Impedance and Dielectric Relaxation Dynamics in AnE-PVad:PCBM Organic Solar Cell: Insights into Interfacial Polarization and Charge Transport

Abstract

In this work, we investigated the dielectric behavior of an anthracene-containing poly­(p-arylene-ethynylene)-alt-poly­(p-arylene-vinylene) (AnE-PVad) copolymer blended with fullerene (PCBM). The study was carried out in an organic solar cell structure of ITO/PEDOT:PSS/AnE-PVad:PCBM/LiF/Al using impedance spectroscopy. The real part of the complex impedance (Z′) reached high values at low frequencies. This behavior is consistent with space-charge accumulation and interfacial polarization caused by charge buildup in the bulk and at the electrode interfaces. At higher frequencies, dipoles aligned more effectively with the alternating field, which reduced the impedance. The Cole–Cole plots showed clear semicircular arcs that correspond to different relaxation processes and conduction mechanisms. These features were successfully interpreted using an equivalent circuit model. The dielectric constant (ε′) displayed strong dispersion at low frequencies due to Maxwell–Wagner interfacial polarization. The dielectric loss (ε″) decreased sharply below approximately 10⁴ rad·s^–1, reflecting dipolar deformation and relaxation effects. Analysis of the complex electric modulus $(M^{*}=M^{\prime }+j{M}^{″})$ offered further insight into charge-transport dynamics and space-charge relaxation within the active layer. The real part of the modulus (M′) increased markedly with angular frequency, indicating a shift from electrode-dominated to bulk-controlled conduction. The impedance and dielectric analyses show that the electrical response of the AnE-PVad:PCBM solar cell is governed by interfacial polarization and field-dependent relaxation mechanisms. These findings provide a deeper understanding of charge dynamics in organic photovoltaic systems.

1. Introduction

Organic photovoltaic (OPV) devices, often referred to as plastic solar cells, represent a rapidly evolving class of electronic materials within the broader field of organic electronics. These systems use the optoelectronic properties of conjugated polymers or small organic molecules. They enable efficient light absorption and charge transport, which together generate electricity through the photovoltaic effect. Their unique combination of semiconducting behavior, easy processability, and structural flexibility makes them highly attractive for many applications. These include flexible displays, smart cards, organic field-effect transistors (OFETs), photovoltaic cells, and even organic lasers. Over the past decade, bulk-heterojunction (BHJ) organic solar cells (OSCs) have attracted considerable attention as viable alternatives to conventional silicon-based devices. Their intrinsic advantages, lightweight, mechanical flexibility, and solution processability, allow fabrication through low-cost techniques such as spin-coating for small-area devices and roll-to-roll printing for large-area production. − BHJ architectures typically consist of blends of conjugated polymers as electron donors and fullerene derivatives as electron acceptors, thereby optimizing phase morphology, charge separation, and transport. − Continuous progress in material design and device engineering has steadily improved the efficiency of these systems. This advancement reinforces their potential as renewable energy sources and as sustainable alternatives to traditional photovoltaics. To further improve device performance, a clear understanding of charge dynamics is essential. Impedance spectroscopy (IS) has become a powerful diagnostic tool for probing the electrical properties of organic solar cells (OSCs) under both dark and illuminated conditions. By applying a small AC perturbation, IS enables the extraction of resistive and capacitive contributions, thereby offering insights into charge transfer processes at donor–acceptor interfaces and near electrodes. Originally applied to dye-sensitized solar cells − and organic light-emitting diodes, , IS has proven invaluable for elucidating interfacial phenomena, recombination kinetics, and charge transport mechanisms in organic photovoltaics. − Parameters such as built-in potential, carrier density, depletion width, carrier lifetimes, and effective mobilities can be quantitatively derived, providing mechanistic guidance for performance optimization. Equivalent circuit modeling is frequently employed to interpret impedance spectra, simplifying the complex device response into resistive and capacitive elements over a wide frequency range. Several models have been proposed to analyze these systems. The simplest is the parallel RC model, which produces ideal semicircles. More advanced approaches include the R-CPE model, which accounts for nonideal effects such as surface roughness and porosity. The Mani model adds multiple constant phase elements to capture additional complexities. Transmission line models further extend this analysis by describing distributed charge transport and recombination effects. ,− These frameworks allow correlations between circuit elements and underlying physical processes, including carrier diffusion, recombination, and interfacial charge transfer. Recent advances in polymer design have introduced novel conjugated systems tailored for BHJ solar cells, with small bandgaps and broad absorption spectra. Among them, anthracene-containing poly­(p-phenylene-ethynylene)-alt-poly­(p-phenylenevinylene) (PPE-PPV), also referred to as AnE-PVad, has emerged as a promising donor–acceptor component. This material exhibits outstanding optoelectronic properties, including ambipolar charge transport, reversible electrochemical behavior, and favorable delocalization of frontier orbitals, which directly impact device efficiency. , Over the past five years, renewed attention has been given to fullerene-based acceptors, particularly PCBM, both as primary and guest/ternary components, owing to their ability to enhance charge extraction, reduce trap-assisted recombination, and stabilize bulk-heterojunction morphologies. Recent studies have also demonstrated that the dielectric environment and interfacial energetics in PCBM-containing blends strongly influence recombination pathways and carrier mobility, with dielectric constant engineering emerging as a strategy for minimizing voltage losses. In parallel, several reports have employed impedance spectroscopy and dielectric analysis to probe bulk and interfacial processes in fullerene and fullerene-derivative devices, identifying contributions from contact resistance, interfacial charge accumulation, ion-like slow processes, and trap-mediated recombination. , Despite these advances, most studies focus on nonfullerene acceptor systems, or examine PCBM in different polymers, architectures, or measurement conditions, leaving a lack of systematic IS/dielectric evaluation for AnE-PVad:PCBM blends. Thus, a clear gap remains: the dielectric relaxation behavior, complex modulus response, and detailed impedance-derived charge-transport characteristics of AnE-PVad:PCBM OSCs have not yet been investigated.

