‘tunability’ of VOC indeed allows ternary OPVs to outperform binaries. Up to now, simulations have been based on the assumption that occupation is constant for all compositions, a fact that does not allow addressing the key (supposed) advantage of ternaries, a better overlap with the solar spectrum, leading to higher jSC and PCE. In the next section, we will therefore extend our model to include the composition dependent absorption.
(6a) |
(6b) |
(7) |
The effective absorption length Leff for the blend is given by
(8) |
(9) |
(10) |
In order to correlate the above with experiments as straightforward and transparent as possible, we adopt a phenomenological transport model. This avoids explicitly addressing the complicated charge transport in the blend, including morphological effects, (reduced) bimolecular and trap-assisted recombination, density and field dependent mobilities, etc. The free carrier concentration is approximated by multiplying the carrier flux ṅ or ṗ with the respective lifetime τel or τhole:
n = ṅ·τel | (11a) |
p = ṗ·τhole | (11b) |
V OC is calculated from the occupation and quasi Fermi levels as described earlier in eqn (3)–(5). Finally, the short circuit current jSC and the power conversion efficiency PCE are calculated as
jSC = q·ṗ·Ldevice | (12a) |
Pout = FF(⋯)·VOC·jSC | (12b) |
PCE = Pout/Pin | (12c) |
As the first test, by implementing the optical model using the parameter values in Table S1 in the ESI,† the calculated VOC, jSC and PCE closely fit the trends in the experimental data of the TQm6:TQm12:PC71BM system, as seen in Fig. 4. The simulation results show the expected increasing current with decreasing open circuit voltage due to an increased absorption. The fill factor for this specific blend was measured to be fairly constant at 0.45 and this value was used in the simulations. As mentioned above, the three donor polymers were selected to give, in combination with PCBM, two ternary systems with weak and strong composition dependence of VOC, respectively, see Fig. 2. At the same time, the rather similar absorption spectra lead to the absence of clear trends in jSC and PCE for the systems where TQp6 is mixed with TQm6 and TQm12 polymers, that can, however, still be surprisingly accurately reproduced given the simplicity of the model presented above (see ESI,† Fig. S9, S10 and Tables S6, S7).
Fig. 4 Simulation (lines) and experimental (symbols) data for VOC (a), jSC (b) and PCE (c) vs. composition for the TQm6:TQm12:PC71BM ternary OPV system. |
In these simulations, the LUMO levels for both donors 1 and 2 are varied between −2.5 eV and −4.1 eV, while their HOMO level is fixed at −5.4 eV. The acceptor LUMO level for PC71BM is set at −4.1 eV. Wherever possible we used parameters that correspond to ref. 15 (see ESI,† Table S8). The results of the simulations are shown in Fig. 5, with the left panel showing the optimal D1 fraction for the given LUMO level combination and the right panel the corresponding PCE, i.e. at the optimal D1 fraction.
In agreement with ref. 15, for most D1–D2 combinations the optimal composition is a ternary one, i.e. in Fig. 5a bright yellow (pure D1) and blue (pure D2) regions are relatively rare and do not come near the overall optimal PCE of 8.75% that is found for a ternary system with a D1:D2 ≈ 1:1. The latter is rather close to the value of 8.5% that is reported by Yang et al. for (PTB7:PBDTT-SeDPP = 1:1):PC71BM. The donor LUMO levels for which the optimal PCE is found in the simulations, ∼−3.25 eV and ∼−3.85 eV are very consistent with the −3.31 eV and −3.70 eV of PTB7 and PBDTT-SeDPP, respectively.
The reason why, in the case of a fixed and common donor HOMO level, ternary systems outperform binary ones is the following. The constant HOMO energy makes VOC essentially constant, so the only thing to be optimized is the overlap with the solar spectrum. For a given finite absorption width two donors are, in virtually all cases, better at that than a single one. For the used parameters, the results indicate that ternary devices are the better choice over binary ones and that they can increase the PCE by ∼33% as the best binary device has a PCE of ∼6.5%, whereas best ternary device has 8.75%. For comparison, Yang et al. found binary PCEs between 6.2% and 7.2%, again consistent with our model. It should, however, be stressed that the superiority of ternary OPVs is not a general result; especially when not the donor HOMO but the donor LUMO is kept fixed. In this case, higher performances can be achieved leading to a dramatically changed picture.
