Figures of Merit Guiding Research on Organic Solar Cells - The

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Cite This: J. Phys. Chem. C 2018, 122, 5829−5843

Figures of Merit Guiding Research on Organic Solar Cells Thomas Kirchartz,*,†,‡ Pascal Kaienburg,† and Derya Baran†,§ †

IEK5-Photovoltaics, Forschungszentrum Jülich, 52425 Jülich, Germany Faculty of Engineering and CENIDE, University of Duisburg-Essen, Carl-Benz-Str. 199, 47057 Duisburg, Germany § Physical Sciences and Engineering Division, KAUST Solar Center, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia

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‡

ABSTRACT: While substantial progress in the efficiency of polymer-based solar cells was possible by optimizing the energy levels of the polymer and more recently also the acceptor molecule, further progress beyond 10% efficiency requires a number of criteria to be fulfilled simultaneously, namely, low energylevel offsets at the donor−acceptor heterojunction, low open-circuit voltage losses due to nonradiative recombination, and efficient charge transport and collection. In this feature article we discuss these criteria considering thermodynamic limits, their correlation to photocurrent and photovoltage, and effects on the fill factor. Each criterion is quantified by a figure of merit (FOM) that directly relates to device performance. To ensure a wide applicability, we focus on FOMs that are easily accessible from common experiments. We demonstrate the relevance of these FOMs by looking at the historic and recent achievements of organic solar cells. We hope that the presented FOMs are or will become a valuable tool to evaluate, monitor, and guide further development of new organic absorber materials for solar cells. In solar cell research, efficiency (PCE or η), open-circuit voltage (Voc), short-circuit current (Jsc), and fill factor (FF) are the four dominant figures of merit that are used to judge device quality; however, taken in isolation they lack informative value. An open-circuit voltage of 1 V, for instance, is relatively meaningless without information about the shape of the absorption edge, the band gap (Eg), and the type of material used. Thus, a valuable figure of merit might be based on the four main device parameters mentioned above, but in addition it will create the context necessary to allow comparison between different devices and materials. Here we aim to give an overview over various FOMs that have been usedimplicitly or explicitlyas a guideline for improving organic solar cell efficiencies and show how the technology and therefore also these FOMs are likely to develop in the future. Understanding the reasons for high or low solar cell efficiencies is a task that may be approached considering different layers of abstraction and complexity. Of course, the final goal of understanding would ideally be one that connects what we know about the properties of molecules and their microstructure after film formation with properties such as recombination coefficients, mobilities, absorption coefficients, and energy-level alignment. Finally, one could then relate the parameters describing recombination, transport, and absorption with the key performance parameters of the photovoltaic device. The scope of this article is to focus on the second step rather than the first one and thus on the issues that are close to the properties of the solar cell itself. After our discussion on the

I. INTRODUCTION Power conversion efficiencies (PCE) of polymer-based solar cells (PSC) have risen steadily in the last 15 years, and nowadays there are several material combinations with efficiencies exceeding 10%1−10 and several with more than 12%.11,12 However, the increase of peak efficiencies of polymer−fullerene solar cells has decelerated, with substantial progress being made with novel non-fullerene acceptors that now start surpassing efficiencies of polymer−fullerene solar cells.11 Despite the promising development of non-fullerene acceptors, progress substantially beyond the 10% level will be more difficult than the path toward 10%. During different times in the development of solar cell technologies in general and organic photovoltaics in particular there have been certain guidelines and optimization criteria that technology development was based on. One obvious example in the case of organic photovoltaics is the redshift of the absorption onset from polymers with absorption onsets ∼2.0 eV like PPV or P3HT to novel lower band gap polymers with absorption onsets in the 1.4−1.6 eV range13,14 that lead to a better match with the solar spectrum. Another example is the optimization of energy levels at the donor−acceptor heterointerface13,15−18 leading to increased open-circuit voltages that drove much of the development in efficiencies. Whenever there are such guidelines or optimization criteria, a research community will create ideally quantitativefigures of merit (FOMs) that can be used as a measuring stick to evaluate progress, to find outstanding materials or devices, and to identify either the potential for further improvement or the necessity to change or expand the optimization criteria used. © 2018 American Chemical Society

Received: February 14, 2018 Published: March 2, 2018 5829

DOI: 10.1021/acs.jpcc.8b01598 J. Phys. Chem. C 2018, 122, 5829−5843

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The Journal of Physical Chemistry C

extremely low as compared to the situation a couple of years ago.

thermodynamics of photovoltage losses, the energy-level alignment in donor−acceptor solar cells and the question of electronic quality and high fill factors, we will conclude with a brief conclusion and outlook of recent developments and how further research can overcome the existing barriers in terms of microstructure and charge collection losses.

III. THERMODYNAMIC CONSIDERATIONS Before we will focus on the specific figures of merit for organic solar cells, we will introduce the general thermodynamic limitations of single-junction solar cells, which is applicable to any type of solar cell independent of specific details of the absorber material. The specific properties of organic solar cells will all lead to losses in photovoltage or photocurrent relative to the thermodynamic limit and will be discussed in Sections IV and V. Solar cells are typically analyzed by studying the basic parameters extracted from current density−voltage (J−V) curves under illumination, namely, efficiency η, open-circuit voltage Voc, short-circuit current density Jsc, and fill factor FF. These can be compared, for instance, with the thermodynamic limits for the respective parameters, which follow from the Shockley−Queisser (SQ) theory35 or variations thereof if realistic absorptances,36−40 multijunction solar cells,41−43 multiple exciton generation,44,45 hot carrier effects,46,47 or up- and down-conversion are taken into account.48,49 The classical SQ theory has the huge advantage that the device parameters would only depend on the temperature (usually kept constant at 300 K) and the band gap Eg of the solar cell. Any internal material properties, such as complex refractive index, mobility, and lifetime, are made redundant by assuming that every photon with energy above the band gap energy creates one electron−hole pair, which will be collected with 100% efficiency, and that the only relevant recombination mechanism controlling the open-circuit voltage would be radiative recombination as required by the principle of detailed balance.50 Under these assumptions, the equations for the saturation current density J0,SQ, the short-circuit current density Jsc,SQ, and the open-circuit voltage Voc,SQ in the SQ limit become quite simple and are given by

