Introduction

Since the first report on bulk-heterojunction (BHJ) devices in 19951, the performance of organic solar cells (OSCs) have improved steadily and power conversion efficiency (PCE) increased as high as 18.22%2. Parallel progress in material development2,3,4,5,6,7, device structure innovation4,6, and fabrication process engineering4,7,8 has contributed to steady improvement of OSC performance. Elucidation of mechanisms that limit the operation of OSCs has contributed similarly in developing advanced version of OSCs8,9,10,11,12,13,14,15,16,17.

It is essential to understand both optical and electrical processes to describe OSC operation because it consists of generation, transport, and extraction of charge carriers2,17,18,19,20,21. Tracking light-intensity dependence of J–V characteristics is an efficient strategy to study essential mechanisms controlling OSC performance because variations in optical and electrical processes can occur simultaneously in response to light intensity changes10,11,12,22. Combined with systematic simulations that can reproduce a measured set of J–V curves, light intensity-dependent studies can be useful in identifying key processes that determine J–V characteristics and elucidating the origin of variations in OSC performance parameters.

In this study, we measured and simulated the operation of BHJ-type OSCs with a ternary active layer (AL) that consisted of PM6, Y6, and PC71BM, together with an inverted device architecture of ITO/ZnO/AL/MoO3/Ag. For device simulation corresponding to operation under various illumination conditions, we first simulated position- and wavelength-dependent exciton generation rates in an AL, which resulted from photon absorption. This optical part of simulation was done by using a multilayer OSC structure together with pre-determined optical constants of each constituent layer21. We used a device simulator SCAPS for electrical part of simulation after importing the results of optical simulations. The key element of our electrical simulations was the inclusion of Shockley–Read–Hall (SRH) type processes for mono-molecular recombination losses.

Results and discussion

Figure 1 shows systematic variation in J–V characteristics of the OSC with respect to the illumination intensity of a solar simulator. Both short-circuit current density Jsc and open-circuit voltage Voc grow larger with increase in light intensity. However, there is subtle difference between light-intensity dependence of Jsc and Voc. Unlike Jsc that increases monotonically across all light intensities, the rate of Voc increase in high intensity light is about half of the rate in low intensities. Additionally, there is a non-monotonic variation in the “squareness” of the J–V curves, which we typically represent by fill factor (FF) parameters23.

Figure 1
figure 1

Light intensity dependence of J–V characteristics of the OPV.

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Such variations in Jsc, Voc., and FF combine to result in the light-intensity dependence of PCEs23. Quantitatively, the decrease in FF in high intensities is sufficient to counteract the increases in both Jsc and Voc and to show the saturating behavior of PCEs following a steady increase up to ~ 13.4% as shown in Fig. 2a. Other groups previously attributed the slope change in a semi-log plot of Voc versus light intensity to the discrepancy in recombination mechanisms12,13,22,24,25,26,27. More specifically, an ideality factor converted from the slope of aforementioned semi-log plots should be 1 if bi-molecular recombination dominates, but 2 if mono-molecular recombination is dominant. Interestingly, the ideality factors corresponding to the slopes of two linear segments in Fig. 2b are 1.12 and 1.86 to suggest such a switch in recombination-loss mechanisms in response to light intensity increase. A two-segment feature is also evident in the plot of FF with respect to light intensity in Fig. 2c. However, the demarcations between two segments for Voc and FF do not appear at the identical light intensity. Moreover, there has been no report on the origin of systematic changes in FF28. In addition to the discrepancy between Voc and FF variations, a quasi-linear Jsc increase in Fig. 2d indicates that qualitative arguments based on two recombination mechanisms are insufficient to manifest light-intensity dependence of the OSC operation.

Figure 2
figure 2

Light-intensity dependent solar cell parameters: (a) power conversion efficiency PCE, (b) open-circuit voltage Voc, (c) fill factor FF, and (d) short-circuit current density Jsc.