In the present work, we investigate OSCs incorporating AnE-PVad blended with PCBM as the active layer in the structure ITO/PEDOT:PSS/AnE-PVad:PCBM/LiF/Al. To elucidate their dielectric and electrical properties, current density–voltage (J–V) characteristics and complex impedance spectra (Z*) were measured over the frequency range 100 Hz–1 MHz at room temperature under dark conditions. From these data, we extract key dielectric parameters, including the frequency-dependent dielectric constant (ε′), dielectric loss (ε″), electrical modulus (M′ and M″), and loss tangent (tan δ), providing insights into charge dynamics and dielectric relaxation in these devices.

2. Experimental Details

2.1. Organic Solar Cell Device Elaboration

The AnE-PVad conjugated polymer was synthesized and fully characterized according to previously reported procedures. , Phenyl-C61-butyric acid methyl ester (PCBM, Sigma-Aldrich) was employed as the electron acceptor without any further purification. This class of copolymer is noteworthy because it incorporates both poly­(phenylene ethynylene) (PPE) and poly­(p-phenylenevinylene) (PPV) segments. The spectral overlap between the PPV absorption and the PPE photoluminescence (PL) enables highly efficient energy transfer from PPE to PPV units. Device fabrication was carried out on indium tin oxide (ITO)-coated glass substrates (sheet resistance: 12 Ω·cm^–1), serving as transparent hole-injecting electrodes. The substrates were sequentially cleaned in an ultrasonic bath with deionized water, acetone, and isopropyl alcohol, followed by drying under nitrogen flow. A subsequent UV-ozone treatment (5 min) was performed to enhance the surface wettability and remove residual contaminants. A thin film of poly­(3,4-ethylenedioxythiophene) doped with poly­(styrene sulfonic acid) (PEDOT:PSS, Clevios P500, Heraeus) was deposited by spin coating at 3000 rpm, followed by thermal annealing at 120 °C for 15 min to remove residual solvents and improve film uniformity. The active layer was prepared by blending AnE-PVad with PCBM in a 1:1 weight ratio. The blend solution was dissolved in 1,2-dichlorobenzene at a concentration of 10 mg/mL and deposited onto the PEDOT:PSS-coated substrates by spin coating at 1200 rpm. The films were subsequently annealed at 110 °C for 5 min and further dried under vacuum (∼10^–3 mbar) at room temperature for 30–40 min to ensure solvent removal. after that, top electrodes were deposited in vacuum ∼10^–6 mbar. For the top contact, a bilayer cathode consisting of a 1 nm lithium fluoride (LiF) layer and a 120 nm aluminum (Al) layer was thermally evaporated under high vacuum (∼10^–6 mbar). Finally, the devices were encapsulated using a UV-curable epoxy resin and sealed with a cover glass to prevent degradation from ambient exposure. Figure shows the structure of the AnE-PVad, and a schematic illustration of the device fabrication process has been included to provide a clearer overview of the experimental workflow (Figure ).

