Simulation of the degradation behavior of small-molecule solar cells based on p-DTS(FBTTh2)2 as the donor material

The use of organic solar cells (OSCs), particularly those based on small-molecule materials, has gained recognition as being promising in photovoltaic applications. However, despite notable advances, persistent challenges in relation to the long-term stability and energy-conversion efficiency of these materials continue to pose significant obstacles to their widespread adoption. The aim of this study was to enhance the efficiency and durability of such cells under ambient conditions. To elucidate whether cells with small-molecule donor materials provide higher benefits and opportunities than cells with polymer donor materials, this study compares the electrical parameters of cells with both types of donor materials. OSCs based on 7,7′-(4,4-bis(2-ethylhexyl)-4H-silolo[3,2-b:4,5-b′]dithiophene-2,6-diyl)bis(6-fluoro-4-(5′-hexyl-[2,2′-bithiophene]-5-yl)benzo[c][1,2,5]thiadiazole): [6,6]-Phenyl C71 butyric acid methyl ester (p-DTS(FBTTh2)2:PC70BM) and 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]]: [6,6]-Phenyl C71 butyric acid methyl ester (PTB7:PC70BM) were manufactured and their electrical characteristics under ambient conditions determined after various time intervals. Numerical simulations based on the metal–insulator–metal (MIM) model were then performed to optimize the performance of the cells and to analyze their internal electrical dynamics in detail. The findings of this study reveal a direct relationship between solar cell degradation and the anode interface, thus enhancing understanding of the degradation mechanisms that occur in OSCs.


Introduction
Solar energy has emerged as a highly promising renewable energy technology due to its abundance and widespread availability.Until now, solar cells based on inorganic materials have dominated the market; however, intrinsic limitations related to the cost, flexibility, and environmental sustainability of these cells have spurred the quest for innovative alternatives, and organic solar cells (OSCs) have thus garnered substantial interest [1][2][3][4][5].However, despite notable advances, there are also challenges associated with OSCs, with degradation being a primary concern due to its adverse impact on the efficiency and operational lifespan of the cells.The degradation mechanisms that occur in OSCs are complex and are associated with a range of factors, such as environmental conditions, material quality, and device architecture.Understanding these mechanisms and developing strategies to mitigate them constitute a critical ongoing area of research [6][7][8][9][10][11][12][13][14].
Numerical simulation has become an essential tool for describing and interpreting the complex physical processes intrinsic to the operation of solar cells, including the generation, diffusion, recombination, and collection of charge carriers.Electrical models provide a simplified yet robust framework that explains the electrical behavior of solar cells under various operational conditions.These models play a fundamental role in predicting solar cell performance and in the optimization of their design to enhance efficiency.In the context of solar cells, numerical simulation and electrical models are thus indispensable resources for exploring new materials and technologies [18][19][20][21].
To reveal the parameters of a solar cell that are influenced by the degradation of organic materials under environmental conditions, this study investigated small-molecule inverted bulk heterojunction organic solar cells (SM-iOSCs) along with polymer solar cells for comparison.The electrical characteristics and degradation of the cells were analyzed via numerical simulations of their current-voltage (J-V ) characteristics.The cell donor materials consisted of either p-DTS(FBTTh 2 ) 2 or PTB7; PC 70 BM served as the acceptor material in the active layer in both cases.Poly [(9,9-bis(3'-(N, N-dimethylamino)propyl)-2,7-fluorene)-alt-2,7-(9,9-dioctylfluorene)] (PFN) and vanadium oxide (V 2 O 5 ) formed the electron transport layer and the hole transport layer, respectively, and indium tin oxide (ITO) and silver (Ag) were used for the electrodes.The electrical characteristics of the cells were measured under the standard AM 1.5 G spectrum.
Although the performances of both small-molecule and polymer cells degrade over time, the deteriorations differ under factors related to the molecular structures of the two materials.We demonstrate that cells based on small-molecule donor materials notably reduce the rate of cell degradation compared with those based on polymer donor materials.