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We quantitatively confirmed switching between bi- and mono-molecular recombination dominance with increase in light intensity using a device simulator SCAPS. In this simulation, we assume SRH-type processes for mono-molecular recombination with neutral defects. Details of SCAPS simulation parameters are specified in Tables S1 (see Supporting Information).

For reliable J–V curve simulations, it is essential to use proper exciton generation profiles that show position- and wavelength-dependent exciton generation rates in an AL, which resulted from photon absorption19. Figure 3a shows a set of position-dependent absorption spectra within an AL, which we simulated based on a multilayer OSC structure in the inset of Fig. 3b and optical constants of constituent layers21,29. Integration of an absorption spectrum over the whole wavelength range at each position resulted in the depth profile of exciton generation rates in Fig. 3b. On the other hand, integration of a spatial absorption profile over the whole AL depth produced the light-harvesting efficiency (LHE) spectrum in Fig. 3c. Good agreement between the spectra of measured incident photon-to-electron conversion efficiency (IPCE) and calculated LHE is convincing evidence for the conversion of all absorbed photons into excitons and near 100% internal quantum efficiency (IQE), which indicates that germinate recombination is highly unlikely and that charge-carrier extraction is almost complete21,30.

Figure 3
figure 3

Optical simulation results: (a) position-dependent absorption spectra within an active layer; depth corresponds to the distance from the interface between ETL and AL, (b) depth profile of exciton generation rates and a multilayer OSC structure (inset), and (c) the comparison of spectra of light-harvesting efficiency and measured incident photon-to-electron conversion efficiency.

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A set of preliminary simulations showed that defect density is the most critical parameter in reproducing light-intensity dependence of measured J–V curves. On the contrary, other parameters did not change simulation results noticeably as long as their order of magnitudes were kept to literature values31,32,33,34,35. Figure 4 shows that improper choice of defect density fails to reproduce experimental J–V curves. Specifically, failure appears prominently near an inflection point in the case of the dark J–V curve, and simultaneous agreement between simulated and measured J–V curves corresponding to weak (0.01 sun), medium (0.28 sun), and strong (1 sun) illumination conditions appear only when defect density of \(5 \times 10^{12} {\text{ cm}}^{ - 3}\) was used. We note that the defect density of \(5 \times 10^{12} {\text{ cm}}^{ - 3}\) is comparable to those in PM6:Y6 devices reported by T-Q Nguyen33.

Figure 4
figure 4

Comparison of simulated and measured J–V curves. We simulated a set of J–V curves corresponding to large defect-density variations that span four orders of magnitude. Simulations agreement of simulation results with experimental J–V curves measured in the dark, and at weak (0.01 sun), medium (0.28 sun), and strong (1 sun) illumination conditions appear only with defect density of \(5 \times 10^{12} {\text{ cm}}^{ - 3}\).

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In Fig. 5a,b, we show the full set of simulated J–V curves (solid lines) together with the corresponding data (symbols) measured at 9 different light intensities and also in the dark. Regardless of substantial changes in short-circuit currents, all simulated J–V curves show good agreement with the experimental data to confirm the validity of our OSC simulations. One of the advantages of simulation studies is that we can identify contributions of generation (Jgen) and recombination current (Jrec) components to J–V curves during OSC operation at light intensity L. Moreover, we can separate Jrec into SRH recombination (JSRH), and bimolecular recombination current (Jbi) components:

Figure 5
figure 5

Comparison of simulated J–V curves (solid lines) with the corresponding data (symbols) measured at 9 different light intensities and also in the dark: (a) from 0.18 to 1.00 sun, and (b) below 0.09 sun and in the dark. (c) Comparison of simulated recombination current curves, Jrec–V (solid lines), with the sum (symbols) of measured J(V) and simulated generation current Jgen(L) at each light intensity L. (d) Variations of normalized current densities Jnorm with respect to applied voltages: \(J_{norm} = J/J_{sc}\).

