Light intensity dependence of organic solar cell operation and dominance switching between Shockley–Read–Hall and bimolecular recombination losses

We investigated the variation of current density–voltage (J–V) characteristics of an organic solar cell (OSC) in the dark and at 9 different light intensities ranging from 0.01 to 1 sun of the AM1.5G spectrum. All three conventional parameters, short-circuit currents (Jsc), open-circuit voltage (Voc), and Fill factor (FF), representing OSC performance evolved systematically in response to light intensity increase. Unlike Jsc that showed quasi-linear monotonic increase, Voc and FF showed distinctive non-monotonic variations. To elucidate the origin of such variations, we performed extensive simulation studies including Shockley–Read–Hall (SRH) recombination losses. Simulation results were sensitive to defect densities, and simultaneous agreement to 10 measured J–V curves was possible only with the defect density of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5 \times 10^{12} {\text{ cm}}^{ - 3}$$\end{document}5×1012cm-3. Based on analyses of simulation results, we were able to separate current losses into SRH- and bimolecular-recombination components and, moreover, identify that the competition between SRH- and bimolecular-loss currents were responsible for the aforementioned variations in Jsc, Voc, and FF. In particular, we verified that apparent demarcation in Voc, and FF variations, which seemed to appear at different light intensities, originated from the same mechanism of dominance switching between 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 J sc and open-circuit voltage V oc grow larger with increase in light intensity. However, there is subtle difference between light-intensity dependence of J sc and V oc . Unlike J sc that increases monotonically across all light intensities, the rate of V oc 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) parameters 23 .
Such variations in J sc, V oc ., and FF combine to result in the light-intensity dependence of PCEs 23 . Quantitatively, the decrease in FF in high intensities is sufficient to counteract the increases in both J sc and V oc 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 V oc versus light intensity to the discrepancy in recombination mechanisms 12,13,22,[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 V oc and FF do not appear at the identical light intensity. Moreover, there has been no report on the origin of systematic changes in FF 28 . In addition to the discrepancy between V oc and FF variations, a quasi-linear J sc increase in Fig. 2d indicates that qualitative arguments based on two recombination mechanisms are insufficient to manifest light-intensity dependence of the OSC operation.
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 positionand wavelength-dependent exciton generation rates in an AL, which resulted from photon absorption 19 . 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 layers 21,29 . 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 complete 21,30 .
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 values [31][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 × 10 12 cm −3 was used. We note that the defect density of 5 × 10 12 cm −3 is comparable to those in PM6:Y6 devices reported by T-Q Nguyen 33 .   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 (J gen ) and recombination current (J rec ) components to J-V curves during OSC operation at light intensity L. Moreover, we can separate J rec into SRH recombination (J SRH ), and bimolecular recombination current (J bi ) components: J gen 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% IQE 30 . We want to emphasize that isolation of J SRH and J bi is important for quantitative elucidation of the aforementioned V oc and FF variations.
We compare a set of simulated J rec -V curves (solid lines) with the corresponding sum of measured J(V) and simulated J gen (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 J rec variations. In Fig. 5d, we show normalized current densities J norm with respect to applied voltages for easier recognition of systematic variations in V oc and FF, independent of a quasi-linear J sc increase:J norm = J/J sc .
To manifest the origin of V oc 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 J gen and V oc , respectively, to emphasize systematic changes in J SRH and J bi , and their contributions to V oc . At 1 sun, V oc is determined mostly by J bi because of their dominance in exponentially increasing currents as shown in Fig. 6a. On the contrary, J SRH dominates over J bi at 0.01 sun and determines J rec . However, the contributions of J bi and J SRH become comparable at 0.18 sun. Systematic variations in recombination currents at V oc in Fig. 6d show that a dominant current-loss mechanism switches from SRH to bimolecular recombination at around 0.18 sun. Accordingly, V oc 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.
Next, we extended the analysis of J SRH and J bi variations to identify the origin of the FF variation in Fig. 2c. Figure 7a,b show the variations of J SRH and J bi that are normalized by J gen with respect to applied voltages normalized www.nature.com/scientificreports/ by V oc . The most prominent discrepancy between J SRH and J bi variations is the systematic shift of knee points.
