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Timestamp: 2019-04-24 10:19:27+00:00

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Impact of charge transport on current–voltage characteristics and power-conversion efficiency of organic solar cells – topic of research paper in Nano-technology. Download scholarly article PDF and read for free on CyberLeninka open science hub.
Impact of charge transport on current–voltage characteristics and power-conversion efficiency of organic solar cells Academic research paper on "Nano-technology"
2017 / Valerio Sarritzu, Nicola Sestu, Daniela Marongiu, Xueqing Chang, Sofia Masi, et al.
2015 / O V Slobodyan, E L Danielson, S J Moench, J A Dinser, M Gutierrez, et al.
Academic research paper on topic "Impact of charge transport on current–voltage characteristics and power-conversion efficiency of organic solar cells"
This work elucidates the impact of charge transport on the photovoltaic properties of organic solar cells. Here we show that the analysis of current-voltage curves of organic solar cells under illumination with the Shockley equation results in values for ideality factor, photo-current and parallel resistance, which lack physical meaning. Drift-diffusion simulations for a wide range of charge-carrier mobilities and illumination intensities reveal significant carrier accumulation caused by poor transport properties, which is not included in the Shockley equation. As a consequence, the separation of the quasi Fermi levels in the organic photoactive layer (internal voltage) differs substantially from the external voltage for almost all conditions. We present a new analytical model, which considers carrier transport explicitly. The model shows excellent agreement with full drift-diffusion simulations over a wide range of mobilities and illumination intensities, making it suitable for realistic efficiency predictions for organic solar cells.
With the development of new photoactive materials and the optimization of device architectures, the performance of organic solar cells has significantly increased over the last 5 years. However, their power-conversion efficiency (PCE) remains well below the Shockley-Queisser limit1. This raises the question about the physical processes limiting the efficiency. In the past, several models have been put forward, mainly considering losses due to geminate recombination2'3, limiting the short-circuit current JSC, or due to non-radiative recombination pathways reducing mainly the fill factor (FF) and the open-circuit voltage VOC (refs 4,5). Recent experimental and theoretical work, however, led to conclude that the performance of different polymer:fullerene blends to be largely affected by inefficient charge extraction due to low mobilities, in particular in systems with effective charge generation and/or large active layer thickness6-8.
where ni is the intrinsic charge-carrier density, d the thickness of the photoactive layer and J0 = ekrn;b d is the corresponding dark-generation current density.
For direct recombination, the rate is given by R = kdirnenh, with kdir being the coefficient for direct recombination, and the ideality factor nid = 1 in this case. For Shockley-Read-Hall recombination17, it is nid = 2 and for Auger recombination18 nid = 2/3.
As transport was not considered in the derivation of equation (1), it can be regarded as an idealization that describes a device with infinitely large conductivities (and hence mobilities) of electrons and holes. When Shockley and co-workers9 derived their expression this was a reasonable assumption, as their aim was to describe the behaviour of diodes. By that time, diodes were solid-state devices comprising pn-junctions made from highly crystalline inorganic materials with rather high mobilities such as, for example, Ge, Si or GaAs.
In contrast to crystalline inorganic semiconductors, organic semiconductors display quite low mobilities19,20. Hence, the basic assumption of equation (4) is not fulfilled for organic solar cells.
To investigate the effect of limited transport properties, numerical simulations were performed with the semiconductor device simulation tool TCAD Sentaurus from Synopsys Inc.21. The model is based on mimicking the photoactive layer by a one-dimensional effective semiconductor with the ETL corresponding to the LUMO of the acceptor phase and the HTL to the HOMO of the donor phase22. The electrodes are defined by their work functions and the surface recombination velocities of electrons and holes. As state-of-the-art organic solar cells employ thin interlayers from, for example, TiOx, ZnO, MoO3, NiO and V2O5 to enhance charge-carrier selectivity of the contacts23-26, electron- and hole-selective layers were included into the one-dimensional stack. For the electron-selective layer the ETL is aligned to the ETL of the photoactive layer, whereas the holes encounter a large energetic barrier of 1.7 eV and vice versa for the hole-selective layer (Supplementary Fig. 1), thus suppressing surface recombination at the electrodes. The parameters are summarized in Table 1 and realistic values were used27,28. Intragap states were not considered; only direct (bimolecular) recombination was taken into account according to R = kdirnenh.