An important technicality that needs to be addressed here is the sensitivity of the model results to the choice of parameters. First, all results presented in this work are robust to parameter variations in the sense that the qualitative conclusions remain unaffected. However, the quantitative results depend on parameter choices and especially on the shape of the absorption profile. For the calculation of Fig. 5 above quantitative agreement with ref. 15 in Fig. 5 is best when a nm-axis is used. The reason for that is likely the fact that the actual absorption profiles are rather symmetric on a nm-axis. For the present calculations (variable HOMO), it turns out that evaluating eqn (7) on a nm-axis leads to the results that are in conflict with experimental observations. Therefore in the following section an eV-axis will be used; otherwise all parameters are kept as in Fig. 5.
The results of Fig. 6 indicate a highest achievable PCE of ∼13%. Surprisingly, this is found for binary devices – in Fig. 6b the superiority of binary devices is shown as a yellow cross. Mapping this cross on a panel shows that the horizontal and vertical branches correspond to pure D1 and pure D2, respectively. The two small ternary regions, indicated by dashed ellipses, show that for certain polymer combinations optimized ternary systems can have an improved PCE over the corresponding binaries. At the same time, these specific ternaries do not give an optimal overall PCE.
There are multiple reasons for the abrupt jumps in the optimal composition in Fig. 6a. The jump around the ‘binary line’ (dashed diagonal) reflects the fact that the overall-optimal device is binary: for D1,2 combinations where neither donor is optimal, still the optimal D1:D2 ratio is the one where one has as much as possible from the donor that comes closest to the optimal donor, i.e. again a binary system. In other words, disadvantages in terms of reduced current or VOC outweigh any advantages of having a ternary system. The other jumps are associated with the presence of two maxima in the PCE vs. composition curve as explained at Fig. S11 in the ESI.†
It is important that the maximum PCE is now predicted to be substantially larger than in the previous variable-LUMO case. The reason is that in the present case energy losses associated with electron transfer to the acceptor are much reduced. This is equivalent to the fact that increasing the bandgap in this (variable HOMO) case does, but in the other (variable LUMO) case does not lead to an increased VOC, while having the same effect on the short circuit current.
Comparing to the work of Scharber et al. on donor selection rules,16 where they predict a PCE of 10% for binary devices, the higher value of 13% that is found here can mostly be attributed to the used higher IQE of 85% (instead of 65%). A close fitting of the present model to the one of Scharber et al. is included in Fig. S12 (ESI†) using the parameters of Table S9 (ESI†).
A remarkable observation in Fig. 6 is the position of the optimal HOMO level at −5.78 eV, corresponding to a bandgap of ∼2.0 eV. The difference with experimental findings where optimal HOMO energies around −5.3 eV are typically found1,2,15 is partially due to the difference in the way the bandgap and HOMO and LUMO energies are defined. Here, central energies are used; the parameters in Fig. 6 give in fact rise to an absorption onset at ∼1.5 eV (∼830 nm), in good agreement with the PTB7 absorption spectrum in ref. 15 that we took as the reference for the absorption width. At the same time, the present results indicate that substantial improvement in PCE can be obtained for a PTB7-like material with the same bandgap but downward-shifted HOMO and LUMO levels – PTB7 has a LUMO at ∼−3.3 eV, giving rise to a large charge transfer energy loss. This suggestion is corroborated by the results of He et al. who showed that PTB7-Th, having slightly deeper HOMO and LUMO levels, indeed gives improved performance.2
Using parameters that correspond to current state-of-the-art donor materials, ternary compositions show no improvement in PCE over binaries for the vast majority of energy level positions (Fig. 6). The picture becomes different if a less optimal absorber is used. Setting the absorption FWHM from 0.8 eV in Fig. 6 to 0.5 eV leads to a situation where the overall optimal PCE is produced by a ternary blend, see Fig. 7. Note that this FWHM corresponds to ref. 10 where, at the same time, rather optimistic absorption lengths of 10–20 nm were used in combination with a 200 nm device thickness. In Fig. 7b a clear cross shape corresponding to near-optimal binaries is visible. As a general design rule, we find that narrow but strong absorbers give rise to systems where ternary compositions offer improved performance over binary ones; broadening the absorption (cf.Fig. 6 and 7) or weakening the absorption length shifts the balance to binary-dominated ones. This is further illustrated in Fig. S13 of the ESI.† The rationalization of this rule consists of two parts. First, for strong absorbers the penalty for diluting the absorber that is closest to the optimal donor by adding a small fraction of another donor, is not so large as most light will still get absorbed. Second, for narrow absorbers the gain of adding another absorption band is relatively large, especially if the added absorber is a strong one.
