Thickness-dependent internal quantum efficiency of narrow band-gap polymer-based solar cells

Solar Energy Materials & Solar Cells 143 (2015) 242–249

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Thickness-dependent internal quantum efficiency of narrow band-gap polymer-based solar cells Hoon Park a, Jongdeok An a, Jongwoo Song b, Myounghee Lee a, Hyuntak Ahn b, Matthias Jahnel c, Chan Im a,b,n a Konkuk University – Fraunhofer Institute for Solar Energy Systems Next Generation Solar Cell Research Center (KFnSC), Konkuk University, 120 Neungdong-ro, Gwangjin-gu, Seoul 143-701, Republic of Korea b Department of Chemistry, Konkuk University, 120 Neungdong-ro, Gwangjin-gu, Seoul 143-701, Republic of Korea c Fraunhofer Institute for Organic Electronics, Electron Beam and Plasma Technology FEP, 01199 Dresden, Germany

art ic l e i nf o

a b s t r a c t

Article history: Received 18 April 2015 Received in revised form 1 July 2015 Accepted 6 July 2015

Active layer thickness-dependent internal quantum efficiencies (IQE) of photocurrent within bulk heterojunction organic photovoltaic (OPV) devices were characterized. These active layers consisted of an electron-donating narrow band-gap polymer and an electron-accepting fullerene derivative. In order to calculate IQE spectra as a function of active layer thickness, incident photon-to-current conversion efficiency (IPCE) spectra and internal absorptance spectra of active layers with various thicknesses were estimated in these solar cell devices. The transfer matrix method (TMM) was used to calculate the internal absorptance spectra of active layers by using experimental optical constants of thin layers typical for these types of OPV devices including narrow band-gap polymer blend film. In addition, spatially resolved absorptance spectra were used to analyze obtained IPCE spectra as well as OPV device parameters (e.g., short circuit current density) at various active layer thicknesses. Finally, charge-carriercollecting probability as a function of active layer thickness was suggested with which the relationship between initial exciton generation and final power conversion efficiency can be more quantitatively described. & 2015 Elsevier B.V. All rights reserved.

Keywords: Organic photovoltaics Internal quantum efficiency Narrow band-gap PTB7 PC71BM

1. Introduction Recently, a polymer-based bulk-heterojunction (BHJ) solar cell exceeded 9% power conversion efficiency (PCE) [1]. However, this achievement already seems like “old news” due to the success of perovskite solar cells and their impressive PCE values compared with other novel solar cell designs [2]. Nevertheless, polymerbased organic photovoltaic (OPV) cells may have their own unique advantages compared with novel perovskite solar cells, or even traditional silicon-based solar cells. OPV cells, with their increasing importance as sustainable renewable energy sources [3,4], may establish their own market segment among these many diverse types of solar cells. Therefore, it is crucial to understand the precise operating mechanism for OPV cells, and other factors related to their PCEs to understand the operational limit for OPV cells. Usually PCE can be expressed in terms of some basic solar cell properties such as photon absorption (photogeneration of excitons in the active layer), generation of charge carriers (CCs) from these n

Corresponding author. E-mail address: [email protected] (C. Im).

http://dx.doi.org/10.1016/j.solmat.2015.07.002 0927-0248/& 2015 Elsevier B.V. All rights reserved.

excitons, the subsequent transport of these CCs towards the counter electrodes before they are dissipated, and finally CC extraction across the interfaces formed between electrodes and various layers depends on the specific device structure. Hence, it is crucial to know how many photons can be captured in an active layer of a solar cell, at least at the initial stage, to understand and compare the performance of different types of solar cells. As next stage, the maximum ability of an active layer to capture a photon (internal absorption) is compared to the photocurrent generated by means of PCE or spectrally resolved IPCE to gain additional insight into how various types of solar cells perform. Another way to accomplish this comparison is to calculate the internal quantum efficiency (IQE) of the photocurrent (the ratio of the number of extracted electrons converted from the current to the number of photons absorbed in an active layer). Hence, an accurate quantity of excitons lost from either (1) excitons photogenerated in an active layer during CC generation, (2) transport to counter electrodes, and/or (3) extraction through interfaces can be estimated. An accurate ratio of the total number of electrons lost to the total number of electrons initially generated is a key factor for improving the PCE of polymer-based solar cells.