II. SPECIFIC PROPERTIES OF ORGANIC SOLAR CELLS There have been numerous reviews on the physics and chemistry of organic solar cells.19−29 Thus, we will here only briefly discuss some specific properties of organic solar cells that are of high relevance to the figures of merit that we will discuss in the following. Organic materials often allow quite high absorption coefficients, at least in a certain spectral region,30 but the typically low dielectric permittivities (εr ≈ 3 to 4) ensure that the photogenerated electron−hole pair is initially still a Coulombically bound exciton. Splitting this exciton is possible via introducing a network of two intimately mixed types of molecules. These molecules need to form a type II heterojunction as shown in Figure 1; that is, one molecule

Figure 1. Donor−acceptor heterojunction (Type II) band diagram illustrating the classical understanding of exciton dissociation, charge transfer followed by dissociation of the charge transfer state, and finally creation of separated charge carriers that may drift or diffuse to the electrodes to be collected.

∫E

J0,SQ = q

∞

ϕbb(E , T = 300 K) dE

g

needs to have both a higher electron affinity and a higher ionization potential than the other to allow injection of electrons from one molecule to the other but not of holes (or vice versa: injection of holes but not of electrons). The two molecules are usually called the donor and acceptor, with the donor injecting electrons into the acceptor molecule but also (for excitons photogenerated on the acceptor) the acceptor injecting holes into the donor. This donor−acceptor blend typically called a bulk heterojunctionallows ultrafast exciton separation with time constants on the order of hundreds of picoseconds or faster.31,32 Thus, photocurrent generation in organic solar cells can be quite efficient. However, the price that must be paid is typically a reduction of the achievable opencircuit voltage (due to the energy-level offsets at the heterojunction) and a reduction of mobilities33,34 in these blend systems relative to systems based on pure molecules used, for example, for transistor applications. Traditionally, the low mobilities and the voltage loss due to the donor−acceptor interface have been considered to be intrinsic problems of organic solar cells that impose a strong limit on the attainable solar cell efficiency. We will see in later parts of the article that low mobilities indeed remain a problem, while the voltage loss at the heterojunction can be reduced to levels that are

Jsc,SQ = q

∫E

(1)

∞

ϕsun(E) dE

(2)

g

and Voc,SQ =

⎛ ⎞ kT ⎜ Jsc,SQ ln⎜ + 1⎟⎟ q ⎝ J0,SQ ⎠

(3)

Here, we use the photon energy E, thermal energy kT, the AM1.5G solar spectrum ϕsun, used for the standardized testing of terrestrial solar cells,51 and the blackbody spectrum52 used for the radiation from the cell at room temperature ϕbb(E) =

⎛ −E ⎞ 2πE2 1 2πE2 ⎟ ≈ exp⎜ 3 2 3 2 ⎝ kT ⎠ h c [exp(E /kT ) − 1] hc (4)

Here, h is Planck’s constant, and c is the speed of light. The current density−voltage curve under illumination in the SQ limit can be written as ⎡ ⎛ qV ⎞ ⎤ J = J0,SQ ⎢exp⎜ ⎟ − 1⎥ − Jsc,SQ ⎝ ⎠ ⎣ ⎦ kT 5830

(5)


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Figure 2. Comparison between the SQ limit and experimental results for (a) η, (b) Voc, (c) Jsc, and (d) FF. Black symbols represent data for typical inorganic solar cells taken from ref 17. Colored symbols represent data points collected for organic solar cell materials with different acceptors (fullerenes, polymer acceptors, or small molecule but non-fullerene acceptors). The blue shaded area is a guide. It is defined as 80% of Jsc,SQ, 85% of FFSQ, and as Voc,SQ − 0.3 V, respectively. The blue line for efficiency is then given by the product of these three lines in (b−d). While organic solar cells come close to or exceed the blue line in (b−d), this does not happen in (a), showing that it is difficult to achieve high values for Voc, Jsc, and FF simultaneously.

Vocs that currently limit efficiencies to ∼26%55,56 and therefore to slightly lower values than for GaAs solar cells (28.8%).57 However, the set of organic solar data presented in Figure 2 is substantially lower than the SQ limit in Jsc, Voc, and FF, and therefore, efficiencies substantially above 10% are still rare in organic photovoltaics. The blue shaded area in Figure 2 serves as a guide, and its upper boundary is defined as 80% of Jsc,SQ, 85% of FFSQ, and as Voc,SQ − 0.3 V, respectively. The upper boundary for the blue shaded area for the efficiency is then calculated from the product η = FFJscVoc. While there are organic solar cells that are at the upper boundary or even beyond for either Jsc, Voc, or FF, none come even close in terms of efficiency, indicating that in organic photovoltaics photocurrent and photovoltage are not easily maximized in one and the same device even if the influence of the band gap is considered. Figure 3 provides a closer look at the spectrally resolved losses in photocurrent and photovoltage by comparing two recently published organic solar cells7,17 with the SQ limit and a recent Pb-halide perovskite solar cell. All three devices are based on absorber materials with band gaps around 1.6 eV, which is therefore used for the calculation of the SQ limit. Figure 3a shows the external quantum efficiencies (EQEs) of the three cells and the step function that is used in the SQ model. To assess the actual impact of the EQE on the cell’s efficiency Figure 3b shows the product EQE(E)ϕsun(E) of EQE and AM1.5G spectrumand therefore the number of absorbed photonsthat is used to calculate the short-circuit current density in a general case via

In the SQ model and in any other case, the extracted power density P follows from the JV curve via P = −JV. The efficiency is then the ratio of the maximum electrical power density versus the incoming power density, that is η=

max(P) ∞

∫0 Eϕsun(E) dE

(6)

The efficiency η, the short-circuit current density Jsc, and the open-circuit voltage Voc are three of the four main figures of merit used to compare photovoltaic performance. The fourth one, the fill factor FF, is not an independent parameter but follows from the other three via FF =

max(P) Jsc Voc

(7)