Method
In this study, the following two inverted organic photovoltaic structures based on different donor materials were fabricated.
Small molecule: ITO/PFN/p-DTS(FBTTh 2 ) 2 : PC 70 BM/V 2 O 5 /Ag Polymer: ITO/PFN/PTB7: PC 70 BM/V 2 O 5 /Ag The details of how these devices were fabricated are described in [22,23].The devices were encapsulated between glass plates that were sealed using NOA 68 UV-curing adhesive.The devices were then studied at ambient conditions (a temperature of (23 ± 2) °C and a relative humidity of (50% ± 5)%).The current-voltage (J−V ) curves for the two OSCs were obtained under the standard AM 1.5 G spectrum and one-sun (100 mW cm −2 ) illumination conditions; the effective cell area was 9 mm 2 in both cases.
The J-V characteristics were simulated using two methods.Data related to the electric charge transport through the heterostructure were obtained by performing drift-diffusion simulations using the Silvaco/ATLAS TCAD simulator.Additional information on the primary factors influencing the electrical performance of OSCs was obtained through simulations using the three-diode equivalent circuit model (figure 1) and the tanh function-based approach.The simulation parameters of the material were kept constant while the anode work function (WF anode) and electron mobility of the charge carriers (μ e ) for the former method were varied.The values of the energy gap (E gap ) and thickness of the active layer (τ) were derived from experimental data previously obtained by our research group.The optical energy gaps for both types of solar cells were calculated by extrapolating the linear portion of the graph of (αhυ) ½ versus hυ using the Tauc method [24,25].
An alternative method of accurately simulating the J−V characteristics in both J and S forms, specifically tailored for modern solar cells that exhibit various types of current kinks, was proposed by Huang et al [18].The method is based on P. J. Roland's three-diode equivalent circuit model, complemented by a strategic regional approach designed to circumvent the necessity for iterative algorithms.As shown in figure 1, the terminal voltage (V ) of the equivalent circuit model is formulated as where This approach involves determining V 1 and V 2 .V 1 can be found analytically by employing the principal branch of the Lambert W 0 function when x > 0: For this purpose, we require the reverse saturation currents J 01 , J 02 , and J 03 and the ideality factors n 1 , n 2 , and n 3 representing the deviations from the ideal diode characteristics of D 1 , D 2 , and D 3 , respectively.The thermal voltage V t is equal to kT/q, where k is the Boltzmann constant, T is the absolute temperature, and q is the electron charge.The shunt resistance R sh represents the leakage current across the PN junction of a conventional solar cell, while the resistance R p enables the simulation of J-V characteristics with current kinks, allowing the creation of J-shaped and S-shaped curves.
In contrast, V 2 generally eludes analytical solution due to the combined effect of the exponential and linear terms in equation (4).However, for specific operational domains, namely, V 2 < 0 V and V 2 > 0 V, there exist asymptotic solutions that can be derived analytically.Furthermore, V 2 can be expressed using the following piecewise function: In this study, an alternative approach based on the use of the hyperbolic tangent function (tanh) was used.Unlike the method proposed by Huang et al this approach does not make use of the Schröder series.
The tanh function is well-suited for delineating gradual transitions owing to its sigmoidal shape, which enables smooth shifts between states.The computational simplicity of the tanh function also renders it an attractive choice, potentially offsetting the Schröder series, despite some slight differences in precision in specific scenarios.
We can express V 2 using the following expression, which is applicable across all operating regimes: In circuit simulation, the iterative assessment of the application of model equations to diverse operational scenarios is a recurring necessity.A more streamlined model can expedite simulations and accommodate complex circuitry.In this context, the computational efficiency of the tanh function is an advantage.