For sake of simplicity, the generation rate was restricted to the photoactive layer and assumed to be spatially homogeneous. Only balanced mobilities (me = mh = m) were considered and series or parallel resistances were not regarded in the simulations (RS = 1/RP=0). Here we analyse the effect of charge-carrier transport on the current-voltage characteristics and PCE of single-junction photovoltaic devices. We demonstrate that it is meaningless to apply the Shockley equation to current-voltage curves under illumination and to extract information on physical parameters such as the recombination order or the apparent shunt resistance Rp. Further, we propose a new analytical approach, which is suited to accurately reproduce simulated current-voltage characteristics for a wide range of parameters and thus to predict achievable PCEs.
Drift-diffusion simulations of JV curves. The simulated JV curves under an intensity of '1 sun' are plotted in Fig. 1a as thin lines with symbols. The thick solid lines are results of our analytical model, which will be explained in detail further below.
Table 1 | Parameters used for the numerical simulations.
etl, electron transport level; htl, hole transport level.
Figure 1 | Effect of the charge-carrier mobility on the JVcharacteristics, (a) JV curves for six different charge-carrier mobilities. Thin lines with symbols show drift-diffusion simulations with the parameters in Table 1, while thick lines are the results of our analytical approximation. (b,c) show the corresponding energy diagrams under short-circuit conditions (Vexl = 0 V) for /1 = 1 and 10 ~ 6 cm2(Vs)respectively, (d) Internal voltage Vinl (left y axis) versus external voltage Vexl as extracted from the simulated JV curves with equation (6) for three different mobilities, compared with the Shockley equation (dotted line). The right y axis shows the corresponding recombination rate R. All graphs correspond to an illumination intensity of '1 sun'.
mobilities first affects the FF, but JSC is also significantly reduced for m < 10 - 5 cm2(Vs) - 1. In addition, the forward current density decreases strongly with lower mobilities.
These changes go along with a drastic violation of the main condition in equation (4). Figure 1b,c plot calculated band diagrams for two different mobilities under '1 sun' illumination at 0 V (short-circuit conditions). If the conductivities were infinitely large, no separation of the quasi Fermi levels would occur in the active layer, which is indicated by the dashed horizontal lines, hence corresponding to the assumption of the Shockley equation. In contrast, even for a high-mobility me = mh = 1cm2(Vs) -1, the quasi Fermi level splitting Efe — EFH in the bulk is considerably large and increases progressively with decreasing mobility. This proves that for all mobilities considered here, the quasi-Fermi level splitting is significantly larger than the external voltage Vext in the voltage range 0 < Vext < VOC. This has been confirmed recently by Schiefer et al.6,7 and Albrecht et oZ.8. The large splitting of the quasi-Fermi levels is the consequence of the accumulation of free charge carriers due to poor transport properties. As a result, non-geminate recombination is increased. This is the main cause for the continuous reduction of the FF and the short-circuit current density.
Here, eVint is the quasi-Fermi level splitting, which, if being constant throughout the entire active layer, would cause the same Jrec. Figure 1d shows Vint as a function of the external voltage Vext under '1 sun' illumination for the Shockley equation (where Vint=Vext) and exemplarily for three different mobilities. For almost all conditions, Vint is significantly larger than the external bias. Therefore, an important conclusion is that for typical mobilities in organic semiconductors, the Shockley equation massively underestimates the quasi-Fermi level spitting in the bulk and thereby the carrier density. High carrier densities have been reported by several authors even at short-circuit conditions, supporting the above findings29,30. For example, for the lowest mobility m= 10 - 6cm2(Vs)- 1 and at Vext = 0, the device is internally almost under open-circuit conditions, causing ~95% of the photogenerated carriers to recombine. Even for m = 1 cm2(Vs)- 1, the internal voltage Vint has a considerably high value of 552 mV under external short-circuit conditions. The above described effects are even more pronounced for increased thickness of the photoactive layer as well as for higher illumination intensities as can be seen in Supplementary Fig. 2a-e.
applicable and the often-used approach to extractP the shunt resistance Rp from the slope of Jillu near short circuit is not useful. Finally, the PCE becomes not only a function of the bandgap but also of the mobility, even if the generation of charge carriers is field independent and non-geminate recombination is slow. These three issues will be considered in more detail in the following.