The SQ model serves as a useful first reference to compare the actual performance of solar cells with different band gaps. Figure 2 compares experimental data of organic and inorganic solar cells with the Shockley−Queisser limit for (a) efficiency η, (b) open-circuit voltage Voc, (c) short-circuit current density Jsc, and (d) fill factor FF. Both Jsc and Voc are strongly band-gapdependent in the SQ model, with Jsc increasing and Voc decreasing with decreasing band gap. Lower band gaps lead to a spectrally wider absorption range and thus a higher Jsc, while lower band gaps also lead to exponentially higher saturation current densities as given by eq 1. Because J0,SQ increases much more strongly with lower band gaps than Jsc,SQ the open-circuit voltage decreases for lower band gap. The fill factor is weakly increasing with band gap. Thus, the efficiency in the SQ model has a maximum, which is however rather broad and leads to highest efficiencies from ∼1.1 to 1.45 eV, where typical photovoltaic materials such as crystalline Si (c-Si), GaAs, and CdTe can be found. Especially the GaAs and c-Si record cells are close to the SQ limit in Jsc, Voc, and FF. In the case of c-Si, an additional intrinsic recombination process, namely, Auger recombination,36,38,53,54 leads to slightly reduced

Jsc = q

∫0

∞

EQE(E)ϕsun(E) dE

(8)

Comparison of Figure 3a,b shows that a quantum efficiency less than 1 has a substantially different impact on Jsc depending on the photon energy range, where it appears due to the multiplication with the solar power density spectrum, which is decaying strongly toward higher energies. Thus, contribu5831


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when studying Figure 3, it is clear that in relation to the SQ limit, the highest efficiency losses for the perovskite solar cell and the PTB7-Th:IDTBR:IDFBR cell are due to the last step, when the spectrally resolved photocurrent is converted into the spectrally resolved electric power density that is extracted from the cell. Figure 3 highlights a series of effects that have an impact on the efficiency and the efficiency limitations of organic solar cells that we will focus on in the following sections. In particular, we note that high open-circuit voltages can coincide with reduced EQE values, as seen for the case of the PffBT4T-2DT:FBR cell. In addition, it is possible to have strong absorption even in extremely thin organic films of ∼100 nm thickness but not necessarily over the whole spectral range covered by inorganic semiconductors. This effect is seen in the PTB7-Th:IDTBR:IDFBR-based solar cell. In addition, even for organic solar cells with high open-circuit voltages the product FF × Voc is substantially smaller than, for instance, for the perovskite solar cell with nearly the same band gap (see Table 1). In the Table 1. Photovoltaic Parameters for the Solar Cells Whose Data Are Presented in Figure 3

Figure 3. (a) Quantum efficiency of three solar cells (one perovskite58 and two organic7,17) with a band gap Eg ≈ 1.6 eV compared with the step-function like quantum efficiency defining the SQ limit. (b) Multiplication of the quantum efficiency with the solar spectrum ϕsun illustrates how strongly different regions of the solar spectrum contribute to the photocurrent. Generally, the low-energy regions close to the band gap are substantially more important than the spectral region in the blue. The areas under the curves are proportional to the short-circuit current density Jsc. (c) If we now further multiply the areas from (b) with the energy-independent product VocFF, we obtain areas that are proportional to the solar cell efficiency. The photovoltaic device parameters of the four cells are summarized in Table 11.

absorber material

Jsc (mA cm−2)

Voc (V)

FF

PCE (%)

SQ limit (FA,MA)Pb(I,Br)3 PTB7-Th:IDTBR:IDFBR PffBT4T-2DT:FBR

25.5 23.2 17.2 10.5

1.32 1.13 1.03 1.12

0.91 0.76 0.60 0.61

30.5 19.9 11.0 7.2

following, we will first focus on the issue of the open-circuit voltage in general, the relation between the open-circuit voltage versus photocurrent generation, and then discuss figures of merit for charge transport.

IV. THERMODYNAMIC LIMITATIONS OF THE OPEN-CIRCUIT VOLTAGE The open-circuit voltage of any real solar cell is reduced relative to the SQ limit given by eq 3 mostly due to (i) the effect of the solar cell quantum efficiency being different from the idealized step-function of the SQ limit and due to (ii) nonradiative recombination. A simple way of expressing these losses is via59

tions to the photocurrent are strongest for absorption close to the band edge of 1.6 eV. For instance, the low EQE of the PffBT4T-2DT:FBR solar cell below 2 eV leads to substantial losses in Jsc, while the strong reduction in EQE for both organic solar cells above 2.5 eV is less of a concern. The perovskite solar cell comes already very close to the Shockley−Queisser limit mostly thanks to its extremely steep absorption onset. While a gradual absorption onset is also observed for several inorganic solar cells, dips and drops in the EQE at higher photon energies are more specific to organic solar cells where the absorption bands of the constituent materials are relatively narrow. Figure 3c shows the product FFVocEQE(E)ϕsun(E), which integrated over energy gives the maximum electric power density and is therefore directly proportional to the efficiency η. The two organic solar cells are based on blends of polymers with non-fullerene acceptors and were chosen because of their high open-circuit voltages relative to their band gaps. For both devices, the open-circuit voltage exceeds 1 V, which is an excellent value when compared with other organic solar cells as seen in Figure 2b. The same holds true for the perovskite solar cell with its high open-circuit voltage of 1.12 V.58 However,

Voc =

⎛ J0,SQ J0,rad ⎞ J kT ⎛ Jsc ⎞ kT ⎜ Jsc,SQ ⎟ × sc × × ln⎜⎜ ⎟⎟ = ln⎜ q q Jsc,SQ J0,rad J0 ⎟⎠ ⎝ J0 ⎠ ⎝ J0,SQ

= Voc,SQ −

⎛ ⎞ ⎛ ⎞ kT ⎛ Jsc,SQ ⎞ kT ⎜ J0,rad ⎟ kT ⎜ J0 ⎟ ⎟⎟ − − ln⎜⎜ ln⎜ ln ⎜J ⎟ ⎟ q q q ⎝ Jsc ⎠ ⎝ 0,rad ⎠ ⎝ J0,SQ ⎠ (9)

where the index “rad” refers to quantities that are calculated in analogy to the SQ method discussed above, however, taking the real quantum efficiency into account. The respective equation for the saturation current density J0,rad in the radiative limit is given by60,61 J0,rad = q

∫0

∞

EQE(E)ϕbb(E) dE

(10)

The integrand in eq 10 specifies the photon flux emitted by pn junction at equilibrium, and J0,rad is the current that must flow to make this emission possible. While eq 9 is not strictly valid62,63 in mostly or fully depleted solar cells like organic solar cells, it is suitable for the purpose of studying voltage losses in organic solar cells.64 5832


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Figure 4. (a) Comparison between the Voc in the SQ limit and the actually measured Voc split up in loss terms as discussed in eq 9 and in ref 59 for a range of different polymer-based solar cells. (b) Voltage loss due to nonradiative recombination as a function of the radiative Voc illustrating the energy gap law, which states that voltage losses are likely to be reduced for solar cells with higher energetic distances between the energy of the recombining charge carriers and the ground state. Data for (a) are taken from refs 17, 59, and 67, and data for (b) were taken mostly from the tables in the Supporting Information of ref 69, to which some points were added from refs 17 and 67. The legend in (b) indicates the acceptor molecule used. “Small molecule” always implies non-fullerene small-molecule acceptors.