Results and discussion
Figure 2 shows the experimental J-V curves for the small-molecule solar cell structure together with those simulated based on the drift-diffusion model at different times: 0 h, 1344 h, 2376 h, 3360 h, and 5832 h.A notable agreement between the simulated and experimental curves can be seen in the fourth quadrant for operating voltages in the range 0.0-0.8V, and there are no S-shaped kinks in the curves.The simulations yielded the following electrical performance values for the fresh (0-h) cell: short-circuit current (Jsc) = 14.91 mA cm −2 , open-circuit voltage (Voc) = 0.806 V, fill factor (FF) = 0.54, and power conversion efficiency (PCE) = 6.53%.These parameter values are consistent with those reported in our previous study [22].
The measured values show a decrease in all performance parameters over the period of the experiment, indicating a decline in the ability of the small-molecule solar cell to function effectively over an extended period.Specifically, the short-circuit current decreases by 12.27%, reflecting a reduction in the capacity of the cell to produce a current under conventional lighting conditions.V OC decreases by only 3.23%, whereas the FF drops by 26.12%-a significant decrease.This reduction suggests a decline in the operational efficiency of the solar cell, which affects its overall power-generating capability, as evidenced by the decrease in the PCE of 36.45% by 5832 h.The electrical performance parameters of the small-molecule solar cell after different time intervals are listed in table S1 in the Supplementay Material.
The simulated J-V curves were obtained by adjusting the work function of the silver metal (WF Ag) and the electron mobility (μ e ) while keeping the work function of the ITO material constant.The other simulations parameters where the effective densities of states in the valence and conduction bands (N V and N C , respectively), the separation distance between electrons and holes (a.singlet), decay rate (Knrs.exciton),singlet-exciton binding energy (s.binding), scale factor of the photogeneration rates (b1), and hole mobility (μ h ).
Over the operational period, from the initial measurement at 0 h to 5832 h, the simulated performance parameters of the OSC show significant changes (see table 1).
These changes again signal a degradation in the electrical properties of the cell and a decline in the efficiency of the conversion of solar energy into electrical energy.The initial value of WF anode is 5.145 eV, and this value remains constant until 1344 h, suggesting stability during the initial phase of the life of the solar cell.However, from 2376 h onwards, there is a gradual decline in WF anode to 5.08 eV at 5832 h.This decrease in the work function may be attributable to factors such as changes in the surface state of the anode material, a buildup of surface contaminants, or interfacial changes at the anode layer.A decrease in the work function implies that the energy barrier to electron injection increases, potentially impeding the efficient extraction of charge carriers and reducing Voc.
The electron mobility (μ e ) exhibits a more pronounced decrease from 7.00 × 10 −5 cm 2 /Vs at 0 h to 9.50 × 10 −6 cm 2 /Vs at 5832 h.This marked decrease suggests degradation of the transport pathways, possibly due to morphological changes in the active layer or the formation of traps that impede the flow of electrons.As electron mobility is related to the current generation and FF, this drop could be significantly contributing to the overall efficiency loss.The hole mobility (μ h ) also experiences a decrease, albeit to a lesser extent, from 1.10 × 10 −5 cm 2 /Vs at 0 h to 8.20 × 10 −6 cm 2 /Vs at 5832 h.This relatively modest reduction in hole mobility may indicate a less severe impact on the hole transport.However, any imbalance between electron transport and hole transport can result in charge accumulation, increased recombination, and a subsequent decrease in Jsc and the overall PCE.
Figure 3 depicts the experimental and simulated J-V curves for the inverted polymer solar cell for the voltage range 0.0-0.7 V. Substantial differences can be observed between the efficiency parameters of the polymer cell and the small-molecule cell (see table S2 in the Supplementary material).The polymer cell has a higher initial Jsc of 18.31 mA cm −2 , but this subsequently decreases rapidly to 12.64 mA cm −2 over a period of 5856 h.Voc initially remains stable, but subsequently decreases significantly to 0.57 V.There is also a significant deterioration in the FF and PCE of the polymer cell, with the FF dropping from 70.68% to 25.50% and the PCE decreasing from 9.28% to 0.20%.Notably, the solar cell measurements performed at 3912 and 5856 h show an S-shaped anomaly in the J-V curves, indicating considerable degradation in the performance of the polymer cell.This anomaly is accompanied by a substantial drop in the values of all the electrical parameters compared with their initial values.In contrast, the small-molecule solar cell exhibits a gradual decline in efficiency, which may be attributable to its inherent robustness against degradation over time.
The stability of Voc across various degradation stages can be attributed to the robustness of electrode materials and their interfaces.It has been established that Voc is primarily determined by the potential difference between the electrodes of a solar cell.In our configurations, the V 2 O 5 /Ag and ITO/PFN interfaces exhibited outstanding stability as unaffected by environmental exposure and operational stress, highlighting the effective preservation of the charge-extraction efficiency at the interfaces.Although the polymer solar cell exhibits higher initial values of Jsc and PCE, the decline in its performance is more rapid than the small-molecule solar cell, possibly because of its material properties and susceptibility to operational stresses such as oxidation or   morphological instability.The considerable decline observed in Jsc is primarily attributed to the deterioration of the active layer within the solar cells.Over time, operational stresses lead to the accumulation of defects that serve as traps, impeding the free movement of