In the case of J SRH -V curves, the knee points move to the lower right direction with increase in light intensity. On the contrary, the knee points of J bi -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 J SRH and J bi to the maximum power, we show powers resulted from each current component in Fig. 8. All powers are normalized by P sq that is defined as the product of J sc and V oc . It is straightforward to see that the difference between generated power (P gen ) and power losses (P SRH and P bi ) is the power output delivered by the OSC at each light intensity. At 0.01 sun, P SRH is 7.1 times larger than P bi at the MPP, and accordingly FF is mostly determined by P SRH . With increase in light intensity, the dominance of P SRH over P bi decreases, but P SRH remains 2.2 times larger than P bi at 0.18 sun. However, P bi becomes comparable to P SRH at 0.50 sun and eventually becomes 1.7 times larger than P bi at 1 sun. For more quantitative comparison, we show the relative contributions of P SRH and P bi to the total power loss P loss at the MPPs in Fig. 9a. P SRH /P loss decrease steadily from 86.1% at 0.01 sun to 37.3% at 1 sun, and coincide with P bi /P loss at 0.50sun. Motivated by switching between P SRH and P bi dominance in power loss, we estimate FFs that would appear if only P SRH or P bi were responsible for power loss: It is interesting to note that the crossing of FF SRH and FF bi variations occur at around 0.50 sun as shown in Fig. 9b, Moreover, the variation of FF is close to that of FF SRH for light intensities lower than 0.09 sun, but follows (2) FF SRH = P gen − P SRH max /P sq (3) FF bi = P gen −P bi max /P sq  show that both the V oc 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 J sc , V oc , 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 × 10 10 cm −3 ) and high (5 × 10 13 cm −3 ) defect densities, V oc , and FF show relatively simple variations because either J bi or J SRH dominates loss currents. On the contrary, more subtle variations occur for defect densities of 5 × 10 11 and 5 × 10 12 cm −3 as the switching between J bi and J SRH dominance occurs. However, J sc show quasi-linear variation with respect to light intensity regardless of defect densities. Quantitatively, J bi normalized to J gen is only ~ 1%, and, consequently, J SRH determine the offsets of J sc from J gen . However, J SRH is less than 1% for defect densities of 5 × 10 10 and 5 × 10 11 cm −3 , and J sc normalized to J gen remains close to 1 to make J sc -L variation almost linear. On the contrary, J SRH normalized to J gen become as large as 7.4% and 21.6% at 0.01 sun for the respective defect densities of 5 × 10 12 and 5 × 10 13 cm −3 while J SRH /J gen decrease monotonically with increase in light intensity. Consequently, the discrepancies between J sc and J gen is noticeable at low light intensities, and the ratio J sc /J gen increase monotonically with increase in light intensity to result in slightly super-linear J sc -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 J sc , V oc , and FF, the three conventional parameters to represent performance of a solar cell. Specifically, J sc showed a quasi-linear increase, but V oc , and FF showed non-monotonic variations with increase in light intensity. Moreover, apparent demarcation in V oc , and FF variations seem to appear at different light intensities. However, extensive OSC simulations showed that all variations in J sc , V oc , 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 www.nature.com/scientificreports/ formation and, therefore, the control of OSC-fabrication environment is very important for the fine control of OSC performance in addition to improving device longevity [36][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 PC 71 BM (Sigma Aldrich) on an ITO-coated (10 Ω sq −1 ) glass substrates based on an inverted device architecture of ITO/ZnO/AL/MoO 3 /Ag. ITO-cathode and Ag-anode patterns defined the square solarcell area of 0.4 × 0.4 cm 2 . ZnO and MoO 3 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 PC 71 BM 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 MoO 3 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 MoO 3 layers www.nature.com/scientificreports/ 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 literature 40 after slight modification to fit reflectance spectra of an actual AL that we formed according to the aforementioned recipe.    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  www.nature.com/scientificreports/ 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 PM6 19 . In this regard, the third component PC 71 BM that does not form a separate percolating phase only serves the role of an absorption enhancer without altering absorption ranges 17 . In accordance, our ternary device's V oc 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 groups 41,42 . All other parameter values were either set at literature values [31][32][33][34][35] .