On the basis of eq 9, the difference between Voc,SQ and Voc rad nr can be expressed via three loss terms (ΔVSC oc , ΔVoc , ΔVoc) that represent (from left to right in eq 9) the loss in short-circuit current (Jsc < JSQ) due to a quantum efficiency below unity, the change in radiative recombination current (J0,rad < J0,SQ) mostly affected by the nonstep-function like quantum efficiency as discussed below and the loss due to nonradiative recombination (J0 < J0,rad). The latter is typically often related to the external light-emitting diode (LED) quantum efficiency QLED via61,65 Voc =

absorption onset of donor and acceptor molecules, and the stronger this shift is the higher are the associated voltage losses. The last loss due to nonradiative recombination is typically greater than 250 mV in organic solar cells and has recently69 been shown to correlate with the energy of the CT state (higher CT state energy leading to lower losses) or the radiative open-circuit voltage Voc,rad, which is closely correlated to the CT state energy. Figure 4b shows that, for higher values nr of V oc,rad, the voltage loss ΔV oc due to nonradiative recombination over a big range of organic solar cells goes down. This correlation has been explained by theories69,70 for nonradiative recombination via multiple vibrational modes, which predict a dependence of the nonradiative recombination rate on 1/p!, where p is the number of vibrational modes. Thus, for higher CT state energies, the number of vibrational modes that must be excited simultaneously to allow a nonradiative transition to occur becomes higher, and therefore the recombination rate goes down drastically. Among the three losses discussed above, ΔVrad oc is closely correlated empirically to the achievable photocurrent. The following section will therefore focus on this correlation.

⎛ J0,rad ⎞ kT ⎛ Jsc ⎞ kT ⎜ Jsc ⎟ ln⎜⎜ ⎟⎟ = ln⎜ × q q J0 ⎟⎠ ⎝ J0 ⎠ ⎝ J0,rad

= Voc,rad +

kT ⎛ J0,rad ⎞ kT ⎟⎟ = Voc,rad + ln⎜⎜ ln(Q LED) q J q ⎝ 0 ⎠

(11)

Experimentally, the discrimination of losses as proposed in eq 9 requires measurements of the external solar cell quantum efficiency EQE and the electroluminescence spectrum. Detailed descriptions of the method can be found in refs 66 and 67. While these quantities are measured regularly, not every research group has access to luminescence spectroscopy with sufficient spectral range (into the near-infrared) and sufficient signal-to-noise ratio. Therefore, experimentally, often only the difference between the band gap of the donor molecule and the measured Voc is compared. We will discuss this type of voltage loss further in the next section. As seen in Figure 4a, the voltage losses due to a reduction of Jsc (first term subtracted in eq 9) are hardly relevant in all reasonably efficient solar cells. This is because Jsc always must be of the same order of magnitude as Jsc,SQ, because Jsc enters the efficiency linearly but the voltage losses only logarithmically. The second loss ΔVrad oc = (kT/q) ln(J0,rad/J0,SQ) due to an increase in J0 from the SQ limit (step function absorptance) to the radiative limit (real shape of the absorption edge) can be quite substantial in organic solar cells. This is because radiative recombination in organic solar cells is often dominated by radiative emission from the charge-transfer (CT) state shown in Figure 1, which causes an increase of J0,rad relative to J0,SQ.39,68 This CT state is shifted to lower energies relative to the

V. RELATIONS BETWEEN OPEN-CIRCUIT VOLTAGE AND PHOTOCURRENT LOSSES The type II heterojunction as shown in Figure 1 is necessary for exciton separation butas explained aboveit may lead to substantial losses in open-circuit voltage if the energetic offset at the heterojunction is too high. In contrast, if the offset is too low at some point photocurrent generation will be reduced, because exciton separation will become less likely.15,16,18,71 Thus, the offsets of the type II heterojunction are an important design criterion for organic solar cells that implies a compromise between photocurrent and photovoltage. While there have been many studies on the relation between photocurrent and photovoltage as a function of the energylevel offsets at the heterojunction, we want to stress here the work of Li et al.72 relating the maximum achievable quantum efficiency (which is roughly proportional to the photocurrent) to the voltage loss Eg/q − Voc for a large set of samples. Figure 5a shows a modified version of the original Li-Plot using data 5833


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Figure 5. (a) Maximum EQE vs voltage loss defined as optical band gap Eg,opt/q − Voc for the data from ref 17. As a gray background, we highlighted the area Li et al.72 suggested being the one where most organic solar cells would fit in. (b) Maximum EQE vs the voltage loss now defined via the inflection point of the EQE; i.e., Eip/q − Voc for a data set including only rather recently published2,7,8,11,12,14,17,75,106−110,126−142 organic solar cells including a substantial amount of blends using non-fullerene acceptors. Highlighted in gray is a rectangle similar to the one implicitly used by Scharber in ref 13. (c, d) The color maps show the efficiency predictions ηSch and ηSch‑Li that result from the rectangles in (a, b), respectively. We assumed an FF of 70% for both panels. The older experimental data from (a) are plotted in (c), and the newer data from (b) with the altered definition of band gap are plotted in (d). The reported device efficiency η is coded in symbol size and color.