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$$J\left(V,L\right)={J}_{rec}(V,L)-{J}_{gen}\left(L\right)={J}_{SRH}\left(V,L\right)+{J}_{bi}(V,L)-{J}_{gen}(L)$$
(1)

Jgen that we calculate by integrating the generation rate in Fig. 3(b) over the AL depth does not depend on applied voltages because the AL is thin enough so that all absorbed photons are converted to excitons with ~ 100% IQE30. We want to emphasize that isolation of JSRH and Jbi is important for quantitative elucidation of the aforementioned Voc and FF variations.

We compare a set of simulated Jrec–V curves (solid lines) with the corresponding sum of measured J(V) and simulated Jgen (symbols) in Fig. 5c. In addition to dark currents that span 5 orders of magnitude, the whole set of photocurrent data show good agreement to simulated Jrec variations. In Fig. 5d, we show normalized current densities Jnorm with respect to applied voltages for easier recognition of systematic variations in Voc and FF, independent of a quasi-linear Jsc increase:\({J}_{norm}=J/{J}_{sc}\).

To manifest the origin of Voc variation in Fig. 2b, we show two recombination current components separately with respect to applied voltage in Fig. 6a–c. In these figures, currents and applied voltages are normalized by Jgen and Voc, respectively, to emphasize systematic changes in JSRH and Jbi, and their contributions to Voc. At 1 sun, Voc is determined mostly by Jbi because of their dominance in exponentially increasing currents as shown in Fig. 6a. On the contrary, JSRH dominates over Jbi at 0.01 sun and determines Jrec. However, the contributions of Jbi and JSRH become comparable at 0.18 sun. Systematic variations in recombination currents at Voc in Fig. 6d show that a dominant current-loss mechanism switches from SRH to bimolecular recombination at around 0.18 sun. Accordingly, Voc variations with respect to light intensity is consistent with the SRH recombination up to 0.18 sun, but with the bimolecular recombination at higher light intensities as shown in Fig. 2b.

Figure 6
figure 6

Variations of simulated SRH, bimolecular, and total recombination currents with respect to applied voltages correspond to (a) weak (0.01 sun), (b) medium (0.18 sun), and (c) strong (1 sun) illumination conditions. Recombination currents are normalized by generation currents Jgen(L), and applied voltages are normalized by Voc. (d) Variations of SRH- and bimolecular -recombination currents at Voc with respect to light intensities.

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Next, we extended the analysis of JSRH and Jbi variations to identify the origin of the FF variation in Fig. 2c. Figure 7a,b show the variations of JSRH and Jbi that are normalized by Jgen with respect to applied voltages normalized by Voc. The most prominent discrepancy between JSRH and Jbi variations is the systematic shift of knee points. In the case of JSRH-V curves, the knee points move to the lower right direction with increase in light intensity. On the contrary, the knee points of Jbi–V curves move to the upper left direction in response to light-intensity increase. Results of such shifts are apparent changes in squareness of the J–V curves at the maximum power points (MPPs). For quantitative comparison between the contributions of JSRH and Jbi to the maximum power, we show powers resulted from each current component in Fig. 8. All powers are normalized by Psq that is defined as the product of Jsc and Voc. It is straightforward to see that the difference between generated power (Pgen) and power losses (PSRH and Pbi) is the power output delivered by the OSC at each light intensity. At 0.01 sun, PSRH is 7.1 times larger than Pbi at the MPP, and accordingly FF is mostly determined by PSRH. With increase in light intensity, the dominance of PSRH over Pbi decreases, but PSRH remains 2.2 times larger than Pbi at 0.18 sun. However, Pbi becomes comparable to PSRH at 0.50 sun and eventually becomes 1.7 times larger than Pbi at 1 sun.

Figure 7
figure 7

Light-intensity dependent variations of normalized SRH- and bimolecular -recombination currents with respect to normalized applied voltages: (a) JSRH/Jgen versus V/Voc and (b) Jbi/Jgen versus V/Voc.

