Charge-Transfer State Energy and Its Relationship with Open-Circuit

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The Charge-Transfer State Energy and Its Relationship with Open-Circuit Voltage in Organic Photovoltaic Device Zhiqiang Guan, Ho-Wa Li, Yuanhang Cheng, Qing Dan Yang, Ming-Fai Lo, Tsz-Wai Ng, Sai-Wing Tsang, and Chun-Sing Lee J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b02375 • Publication Date (Web): 13 Jun 2016 Downloaded from http://pubs.acs.org on June 15, 2016

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The Journal of Physical Chemistry

The

Charge-Transfer

State

Energy

and

Its

Relationship with Open-Circuit Voltage in Organic Photovoltaic Device. Zhiqiang Guan,†,‡,§ Ho-Wa Li,‡,§ Yuanhang Cheng,‡ Qingdan Yang,†,‡ Ming-Fai Lo,†,‡ Tsz-Wai Ng, †, ‡

†

Sai-Wing Tsang*,‡ and Chun-Sing Lee*,†,‡

Center of Super-Diamond and Advanced Films (COSDAF), City University of Hong Kong,

Hong Kong SAR, P. R. China ‡

Department of Physics and Materials Science, City University of Hong Kong, Hong Kong SAR,

P. R. China

ACS Paragon Plus Environment

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ABSTRACT: Charge-transfer state (CTS) plays a very important role in organic photovoltaic (OPV) devices. Especially the relationship between open-circuit voltage (VOC) and CTS has been widely discussed. It is proposed that the CTS energy (ECT) directly determines the VOC value, however, the ECTs measured from different techniques often show considerable discrepancy. Here four methods are applied to probe the ECT values in five different bulk-heterojunction polymer:fullerene OPVs. It is found that linear relationships exists between different ECTs and VOC values. The detailed energetic meanings of the ECT values measured from different techniques are discussed and the origin of their discrepancy is analyzed. Lastly, based on a proposed energy model, a relationship is summarized to estimate VOC loss by considering the energetic broadening of CTS, bimolecular recombination and dielectric effect. The results provide a guideline to forecast the VOC and investigate its loss in OPV.


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1. Introduction Organic photovoltaic (OPV) devices based on donor:acceptor (D:A) bulk-heterojunctions (BHJs) show great potential as the next-generation photovoltaic technology due to their advantages of low cost, flexibility, light weight and high-throughput roll-to-roll production.1-5 Recently, lots of attentions are focused on charge-transfer states (CTSs) and their roles on photovoltaic process.6-14 Specifically, the relationship between CTSs and open-circuit voltage (VOC) of OPV devices has been widely discussed.15-18 Moreover, it has been proposed that the CTS energy (ECT) directly determines the VOC value.19 ECT is determined as the free-energy difference between the CTS ground state and the CTS excited state.19 However, this energy is not easy to measure, partly due to the weak coupling between ground state and excited state.18 In addition, the existing of reorganization energy19 and energetic disorder17 usually leads to a broadening of several hundreds of meV in measurement spectrum. In Marcus theory, the reorganization energy is defined as the energy required to bring reactant to the equilibrium geometry of product.11 In order to probe the energy distribution of CTSs, many methods have been applied, such like IR absorption,20,21 radiative recombination spectrum,22,23 external quantum efficiency (EQE),19,24 ultraviolet photoemission spectroscopy (UPS)6,25 and charge modulated electroabsorption spectroscopy (CMEAS)9,16. But ECTs measured with these techniques often show considerable discrepancy, leading to inconsistent pictures of the photovoltaic processes.16 For this reason, much active research on this area is being carried out. In this report, we measure ECTs from five different polymer:fullerene BHJs using four methods, namely, EQE fitting based on Marcus theory (EQE (Marcus)),19,24,26,27 EQE fitting with Gaussian function (EQE (Gaussian)), UPS6,25 and CMEAS9,16. VOC of the corresponding devices are measured at different temperatures and luminescent exposures. ECT values measured from the