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IQE can be calculated from ultraviolet–visible (UV–vis) absorption spectra and IPCE spectra. However, the complexity of the IQE calculation arises rapidly because the solar cell structure is based on a sandwiched thin film structure that has a typical thickness range from tens to hundreds of nanometers. Such a wide variation of thicknesses in conjunction with the presence of a highly reflective metallic top electrode will cause complicated internal reflections and significant interferences between waves propagated in the active layer. The active layer is where most CCs are generated and the incident light power extinguished. This is the reason why the internal absorptance in the active layer (Q) in an actual device structure cannot be calculated using simple UV– vis absorption spectra of a sample with a single active layer (e.g., on a glass substrate). In addition, there are plenty of complicated difficulties involved in estimating accurate optical constants for pristine and blended π-conjugated polymer films, as described by Klein et al. [5]. More than two decades ago, Pettersson et al. showed that the photocurrent action spectra of devices consisting of an active photoelectron-generating bilayer structure could be accurately calculated using the transfer matrix method (TMM) together with proper optical constants determined by spectroscopic ellipsometry [6]. With these results, the influences of the geometric structure on the efficiency of thin film devices can be quantitatively modeled. A few years later, Hoppe et al. showed Q spectra calculated by TMM, but for only BHJ OPV devices consisting of a poly(2methoxy-5-{3′,7′-dimethyloctyloxy}-p-phenylene vinylene):1-(3methoxycarbonyl)propyl-1-phenyl[6,6]C61 (MDMO-PPV:PCBM) blended active layer [7]. They reported calculated short circuit currents (ISC) for various active layer thicknesses assuming an internal quantum efficiency of unity. Thus, their calculated ISC values became a theoretical upper limit for the experimental values [8,9]. Other related studies for these BHJ OPV systems have also been done. For example, Sievers et al. [10] used a π-conjugated polymer, poly(2‐methoxy‐5(2′‐ethyl)hexoxy‐phenylenevinylene) (MEH‐PPV), and a fullerene derivative blend system; and Moulé et al. [11] and Monestier et al. [12] studied the poly (3hexylthiophene) (P3HT):PCBM system. Sievers et al. also compared the measured and calculated ISC for a model improved by adding the exciton dissociation probability. Moulé et al. examined BHJ active layer blend ratios in combination with the thickness dependence of device performance. This latter work was done both experimentally and computationally. Yang et al. [13], to improve the PCE in OPV cells by structural modification of its layers in order to increase its photon capturing capability, extended these TMM-related studies. Dennler et al. [14] exploited the angle dependence of the PCE for OPVs. This work was followed by an intensity-dependent photocurrent generation study done by Moulé et al. [15]. Later, IQE-related studies were continued by Burkhard et al. [16,17], in which TMM tools were used to investigate the role of fullerene derivatives in OPV cells. At about the same time as Burkhard et al.'s work, Liu et al. [18] did a study on high IQEs in fullerene solar cells, and Betancur et al. [19] did a study comparing EQEs and IQEs. Meanwhile, Grancini et al. presented a study on hot exciton dissociation in polymer solar cells [20]. Grancini et al.'s work caused an important scientific discussion about hot exciton dissociation in which the complete understanding of photon energy-dependent IQE behavior is crucial. On this topic, Scharber et al. [21] noticed some important critiques of the IQE calculations reported by Grancini et al. and similar arguments given by Armin et al. [22]. Additional results were reported later using these similar methods [23,24]. Many experiments have been done to understand the complex situation within OPV devices. However, there are still some additional studies that could be done using experimental

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thickness-dependent IPCE data, e.g., to correlate further the thickness dependence of the IQE calculation. In addition, a novel narrow band-gap polymer, poly[4,8-bis[(2-ethylhexyl)oxy]benzo [1,2-b:4,5-b′]dithiophene-2,6-diyl][3-fluoro-2-[(2-ethylhexyl) carbonyl]thieno[3,4-b]-thiophenediyl] (PTB7), has not yet been characterized in this way although this material is one of the highest PCE donor material of a single BHJ layer device. Therefore, to gain a deeper insight into narrow band-gap device performance, we have decided to perform a wide range (66–320 nm) thickness-dependent device characterization with IPCE measurements to obtain a complete set of thickness dependent IQE spectra. For example, we will calculate the CC collection probability as a function of active layer thickness for OPV devices.