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Figure 8
figure 8

Variations of normalized power components with respect to normalized applied voltages corresponding to light intensities of (a) 0.01, (b) 0.18, (c) 0.50, and (d) 1.00 sun. Each power component is normalized by Psq that is defined as the product of Jsc and Voc, and applied voltages are normalized by Voc.

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For more quantitative comparison, we show the relative contributions of PSRH and Pbi to the total power loss Ploss at the MPPs in Fig. 9a. PSRH/Ploss decrease steadily from 86.1% at 0.01 sun to 37.3% at 1 sun, and coincide with Pbi/Ploss at 0.50sun. Motivated by switching between PSRH and Pbi dominance in power loss, we estimate FFs that would appear if only PSRH or Pbi were responsible for power loss:

$$FF_{SRH} = \, \left( {P_{gen} - \, P_{SRH} } \right)_{max} /P_{sq}$$
(2)
$$FF_{bi} = \left( {P_{gen} {-}P_{bi} } \right)_{max} /P_{sq}$$
(3)
Figure 9
figure 9

(a) Variations of the relative contributions of power losses PSRH and Pbi to the total power loss Ploss at the maximum power points with respect to light intensities. (b) Variations of fill factors (FFs) with respect to light intensities. FFSRH and FFbi are FFs that would appear if only PSRH or Pbi were responsible for power loss.

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It is interesting to note that the crossing of FFSRH and FFbi variations occur at around 0.50 sun as shown in Fig. 9b, Moreover, the variation of FF is close to that of FFSRH for light intensities lower than 0.09 sun, but follows the trend of FFbi for light intensities above 0.50 sun. However, FF does not change noticeably for intermediate light intensities, in which FFSRH and FFbi are comparable.

Discussions related to Figs. 6 and 8 show that both the Voc and FF variations with respect to light intensity originate from the competition between SRH and bimolecular recombination-loss mechanisms. Because SRH recombination loss is sensitive to defect density, we expect systematic evolutions of Jsc, Voc, and FF in response to defect density variations. A series of simulations that cover 4 orders of magnitude variation in defect density confirms our expectations as shown in Figs. S2 and S3 in Supporting Information. With low (5 × 1010 cm−3) and high (5 × 1013 cm−3) defect densities, Voc, and FF show relatively simple variations because either Jbi or JSRH dominates loss currents. On the contrary, more subtle variations occur for defect densities of 5 × 1011 and 5 × 1012 cm−3 as the switching between Jbi and JSRH dominance occurs. However, Jsc show quasi-linear variation with respect to light intensity regardless of defect densities. Quantitatively, Jbi normalized to Jgen is only ~ 1%, and, consequently, JSRH determine the offsets of Jsc from Jgen. However, JSRH is less than 1% for defect densities of 5 × 1010 and 5 × 1011 cm−3, and Jsc normalized to Jgen remains close to 1 to make Jsc-L variation almost linear. On the contrary, JSRH normalized to Jgen become as large as 7.4% and 21.6% at 0.01 sun for the respective defect densities of 5 × 1012 and 5 × 1013 cm−3 while JSRH/Jgen decrease monotonically with increase in light intensity. Consequently, the discrepancies between Jsc and Jgen is noticeable at low light intensities, and the ratio Jsc/Jgen increase monotonically with increase in light intensity to result in slightly super-linear Jsc-L variations.

Conclusion

We measured J–V characteristics of an OSC in the dark and at 9 different illumination intensities and found systematic variations in Jsc, Voc, and FF, the three conventional parameters to represent performance of a solar cell. Specifically, Jsc showed a quasi-linear increase, but Voc, and FF showed non-monotonic variations with increase in light intensity. Moreover, apparent demarcation in Voc, and FF variations seem to appear at different light intensities. However, extensive OSC simulations showed that all variations in Jsc, Voc, and FF are attributable to the same origin. In short, we were able to verify that the competition between bimolecular- and SRH-recombination losses are responsible for the aforementioned variations. Unlike bimolecular recombination that is intrinsic to any AL material, SRH recombination occurs because of defects. Consequently, defect control during OSC fabrication emerges ever more important. AL-material oxidation is the most likely source for defect formation and, therefore, the control of OSC-fabrication environment is very important for the fine control of OSC performance in addition to improving device longevity36,37,38,39.