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four approaches used here show obvious inconsistency in term of their quantities. Nevertheless, we observe for the first time that the ECT values from the four methods do show similar linear relationships (all have almost the same slope) with the devices’ VOC. Based on these results, we discuss the detailed energetic meanings of the ECT values measured from different techniques as well as the origins of their discrepancy. With a model proposed based on experimental results, we distinguish the different energetic losses of VOC from ECT in OPV device. 2. Experimental Methods Device Fabrication. OPV devices were fabricated by spin-coating polymer:fullerene blend solutions on poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) coated indium tin oxide (ITO) substrates. The active layer preparation process is described in Supporting Information. The treated samples were then transferred to a deposition chamber directly. Bathocuproine (Lumtec) (7 nm) and Al (80 nm) were deposited onto the samples films with the active device area of 0.1 cm2. All the devices were encapsulated in a glove box after Al deposition. Charge Modulated Electroabsorption Spectroscopy (CMEAS). A monochromatic parallel beam probes the sample through the ITO side at an incident angle of 45o and is reflected by the Al electrode. A small sinusoidal voltage with the a peak-to-peak voltage amplitude of 0.5 V and a frequency of 1 kHz was superimposed with another negative DC bias to modulate the internal electric field in the devices. The negative DC bias applied here is to guarantee the free charges are all extracted from the solar cell instead of injection from electrodes. The reflected light was collected by calibrated silicon or germanium photo detectors. Current amplifier (Agilent 33250A) and lock-in amplifier (SR 830) were connected to the detector for


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measurements. The final signal ∆T/T was the ratio of the signals with and without AC field modulation. The devices used in CMEAS measurement were without PEDOT:PSS in order to rule out the influence of interfacial charges. All measurements were carried out at room temperature. J-V and External quantum efficiency (EQE). J-V characteristics were measured with a programmable Keithley model 237 power source. Light characteristics were measured under illumination with an intensity of 100 mW/cm2 from an Oriel 150 W solar simulator with AM1.5G filters. For temperature dependence experiment, the samples were put in vacuum inside a cryostat. Temperature varied in the range between 150 K to 325 K. EQE characteristics were measured with a 1000 W Xe light source, monochromator (Zolix), optical chopper, calibrated Newport detectors and lock-in amplifier. The high-sensitivity lock-in technique provides a sensitivity up to 10-5%. Ultraviolet photoelectron spectroscopies (UPS). UPS was carried out using a VG ESCALAB 220i-XL ultra-high vacuum surface analysis system equipped with a He-discharge lamp providing He-I photons of 21.22 eV. The base vacuum of the system is 10−10 Torr. Organic samples for UPS measurements were prepared by spin-coating polymer:fullerene blend solutions on ITO-coated glass substrates. The treatments of blend films are as same as in device fabrication. In UPS spectra, the onset position is defined as the point of intersection of two tangent lines. 3. Results In this work, we study BHJs formed between an acceptor [6,6]-phenyl C71 butyric acid methyl ester (PC71BM) and five different polymeric donors, namely, poly[2-methoxy-5-(2-


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ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV), poly(3-hexylthiophene) (P3HT), poly[[9(1-octylnonyl)-9H-carbazole-2,7-diyl]-2,5-thiophenediyl-2,1,3-benzothiadiazole-4,7-diyl-2,5thiophenediyl] (PCDTBT), poly[[4,8-bis[(2-ethylhexyl)oxy]benzo[1,2-b:4,5-b’]dithiophene-2,6diyl][3-fluoro-2-[(2-ethylhexyl)carbonyl]thieno[3,4-b]thiophenediyl]] (PTB7) and poly[(5,6dihydro-5-octyl-4,6-dioxo-4H-thieno[3,4-c]pyrrole-1,3-diyl)[4,4-bis(2-ethylhexyl)-4Hsilolo[3,2-b:4,5-b';]dithiophene-2,6-diyl]] (PDTS-TPD). The chemical structures are shown in Figure 1a and normalized absorption spectra of the pristine materials as well as the blend polymer:fullerere films are shown in Figure S1.