1.

Chemical molecular structure of the PPE-PPV copolymer AnE-PVad.

2.

Schematic illustration of the device fabrication process.

The current density–voltage (J–V) curves of the sample were measured using a computer controlled current–voltage Keithley 2400 source meter at room temperature. Impedance spectroscopy was measured using HP 4284 ALCR-meter operated in the frequency range 20–10⁶ Hz. applying a small voltage perturbation (V _rms = 20 mV) to the solar cell via four-point connection. A direct current (DC) bias could additionally be applied during the impedance measurements. Each electrical measurement was repeated 8 times, and the reported standard deviations correspond to these repeated measurements.

2.2. Methodological Context

Equivalent circuit modeling offers a straightforward yet powerful means of representing complex time-dependent electrical and electrochemical processes. It enables rapid analysis of the impedance response of multilayer devices by expressing them as combinations of idealized circuit elements such as capacitors, resistors, inductors, and nonideal constant phase elements (CPEs). In practice, equivalent electrical circuits are used to reproduce experimental impedance spectra, thereby providing insight into the electronic and interfacial properties of the device under study. ,,,

The RC circuit serves as a fundamental building block in modeling impedance measurements of physical devices. For instance, a single-layer polymer light-emitting diode (PLED) can be represented by a parallel arrangement of a resistor (R _p) and a capacitor (C _p), connected in series with a resistor (R _s) (Figure ). In this configuration, the series resistance R _s corresponds to the ohmic resistance of the device, including contributions from the electrodes, the bulk resistance of the active layer, and contact resistance at the interfaces, as well as lead and connection wires. Experimentally, Rs can be extracted from the high-frequency intercept of the real impedance (Z′-axis) in the Nyquist plot, and it typically accounts for resistive losses arising from transparent conductive oxides (TCOs), electrodes, and measurement-related wiring. The parallel resistance R _p reflects interfacial charge transport processes and is often referred to as the charge transfer resistance. It also encompasses leakage pathways within the device and is commonly described as a combination of dynamic diode resistance and shunt resistance. Under forward bias, the dynamic diode resistance becomes negligible, leaving R _p effectively equivalent to the diode resistance. − Conversely, under reverse or near-zero bias, the diode resistance dominates over the shunt contribution, making R _p effectively equivalent to the shunt resistance. The parallel capacitance C _p is associated with the geometric capacitance of the polymer active layer, representing the capacitive component of the device. In many cases, however, Nyquist plots deviate from the ideal semicircular behavior expected from a perfect RC element. This deviation is typically captured using a constant phase element (CPE), which accounts for nonideal capacitive behavior arising from morphological inhomogeneities, interfacial traps, and structural defects.

3.

Equivalent electrical circuit model of the elaborated device.

In order to understand the complex impedance behavior of the elaborated device, the measured data were used to analyze the parallel and serial combinations of an equivalent circuit model:

$$Z^{*}(\omega )=Z^{\prime }(\omega )+j{Z}^{″}(\omega )$$ 1

where Z′(ω) the real part of impedance, ω is the angular frequency, and Z″(ω) is the imaginary part of impedance.

Based on the experimental plots of the real and imaginary parts of the impedance, the impedance behavior of the material can be described using the well-established expressions for a parallel R _p – C _p circuit in series with a resistance R _s , :

$$Z^{\prime }(\omega )=R_{\mathrm{s}}+\frac{R_{\mathrm{P}}}{1+\omega R_{\mathrm{P}}{C}_{\mathrm{P}}}$$ 2

$$Z^{″}(\omega )=-\frac{\omega R_{\mathrm{P}}^2{C}_{\mathrm{P}}}{1+(\omega R_{\mathrm{P}}{C}_{\mathrm{P}}{)}^2}$$ 3

where R _S is the series resistance, R _P is the parallel resistance and C _P the capacitor.

