Figures of Merit Guiding Research on Organic Solar Cells - The

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Figures of Merit Guiding Research on Organic Solar Cells Thomas Kirchartz, Pascal Kaienburg, and Derya Baran J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01598 • Publication Date (Web): 02 Mar 2018 Downloaded from http://pubs.acs.org on March 4, 2018

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The Journal of Physical Chemistry

Figures of Merit Guiding Research on Organic Solar Cells Thomas Kirchartz1,2, Pascal Kaienburg1, and Derya Baran1,3 1

IEK5-Photovoltaics, Forschungszentrum Jülich, 52425 Jülich, Germany Faculty of Engineering and CENIDE, University of Duisburg-Essen, Carl-Benz-Str. 199, 47057 Duisburg, Germany 3 Physical Sciences and Engineering Division, KAUST Solar Center (KSC), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia 2

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 energy level offsets at the donor-acceptor heterojunction, low open-circuit voltage losses due to non-radiative 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.

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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 towards 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 are the redshift of the absorption onset from polymers with absorption onsets around 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 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. 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 2 ACS Paragon Plus Environment

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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 figures-of-merit 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 now 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 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.

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 region30 but the typically low dielectric permittivities (εr ~ 3 to 4) ensure that the photogenerated 3 ACS Paragon Plus Environment


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; i.e. one molecule needs to have both a higher electron affinity and a higher ionization potential than the other in order 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 donoracceptor 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 has to be paid is typically a reduction of the achievable open-circuit 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 e.g. 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 extremely low as compared to the situation a couple of years ago.

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

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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 effects46,47 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 ∞

J 0,SQ = q ∫ φbb ( E , T = 300 K )dE ,

(1)

Eg

∞

J sc,SQ = q ∫ φsun ( E )dE ,

(2)

Eg

and

Voc,SQ =

 kT  J sc,SQ ln + 1 .  q  J 0,SQ 


(3)


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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 black body spectrum52 used for the radiation from the cell at room temperature

φbb ( E ) =

2πE 2 1 2πE 2 −E ≈ exp . 3 2 3 2 h c [exp(E / kT ) − 1] h c  kT 

(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 = J 0,SQ exp  − 1 − J sc,SQ .   kT  

(5)

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 vs. the incoming power density, i.e.

η=∞

max(P )

.

(6)

∫ Eφ (E )dE sun

0

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) . J scVoc

(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 gap dependent 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.


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(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 at around 1.1 eV 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 VocsQ that currently limit efficiencies to about 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 Fig. 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 to the eye 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 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 comes 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 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 external quantum efficiency EQE and AM1.5G 7 ACS Paragon Plus Environment


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spectrum – and therefore the number of absorbed photons - that is used to calculate the shortcircuit current density in a general case via ∞

J sc = q ∫ EQE (E )φsun ( E )dE .

(8)

0

Comparison of figs. 3a and 3b show that a quantum efficiency < 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 towards higher energies. Thus, contributions 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 FFVoc EQE(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 Fig. 2b. The same holds true for the perovskite solar cell with its high open-circuit voltage of 1.12 V.58 However, 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. 8 ACS Paragon Plus Environment

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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 about 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 I). In the following, we will first focus on the issue of the open-circuit voltage in general, the relation between the open-circuit voltage vs. 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) non-radiative recombination. A simple way of expressing these losses is via59  J J J kT  J sc  kT  J sc,SQ  = ln ln × sc × 0,SQ × 0,rad  q  J 0  q  J 0 ,SQ J sc,SQ J 0,rad J 0  . kT  J sc,SQ  kT  J 0 ,rad  kT  J 0  = Voc,SQ − ln − ln − ln q  J sc  q  J 0,SQ  q  J 0,rad 

Voc =

(9)

where the index ‘rad’ refers to quantities that are calculated using 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



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∞

J 0,rad = q∫ EQE( E)φbb ( E)dE .

(10)

0

The integrand in Equation (10) specifies the photon flux emitted by pn-junction at equilibrium and J0,rad is the current that has to 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 Based on Eq. (9), the difference between Voc,SQ and Voc can be expressed via three loss terms ( ∆VocSC , ∆Vocrad , ∆Vocnr ) that represent (from left to right in Eq. (9)) the loss in short circuit

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TOC Graphic: 104

13

PffBT4T

efficiency η (%)

PNTz4T

electronic quality Q (cm1.6V-2s1.2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


11

103

PTB7-Th:BTR:PCBM

P3HT

102

9

FTAZ:ITIC-Th1

PBDB-T:IT-M:BisPCBM

101

PBDB-T-SF:IT-4F

7

PCE10:IDTBR:IDFBR

5

PTB7 MDMO-PPV PCDTBT

100 4

6

8

10

12

14

energy level matching ηScharber (%)



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. Pascal Kaienburg is a PhD student at the Research Centre Jülich (Institute for Energy and Climate Research: Photovoltaics). He previously received a Master’s degree in physics from RWTH Aachen University for his thesis on radio-frequency studies on graphene. His current work covers the evaluation of novel materials for photovoltaics via device simulations as well as the fabrication and characterization of solution-processed hybrid inorganic/polymer solar cells with the aim of identifying limitations to device performance.

Derya Baran received a Helmholtz Postdoctoral Fellowship in 2015 and pursued post-doctoral 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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Figures of Merit Guiding Research on Organic Solar Cells - The

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