Figure 1. (a) Chemical structures of organic materials used in this work. (b) EQE (Marcus) fits of five blend OPV devices in sub-bandgap region.


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3.1. EQE fitting based on Marcus theory A semi-classical non-adiabatic electron transfer theory developed by Marcus28 has been applied to many chemical systems and extended to the organic charge transfer process.29,30 Recently, a Marcus formalism used to characterize the properties of CTS has been raised by Vandewal et al.19 and widely used24,26,27 to investigate the ECTs, as shown in Equation 1.

EQE ( E ) =

 −( ECT + λ − E ) 2  ⋅ exp   4λ k BT E ( 4πλ k BT )   f

(1),

where f is a prefactor determined by internal quantum efficiency, density of state (DOS) of CTS, film thickness and electronic coupling matrix element, E is photon energy, λ is the reorganization energy associated with CTS absorption process, kB is the Boltzmann constant and T is the temperature. The parameters ECT, λ and f can be extracted through fitting the EQE curve in the sub-bandgap region. With this Marcus theory, we firstly determine ECT values (ECT (Marcus)) of the five different polymer:fullerene blends by fitting EQE spectra of their corresponding OPV devices. The measured EQE data (open symbols) and fitted curves (solid lines) at 300 K are shown in Figure 1b. The fitting results are satisfactory over the sub-bandgap region. Fitting parameters of ECT, λ and f are listed in Table 1. Table 1. Parameters used in fitting the sub-bandgap EQE curves with Marcus theory for five blend devices.

Parameters ECT (eV) λ (eV)

MEH-PPV: PC71BM 1.4 0.18

P3HT: PC71BM 1.14 0.22

PCDTBT: PC71BM 1.42 0.18

PTB7: PC71BM 1.35 0.18

PDTS-TPD: PC71BM 1.5 0.15


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f (eV2)

8×10-2

3.5×10-3

5×10-2

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2×10-1

4×10-2

3.2. EQE fitting based on Gaussian function In addition to the Marcus form, it has also been proposed that the CTS distribution should has a Gaussian shape due to the fact that CT states are combinations from the Highest Occupied Molecular Orbital (HOMO) of donor and the Lowest Unoccupied Molecular Orbital (LUMO) of acceptor, both of which can be well-described with Gaussian distributions.17,31,32 Therefore, we next carry out a “global” EQE fitting method by fitting the EQE spectra from the sub-bandgap region to the excitation absorption edge with isolated Gaussian functions contributed from the donor, the acceptor and their CTSs. The general Gaussian model used in the fitting process is described in Equation 2.

 ( x − µ )2  A ⋅ exp  − f =  2   σ 2 2πσ  

(2),

where µ represents the peak position of the Gaussian distribution, σ is the standard deviation and A is the proportional constant. Gaussian shapes of the excitonic transitions in the pristine materials are firstly determined by fitting EQE spectra of the polymer-only and the fullerene-only devices. Fitting results and parameters are summarized in Figure S2 and Table S1. With the excitonic state distributions fixed, the profile of CTS peak can be obtained by fitting EQE spectra of the polymer:fullerence devices through tuning the fitting parameters for the CTSs. The parameters for the best-fitting results are listed in Table 2. The results of the Gaussian fitting are shown in Figure 2. The solid lines represent the total fitting curves with contributions from the S0 to S1 excitonic transitions in