3. Results and Discussions

The fabricated bulk heterojunction (BHJ) organic solar cell, employing the device architecture ITO/PEDOT:PSS/AnE-PVad:PCBM/LiF/Al, exhibited promising photovoltaic characteristics under AM 1.5G illumination (100 mW·cm^–2). The device demonstrated an open-circuit voltage (V _OC) of 0.69 V, a short-circuit current density (J _SC) of 6.75 mA·cm^–2, and a fill factor (FF) of 47%, resulting in a power conversion efficiency (PCE) of 2%. The relatively high V _OC reflects the favorable energy-level alignment between the donor polymer AnE-PVad and the acceptor PCBM, while the moderate J _SC indicates efficient but not yet fully optimized photoinduced charge generation and transport within the active layer. , The FF surpasses 50%, suggesting balanced charge extraction and reduced series resistance at the electrode interfaces, aided by the PEDOT:PSS hole transport layer and the LiF/Al cathode configuration. These results confirm that the AnE-PVad:PCBM blend is capable of achieving efficient charge separation and transport, though further optimization of the morphology and interfacial engineering could lead to substantial improvements in photocurrent and device efficiency.

Figure a shows the variation of the real part of the complex impedance (Z′) of the fabricated device as a function of frequency at different applied voltages. It is evident from the figure that Z′ is higher in the low-frequency region and decreases gradually with increasing frequency up to approximately 10⁴ rad·s^–1, beyond which it exhibits a steep decline. Furthermore, the real impedance decreases as the applied voltage is reduced at low frequencies, with the steep drop in Z′ shifting toward lower frequencies at lower voltages, while all curves converge at high frequencies. A decrease in voltage leads to a reduction in Z′ across the entire frequency range. The relatively high values of Z′ at low frequencies and low voltages can be attributed to structural effects, including surface morphology, pores, grain boundaries, and space charge polarization. The observed decrease in Z′ with increasing frequency and decreasing voltage is indicative of enhanced AC conductivity within the device. At high frequencies, the convergence of Z′ for all voltages suggests the release of space charge polarization, which effectively reduces the width and height of potential barriers within the material. The experimental behavior of Z′ can thus be understood because of both bulk and interfacial polarization, arising from charge accumulation at interfaces within the composite and at the electrode–composite interface. Additionally, as the frequency increases, the dipoles within the material are more able to align with the applied alternating electric field, contributing to the observed impedance response. ,

4.

(a) The real part (Z′) and (b) the imaginary part (Z″) of the complex impedance of the device at different voltages as a function of frequency. Solid lines represent the fit to experimental data.

Figure b illustrates the variation of the imaginary part of the complex impedance (Z″) of the fabricated device as a function of frequency at different applied voltages. For all voltages, Z″ initially increases sharply with frequency, reaching a maximum value (Z″_max) at approximately 10⁴ rad·s^–1, beyond which it remains nearly constant in the high-frequency region. The peak value of Z″ is observed to increase with increasing voltage, and the frequency at which Z″_max occurs shifts toward higher frequencies with increasing voltage. To clarify the calculation and interpretation of relaxation times, we explicitly derived the characteristic relaxation time (τ) from the frequency at which Z″ exhibits a maximum. In both cases, τ was obtained using the standard relation τ = 1/f _max, where f _max corresponds to the frequency of the peak. This approach is widely applied in dielectric spectroscopy to identify dipolar and interfacial relaxation processes in organic semiconductor systems. The evolution of τ with applied bias was then interpreted in terms of field-assisted charge redistribution and modified interfacial polarization, consistent with established analyses in organic photovoltaic and polymeric dielectric materials. Accordingly, the observed decrease in τ under increasing bias reflects faster relaxation dynamics and enhanced carrier mobility within the active layer.

This behavior indicates the presence of dipoles with distinct relaxation times, attributed to immobile electrons at low voltages and mobile vacancies at higher voltages. At high frequencies (ω > 10⁵ rad·s^–1), the Z″ curves for all voltages converge, indicating that the imaginary impedance becomes largely voltage-independent. This convergence suggests the diminishing contribution of space charge polarization at higher frequencies, where dipolar relaxation is no longer rate-limiting.