that are not always reported along with EQE results. Figure 5b displays more recent results from polymer:non-fullerene blends (green) along with polymer−fullerene blends with low voltage loss (red) and results from polymer−fullerene blends that marked a record efficiency at the time of their publication (blue). By defining voltage losses via the EQE inflection point a sharp cutoff at 0.6 V becomes visible for the depicted data. Thus, state-of-the-art technology cannot produce efficient organic solar cells with voltage losses smaller than 0.6 V. Apart from this threshold no correlation between voltage loss and maximum attainable EQE can be identified. Especially the more recently published non-fullerene acceptor (NFA) blends show low Voc losses and high peak EQEs at ∼80%. While incomplete exciton splitting does not limit the EQE and Jsc of these devices, their low thickness of ∼100 nm prevents complete absorption of incident light as will be discussed later. One important figure of merit to optimize band gaps and in general energy levels in organic photovoltaics is the so-called Scharber plot.13 The energy levels of polymers are a necessary but not sufficient criterion for optimizing photocurrent (via the band gap of the polymer) and open-circuit voltage (via the band alignment between the polymer and the acceptor molecule). Scharber et al. calculated device efficiencies as a function of the smaller band gap in the blend systemwhich was always the polymer at that timeand the lowest unoccupied molecular orbital (LUMO)−LUMO offset between donor and acceptor that can be directly translated into a voltage loss. The authors assumed a difference between the charge transfer state energy Ect and qVoc of 0.3 eV as nonradiative loss

from ref 17. Figure 5a shows that a decrease in the voltage loss most of the time results in a reduction of the maximum external quantum efficiency EQEmax. In the original paper by Li et al. the gray area was suggested as an empirical upper limit and a voltage loss of 0.6 V as an empirical limit below which values for EQEmax are dramatically reduced. In recent years, several polymer−fullerene and especially non-fullerene polymer:smallmolecule blends have enabled the fabrication of organic solar cells with values outside of the gray box. However, it has also been shown that the lack of a common definition of “band gap”59,73 reduces the usefulness of the version of the graph shown in Figure 5a. While the band gap is a well-defined quantity in a crystalline material like Si, the band gap may be defined in different ways in the context of organic solar cells. Often fits to absorption or quantum efficiency spectra are used to determine the band gap, but without a standard definition and analysis method of the band gap the voltage loss is difficult to compare, and the points in Figure 5a can shiftto some extentalong the voltage-loss axes. For Figure 5b we obtain a consistent analysis and comparable results by following the rationale of ref 59 and define the band gap as the inflection point Eip of the EQE spectrum at long wavelengths.59 Note that this definition of band gap via the EQE of the bulk heterojunction solar cell makes no statement about whether it is donor molecule, acceptor molecule, or a combination of both that most strongly affects the absorption onset. At the same time this enables the analysis of voltage losses of literature reports solely based on EQE measurements and does not require additional datathat is, from optical measurements 5834


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energies, and the most efficient cells have voltage losses that are 0.1 V higher than the predicted optimum. The reason for the deviation between predicted optimum and prevalent experimental development will be discussed in the next section. Figure 5d thus suggests further room for improvement for today’s best-performing NFA-based solar cells with peak EQEs independent of their voltage loss. Note that, to predict efficiency from energy levels, Figure 5b,d makes the important simplification of using the band gap or inflection point as an important reference point for the voltage loss but also for the maximum Jsc. In addition, we saw in Figure 3 that the quantum efficiency in reality is not a step function and that, in particular, losses close to the absorption onset or band gap may be substantial for the photocurrent because of the high photon flux per energy interval in the nearinfrared part of the solar spectrum. There are three problems with the efficiency assessment following Scharber: (i) The model uses a step-function like quantum efficiency, and, in particular, the new non-fullerene acceptors often lead to quantum efficiencies that are very high in the lower energy part of the spectrum and low in the higher energy part of the spectrum (see, e.g., Figure 3). While there are substantially fewer photons per energy interval in the higher energy part of the spectrum, the reduced EQE would still lead to losses that should be taken into account if the band gap was reduced further. (ii) As described in Section IV, lower CT state energies lead to higher nonradiative recombination losses, which will favor higher band gaps relative to the models described above, where voltage loss is a free parameter and is not assumed to be a function of band gap or CT energy. (iii) Collection problems that demand low device thickness are only taken into account by a relatively low FF of 70% and are otherwise neglected.

and a LUMO−LUMO offset of at least 0.3 eV. Thus, ref 13 was already based on a minimum voltage loss (Eg/q − Voc)min = 0.6 V. Additional voltage losses result from LUMO−LUMO offsets larger than 0.3 eV. By assuming a step-function like quantum efficiency with EQEmax = 0.65 and a 65% FF, the efficiency of any polymer when blended with PCBM could be calculated via Jsc = q0.65

∫E

∞

ϕsun(E) dE

g

, Voc = Ect/q − 0.3 V, and η = 0.65JscVoc. In Figure 5c,d we combine Scharber’s approach with the relations between EQEmax and voltage loss as indicated in Figure 5a,b. Thus, for Figure 5c we use Jsc = q

∫E

∞

EQEmax (Eg,opt /q − Voc)ϕsun(E) dE

g,opt

with higher voltage losses leading to higher EQEmax values as given by Figure 5a, Voc is given by the difference between optical band gap and the voltage loss on the y-axis of Figure 5c, and the FF is fixed at 70%; thus, the efficiency is given by η = 0.7JscVoc. For Figure 5d we use the inflection point of the EQE as a measure of band gap and use the gray box in Figure 5b to relate EQEmax with voltage loss. Thus, the calculation now uses Jsc = q0.8