2. Experimental 2.1. Sample preparation All chemicals were used as they were purchased without further purification. Pre-patterned indium tin oxide (ITO)-covered glass substrates (10 Ω/sq, 180-nm thickness from Samsung Corning) were ultrasonically cleaned for about 20 min in deionized water with o2% detergent (Mucasol, Sigma Aldrich) followed by ultrasonic cleaning in deionized water, acetone, and isopropanol, consecutively, for about 20 min. Then the ITO substrates were treated with O2 plasma for about 10 min. A poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate) (PEDT:PSS) (Clevios P VP AI 4083) layer of 50-nm thickness was spin-coated at 2700 rpm onto pre-treated ITO-covered glass substrates and then baked at 140 °C for over 10 min under ambient conditions. PTB7 (1-Material Inc.) and [6,6]-phenyl-C71-butyric acid methyl ester (PC71BM, Nano-C Inc.) were used as an electron donor and an electron acceptor, respectively. The chemical structures of PTB7 and PC71BM are shown in Ref. [1]. 2.16-wt% or 4.00-wt% chlorobenzene (CB) with 1,8-diiodooctane (DIO) co-solvent of 3 vol% solution of a donor/acceptor mixture (D:A) were stirred under a nitrogen atmosphere at 60 °C overnight. The blend ratio of PTB7:PC71BM was 1:1.5 by weight. The prepared D:A blend solution was filtered through a 0.45 μm syringe filter and spin-coated with different rpms onto the PEDT:PSS-covered ITO substrates. The thicknesses of the resulting BHJ photoactive layers were in the range 66–320 nm. The top electrode was prepared by thermally evaporating a combination of 0.3 nm lithium fluoride (LiF) and 120 nm aluminum (Al) layers under 10
6 mbar vacuum. Each device in this study was encapsulated with an engraved cover-glass using a commercial getter under N2 atmosphere. The prepared device structure was glass(1.1 mm)/ITO (180 nm)/PEDOT:PSS(50 nm)/PTB7:PC71BM(66-320 nm)/LiF(0.3 nm)/ Al(120 nm) as schematically shown in Fig. 1. The current-density versus voltage (J–V) characteristics of the OPV devices used in this study were measured by a Keithley 2410 source measure unit (SMU) under illumination by a Newport 94062A solar simulator in a clean room kept slightly below 25 °C. In order to maintain conventional standard test conditions (Air Mass 1.5 for the spectral irradiance distribution; 1000 W/m2 for radiant intensity), the solar simulator was calibrated with a

Fig. 1. The structure of the device used in this study.

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reference cell certificated by the National Renewable Energy Laboratory (NREL, USA). Single-layer samples on glass or silicon substrates were prepared as described above for the ITO-covered glass substrates in order to keep consistent film quality between different preparation conditions. These samples were used for a variety of optical characterizations. UV–vis absorption and transmittance spectra of D:A blend films spin-coated on a glass substrate were recorded with a Nenosys-2000 spectrophotometer (Scinco). Additional transmittance and reflectance spectra were obtained with an AvaSpec-ULS2048 spectrometer (Avantes). The latter spectra were done to obtain reflectance spectra for devices with an opaque Al top electrode. The IPCE spectra were obtained with commercial IPCE equipment (QEX7, PV measurement Inc.). Preliminary thicknesses were measured using a surface profiler (XP-200, AMBiOS) and later corrected with an optical non-contacting TMM fitting process. Due to the mechanical nature of the surface profiler, significant errors can occur during the measurement of soft and rough polymeric D: A blend films that can lead to under-estimated thicknesses due to drift of the detecting needle on these films. 2.2. Internal absorptance calculation In order to calculate an accurate internal absorptance of the active layer (Q) in a device, we first extracted optical constants such as the refractive index (n) and extinction coefficient (k) for ITO, PEDT:PSS, and PTB7:PC71BM blend film by analysis of data obtained from variable-angle spectroscopic ellipsometry (VASE) with an analyzer (NIR–vis–UV VASE, J.A. Woollam Co., Inc.). Values for aluminum were taken from the widely accepted data provided by the J.A. Woollam Co. It should be mentioned, however, that the LiF layer's n and k values were not explicitly taken into account in the TMM calculations because the thickness of the LiF layer (0.3 nm) was practically negligible in most optical calculations done in this study. Although many measurements were needed to obtain reasonable values for the variables just discussed, details of the ellipsometric modeling process is not discussed here because this was outside the main scope of this study. Therefore, this paper focuses on a thorough analysis of our verifying methods and results. Since a direct comparison of n and k spectra with the optically observable spectra of, e.g., UV–vis absorption, is not possible, extracted n and k values were used to calculate the absorptance spectra of whole devices using TMM. Then, these spectra were compared with the experimentally estimated absorptance spectra as shown in Fig. 5. This comparison is possible because the optics can be modeled for the structure depicted in Fig. 1. Incident light cannot be transmitted due to the opacity of the top metal electrode. Hence, for Fig. 1, the simple relation “1
reflectance (R)
transmittance (T)¼ absorptance (A)” can be reduced to “1
R¼A.” Therefore, A spectra could be prepared as soon as R spectra were available. We found that there are serious deviations for n and k values in the literature due to the complexity of the active layers' optical properties. Hence, such a verification process as discussed above is very important. For the practical calculation of TMM spectra, we used a home-made program in addition to the stable public domain program “OpenFilter” [25] and a program with n and k values provided by the McGehee group [26]. After careful verification of the ellipsometrically obtained n and k values, the spatially and spectrally resolved optical electric field strength of the entire device, from the front surface of the glass substrate to the rear surface of the Al top electrode, can be calculated using TMM with a spatial resolution of 1 nm for wavelengths from 900 to 300 nm. By proper calculation and integration of the values for the active layer, one can obtain the internal