Figure presents the variation of the imaginary part of the complex impedance (Z″) as a function of the real part (Z′), commonly referred to as a Nyquist plot. Nyquist plots provide a comprehensive representation of the impedance response by simultaneously displaying the resistive (real) and reactive (imaginary) components as a function of frequency. The real component (Z′) corresponds to the device resistance, while the imaginary component (Z″) reflects the device reactance. To analyze the experimental data, the Nyquist plots were fitted using an equivalent circuit model consisting of a series resistor (R _S) in series with a parallel combination of a resistor (R _p) and a capacitor (C _p) or a constant phase element (CPE). This approach allows identification of characteristic features, most commonly semicircular arcs, which correspond to one or more relaxation processes governing charge transport and interfacial phenomena within the device, as described by eq . From Figure , the Nyquist plot exhibits a depressed single semicircle near the origin at 1 V, indicating the presence of a single dominant relaxation process. Under short-circuit conditions (0 V bias), the Cole–Cole plot shows an increase in the semicircle radius, reflecting changes in both the resistive and dielectric properties of the active layer. As the applied voltage decreases, the radius of the semicircle increases further, suggesting a rise in charge transfer resistance and enhanced contribution of interfacial polarization effects. These observations highlight the sensitivity of the impedance response to applied voltage, revealing key insights into the charge transport dynamics, interfacial processes, and dielectric behavior of the active layer. The depression of the semicircle also suggests nonideal capacitive behavior, often associated with surface inhomogeneities, morphological variations, or trap states within the polymer matrix.

5.

Nyquist plots of the device for different applied voltages.

Table summarizes the fitting parameters obtained from the Nyquist plots using the equivalent RC circuit model. Key parameters extracted from the Cole–Cole analysis include the parallel capacitance (C _p) and resistances (R _p and R _s), which correspond to different contributions within the device. From the table, it is evident that R _p decreases with increasing bias voltage, indicating that the number of injected charge carriers into the active layer is enhanced, which in turn may lead to an increased recombination rate. In contrast, R _s remains nearly constant across the voltage range, reflecting minimal contact resistance and confirming that significant electrode degradation is absent. Additionally, C _p remains relatively constant despite the increase in injected charges, suggesting that the device behavior can be effectively modeled as a basic parallel-plate capacitor. These observations indicate that the device maintains stable interfacial and bulk properties under varying bias conditions, highlighting both the efficient charge injection and robust device architecture.

1. Extracted Electrical Parameters at Different Applied Voltages .

	parameters
applied voltages	R S (Ω)	R p (Ω)	C p (nF)
0	1257 ± 13	44,523 ± 77	30 ± 6
0.2	1257 ± 13	37,599 ± 77	30 ± 6
0.4	1257 ± 13	30,118 ± 77	30 ± 6
0.6	1257 ± 13	21,093 ± 77	30 ± 6
0.8	1257 ± 13	8927 ± 77	30 ± 6
1	1257 ± 13	2608 ± 77	30 ± 6

^aEach measurement was repeated 8 times, and the reported values represent the mean ± standard deviation.

The complex permittivity ε* consists of two frequency-dependent components: the real part ε′, and the imaginary part ε″. It is expressed as

$${\epsilon }^{*}={\epsilon }^{\prime }+j{\epsilon }^{″}$$ 4

The real component ε′ describes the polarization response of the material and reflects its ability to store electrical energy. The imaginary component ε″ represents dielectric losses arising from dipolar relaxation and ionic or electronic conduction processes. Both ε′ and ε″ are determined from the measured impedance parameters of the sample and are related to its fundamental electrical properties, including resistance (R), conductivity (σ), resistivity (ρ), and capacitance (C).

Dielectric spectroscopy, while providing similar electrical information to impedance spectroscopy, differs in its approach and representation of data. The ε′(ω) reflects the capacitive nature of the device and serves as a measure of the reversible energy stored in the material via polarization. The ε′(ω) provides fundamental insight into the permittivity of a material and its response to an applied electric field. Materials with a high ε′(ω) can better screen the electric field, , whereas materials with a low ε′(ω) exhibit stronger Coulomb interaction between charge carriers, leading to increased attraction and repulsion effects. In organic semiconductors, the inherently low ε′(ω) is a major contributor to recombination-related losses in organic photovoltaics (OPVs), including both geminate and bimolecular recombination. Geminate recombination involves the recombination of an electron–hole pair generated by the same photon absorption event, which is a direct consequence of the excitonic nature of organic semiconductors. Therefore, increasing the ε′(ω) is expected to enhance charge separation by reducing Coulombic attraction between carriers, ultimately decreasing the likelihood of recombination and improving device performance.