∫E

∞

ϕsun(E) dE ip

, Voc is given by Eip/q minus the voltage loss on the y-axis of Figure 5d, while the efficiency is then given by η = 0.7JscVoc (again assuming 70% FF). We also plot all experimental data points shown in Figure 5a,b into Figure 5c,d, respectively. The band gap is defined according to the corresponding model in Figure 5a,b. The actual efficiency of the reported data is encoded in symbol size and color. Since Figure 5b,d includes more recent results, generally higher efficiencies are achieved. In Figure 5c, we observe that most of the data points from Figure 5a lie in the broadened middle of the range of highest efficiencies. The center of the plot is approximately a band gap of 1.6 eV and a voltage loss around 0.8 V, that is, values that are typical for the best polymer−fullerene devices. The more realistic case for recently reported NFAs with high efficiencies where EQEs are independent of voltage loss is displayed in Figure 5d. To compare the results of Figure 5c,d, note that a band gap definition via the inflection point Eipas chosen in Figure 5b,dsystematically shifts data to larger band gaps and therefore higher voltage losses compared to optically defined band gaps Eg,opt in Figure 5a,c. Bearing this systematic shift in mind, Figure 5d predicts a slightly lower optimum band gap of Eip = 1.5 eV and a lower optimum voltage loss of 0.6 V, which marks the cutoff for today’s efficient organic solar cells. This is consistent with the efficiency development of organic solar cells with very low voltage losses. While already in 2009 there were polymers like PDPP3T74 or (in 2012) isoindigobased polymers71 that enabled very low voltage losses, only recently there were also cases7,11,12,75 where low voltage loss blends (mostly using non-fullerene acceptors) showed efficiencies ∼11% and higher, that is, even outperforming the best efficiencies for blends with higher voltage losses. However, while the best-performing cells presented in Figure 5c closely match the predicted optimum band gap and voltage loss for a voltage-loss-dependent EQE, most experimental data points in Figure 5d are slightly offset toward higher inflection point

VI. FILL FACTOR AND CHARGE COLLECTION LOSSES Figure 2d shows that fill factors in organic solar cells are typically much lower than theoretically possible with rather few data points above 75%. While reductions in FF in highefficiency solar cells like crystalline Si are often due to simple resistive effects, in organic and other thin-film solar cells made from intrinsic or lowly doped absorber materials, charge collectionand therefore photocurrentdepends on the electric field in the absorber, which naturally changes with applied voltage implying an impact on the FF. The first type of solar cell, where field-dependent charge collection was studied extensively, was amorphous Si, prepared in a so-called p-i-n type of structure with a few hundred nanometers of intrinsic amorphous Si sandwiched by ∼20 nm thick layers of doped Si. In amorphous Si, the most dominant defects are typically dangling Si bonds not passivated by H, which create broad distributions of deep defects.76−78 Thus, the first models79−81 describing voltage-dependent charge collection in p-i-n-type structures were treating the case of Shockley−Read−Hall recombination via a deep defect as the dominant recombination mechanism. This led to analytical approximations that describe charge collection as a function of the ratio between drift length Ldr and thickness d. In the approximation of a constant field, this ratio could be expressed by79,80 Ldr V −V = μτ bi 2 d d

(12)

and the photocurrent would be79,82 5835


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The Journal of Physical Chemistry C Jph = 2qG̅ μτ

⎛ ⎞⎞ Vbi − V ⎛ d2 ⎜⎜1 − exp⎜ − ⎟⎟⎟ d ⎝ ⎝ 2μτ(Vbi − V ) ⎠⎠

(13)

where G̅ is the average generation rate of free charge carriers, μ and τ are the charge carrier mobility and lifetime, respectively, Vbi is the built-in voltage, and V is the applied voltage. Equation 13 already shows the importance of the product of mobility and lifetime as the major material properties that govern the collection of photogenerated charge carriers. In organic materials, the same equations have also been applied,82−85 but it was recognized that the recombination via deep defects may in many cases not be the dominant mechanism. Ideality factors derived from the light intensity dependence of the open-circuit voltage were only in rare cases showing values close to 2,86,87 while values closer to 1 were much more frequently observed. This hints at a dominance of recombination between states that lie above and below the two quasi-Fermi levels of electrons and holes and not between them as in the case of a deep defect. This can be rationalized with recombination via several phonons or vibrational modes discussed above. The equations used for molecular semiconductors69,70 and for inorganic semiconductors88−93 are very similar and agree that the number of phonons needed for the electronic transition to a lower energy state has a strong effect on the probability and rate of the transition. However, the larger energies of the vibrational modes in organic semiconductors (∼160 meV)69 relative to the energies of phonons in inorganic semiconductors (e.g., ∼60 meV for optical phonons in Si) make direct recombination in organic semiconductors much more likely than in inorganic ones, which are much more likely to require intermediate states to reduce the number of phonons needed per transition. In addition, often recombination in organic semiconductors was found to be nonlinear in carrier concentration,94−97 leading, for instance, to fill factors that are reduced with higher light intensities.98 This is an effect that a constant (charge carrierdensity independent) lifetime in eq 13 cannot reproduce. Therefore, other models were developed based on nonlinear direct recombination with a rate R following the equation R = knp, where k is the recombination coefficient (sometimes called bimolecular or direct recombination coefficient), and n and p are the electron and hole concentrations. While the calculation of current−voltage curves from parameters like the recombination coefficient k or the mobility μ is relatively easy to do via numerical simulations, there were also successful attempts to analytically describe the current voltage curve of p-i-n-like devices in the presence of bimolecular recombination.99,100 In both cases of linear Shockley-Read-Hall (SRH) recombination via deep defects or nonlinear bimolecular recombination, any increase in thickness will typically lead to a strong reduction of the FF.85,101 A larger thickness both increases the distance the carriers have to travel and reduces the electric field at a given voltage V and built-in voltage Vbi. Both aspects lead to a longer transit time for charge carriers through the active layer, which increases their chance to recombine. The thickness dependence of the FF is depicted qualitatively in Figure 6a. Up to which thickness high fill factors can be maintained depends heavily on the electronic quality Q of the material blend. The electronic quality is given, for instance, by the recombination coefficient k and the mobility μ or by the more conventional μτ product that is typically used in inorganic semiconductors and will be defined in the following. As a consequence of a low

Figure 6. (a) Thickness dependence of the FF for different values of electronic quality Q. (b) Correlation between the FF normalized to Voc and the collection coefficient γ. The small dots result from driftdiffusion simulations over a large ensemble of input parameters typical for organic solar cells. A model for the collection coefficient is fitted to the simulated data leading to the red line, which then allows the determination of electronic quality from experimentally obtained FFs. The experimental data points2,7,11,12,75,103,104,106−109 in (a, b) are a selection from recent NFA (small-molecule) blends and fullerenebased blends that reflect the historic development of organic solar cells. Higher Qs lead to higher FFs and at some point allow device thicknesses beyond the first interference maximum.