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PC71BM (dotted line) and in polymers (dash-dotted line) as well as the ground state to CTSs excitations (dashed line). All the EQE spectra can be satisfactorily fitted with a single CTS peaks except the case in P3HT:PC71BM (Figure 2b), which requires two CTS peaks to give acceptable fitting. The reason may be that there exists two kinds of CTSs with different energetic distributions at the P3HT/PC71BM interface. As previously reported, P3HT shows high crystallinity in both adirection (edge-on) and b-direction (face-on) stacking in film.33,34 It thus generates two kinds of donor/acceptor interfaces: one is that fullerene and P3HT backbone are separated with alkyl side chains and another is that fullerene and P3HT backbone are adjacent. For the first case, the distance between hole and electron in CTS is longer than the distance in second case. Longer hole-electron distance leads to a higher ECT based on Onsager model.11 For MEH-PPV:PC71BM, there appears two PC71BM peaks. One is at 1.79 eV, similar with other combinations; another one is at 2.0 eV.35 After obtaining the best fit, the peak position of the CTSs’ Gaussian peak is taken as the ECT (ECT (Gaussian)) (Table 2).


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Figure 2. EQE curves (open square) and Gaussian fitting results of five blend devices. (Solid lines: total fitting curves; dashed lines: peaks of CTS; dotted lines: S0 to S1 excitonic transitions in PC71BM; dash-dotted lines: excitonic transitions in polymers.) Table 2. Parameters used in EQE fitting with general Gaussian functions for five blend devices.

CTS PC71BM-1 PC71BM-2 MEH-PPV CTS PC71BM PCDTBT CTS PDTS-TPD

µ (eV) σ MEH-PPV:PC71BM 1.61 0.1 1.79 0.08 2.0 0.095 2.36 0.15 PCDTBT:PC71BM 1.6 0.095 1.82 0.06 2.04 0.12 PDTS-TPD:PC71BM 1.65 0.11 1.86 0.076

µ (eV)

Α 0.015 0.065 0.2 1.2

CTS-1 CTS-2 PC71BM P3HT

0.006 0.2 2.3

CTS PTB7

σ

P3HT:PC71BM 1.35 0.11 1.79 0.17 1.79 0.06 2.1 0.09 PTB7:PC71BM 1.55 0.1 1.8 0.092

Α 0.00021 0.04 0.015 1 0.03 2.2

0.0097 0.56


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3.3. CMEAS We then apply CMEAS to probe the ECT.9,16 CMEAS has been previously used to probe the energy of charges generated from CTSs, therefore provides information of the energetic distribution of CTS.9,16 The measuring process is described in Experimental Methods and the detailed working principle can be found in Supporting Information. Figure 3 shows CMEAS results from the five polymer:fullerene OPV devices. Positive peaks in the CMEAS spectra are due to Stark shifts from the excitonic states in the constituting materials or from the CTSs. Those due to the constituting materials are typically stronger peaks at higher energy (near bandgap energy), while the weak peaks at low sub-bandgap energies are from the CTS.9,16 As described in Supporting Information, in mathematic analysis, CMEAS signals can be expressed with derivatives of absorption coefficient. Therefore the excitonic Stark peaks in five blends are near the onset positions of absorption spectra, as shown in Figure S1 (Supporting Information). On the other hand, while the CTS peaks positions from the two approaches also agree in general, due to wide peak spread and low intensity in the CMEAS spectra, detailed comparison are less meaningful. We also mark the onset positions of the CMEAS signals (CMEASonset) of the CTS in each plot of Figure 3. The CMEASonset position is determined as the first point that ∆T/T signal decreases to zero. These onset positions (Table 3) are regarded as the lowest energies of the CTSs (ECT (CMEAS)) at the D/A interface.9 3.4. UPS UPS technique has been previously used to study interface electronics in organic electronic devices.6-8,36-38 Recently, the accurate electronic structures at blend polymer:fullerene


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BHJ interfaces have been successfully probed with a very high PC71BM ratio by our group.39 HOMO energies of the polymer donors (HOMOD) in the polymer:fullerene blends were measured with UPS and the offsets between the HOMOD values and the LUMO of PC71PM (LUMOA) were compared with VOCs of corresponding OPV devices. Considering the direct relationship between HOMOD-LUMOA offset and ECT,15 here we regard the HOMOD-LUMOA offset as the ECT values (ECT (UPS)). These ECT (UPS) values are cited from Ref. 39 and compared here in order to provide a full energetic picture of CTS. The cited ECT (UPS) values are listed in Table 3, the UPS spectra and the energetic diagrams of five polymer:fullerene BHJs are shown in Figure S3 and Figure S4, respectively.