absorptance spectra for an active layer, Q, in a specific device, which can be used for further calculations. Using partial integration of the map of optical electric field strength allows intuitive visualization of interesting spatial and/or spectral distribution of the generated excitons in, e.g., the central or interfacial parts of the layer and/or higher or lower photon energy, etc., that can be further analyzed based on the data presented in this study.

3. Results and discussion UV–vis absorption spectra of D:A blend films on glass substrates with active layer thicknesses in the range 66–320 nm are shown in Fig. 2. Absorbance values at four selected wavelengths (378, 470, 623, and 678 nm), shown in the inset of Fig. 2, depict a virtually linear relationship between the measured absorbance and estimated thickness values obtained by using a surface profiler. This means that absorption is increasing with increasing thickness according to the Beer–Lambert law in such single layer on a non-coherent substrate without a top metal electrode, as expected. However, there is also a marginal but detectable interference effect. This effect might be due to a small periodic deviation from linearity of the absorbance as a function of active layer thickness. It is noteworthy that the shapes of the spectra were superimposable upon each other independent of the active layer thickness. This is a sign that the blending ratio of D:A in the active layers was almost constant. It is also noteworthy that the spectral shape of the blend was a superimposition of the spectra of pure PTB7 and pure PC71BM as shown in Fig. 1 of the Supplementary information (SI). It should be noticed that the rapid increase of absorbance at wavelengths shorter than 330 nm is due to the absorption of PC71BM and the glass substrate. In Fig. 3, all measured current-density versus voltage (J–V) data are presented. In the inset of Fig. 3, a plot of resistance (RS, Ω cm2) as a function of active layer thickness extracted from these data is presented as well. These RS values increase virtually linearly with increasing active layer thickness. All important solar cell device parameters, i.e., PCE, short circuit current-density (JSC), open circuit voltage (VOC), and fill factor (FF) (in addition to RS and shunt resistance (Rsh) from Fig. 3) are listed in Table 1 and plotted as functions of active layer thickness in Fig. 4 (a) and (b). Parameters are defined in Eqs. (1) and (2).

PCE = (FF×JSC× VOC)/PSun

(1)

Fig. 2. UV–vis absorption spectra of PTB7:PC71BM blend films on glass substrates with thicknesses ranging from 66 to 320 nm. Inset: Absorbance as a function of active layer thickness.

H. Park et al. / Solar Energy Materials & Solar Cells 143 (2015) 242–249

FF=(Jmax× Vmax )/(JSC × VOC )

Fig. 3. Current-density versus voltage (J–V) characteristics of devices with active layer thicknesses from 66 to 320 nm. Inset: A plot of device resistance (RS) as a function of active layer thickness.

Table 1 Estimated solar cell device parameters at various active layer thicknesses. VOC (V) JSC (mA/cm2) FF (%) PCE (%) RSh (Ω cm2) RS (Ω cm2) Active layer thickness (nm) 0.735 0.735 0.720 0.720 0.720 0.735 0.705 0.720 0.720 0.705

14.3 15.2 16.0 14.9 14.2 12.6 12.1 11.6 9.5 6.2

57.4 55.8 52.9 51.1 49.2 50.4 50.3 50.4 50.6 51.2

6.0 6.2 6.1 5.5 5.0 4.7 4.3 4.2 3.5 2.2

414 380 259 241 194 239 225 240 285 392

7.3 7.9 8.5 9.4 10.3 11.3 12.5 12.3 15.1 22.3

20

8

16

6

12

4

8

2

4

0

0

0.8

80

0.6

60

0.4

40

0.2

20

0.0

FF (%)

Voc (V)

PCE (%)

2

10

0 0

50

100

150

200

250

300

350

Active layer thickness (nm) Fig. 4. Plots of PCE (a, filled rectangles), JSC (a, open circles), VOC (b, filled rectangles), and FF (b, open circles) as a function of active layer thickness.