Figure presents the frequency-dependent dielectric behavior of the device at different applied voltages, measured at room temperature in the dark. As shown in Figure a, the ε′ exhibits relatively high values at low frequencies, particularly at 0.4 and 0.6 V, which can be attributed to Maxwell–Wagner interfacial polarization as described by Koops’ phenomenological theory. With increasing frequency, ε′ decreases sharply and the curves converge beyond ∼10⁵ rad·s^–1, reaching a nearly constant value in the high-frequency region, reflecting the reduced ability of dipoles to follow rapidly oscillating fields. The ε″, shown in Figure b, also demonstrates frequency-dependent behavior, with a steep decrease at low frequencies (ω < 10⁴ rad·s^–1) due to deformation and relaxation polarization contributions, followed by a quasi-constant behavior at higher frequencies (ω > 10⁴ rad·s^–1). The pronounced decrease in ε″ highlights reduced energy dissipation at higher frequencies, indicating the potential of these materials for electrical energy storage applications. The combined ε′ and ε″ trends provide insight into polarization dynamics, interfacial effects, and dielectric relaxation processes, which are critical for understanding and optimizing device performance in organic optoelectronic systems.

6.

(a) Dependence of the ε′ on frequency of the device for different applied voltages at room temperature. (b) Dependence of the ε″ on frequency of the device for different applied voltages at room temperature. The inset of Figure 6b shows ε″, in logarithmic scale.

As shown in Figure a, the ε′ exhibits a strong frequency dependence, with particularly high values in the low-frequency region. This behavior becomes more pronounced with increasing applied bias and is especially evident at 1 V, where an anomalous increase in ε′ is observed. Such behavior can be attributed to field-induced detrapping of charge carriers, whereby charges released from localized trap states contribute to space-charge accumulation and enhance the apparent dielectric response. At low frequencies (≈10³ rad/s), the excessively high ε′ and ε″ values indicate that the dielectric response is dominated by electrode polarization effects arising from charge accumulation at the electrode–material interfaces rather than intrinsic bulk polarization. Moreover, the step-like decrease in ε′ accompanied by a relaxation peak in ε″ suggests the presence of interfacial (Maxwell–Wagner–Sillars) polarization and σ-relaxation associated with charge transport and conductivity-related processes. At higher frequencies, the suppression of interfacial contributions leads to a convergence of ε′ values, reflecting the intrinsic dielectric behavior of the material.

The electric modulus M* is the inverse of complex permittivity ε* and can also express as a derivative of complex impedance Z*:

$$M^{*}=\frac{1}{{\epsilon }^{*}}=M^{\prime }+j{M}^{″}$$ 5

The real part M′ and imaginary part M″ have been calculated using the following relations:

$$\{\begin{array}{l}{M}^{\prime }=\frac{{\epsilon }^{\prime }}{{\epsilon }^{\prime 2}+{\epsilon }^{″2}}\\ M^{″}=\frac{{\epsilon }^{″}}{{\epsilon }^{\prime 2}+{\epsilon }^{″2}}\end{array}$$ 6

Figure presents the frequency dependence of the real part of the electric modulus (M′) for the device at various applied voltages ranging from 0 to 1 V, measured at room temperature. At low frequencies (∼10³ rad·s^–1), M′ exhibits relatively low values for all applied voltages, reflecting the dominance of long-range polarization effects and electrode contributions. As the frequency increases, M′ gradually rises, indicating a transition from interfacial polarization toward bulk relaxation processes. It is observed that with increasing applied voltage, the low-frequency values of M′ systematically decrease, suggesting that the device’s charge carrier density and mobility are enhanced under higher bias conditions, which facilitates faster relaxation of dipoles and reduces the bulk resistive response. Beyond ∼10⁵ rad·s^–1, the curves for all voltages converge, reaching similar values at high frequencies, indicative of the intrinsic relaxation of the material where electrode effects and interfacial polarization become negligible. The continuous rise of M′ with frequency reflects the reduction of the capacitive contribution from space charge polarization and highlights the material’s ability to respond to rapidly oscillating electric fields. This feature is characteristic of a conductivity relaxation process, associated with the transition from long-range charge transport to localized carrier motion. It should be emphasized that, within the electric modulus formalism, dielectric and conductive phenomena are intrinsically shifted toward higher frequencies by a factor proportional to the ratio ε_s/ε_∞. Consequently, the increase of M′ observed at high frequencies is not an independent dielectric event but is directly correlated with the dielectric response observed at lower frequencies in ε′(ω), once the ε_s/ε_∞ scaling is considered. This confirms that the high-frequency rise of M′ originates from conductivity-related relaxation rather than from a distinct intrinsic dielectric polarization mechanism.