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Figure 3. CMEAS spectra of five OPV devices with marking the position of CMEASonset.

Table 3. ECTs obtained from CMEASonset and UPS measurement, V0s extrapolated from VOCs at 0 K and VOCs measured at room temperature for five blend systems. The ECTs from UPS measurement are cited from Ref. 39.

Parameters CMEASonset (eV) UPS (eV) V0 (V) VOC (V)

MEH-PPV: P3HT: PCDTBT: PC71BM PC71BM PC71BM 1.3±0.07 1.25±0.04 1.32±0.04 1.31±0.05 1.03±0.05 1.45±0.05 1.25±0.05 0.95±0.03 1.35±0.05 0.88±0.02 0.6±0.02 0.92±0.02

PTB7: PC71BM 1.12±0.05 1.23±0.05 1.2±0.06 0.76±0.02

PDTS-TPD: PC71BM 1.23±0.06 1.37±0.05 1.33±0.05 0.94±0.02

4. Discussions With the above measured ECTs from four different methods, we try to clarify their physical meanings and to identify their relationships with VOC of the corresponding OPV devices. As shown in Figure 4a, at open-circuit condition, the quasi-Fermi levels are flat. VOC is


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defined as the difference between quasi-Fermi levels (Efn and Efp) and can be described with bandgap energy and charge carrier concentrations (n for electron and p for hole):  E − EC  n = N 0 exp  fn   kT 

(3),

 EV − E fp  p = N 0 exp    kT 

(4),

 qV − Eg  np = N 02 exp  OC  kT  

(5).

N0 is the density of electronic states, EV and EC are the energies of HOMOD and LUMOA, respectively, Eg is defined as the difference between EV and EC. With these relationships, VOC value is derived as:  N2  qVOC = Eg − kT log  0   np 

(6).

From Equation 6, VOC is determined by the effective bandgap Eg. The second term, which is dependent on temperature, is regarded as bimolecular recombination loss in VOC.40,41 The bimolecular recombination loss can be eliminated by decreasing the temperature to zero to obtained the zero-K VOC (V0). In order to rule out the effect of bimolecular recombination, we firstly measure the VOCs of five OPV devices at different temperatures and light intensities and extract the V0 by extrapolation as shown in Figure S5. Upon extrapolation to 0 K, the VOC values obtained at different light intensities converge to a small range. V0 values are estimated from the middle point of the range and listed in Table 3.


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Figure 4. (a) Energy diagram of BHJ-based OPV devices at open-circuit condition. Solid lines represent the HOMO and LUMO energy levels and dashed lines represent the quasi-Fermi levels for electrons (Efn) and holes (Efp). qVOC is defined as the difference between Efn and Efp. The difference between HOMOD and LUMOA is named as Eg. (b) ECTs obtained from UPS (square), CMEASonset (circle), EQE (Gaussian) fit (up triangle) and EQE (Marcus) fit (down triangle) of five polymer:fullerene systems as the function of V0. The dashed line is drawn as the reference line with slope = 1 and intercept = zero. The solid lines are fitting lines according to two EQE fitting results and parallel with the reference line. (c) ECTs and V0 (diamond) of five polymer:fullerene systems against VOC. The dashed line is drawn as the reference line with slope = 1 and intercept = 0.4. The solid lines are fitting lines according to two EQE fitting results and


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parallel with the reference line. For (b) and (c), error bars are taken from the experimental deviation and shown in the figure to reflect the accuracy.