charge carriers and reducing the current generation efficiency.Concurrently, the active layer materials undergo photo-oxidation and other chemical changes that compromise their electronic properties.These chemical alterations further degrade the ability of the active layer to effectively generate and transport charge.Additionally, morphological changes disrupt established pathways for charge transport, further diminishing the efficiency of current generation.This compound degradation is evident in the data presented in tables S1 and S2, which show a considerable reduction in Jsc.The stability of Voc indicates that the electrode energetics remain largely unaffected, while the decline in Jsc is a result of increased recombination rates and reduced mobility of charge carriers, highlighting the extensive degradation of the active layer.Based on the PCE values after 5000 h of exposure to the environment, it can be inferred that the active layer of the smallmolecule solar cell suffers less degradation than the polymer cell.The S-shaped kink in J-V curves has been associated with different effects, including: (1) a reduction in the extraction efficiency of charge carriers due to the formation of a barrier at the contacts; (2) the formation of interfacial dipoles due to the creation of defects and traps; and (3) the accumulation of charge on the electrode surface due to an imbalance between the mobility of the holes and electrons [26][27][28][29][30].These effects were noted by Tress et al [31] after performing drift-diffusion simulations.It was observed that the S-shaped kink appears in J-V curves due to an imbalance between electron mobility and hole mobility, with a mismatch factor of ≈100.In figure 4, the carrier mobility is plotted against time.In the case of the polymer device, after 3912 h, there is a significant drop in the electron mobility (see table 2), and after 5856 h, the electron and hole mobility differ by two orders of magnitude; this results in the appearance of the S-shaped kink in the J-V curve (figure 3).In contrast, in the case of the small-molecule device,   both the hole mobility and electron mobility values remain of the same order throughout the experiment; consequently, the S-shaped kink does not appear.A deeper insight into the primary factors influencing the FF of various OSC devices was conducted for nonideal illuminated J-V curves by applying the three-diode lumped-parameter equivalent circuit model introduced by Huang et al [18].The polymer solar cell displayed the most significant decrease in the FF, with its J-V curves adopting an S-shaped profile after 3912 h of exposure to ambient conditions.The results shown in table 3 indicate that the reduction in the FF for this device can be attributed to the increase in the series resistance (Rp + Rs).A significant increase in Rp from 1 Ω to 415 Ω and a decline in Rsh from 1.3×10 3 Ω to 643.2 Ω were observed, which suggests an increase in parasitic losses and leakage currents.The small-molecule devices exhibited notable fluctuations in Rp and increases in Rsh at specific intervals, implying that these cells mitigated the leakage currents under certain conditions; however, the reduction in the FF cannot be explained by considering only the increase in the series resistance since, as shown in table 4, there is no clear correspondence between the increase in this resistance and the decrease in the FF.This parameter can, however, also be affected by a reduction in the charge carrier mobility, which leads to a longer carrier extraction time and a higher probability of bimolecular recombination [32].Simulations of polymer solar cells indicate a reduction in the electron mobility confirming that the behavior of the FF is related to both the increase in resistance and the reduction in mobility.In a compound system consisting of small molecules and fullerenes, such as p-DTS(FBTTh 2 ) 2 :PC 70 BM, one cause of the low FF is the inhomogeneous distribution of the donor and acceptor components.Since the surface energy of the conjugated small molecule (p-DTS(FBTTh 2 ) 2 ) is substantially lower than that of the fullerenes (PC 70 BM), the surface exposed to the air is almost exclusively composed of the conjugated small molecule, whereas the fullerenes tend to be deposited on the substrate; this blocks the charge transport and produces a greater barrier to the injection of charge [33].
An analysis of the behavior of the diode ideality factor, n 1 , within the active layer of each cell type revealed differences in the degradation mechanisms.For example, the pronounced increase in n 1 in the small-molecule cells (see table 4) suggests an increase in the amount of recombination within the active layer [22].Indeed, according to the research of Ko Kyaw et al [34], the lower FF value and trap-assisted recombination in the p-DTS(FBTTh 2 ) 2 molecule are directly linked.
To complement the analysis of the cells, we compared the chemical structures of p-DTS(FBTTh 2 ) 2 and PTB7 (diagrams can be consulted on the manufacturer web site).Research by Manceau et al [35,36] suggests three general rules that relate photodegradation to chemical structure.(1) Donor monomers with side chains are more susceptible to photodegradation.The polymer PTB7 has three side chains in its structure, whereas the small molecule p-DTS(FBTTh 2 ) 2 has only one.(2) Molecules containing carbon-nitrogen (C-N) or carbon-oxygen (C-O) single bonds are less stable.PTB7 contains three C-O single bonds, whereas the p-DTS(FBTTh 2 ) 2 molecule does not contain any.(3) Replacing carbon atoms with silicon atoms at the side chain junction improves oxidative stability.In the p-DTS(FB TTh 2 ) 2 molecule, one of the carbon atoms is replaced by a silicon atom.Therefore, it can be considered that the chemical structure of p-DTS(FBTTh 2 ) 2 also helps to give the small-molecule solar cell greater stability than the polymer solar cell containing PTB7.The J-V characteristics simulated using the three-diode lumped-parameter equivalent circuit model reasonably agreed with the experimental curves obtained from both the small-molecule solar cell (see figure S1, Supplementary Material) and the polymer solar cell (see figure S2).