(2)

where PSun is the total power of incident sunlight, Jmax is the current density at maximum output power, and Vmax is the voltage at maximum output power. As shown in Fig. 4, PCEs decrease linearly with increasing active layer thickness except for the initial three lowest thickness values where thickness was less than 100 nm. JSC values increased with increasing thickness, while FF values decreased and VOC remained virtually constant with increasing thickness over these three low thickness points. Hence, the observation of almost constant PCE values at the lowest thickness points can be understood because PCE is dependent upon the product of FF, JSC, and VOC, as defined in Eq. (1). The PCE values at low thicknesses are about 6% and significantly higher than those for thicker devices. It is noteworthy that the PCE presented here is lower than the highest PCE value reported [1] because we paid more attention to maintain consistent preparation conditions over the range of active layer thicknesses studied. Interestingly, the FF values also remained constant as the thickness was increased to more than 120 nm. Since FF is often explained in conjunction with RS according to the ideal diode equation, a monotonically increasing trend is expected with linearly increasing active layer thickness-dependent RS as shown in this study. However, the FFs only slightly decreased and hence the PCEs decreased more slowly than the rapid decrease of JSC values with increasing active layer thicknesses. It should be also noted that the JSC as well as PCE values cannot increase with increasing absorption because the active layer thicknesses increase as shown in Fig. 2. In order to analyze this deviation more quantitatively in conjunction with knowledge of the underlying mechanism, use of Eq. (3) is often more helpful than Eqs. (1) and (2)

ηEQE = η A × ηIQE = η A × ηCG × ηCT × ηCE × …

Jsc (mA/cm )

66 79 90 100 120 158 168 173 218 320

245

(3)

where ηIQE is the IQE; ηA is the exciton generation efficiency (the ratio of absorbed photon number to total incident photon number in the active layer), which should be the same as Q; ηCG is the CC photo-generation efficiency; ηCT is the CC transport efficiency (transport probability of CC to the counter electrodes before CCs are dissipated); and ηCE is the subsequent charge extraction efficiency across the interface to the external circuitry. Such deviations between PCE and the absorption trends as the active layer thickness increases are well-known and have been presented by many previous works discussed in Section 1 [6], [9– 12]. Although absorption in the active layer, Q, can be accurately predicted using TMM by taking into account the various internal reflections and their interferences, JSC and PCE values cannot increase with increasing Q. This means that ηIQE should be significantly reduced as the active layer thickness increases according to Eq. (3). However, ηCG seemed to remain high according to the previous work done on electron scavenging dopant concentrationdependent photoluminescence quenching [27] and the corresponding photocurrent generation studies [28] done with similar disordered polymer systems. Consequently, ηCT and ηCE, together with the CC collection probability, should be primarily responsible for the reduction of IQE, while ηCG should be more or less unity in such optimized D:A blend systems. Therefore, it might be concluded that a serious loss of photo-generated CCs, possibly due to dissipation via non-geminate recombination [29], was taking place as the active layer thickness increased beyond 100 nm. In Fig. 5, experimental and calculated A (A¼ 1
R) spectra in addition to EQE spectra of whole devices and calculated Q spectra of active layers for active layer thicknesses of 79, 168, and 218 nm are shown. Before we begin a detailed analysis of the results in

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H. Park et al. / Solar Energy Materials & Solar Cells 143 (2015) 242–249 100

100

80

80

(W/m2), which can be calculated by multiplying the photon flux by the photon energy as given in Eq. (7)

60

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40

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20

0

0

80

80

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60

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40

20

20

0

0

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80

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60

40

40

20

20

300

400

500

600

700

JSC =

800

Fig. 5. Experimental and calculated absorptance spectra, EQE of whole devices, and Q spectra of active layers in devices with thicknesses of (a) 79 nm, (b) 168 nm, and (c) 218 nm. Solid lines: experimental A (A ¼1
R) spectra, Dash-dot lines: calculated A spectra, Dot lines: EQE spectra, Dash lines: calculated Q spectra.