Figure 4b shows the above measured ECTs with different methods, namely, EQE (Marcus) fit, EQE (Gaussian) fit, CMEAS and UPS, as the function of V0. The dashed line is drawn as the reference line with slope = 1 and y-intercept = zero while the other two solid lines are the fitting lines according to two EQE fitting results and parallel with the reference lines. It can be seen that ECT (UPS) and ECT (CMEAS) basically distribute around the reference line. Except the data from CMEAS (circle), ECTs from the other three methods show good linear relationships with V0 as indicated by the three lines. In fact, even the CMEAS data also give a reasonable linear relationship except the data point from the P3HT:PC71BM system. For the large deviation of ECT (CMEAS) with ECT (UPS) in P3HT:PC71BM, we still do not fully understand the reason. The reason may be due to the complicated P3HT/PC71BM interface. As mentioned above in EQE (Gaussian) fitting results, there exist two kinds of CTSs in high-crystalline P3HT:PC71BM film. Then for UPS measurement, different from other four polymers, only P3HT:PC71BM blend exhibits large band bending. We thus speculate this band bending may be attributed to the generation of the second kind of CTS. In addition, it can be found that in EQE (Gaussian) fit (Figure 2b), the peak intensity of CTS-1 is nearly two orders lower than that of CTS-2. In Marcus theory, EQE is regarded to reflect the absorption of CTS. This lower intensity may be attributed to the low absorption coefficient or inefficient electronic coupling between ground state and CTS-1.19 Therefore, considering that the measurement limitation of CMEAS is not as high as that of UPS, we propose a possibility that UPS detects the low-energy CTS-1 state


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while CMEAS signals are only dominated by the high-energy CTS-2 state. The detailed relationship among these experimental results will be explored in future work. It is interesting that all the linear relationships have the same slope of unity and differ only in their y-intercept. In particular, the reference line reflecting the trends of the ECT (UPS) and the ECT (CMEAS) data is passing through origin, suggesting that the ECT measured with these two approaches can be simply taken as qV0. On the other hand, qV0 can also be estimated as ECT (Gaussian) – 0.32 eV or ECT (Marcus) – 0.15 eV. It should be noted that although the V0 is regarded as the maximum theoretical VOC, this value is impossible to be achieved at room temperature due to the bimolecular recombination. In addition, for OPV, the binding energy of CTS cannot be ignored. This factor further decreases the VOC value as dielectric loss.16 This loss can be directly observed from the saturation in VOC as temperature decreases (Figure S4). The estimated saturation value (Vsat) and Vsat -VOC values are listed in Table S2. It should be noticed that these Vsat -VOC values maybe not reflect the exact dielectric losses due to the temperature limitation in our measurement, but it proves that the CTS binding energy results in the decrease of VOC in OPV devices. To compare the ECTs from different measurements with the VOC values of OPV devices at room temperature, we plot the ECTs and V0 against VOC in Figure 4c. It can be found that the ECT (CMEAS) and ECT (UPS) as well as qV0 distribute around the reference line with slope = 1 and y-intercept = 0.4 eV. This implies that the differences between the V0 and VOC in actual devices are around 0.4 V. We attributed this loss to the sum of bimolecular recombination and dielectric effect. The specific values may vary for different polymer:fullerene systems. The ECT (Gaussian) and ECT (Marcus) also can be described by lines with the slope of 1. The energy differences with


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the qVOCs (y-intercept) are 0.7 eV for the former and 0.53 eV for the latter, i.e. 0.3 eV and 0.13 eV higher than the y-intercept of the first line. These values are very similar with the energy differences obtained in Figure 4b (0.32 eV and 0.15 eV), indicating a consistence for the conditions of 0 K and room temperature. We next try to distinguish the difference of the ECTs obtained from different methods. The mechanism of UPS is to detect the kinetic energy of photoemission electron from HOMO,36 which is the top of occupied electronic states for CTS. CMEAS probes the energy of charge states from CTSs and the onset position of its spectrum indicates the response of the lowest detectable charge state. Different from two EQE fitting methods, which focus on the spectra peak of an electronic state, UPS and CMEAS can provide a definite onset of CTSs. As both methods try to probe the lowest energetic “boundary” of CTS, we expect the measured results should be similar within the measurement limitation. This can be verified by the results in Figure 4b and Table 3, in which CMEASonset and UPS values are very close except for P3HT:PC71BM. The deviation in the case of P3HT:PC71BM, as discussed above, may be due to the existence of another weak CTS, which is beyond the CMEAS measurement limitation. For the BHJ structure OPV devices, especially based on some push-pull co-polymers,42,43 the morphology is amorphous and interpenetrating,44 as shown in Figure 5a, i.e. donor and acceptor domains distribute alternatively (Figure 5b). The alternating LUMOA and HOMOD form a “band-like” energy bandgap for CTS.14 We therefore propose that the measured ECT results from UPS and CMEAS should be the bandgap width of the CTS, EgCT, which is consistent with qV0.