electronic quality, and thus a rapid drop in fill factor beyond a certain thickness, many organic solar cells have their optimum thickness at ∼100 nm, where the absorption of the incident light is far from complete. Thin active layers are also typical for high-efficiency organic solar cells, which can be seen from the data points plotted in Figure 6a, which are based on reports that marked outstanding performance at the respective time of publication. The position of the data points and their colorcoded electronic quality enforces the already mentioned trend: increasing Q values lead to higher fill factors and eventually allow a jump in active layer thickness to the second interference maximum above 200 nm. To reach a quantitative description, there were attempts to predict how the FF would depend on thickness and light intensity for a given electronic quality. First attempts in that direction were done by Barthesaghi et al.99 and others.101,102 While the details of the expressions vary slightly, the general idea is the same. For instance, ref 101 finds that the FF will be roughly the same over a wide range of parameters as long as the collection coefficients 2.0

γdir =

μ2 Voc · k0.8 d3.5Jsc0.5

(14)

for direct recombination, or γSRH = μ2 τ1.6· 5836

2.0 Voc

d 4.3

(15) DOI: 10.1021/acs.jpcc.8b01598 J. Phys. Chem. C 2018, 122, 5829−5843

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The Journal of Physical Chemistry C for SRH recombination via a deep defect are constant. Higher values of the coefficients γ would lead to higher FFs as shown in Figure 6b. The set of data points results from drift-diffusion simulations over a wide parameter range that are typical for organic solar cells. The line is the model fit presented in ref 101. The model produces an unequivocal relation between the collection coefficient and a normalized fill factor FFn that takes the Voc dependence of the highest attainable FF into account. The relation between collection coefficient and fill factor has limitations whenever space-charge effects become important. In this case, the constant field approximation is no longer applicable, and diffusion cannot be neglected anymore. Reference 101 contains a detailed discussion of space-charge effects. Both collection coefficients γ defined in eqs 14 and (15) depend on a material specific part depending only on μ and k or τ and a term depending on thickness, light intensity, and open-circuit voltage. The material specific part defines an electronic quality factor Qdir = μ2/k0.8 for direct and QSRH = μ2τ1.6 for Shockley−Read−Hall recombination, which can vary over several orders of magnitude, while the other term covers ∼1 order of magnitude for typical organic solar cells. Therefore, only materials with a high electronic quality factor can reach high fill factors. The literature reports included in Figure 6a are also entered in Figure 6b by applying the results of the model and calculating the collection coefficient from the (normalized) fill factor. Since Voc, Jsc, and thickness are also known, the electronic quality can be obtained. A rough correlation between electronic quality and collection coefficient and FFn can be seen. The correlation is naturally not perfect, because the collection coefficient is proportional to d−3.5, and thus the device thickness shifts the data points along the curve. Especially devices with the highest Q might have a slightly lower γ and FF, because they can be made much thicker than 100 nm. The slightly lower FF is compensated by a more complete absorption, which is one route to overcome the issue of photocurrent loss at the band edge discussed in Figure 3. The correlation between electronic quality and voltage loss is shown in Figure 7a for the literature data that also Figure 5b is based on. Most importantly, as of today there are no organic solar cell materials that simultaneously reach high electronic qualities above 1000 cm1.6 s1.2/V2 and low voltage losses below 0.8 V. The apparent decline in Q with lower voltage losses might explain why the voltage loss of today’s best-performing solar cells is larger than the optimum of 0.6 V predicted by Figure 5d, where collection problems were neglected. Figure 7b further elaborates on this point and essentially summarizes the last 15 years of organic solar cell development in two relevant figures of merit denoted as electronic quality and energy-level matching. Here we assumed direct, bimolecular recombination to be dominant and therefore used Qdir to quantify electronic quality from values of FF, Jsc, Voc, and thickness under the assumption that space charge effects are not too dominant in high-efficiency solar cells. The energy-level matching axis reflects the efficiency prediction ηScharber as shown in Figure 5d. In 2001 Shaheen et al.103 reported the first organic solar cell based on MDMO-PPV with a notable efficiency of 2.5%, although it scored low for both FOMs. The increase in record efficiency to almost 5% achieved by P3HT:PCBM104 can be mostly attributed to its high electronic quality. This high Q allowed for devices thicker than 200 nm105 and results from the highly ordered film morphology of P3HT:PCBM, which, for several years, remained exceptional for a high-performing solar

Figure 7. (a) Correlation between electronic quality and voltage loss. Small-molecule NFA-based blends with low voltage loss have not reached high electronic qualities, which explains the typical optimum thickness of ∼100 nm of this recent class of organic solar cells. (b) Overview of the development of organic solar cells over the past 15 years expressed in terms of the two FOMs electronic quality and energy-level matching. The actual device efficiency is encoded in the color and the height of the bars. The data selection is the same as in Figure 6. While considerable progress has been made for both FOMs, it remains an open challenge to create material blends that excel in both categories, which would then boost the power conversion efficiency of organic solar cells.

cell. Then followed a phase during which the electronic quality was low but the energy-level matching was improved drastically. Devices based on new polymers such as PCDTBT106 and PTB7107 lead to efficiencies of 6% and 9%, respectively, by narrowing the band gap of the polymer and bringing its LUMO closer to the LUMO of PCBM that was the only wellperforming acceptor material at that time. Only thenroughly a decade after the “high-Q” P3HT emergedpolymers such as PNTz4T108 and PffBT4T2 appeared that had 100 times higher Q than the previous group while retaining a similarly good energy-level matching. These polymers outperform P3HT in terms of Q, have an optimum thickness of ∼300 nm, and were able to reach 10% to 11% efficiency with PCBM as the acceptor material. A little later, reports in which instead of PCBM, small molecules were incorporated in the material blends caused a change in paradigm. These NFAs show low voltage losses leading to even better energy-level matching and efficiencies above 11% despite only moderate electronic qualities below 100 cm1.6 s1.2/V2.7,11,12,75 Again the low Q manifests in optimum thicknesses around 100 nm. With the data selection we want to highlight some remarkable approaches that produced highly efficient solar cells. The ternary blend PTB75837