Fig. 5, some aspects related to EQE, IQE and JSC should be reviewed to avoid any confusion. EQE is the ratio of the number of CCs collected by the solar cell to the total number of incident photons as shown in Eq. (4). Q is the ratio of the number of absorbed photons in the photo-active layer to the number of incident photons or, in other words, the internal absorptance of the active layer, Q, as defined before. Thus, IQE can be easily calculated from the experimental EQE, as written in Eq. (5), if a precise value for Q can be obtained under some ideal simplified conditions. For example, CCs assumed to be photo-generated in the active layer only, as shown in the equation for Q below.

EQE =

n (generated e−) n (total incident photons)

(4)

IQE =

n (generated e−) EQE = n (abs. photons in act. layer ) Q

(5)

n (abs. photons in act. layer) EQE = n (total incident photons) IQE

(8)

where Plight (λ) is the incident light power on a given solar cell. JSC can then be calculated using EQE and the incident light power according to Eq. (9).

Wavelength (nm)

Q=

(7)

JSC (λ ) q qλ ⋅EQE (λ ) = ⋅EQE (λ ) = H hc Plight (λ )

SR (λ ) =

0

0

hc (J ) λ

where h is Planck's constant; c is the speed of light; Φ is photon flux (number of photons per second per square meter). Then, H can be combined with the external quantum efficiency (EQE) to form the spectral response (SR). Indeed, SR is the ratio of the photo-current to the incident power on a given device similar to EQE. And hence SR in amperes produced per watt of incident light (A/W) for a given solar cell can be defined (see Eq. (8))

EQE & Q (%)

Absorptance (%)

H = Φ⋅

(6)

In principal, JSC can also be relatively easily combined into EQE and IQE, if the incident light power is given. Thus, these relationships can be started with the incident light power density, H

∫λ

λ2

1

EQE (λ )⋅SIrr (λ )⋅

λ dλ 1240

(9)

Plight can change along the spectral irradiance (SIrr) spectrum, which is typically estimated under standard test conditions (AM 1.5 distribution and 1000 W/m2 radiant intensity). In Fig. 5, the experimental and calculated A spectra having the same thickness show good agreement, with less than 5% deviation. This means that the corresponding Q value for each active layer thickness is good enough for further analysis because ηA (i.e., Q) can be accurately modeled within the framework of TMM by using our estimated n and k values. However, there are significant deviations between the spectra of EQE and Q as shown in Fig. 5. This means that there are significant deviations between EQE and IQE as the thickness increases as discussed above using Eq. (3). This result becomes the main reason why PCE decreases while Q increases as thickness increases. At thicknesses less than 100 nm, the spectral shapes and amplitudes between EQE and Q in Fig. 5 are similar, while these differ significantly at larger active layer thickness values. The amplitudes of the EQE spectra are gradually reduced as thickness increases relative to those of Q. This means that the IQEs decrease with increasing active layer thickness. This is evidence for a loss channel, which reduces the probability of CCs surviving as the active layer thickness increases. There is enough experimental evidence, however, that the efficiency of CC generation from excitons, ηCG, is high in a BHJ type active layer. This is due to the existence of an optimum population of D:A interfaces within the exciton diffusion length where excitons can be effectively dissociated and then form stable CCs in well-optimized devices [30]. The results of our study are very similar to those of earlier ones mentioned in the introduction and, therefore, we can say that most of the reduction in CC collection probability, product of ηCT by ηCE, as the active layer thickness increases, is responsible for the reduction of PCE in the same manner. The loss channel might be an incoherent or non-geminate CC recombination because of its bipolar transporting character and/or deep traps due to a high degree of disorder in such random solids [31]. The IQE spectra in Fig. 6 were calculated by using Eq. (5). Active layer thickness-dependent IQE plots at five selected wavelengths determined by using the data set extracted from Fig. 6 are shown in Fig. S2 (SI). The active layer thickness-dependent IQE spectra in Fig. 6 also show a decreasing trend, which is similar to that of JSC and PCE values. Indeed, this similarity has already been discussed in Fig. 5. Fig. 6 and Fig. S2 (SI), however, show an additional trend, which is that the spectral dependency of IQE changes with increasing active layer thickness (see Fig. 6). This result is also

H. Park et al. / Solar Energy Materials & Solar Cells 143 (2015) 242–249

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300 0.0 0.1 0.3 0.4 0.6 0.8 0.9 1.1 1.2 1.3 1.5

400

500

600

700

800 0.0

Fig. 6. IQE spectra of devices with active layer thicknesses ranging from 66 to 320 nm.