Methods

Device Fabrication

We fabricated BHJ type OSCs with a ternary AL that consisted of PM6 (1-Material), Y6 (1-Material), and PC71BM (Sigma Aldrich) on an ITO-coated (10 Ω sq−1) glass substrates based on an inverted device architecture of ITO/ZnO/AL/MoO3/Ag. ITO-cathode and Ag-anode patterns defined the square solar-cell area of 0.4 × 0.4 cm2. ZnO and MoO3 were electron- (EELs) and hole-extraction layers (HELs), respectively. Device fabrication started by thoroughly cleaning ITO surfaces according to a conventional recipe. Just prior to spin-coating a dispersion solution of 12-nm ZnO nanoparticles in IPA (Avantama), we treated ITO surfaces with oxygen plasma. ZnO EELs with a thickness of 40 nm were formed following a post annealing step at 80 ˚C for 10 min. We formed ALs similarly by combining spin-coating and post-annealing steps. The precursor solution for ALs was prepared by dissolving 7 mg of PM6, 7 mg of Y6, and 1.4 mg of PC71BM in 1 ml of chloroform, and then adding 0.5 V% of chloronaphthalene to the mixture solution. Post-annealing for 10 min at 90 ˚C completed the formation of 90-nm thick ALs. Finally, we deposited a 10-nm thick MoO3 HEL and a 100-nm thick silver anode in succession using a thermal evaporator equipped with a thickness monitor. We protected fabricated OSCs against exposure to ambient air using epoxy-glass encapsulation.

J–V measurement

J–V characteristics under different illumination conditions were measured with a CompactStat (Ivium) source-measuring unit. We used a solar simulator PEC-L01 (Peccell) operating at 100 mW cm−2, together with a set of neutral filters, to simulate various illumination levels under AM1.5G conditions. For calibration of solar simulator irradiance, we used a silicon reference cell PEC-S101 (Peccell).

Optical simulation

We did optical simulations for OSCs using the RSOFT program that is a numerical solver for Maxwell equations based on a RCWA method. Complex optical constants of ZnO and MoO3 layers used for optical simulations were the results of our previous studies to fit transmittance, reflectance, and/or ellipsometry spectra. In the case of a ternary AL, we used optical constants reported in a literature40 after slight modification to fit reflectance spectra of an actual AL that we formed according to the aforementioned recipe.

Electrical simulation

We conducted electrical simulations for OSC operation at different illumination intensities using the device simulator SCAPS (ver. 3.3.03) developed by Burgelman’s group at the University of Gent. In essence, SCAPS is a drift–diffusion equation solver. We summarized details of electrical simulation parameters in Supporting Information, Table S1. In our simulation, we modeled the BHJ AL as a fictitious semiconductor having the lowest unoccupied (LUMO) and highest occupied (HOMO) molecular orbital that coincide with Y6’s LUMO and PM6’s HOMO, respectively. This model is appropriate to take into account transport of electrons and holes in the OSC because electron and hole transport in the BHJ AL occur separately along a percolating path of Y6 or that of PM619. In this regard, the third component PC71BM that does not form a separate percolating phase only serves the role of an absorption enhancer without altering absorption ranges17. In accordance, our ternary device’s Voc of 0.84 V at 1 sun was almost identical with that of a PM6/Y6 binary device. We set thermal velocities of electrons and holes to typical values for bulk semiconductors throughout the device. For electron and hole mobility in the AL we used literature values with a slight modification to produce simultaneous agreement between simulated and measured J–V curves corresponding to 10 different illumination conditions. The value of bimolecular recombination coefficient that we used for successful reproduction of the complete set J–V curves is similar to that reported by other groups41,42. All other parameter values were either set at literature values31,32,33,34,35.