Generation current and photocurrent. As pointed out above, it is quite common to define 'the' photocurrent, Jph via Jph = Jinu - Jdark. Figure 2a plots this quantity, normalized by the generation current: (Jiliu - Jdark)/Jgen, that is, the relative extraction efficiency of the photogenerated current Jgen (which for an illumination intensity of '1 sun' was set to Jgen = ejjj G(x)dx =12.82 mAcm-2). As expected, providing additional driving force by applying a negative bias voltage helps to extract more photogenerated charge carriers in those cases where the extraction at Vext = 0 is incomplete due to a low mobility. However, the quantity Jillu - Jdark can by no means be interpreted as the generation current, that is, Jgen. This is only true for mobilities being so large that the driving forces for the transport of electrons and holes can be neglected (and if external resistances can be neglected31). In fact, the extraction efficiency decreases strongly with increasing forward bias and the larger the mobilities the higher the voltage where the extraction efficiency starts to decrease. It should be noted here that for an ideal diode obeying equation (1) the difference between current under illumination and current in the dark is independent of voltage and equals the generation current: Jillu - Jdark = - Jgen. The reason for the voltage dependence in forward direction is the fact that the concentration of electrons and holes for a given voltage Vext is higher for an illuminated solar cell than for one in the dark. The additional generation of charge carriers by the light source increases their concentration and hence also their conductivity. As a consequence, a smaller part of the applied voltage Vext is required as driving force for the transport and hence the internal voltage Vint, and thus the (recombination) current is higher. This can lead (depending on the exact parameters) to the often-observed effect of intercepting dark and illuminated JV curves, that is, the JV curve under illumination 'overtakes' the one measured in the dark. In Fig. 2a, this becomes visible by the negative values of (JiUu - Jdark)/Jgen.
effective charge-carrier conductivity ffavjeff = d f 0 \Jse (x)ffh(x) dx is plotted versus the mobility at '1 sun' for short-circuit conditions in Fig. 2b. The conductivity of electrons and holes is given by: ffe h = eme,h x ne h. For a given mobility, the conductivity increases strongly under illumination due to the additional generation of charge carriers. The larger conductivity then leads to larger currents in forward direction and results in the crossing of dark and illuminated JV curves. As expected, the increase in conductivity under illumination and short-circuit conditions is less pronounced for higher mobilities.
Figure 2 | Photoconductivity and ideality factor. (a) Relative extraction rate of the photogenerated current as a function of the external voltage for six different mobilities at an illumination intensity of '1 sun'. (b) Corresponding effective average conductivity (see text) at Vexl = 0 as a function of mobility under illumination and in the dark. (c) Ideality factor nid as a function of light intensity for six different mobilities. (d) Apparent shunt resistance Rp as the function of light intensity as determined from the inverse slope of the simulated Jinu(V) at V = 0. The case of m = 1cm2(Vs)-1 was left out for better visualization.
Hereby, a linear fit (of the logarithmically plotted curve) was performed in the fourth quadrant, that is, 0< V< VOC. The results are plotted in Fig. 2c, showing a very large variation of the ideality factor with charge-carrier mobility and illumination intensity. The only exception is m = 1 cm2(Vs) - 1 where the ideality factor is unity for all light intensities. The lower the value for m, the more the ideality factor deviates from 1 and the lower the intensity where nid starts to increase. Notably, the apparent ideality factor determined via equation (7) can become very large, although direct free charge-carrier recombination was the only recombination pathway in our simulations and, therefore, nid = 1 should be expected. This proves that applying the Shockley equation to the JV curves of low-mobility carrier devices results in ideality factors that lack real physical meaning. As shown in Fig. 2c, this violation becomes most severe for large generation currents (efficient charge generation and/or high illumination intensity) and low mobilities.
is analysed to determine nid32,33. However, as shown in Supplementary Fig. 3, the applicability of this approach becomes questionable for low carrier mobilities and high currents. Alternatively, the analysis can be restricted to the exponential part of dark JV curves, but this requires devices with very-low leakage currents34. A more accurate method is the determination of the ideality factor from the dependence of VOC on the light intensity. Here, the charge-carrier densities vary over several orders of magnitude and thus more information can be extracted35,36. Although these measurements are not influenced by carrier transport, the accurate analysis of the results becomes difficult if the spatial distributions of electrons and holes are strongly asymmetric, which is the case, for example, for a small layer thickness or unintentional background doping13,37,38. In addition, surface recombination will alter the carrier profiles26 and lead to a reduction of the ideality factor.