Wavelength (nm)

depicted as the active layer thickness dependent IQE plots at selected wavelengths in Fig. S2 (SI). It is important to discuss the spectral dependence of IQE values because this is important experimental evidence showing how excess photon energy can affect CC photo-generation from primary excitons in D:A blend solids. It is believed that hot excitons can benefit CC photo-generation because the excess energy from hot excitons can be used to break the strong exciton binding energy typical of pristine πconjugated polymer solids [28]. Actually, accurate Q values for these IQE spectra should not strongly influence a device's optical properties because these Q values already include most of the complicated interference effects within the framework of TMM. Unfortunately it should be noted that there are still some significant errors close to the absorption edge and UV part of the spectrum, namely from 730 to 800 nm and from 300 to 330 nm, respectively. This is mainly due to resolution and sensitivity differences between different equipment used and the steep slopes in those regions. Except for these two steeply sloped spectral regions, the IQE spectra seem quite consistent. However, the slopes of IQE spectra also slightly increase from 66 to 120 nm as photon energy increases. Interestingly, spectral dependence, as the photon energy increases, begins to decrease at 158 nm. The spectral dependence gradually decreases until it becomes almost horizontal at 320 nm thickness, except for a cusp shape close to the absorption edge. These cusp shapes can be explained by means of a higher initial polaron yield for excitation at energetically lower-lying edge ranges as reported by Hermann et al. [32]. It is noteworthy that the difference between IQE values below and above the exciton binding energy is often greater than an order of magnitude [28]. Such sudden slope changes were not observed in this study and hence strong exciton binding energy effects can be excluded for D:A blend systems. In addition, these moderate slope changes, both increasing and decreasing, seen as the photon energy increases cannot easily be connected to the hot exciton effect described in Ref. [20] because the slope trend is not consistent, but rather changes with thickness. Therefore, the change in slope with increasing active layer thickness seems not simply explained by only the excess photon energy concept. In other words, this moderate fluctuation of spectral dependence should be explained in thickness-dependent terms rather than in monotonically excess photon energy terms. Hence, spatially resolved Q spectra were carefully investigated in order to clarify the meaning of this fluctuating trend in IQE spectra. It is also very interesting to compare these results with a similar narrow band-gap polymer blend system, PCDTBT: PC71BM,

0.1

400

0.2 0.3 0.4 0.6 0.7

500

0.8 0.9 1.0

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500

0.6 0.7 0.8

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800 0

50

100

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300

Position in active layer (nm) Fig. 7. Mapping of absorptance values for three active layer thicknesses: (a) 79 nm, (b) 168 nm, and (c) 218 nm.

investigated by Armin et al. [24]. In their thickness dependent IQE spectra, fairly similar behavior, namely, an increase of significant loss pathways with increasing active layer thickness and fluctuation trends of IQE spectra were seen. However, further analysis with spatially-resolved internal absorptance spectra were not provided. In Fig. 7, maps of spatially resolved Q spectra for three active layer thicknesses are shown (Additional maps are shown in Fig. S3 (SI)). Integration of all the absorptance values over the entire length of any active layer is the same as the absorptance spectra in Fig. 5. As shown in Fig. 7, the strength of the internal optical electric field can be visualized, and then the generated exciton population can be set to be proportional to the internal optical electric field distribution. Two different methods can be suggested

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H. Park et al. / Solar Energy Materials & Solar Cells 143 (2015) 242–249

Fig. 8. CC collection probability as a function of the relative position from the center of a given active layer thickness (for comparison of Q and EQE).

the number of absorbed photons in an active layer to the number of total incident photons, Q can be regarded as the ratio of the number of electrons produced to the number of total incident photons, if we assume unity CC photo-generation. However, after multiplying the CC collection probability, the corrected Q and the experimentally obtained EQE are in near perfect agreement as shown in Fig. 9. Use of this triangular CC collection probability function comes from the idea that CC can be more effectively dissipated as the distance of electrons from the metal electrode (or distance of holes from the ITO electrode) is increased. This function can be exchanged with an exponential function, which reflects the physical background more accurately as shown in many text books on silicone-based solar cells. It should be mentioned that Mescher et al. [33] have done a study on the influence of power conversion efficiency upon the change of absorption profile shapes (centered and peripheral) in combination with the drift and diffusion model. They concluded that the spatial distribution of CCs can strongly affect the electrical characteristics of solar cells. We believe that their simulation work could be confirmed by comparing the experimental results of this study as described by the spatially resolved CC collection probability shown in Fig. 8 and the corresponding plots in Fig. 9. Finally, the excellent agreement between corrected Q and EQE were verified again by comparing the calculated photocurrent and experimental photocurrent (typically JSC) under standard test conditions according to Eqs. (9) and (10).