Conclusion
The results of this study indicate that small-molecule solar cells are more stable than polymer solar cells under similar operating conditions.While polymer cells may have a slightly higher initial efficiency, small-molecule cells retain more of their initial performance over time, suggesting that they may be a more dependable option for long-term use.Initially, the solar cells exhibited a short-circuit current (Jsc) of 14.91 mA cm −2 , an opencircuit voltage (Voc) of 0.806 V, a fill factor (FF) of 54.40%, and a power conversion efficiency (PCE) of 6.53%.
In this study, the metal-insulator-metal (MIM) model was used to investigate the internal electrical dynamics of organic solar cells (OSCs).This allowed a comprehensive examination of the complex physical processes, such as generation, diffusion, recombination, and collection of charge carriers, that occur in OSCs.For the small-molecule and the polymer solar cells, the simulation results were consistent with the J-V characteristics found in the experiments.This underscores the critical role that numerical simulations plays in predicting and enhancing the performance of solar cells as they allow the values of parameters such as the metal work function and electron mobility, in case of simulations based on drift-diffusion equations, to be adjusted while maintaining constant values of, for example, the energy gap and the thickness of the active layer.
The degradation analysis highlights the considerable challenges associated with maintaining solar cell performance over time, as evidenced by the substantial reduction in the electron mobility of the small-molecule OSC from 7.00 × 10 −5 cm 2 /Vs in the new cell to 9.50 × 10 −6 cm 2 /Vs after 5832 h.The polymer device also exhibited a notable decline in the FF, and its J-V curves developed an S-shape by 3912 h.This suggests a significant degradation in performance that affects the ability of the polymer device to efficiently convert solar into electrical energy.
In contrast, the decrease in the FF observed in the case of the small-molecule solar cell was less severe than would be expected based only on a consideration of the increase in series resistance.This slight decline indicates that a different underlying mechanism is present.Specifically, in small-molecule cells, the obvious increase in the diode ideality factor, n 1 , suggests that enhanced recombination processes occur within the device.The information provided by the simulations based on the three-diode equivalent circuit model made it possible to obtain these results.

Figure 1 .
Figure 1.Three-diode equivalent circuit of an organic solar cell.

Figure 2 .
Figure 2. Experimental (symbols) and simulated (solid lines) J-V curves for the small-molecule solar cell.

Figure 3 .
Figure 3. Experimental (symbols) and simulated (solid lines) J-V curves for the inverted polymer solar cell.

Figure 4 .
Figure 4. Carrier mobility obtained from the drift-diffusion simulations for (a) the small-molecule device and (b) the polymer device.

Table 1 .
List of parameter values used in the drift-diffusion simulation of the small-molecule solar cell.

Table 2 .
List of parameter values used in the drift-diffusion simulations of the inverted polymer solar cell.

Table 3 .
Values obtained by applying the three-diode lumped-parameter equivalent circuit model to the polymer OSC.

Table 4 .
Values obtained by applying the three-diode lumped-parameter equivalent circuit model to the small-molecule OSC.