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Figure 5. (a) Distributions of polymer and fullerene in BHJ-based OPV devices. (b) (Left) Energy level diagram in BHJ-based OPV device. (Right) Proposed energetic model of CTS and the energy levels obtained with different methods. The alternating LUMOA and HOMOD form a “band-like” energy bandgap of CTS. EgCT is the bandgap width obtained from UPS and CMEASonset and directly determines V0. Ee-pCT is the energy difference between the edge and peak of CTS distribution obtained from EQE (Marcus) fit. Ep-pCT is the energy difference between two distribution peaks obtained from EQE (Gaussian) fit.

For the other two methods based on EQE fit, generally their measured ECTs are higher than those from UPS or CMEAS in energy. Specifically, from the drawn lines in Figure 4b and c, it can be found that these energy differences obtained by EQE (Gaussian) method (~300 meV) are around twice as the differences obtained by EQE (Marcus) method (~150 meV). As described in previous reports19,24,27 and illustrated in Figure S6, for the EQE (Marcus) fitting


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method, ECT is in the middle between the CTS emission peak (Eflmax) and CTS absorption peak (Eabsmax) with the reorganization energy, λ, i.e. ECT = Eflmax +λ and Eabsmax = Eflmax +2λ. As the ECTs (Gaussian) are very similar with the Eabsmaxs obtained through EQE (Marucs) fit, it is reasonable to claim that the energy difference between two ECTs from two EQE fitting methods (~150 meV) is λ. As it has been proposed that λ is related to the width of the CTS absorbance band,27 we here regard the energetic broadening of CTS (λ’) as the sum of λ and the energetic disorder of CTS, σ, i.e. λ’ = λ +σ2/2kT and propose a model to illustrate the difference among ECTs from several methods. In Figure 5b (right), the CTSs mainly distribute above LUMOA and below HOMOD with Gaussian-shaped DOS. As mentioned above, the bandgap of CTS, EgCT, can be probed by UPS or CMEAS. For the ECT (Marucs), as it contains one λ, it should reflect the reorganization energy of one CTS. We attribute the ECT (Marucs) as the energy difference from the edge of one CTS to the peak of another CTS, named Ee-pCT. Similarly, since the ECT (Gaussian) contains two λ, we attribute it as the energy difference between two peaks of two CTSs, named Ep-pCT. Our model is reasonable considering the mechanisms of the used methods and good consistence of data among the results. By clarifying the physical meanings of those different ECTs, our model provides a consistent picture about the CTS distributions in BHJ-based OPV devices. For VOC, this model explains that why the difference between qVOC and ECT measured from different methods always show considerable discrepancy. Even though these methods all probe the CTS, the energies of ECT varies a lot considering the broadening of CTS. Specifically, the reorganization energy of one CTS (HOMOD or LUMOA) can be extracted as λ by applying the EQE (Marcus) fit. We also find that the method of CMEAS and UPS can directly probe the bandgap values of CTS, ruling out the effect of CTS broadening in studying the relationship with


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VOC. The difference between qVOC and EgCT can only be attributed to the losses of bimolecular recombination and dielectric effect, which is around 0.4 eV based on our experiment.