We also find that low mobilities cause an apparent shunt resistance Rp (although 1/RP = 0 in all our simulations). The concept of 'the' shunt resistance is frequently used in the literature to account for the non-zero slope of the Jmu( V) curve at short-circuit conditions: RP = (dJ(V)/dV) - 1|V = 0. The analysis of experimental JV curves with this approach yields values for Rp of typically few tens to several thousand ficm2 (refs 39-41). Our simulations reveal that non-zero slopes of the JV curves are an inevitable consequence of low charge-carrier mobilities. Values for the apparent shunt resistance deduced from the simulated JV curves vary, indeed, over a very wide range, depending strongly on mobility and generation rate (Fig. 2d). The large discrepancy between the value of Rp used in the simulation (infinity) and the one deduced from the slope of the simulated JV curves with the extended Shockley equation again proves its non-applicability to organic solar cells for virtually any typical mobility and illumination intensity.
non-zero currents, the voltage drops related to the transport of electrons and holes through a resistive medium, that is, the photoactive layer, results in large differences between the external voltage Vext, which is applied (and which can be measured directly), and the internal voltage Vint. As only the latter determines the recombination rate, the description of a JV curve with equation (1) using Vext becomes worse as the charge-carrier conductivities get lower, and any approach to relate Jillu to Vext in a trivial form will fail.
However, if we recalculate JV curves with the help of equation (1) but replace Vext with Vint (Vext), the resulting curves are identical to the ones that were simulated with different mobilities. This is of course expected, as we excluded all loss mechanisms other than direct recombination between electrons and holes.
An interesting question is therefore how this internal voltage can be determined for real devices. One approach was followed by Wurfel et a/.42,43 with dye solar cells, where they managed to incorporate a third electrode into a dye solar cell, thus contacting the electron transport material, that is, the nanocrystalline TiOx, on both sides. Thus, they could show directly that under external short-circuit conditions, the internal voltage was already ~75% of the VOC. This is in full accordance with the analysis presented here.
with « being the intrinsic carrier density and meff = V^A being an effective mobility (see Supplementary Note 1 for the derivation of these terms).
By these means, the current density and the external voltage can both be calculated from Vint. As values for m and kr can however be determined separately44-48, the intrinsic charge-carrier density « remains as the only fitting parameter.
As a first test of the applicability of this approach, we have calculated JV curves with the parameters given in Table 1 and compared them with the JV curves from the full drift-diffusion simulations. We find excellent agreement between the simulated and the analytic approach for all mobilities as demonstrated in Fig. 1a.
We also find good agreement when applying this approach to a layer thickness of 300 nm and when changing the illumination intensity to either 0.1 suns or 10 suns (see Supplementary Fig. 2). Thus, for balanced mobilities our analytical approach shall provide an accurate analytical description of JV curves of organic solar cells over a wide range of mobilities and generation currents. The case of unbalanced mobilities is shown in the Supplementary Fig. 4. It can be seen that in this case our approach delivers very reasonable results as well.
with T = 300 K: J0, sq (EG, eff) = jprpc ¡Zf exp'O/tTl- 1 d' where c is the speed of light. This way, we made use of the fact that the absorption via charge transfer (states) does hardly contribute to the overall photogenerated current, while luminescence measurements show that most charge carriers do recombine via the effective semiconductor gap4,50,51. It is noteworthy that our study focuses on the influence of limited charge-carrier transport and the general findings presented here would not be altered even if the absorption via the effective band gap played a more significant role.
Figure 3 | The effect of mobility on the achievable PCE. (a) Scheme of the two band gaps involved. (b) Efficiencies are plotted as a function of effective semiconductor band gap, without an offset between donor and acceptor, that is, EG,abs = EG,eff and (c) with an offset DLL of 0.5 eV. Shown are the results for six different mobilities calculated either via the analytical approach (thin lines with symbols) or via drift-diffusion simulations (thick lines) in comparison with the Scharber model49. For parameters, see text.
radiative pathways4,51. For simplicity, this a = 5564 was used to calculate the dark-generated current for each effective band gap according to j0(£G,eff) = aj0,SQ(£G,eff).