JPhoto (x, λ ) = q⋅

Fig. 9. Comparison of EQE and corrected Q for layer thicknesses of 79 nm (straight line, rectangles), 168 nm (dash lined, circles), and 218 nm (dotted line, triangles).

to exploit the thickness-dependent IQE slope changes. One method is position-dependent CC photogeneration and the second method is position-dependent CC collection. First, the maps in Fig. 7 were used to verify the position dependency of CC photo-generation. Pristine films of π-conjugated polymers have a strong exciton binding energy due to its Frenkel exciton character. Therefore, their excitons could be effectively dissociated to form CCs close to the ITO electrode interface. Therefore, their EQE spectra seem fairly coincident to the spectra constructed by integration of the absorptance near the ITO side, which is typically  10 nm thick. This thickness is comparable to the typical exciton diffusion length for such materials [29]. Finally, it was found that such position-dependent enhanced extrinsic CC photo-generation could be matched with any IQE spectra in this study. This is understandable due to the effective bulk of CC photogeneration within such well-optimized D:A blend systems. Second, the maps in Fig. 7 and a trial function of CC collection probability shown in Fig. 8 were used to support positiondependent CC collection as follows. The corrected Q values were obtained by multiplying the simple linear function by Q in order to take into account the position-dependent CC collection probability shown in Fig. 8. The corrected Q with EQE spectra are shown in Fig. 9. Interestingly, these plots overlap each other well in spite of the extremely simple CC collection probability function. Symmetrically-combined linear CC collection probability plotted as a triangular function relative to the center position of an active layer in a device was used to correct Q. Since Q is the ratio of

d

∫0 ∫λ

λ2

G (x, λ )⋅C (x, λ )⋅dx⋅dλ

(10)

1

Results of these calculations are listed in Table 2 and plots are shown in Fig. S4 (SI). It should be noted that the JSC estimated by J– V characterization is approximately 14% larger than the JSC calculated from EQE, which is even larger than the JSC values obtained from J–V and from the corrected Q. We found that our EQE characterization gave a solar cell size that was about 15% smaller than the actual size of the solar cell's active surface area. This is likely the main source of error in our work, but the functional dependence of the plots shown in Fig. S4 (SI) are in good agreement with each other.

4. Conclusion From experimental EQE spectra and calculated internal absorptance spectra, accurate IQE spectra for a wide range of active layer thickness were obtained. Observed IQE spectra have shown active layer thickness-dependent slope fluctuations for IQE spectra in addition to a significant reduction of IQE with increasing active layer thickness. The latter result means that there are significant non-geminate recombination loss pathways in the active layer. This conclusion results from the data set for PTB7:PC71BM blended films, which was nicely comparable with the results of earlier studies. In addition, spatially resolved absorptance spectra were used to explain the slope fluctuation of the IQE spectra seen as the active layer thickness increased. By adapting a simple positionTable 2 JSC estimated using various methods for three active layer thicknesses. Active layer thickness (nm)

JSC (mA/cm2) J–V curve

JSC (mA/cm2) IPCE

JSC (mA/cm2) calculated

79 168 218

15.2 12.1 9.5

12.8 10.1 8.7

13.4 10.7 9.0

H. Park et al. / Solar Energy Materials & Solar Cells 143 (2015) 242–249

dependent CC collection probability function, EQE spectra could be calculated from internal absorptance spectra, Q, with an assumption of unity ηCG. This calculation produced the same result as the IQE derived from the simple CC collection probability, if Q is known, according to Eqs. (4)–(6). Then, these results were verified by comparing the experimentally estimated JSC with the theoretically calculated JSC, which showed fairy similar values with marginal mismatching. As a concluding remark, it might be pointed out that the excitons should be generated possibly at the center of active layer via device structure optimization due to minimize unfavorable recombination loss in order to improve overall PCE of such narrow band gap based OPV devices. And it should be also mentioned that such CC collection probability study has to be extended with practical modules under the condition of international summit on OPV [34] in order to confront the long term stability issue.

Acknowledgment This study was supported by Konkuk University in 2014.

Appendix A. Supplementary information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.solmat.2015.07.002.

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