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The Journal of Physical Chemistry C TH:IDTBR:IDFBR7 of two NFAs with a polymer shows an extremely high energy-level matching but very low electronic quality and an efficiency of 11%. Another interesting approach is ternary blends that include a polymer, a fullerene, and a small molecule. A blend of PTB7-Th:BTR:PCBM109 reached an electronic quality in the range of well-performing pure fullerene acceptor blends but did not reach the high-energy-level matching of polymer:NFA blends leading to an efficiency of 11.3%. The use of the highly ordered polymer FTAZ with an NFA75 enabled a Q of almost 100 cm1.6 s1.2/V2 together with a good energy-level matching and reached an efficiency of 12.1%. Today’s record efficiency for organic solar cells is marked by a blend of PBDB-T-SF:IT-4F11 with 13.1% device efficiency a moderate Q of ∼40 cm1.6 s1.2/V2 and extremely well-matched energy levels. However, as of today there have been hardly any reports of NFA-based blends reaching high fill factors also at thicknesses ∼300 nm with ref 110 being a notable exception. To conclude, despite continuous success in increasing the two FOMs separately, a material blend that combines the highest degree of energy-level matching and electronic quality has yet to be shown.

these different phases in their drift-diffusion models to explain the specific shape of current−voltage curves.121,122 While the mixed polymer−fullerene phases help charge generation, they lead to reduced fill factors, which indicates charge-collection losses and increased recombination. Recently, Ade et al.123,124 have discussed the relationship between the integrated scattering intensity (ISI) from resonant soft X-ray scattering (R-SoXS), the amorphous−amorphous Flory−Huggins interaction parameter χaa, and the fill factor FF. Their in-depth studies123 show that the FF can be controlled and predicted by the χaa (miscibility between donor and the acceptor) in amorphous donor PCDTBT and various acceptor systems. The authors also comment on the conversion of R-SoXS measurements into χ aa values, which does not consider the polydispersity (molecular weight distribution) of the polymer thus offering room for further development. In addition, the necessity for tedious and complex measurements makes this approach difficult to apply to many samples as a routine measurement, thus suggesting the need for more easily and widely applicable methods.125

VII. CHALLENGES AND OUTLOOK In Section VI, we established the importance of charge collection to achieve high fill factors also at thicknesses greater than 100 nm and identified the need to investigate chargecollection issues, in particular, in polymer:NFA blends. As always in organic photovoltaics, further improvements will be partly based on development of new molecules, but in addition, we can identify a range of challenges that must be tackled in the future from the point of method development. The FOMs discussed in this Feature Article are in part inspired by the requirement of being applicable to a large number of samples without further characterization (just based on the typically available information such as FF and active-layer thickness). Obviously, this can only be the first step and must be complemented by detailed measurements of mobility and lifetime or recombination coefficient. Here, the community is in need to develop new111,112 or further develop existing electrical and optoelectronic characterization and analysis methods. In particular, transient measurements of recombination coefficients have recently been shown113 to be error-prone due to capacitive effects114 that are not or only indirectly related to the actual charge-carrier lifetime. In addition, also a deeper understanding of capacitance-based methods115,116 or the frequently used space-charge limited current measurements117−119 for mobility determinations are needed. In terms of understanding the relations between parameters such as absorption coefficient, lifetime, and charge-carrier mobility and the properties of molecules and the microstructure of the film there has been some progress made recently, but there are still a range of open questions. We now have a better understanding of how optical absorption is related to the persistence length of the polymer,30 and our understanding of nonradiative recombination has been substantially improved69 by considering the role of energy dissipation rather than diffusional encounters. A clear understanding about how microstructure affects charge collection, however, is still at a relatively early stage. It was recognized early on120 that polymer−fullerene blends did not consist just of two phases (pure polymer and pure fullerene) but of mixed phases depending on the crystallinity of the polymer and the volume fraction of polymer and fullerene. Kemerink et al. implemented

VIII. CONCLUSION We presented several figures of merit (FOMs) for organic solar cells that can be used to monitor and evaluate the ongoing development of new organic materials and blends. The FOMs bridge the gap between fundamental material propertiessuch as absorption coefficient, charge-carrier mobility, and lifetime and energy levels of donor, acceptor, and interface statesand the solar cell performance given by efficiency, short-circuit current density, open-circuit voltage, and fill factor. While the short-circuit current of organic solar cells has not reached its full potential, mostly because of a slow EQE onset at the band edge due to the typically low thicknesses, more major limitations stem from losses in Voc and FF. The underlying shortcomings can be quantified by the two figure of merits “energy-level matching” and “electronic quality”. The former is governed by the heterointerface, where charge transfer state(s) and offsets in energy levels lead to voltage losses. The other FOM, electronic quality, is characteristic for the interplay between charge transport and recombination, which governs the FF. Additionally, a low electronic quality reduces the optimum thickness of the active layer and therefore indirectly impacts the number of absorbed photons and the attainable EQE. While considerable progress in both FOMs has been achieved with different organic materials, there is room for efficiency improvement, and the future challenge is to simultaneously reach high performance in both categories.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Thomas Kirchartz: 0000-0002-6954-8213 Derya Baran: 0000-0003-2196-8187 Notes

The authors declare no competing financial interest. 5838


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The Journal of Physical Chemistry C Biographies

Derya Baran received a Helmholtz Postdoctoral Fellowship in 2015 and pursued postdoctoral studies as a joint research associate at Imperial Collage London and Research Center Jülich. Since January 2017, she is an assistant professor of material science and engineering at King Abdullah University of Science and Technology (KAUST). Her current research focuses on the engineering of smart materials for energy conversion applications such as solar cells and thermoelectrics.

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ACKNOWLEDGMENTS T.K. acknowledges support from the DFG (Grant No. KI1571/2-1). D.B. thanks the Helmholtz Association for a Helmholtz Postdoctoral Fellowship. We thank J. Benduhn and K. Vandewal for sharing the data presented in Figure 4b.

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Thomas Kirchartz is a professor of electrical engineering and information technology at the University Duisburg-Essen and the head of the department of analytics and simulation and the group of organic and hybrid solar cells at the Research Centre Jülich (Institute for Energy and Climate Research). Previously he was a Junior Research Fellow at Imperial College London. His research interests cover all aspects regarding the fundamental understanding of photovoltaic devices including their characterization and simulation.

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Figures of Merit Guiding Research on Organic Solar Cells - The

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