Figure 6. Plot of calculated (Cal.) VOC vs. experimental (Exp.) VOC. The Cal. VOCs are obtained with the Equation 7. Parameters used in calculating and Exp. VOC values are taken from the Ref. 45, 46, 24 and 27 as well as this work. All the data used in this figure are listed in Table S3.

To further check the validity of our model, we try to collect previously reported parameters about CTS and compare them with the experimentally obtained VOCs in actual OPV devices. Thanks to the precursor work by Vandewal et al.,19 the EQE (Marcus) fitting method has been widely used to investigate the CTS in OPV.24,27,45,46 Based on the discussions in Ref. 17, the VOC loss can be assigned to a combination of CTS energetic broadening, CTS binding energy, bimolecular recombination and degree of donor:acceptor mixing. However, since the influence of donor:acceptor mixing is still under discussion21,27 and the estimated energetic loss


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is small (less than 100 meV)17, here we mainly consider the other three factors, which have been widely recognized as the contributor to VOC loss.16,17 For the VOC loss due to the energetic broadening, since the disorder degree is difficult to be directly measured and the estimated loss is small (σ of 60 meV only results in the energetic broadening of 70 meV), we regard the reorganization energy as the main loss of energetic broadening of CTS for the estimation of VOC below. We therefore collect the Ee-pCT and λ from some of these literatures and calculate VOCs with Equation 7:

qVOC = EeCT− p − λ −∆Eloss

(7),

where ∆Eloss represents the energy loss due to the bimolecular recombination and dielectric effect at open-circuit condition. As shown in Figure 6 and Table S3, we find a good consistence between the calculated and experimental VOCs with a small deviation of ± 0.08 eV, which verifies our model. It should be noted that for all the compared systems we fixed ∆Eloss at 0.4 eV, as we cannot identify the exact ∆Eloss values in other systems. 5. Conclusion In summary, we obtain the CTS energies (ECTs) from four different methods, namely, EQE (Marcus) fit, EQE (Gaussian) fit, CMEAS and UPS. By comparing these ECT values with the zero-K VOC or VOC measured at room temperature, we find the ECTs from each method exhibit a linear relationship with VOCs. By analyzing the exact energy values of each ECT as well as λ, we propose that the ECT measured from UPS and CMEAS describes the energy difference between the DOS edges of HOMOD and LUMOA in CTS. The ECT extracted from EQE (Marcus) fit is the energy difference from the edge of one CTS to the peak of another CTS, containing the broadening degree of one CTS, meanwhile the ECT from EQE (Gaussian) fit indicates the energy


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difference between the DOS peak positions of two CTSs in HOMOD and LUMOA. Specifically, we find the UPS and CMEAS technique directly probe the bandgap of CTS at D:A interface by ruling out the energetic broadening of CTS. These two methods allow us to extract the loss of bimolecular recombination and dielectric effect from the total loss of VOC. It should be noted that this does not mean the “ineffectiveness” of EQE fit based on Marcus theory in determining ECT. Instead, we find ECTs (Marcus) from previous literatures can be successfully used to estimate VOC. Our results clarify the detailed energetic meanings of the CTSs measured from different techniques and provide a guideline to investigate the VOC and its loss in OPV devices.

ASSOCIATED CONTENT Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org. Active layer preparation; principle of electroabsorption spectroscopy; normalized absorption spectra; EQE fitting results of polymer-only and fullerene-only devices with Gaussian function; energy diagram of five polymer:fullerene BHJs from UPS; temperature dependence of VOC for five OPV devices; schematic of reduced spectra of EQEPV and EL together with the fitting curves based on Marcus formula; comparison between the calculated VOCs from equation 7 and the experimentally obtained VOCs. AUTHOR INFORMATION Corresponding Authors * E-mail: [email protected]. Telephone number: +852 34427826 * E-mail: [email protected]. Telephone number: +852 34424618


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Author Contributions §

Z. G and H. -W. L. are co-first authors with equal contribution to this work.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work is supported by Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11304115 and 21201514), and National Natural Science Foundation of China (No. 51473138).

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