Figure 3b shows the results for equal band gaps of absorber and effective semiconductor, that is, no offset DLL between the LUMO levels of donor and acceptor (and of course also between their HOMO levels for excitons generated in the acceptor), while Fig. 3c corresponds to DLL = 0.5 eV. The results of our analytical approach are well in accordance with the full drift-diffusion simulations, meaning that the assumptions leading to equation (13) remain valid for a wide range of bandgaps and mobilities. The figures also demonstrate the large impact of the charge-carrier mobility on the device efficiency. Efficiencies beyond 25% are predicted only for zero offset, a condition that is rather unlikely to realize with organic donor-acceptor blends. Nevertheless, efficiencies of 12% and higher are within reach for a realistic offset of 0.5 eV, provided that the mobility is in excess of 10 - 3 cm2(Vs)- 1.
These predictions are in good agreement to recent efficiency values. For example, Proctor et oZ. compared mobility and FF values for various solution processed small molecule-based bulk heterojunction solar cells. It is shown that balanced mobilities in excess of 2 x 10 - 4 cm2(Vs) - 1 are needed to achieve high FFs (and PCEs). Notably, a record efficiency of 10.8% was achieved in blends of carefully designed polymers with fullerene53. These blends had exceptionally high hole mobilities of 1.5 - 3.0 x 10 - 2 cm2(Vs) -1. Given the fact that the external quantum efficiency (EQE) was about 0.85 on average and that £G abs was about 1.55 eV, efficiencies of > 13% should be in reach on further optimization of the absorption properties, consistent with our predictions in Fig. 3.
smaller offsets DLL, enabling efficiencies beyond 20%. However, the effect of charge-carrier mobility is not explicitly treated in this work.
As there is no fundamental reason for DLL to be at least 0.5 eV, we also determined the maximum efficiency for smaller offsets. For mobilities of 10 - 2 cm2(Vs) - 1 or larger and DLL = 0.3 eV, we find an efficiency of 18%, and for DLL = 0.2 eV the maximum efficiency is already slightly above 20%. If the recombination coefficient kr could be reduced by one order of magnitude, the VOC would increase by 59.6 mV (at 300 K). As the FF is also improved, the maximum efficiency for DLL = 0.2 eV reaches 22% for mobilities of at least 10 - 2 cm 2(Vs) - 1 and even for mobilities of 10 - 4 cm2(Vs) -1, it still is almost 17%.
We demonstrated that the Shockley equation cannot be applied to low-mobility materials such as those typically used in organic solar cells. The poor transport properties cause accumulation of charge carriers in the photoactive layer and this effect becomes more and more prominent with decreasing mobility. As a consequence, for almost all conditions encountered in organic solar cells, the separation of the quasi Fermi levels in the photoactive layer (internal voltage) differs substantially from the externally applied voltage. For this reason, there is no trivial relation between the charge-carrier concentrations in the illuminated solar cell and the external voltage, which is however an assumption of the Shockley equation. A further consequence is that parameters such as ideality factors or apparent shunt resistance determined via the simple or extended Shockley equation will result in values that lack real physical meaning. Therefore, it is not possible to extract correct information about the reaction order of the recombination process and the photogenerated current, by applying the Shockley equation to current-voltage characteristics of organic solar cells under illumination.
An analytical model is presented that explicitly considers the implication of poor charge-carrier transport. We have obtained excellent agreement of the presented analytical model with the results of full drift-diffusion simulations for a wide range of mobilities, illumination intensities and active layer thicknesses. In contrast to other models, it allows predicting efficiency potentials by explicit consideration of charge-carrier mobilities, which has been very tedious to date in an analytical way.
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photovoltaics'). D.N. and S.A. further acknowledge funding from the BMBF within the PVcomB project (FKZ 03IS2151D).
U.W. and A.S. carried out the simulations. D.N. and U.W. developed and evaluated the analytical approach. U.W., A.S. and D.N. wrote the paper, with input from S.A.
How to cite this article: Würfel, U. et al. Impact of charge transport on current-voltage characteristics and power-conversion efficiency of organic solar cells. Nat. Commun. 6:6951 doi: 10.1038/ncomms7951 (2015).

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