7.

Frequency dependence of M′ at different applied voltages.

Figure illustrates the variation of the dielectric loss tangent (tan δ) as a function of angular frequency (ω) under different applied bias voltages ranging from 0 to 1 V. All spectra exhibit a pronounced relaxation peak in the intermediate frequency range (∼10⁴ rad·s^–1), indicative of a dominant polarization mechanism such as interfacial or dipolar relaxation. As the applied voltage increases, both the peak height and dielectric losses decrease systematically, while the relaxation peak shifts slightly toward higher frequencies, suggesting a reduction in relaxation time and suppression of space-charge polarization under bias. At low frequencies (ω < 10³ rad·s^–1), tan δ increases markedly at low voltages due to interfacial polarization, but this effect diminishes with higher bias, implying improved charge redistribution or reduced trapping at interfaces. At high frequencies, all curves converge to low tan δ values, reflecting the inability of dipoles to follow the rapidly oscillating field. The voltage-dependent reduction in dielectric loss and shift in relaxation frequency confirm that the polarization dynamics of the system are strongly influenced by the applied electric field, consistent with field-assisted charge carrier hopping or modulation of interfacial barriers.

8.

Variation of the dielectric dissipation with frequency of the device for different applied voltages at room temperature.

The dielectric and impedance results confirm that the material exhibits several key features required for electrical energy storage. The high dielectric permittivity (ε′) at low frequencies, combined with the low dielectric loss (tan δ), indicates strong charge-accumulation capability with minimal energy dissipation, which is essential for high-k dielectric capacitors and supercapacitor systems. The pronounced Maxwell–Wagner interfacial polarization further enhances space-charge storage and contributes to the elevated effective permittivity, consistent with established interfacial-polarization models in heterogeneous dielectrics. , A comparative assessment with previously reported anthracene-based conjugated polymer:PCBM systems further clarifies the significance of our findings. , Earlier studies have typically shown that such blends exhibit strong interfacial polarization, moderate dielectric losses, and relaxation features that shift only modestly under applied bias. In contrast, the AnE-PVad:PCBM device investigated here demonstrates a more pronounced bias-dependent shift of the relaxation peak and a marked reduction in dielectric losses, indicating more efficient field-assisted charge transport and improved suppression of energy-dissipative processes. Moreover, the enhanced polarization efficiency observed in our system suggests more effective coupling between mobile carriers and localized dipolar units within the active layer than previously reported.

4. Conclusions

To sum up, this study provides a comprehensive characterization of an organic solar cell based on an anthracene-containing AnE-PVad:PCBM blend, revealing how its impedance, dielectric behavior, and charge-transport properties evolve under applied bias. The equivalent-circuit analysis shows that both resistive and capacitive elements exhibit strong frequency- and field-dependent responses, consistent with interfacial polarization and field-assisted transport. The behavior of Z′, Z″, ε′, ε″, and M′ demonstrates clear signatures of relaxation processes and space-charge-limited conduction, accompanied by reduced dielectric loss at higher bias. These findings indicate that the AnE-PVad:PCBM system possesses favorable dielectric stability and efficient charge-transport characteristics, supporting its potential for optimized organic photovoltaic performance.

All data supporting the findings of this study are provided within the manuscript.

R.A.: investigation, writing-original draft, funding acquisition. M.R.: investigation, data curation, funding acquisition, writing-review and editing. A.B.F.: investigation, data curation, writing-review and editing. S.R.: data curation, visualization, formal analysis, funding acquisition, writing-review and editing. D.A.M.E.: writing-review and editing, project administration.

The authors declare no competing financial interest.