An instructive intermediate situation arises when a material with a wide absorption band, as in Fig. 6, is mixed with the one with a narrow absorption, as in Fig. 7. Intuitively one might expect the narrow band to complement the wide one. It does, but at the price of diluting the wide absorption material. The net result is current and PCE loss with respect to the overall optimal binary device. Alternatively, one can rationalize this result on the basis of Fig. 6 by realizing that adding a narrow absorber must in all cases be inferior to adding a wider one.
The above findings lead to the conclusion that in the case of realistic good absorbers with close to optimal energy levels the enhanced overlap with the solar spectrum cannot be expected to lead to significant improvement in performance of ternary blends of the D1:D2:A type. However, this conclusion depends critically on the assumption that all other parameters are independent of composition. In practice, especially the fill factor can depend significantly on composition, as e.g. in ref. 6, 7 and 17, leading to optimal ternary compositions. Where this is not the case, e.g. in ref. 5 and 18, optimal PCEs are found for close to binary compositions, in agreement with the conclusions from Fig. 6 and 7.
In order to illustrate the critical role the composition-dependent fill factor plays in achieving ternary systems that outperform their binary counterparts, the simulations of Fig. 6 were re-run with a fill factor that is a function of the D1 fraction fD1:
FF(fD1) = afD12 + (FFD1 − FFD2 − a)fD1 + FFD2 | (13) |
In the simulations of Fig. 8, we used typical values of FFD1 = 0.65, FFD2 = 0.5 and a = −0.45, corresponding to a maximum FF of 0.7 at fD1 = 0.66, as shown in Fig. S14 in the ESI.† The calculation results now show that for virtually all HOMO level combinations, including the overall-optimal one, a ternary compound is preferred. Comparison of these results with that in Fig. 6 allows two important conclusions. First, in the case of ternary blending using state-of-the-art absorbers, minor or no improvements due to a better overlap with the solar spectrum can be expected (Fig. 6 and 7), but ‘secondary effects’ that lead to an improved fill factor can give rise to significant improvements (Fig. 8). This is in agreement with the experimentally observed correlation between the optimal fill factor and PCE.6,7,17 Second, in Fig. 8 the overall optimal PCE is still located on the binary line, where both donors have the same HOMO and LUMO. This reiterates the superiority of a single optimal bandgap provided the absorption is sufficiently broad. Hence, the ideal ternary system consists of two heterogeneous donors, both having this optimal bandgap, and showing a synergistic behavior in terms of FF, i.e. a negative a in eqn (13). Experimentally, this may be hard to achieve and one may be forced away from the overall PCE optimum.
Fig. 8 (a) Optimal fraction of donor1 and (b) associated PCE for all different HOMO level combinations. The calculation parameters are same as Fig. 6 but with a composition-dependent fill factor given by eqn (13) with FFD1 = 0.65, FFD2 = 0.5 and a = −0.45, corresponding to a maximum FF of 0.7 at fD1 = 0.66. The dashed ellipse indicates the best overall PCE of ∼14.1% at a D1 fraction of 0.66. |
As for our own experimental system, that was selected to investigate VOC, the virtual absence of spectral differences between the donors and the composition-independent fill factor preclude ternary compositions from having any advantages over binaries.
We shall finally draw an analogy between the present results and the 3-phase morphology encountered in binary OPV systems in which pure and aggregated donor and acceptor phases coexist with an amorphous mixed phase.19 Ignoring complications associated with the fact that charge transfer to the acceptor may be affected for better or worse, the mixed and pure donor phases can be considered as donor1 and donor2 phases, with slightly shifted energy levels due to the aggregation. From the discussion of Fig. 6 and 7 it can be said that such a 3-phase morphology is sub-optimal in the case of a donor with a broad absorption spectrum.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ee03095a |
This journal is © The Royal Society of Chemistry 2016 |