Plasmonic vortex-coupled forward emission (PVCFE): a novel light coupling mechanism in aluminium nanostructures for high-efficiency, stable, and cost-effective organic photovoltaics

Abstract

The dual challenge of enhancing power conversion efficiency (PCE) while ensuring long-term stability is paramount for the commercial viability of organic photovoltaics (OSCs). This work confronts these challenges by identifying a novel, material-dependent light coupling mechanism—termed plasmonic vortex-coupled forward emission (PVCFE)—and embedding it within a holistically designed, stable, and cost-effective device architecture. Through a rigorous multiphysics simulation workflow that accurately isolates useful optical generation from parasitic losses, we discover that non-noble metal nanostructures like aluminium (Al) support complex, hybridized plasmon modes. Phase-resolved electromagnetic field analysis reveals that PVCFE involves the synchronous coupling of a vortical near-field with a directional energy channeling component, which actively “pumps” optical energy deep within the organic active layer. Harnessing this discovery, we computationally designed and optimized an inverted OSC based on a high-performance PTB7:PC₇₁BM active layer with a robust AZO ETL and a chemically inert graphite anode. The final, optimized Al-core/Al₂O₃-shell enhanced device is predicted to exhibit a remarkable 57% relative increase in PCE, reaching a simulated 9.34% compared to the 5.95% intrinsic baseline. This breakthrough is driven by a massive 55.8% increase in short-circuit current to 18.09 mA cm⁻², stemming from the PVCFE mechanism and estimated hot carrier contributions, while impressively maintaining the fill factor. Our findings suggest that Al is a potentially superior plasmonic material for high-performance OSCs and introduce PVCFE as a new design paradigm for engineering light–matter interactions in nanophotonic devices.

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1 Introduction

The global imperative for a sustainable energy future has intensified research into next-generation photovoltaic technologies capable of delivering clean power at a low cost.¹ Organic solar cells (OSCs) represent a highly promising frontier, offering unique advantages such as solution-processability, mechanical flexibility, and lightweight design.² These features make them ideal for emerging applications from wearable electronics to building-integrated photovoltaics, although significant challenges in device stability and efficiency still need to be overcome to achieve widespread commercialization.³ Despite significant progress, the power conversion efficiencies (PCEs) of OSCs are often constrained by incomplete light absorption within their characteristically thin active layers, a limitation imposed by short exciton diffusion lengths and modest charge carrier mobilities of organic semiconductors.^4,5

To overcome the absorption bottleneck, advanced light management is essential. The strategic use of polymers and nanostructures continues to be a vibrant area of research for pushing the performance limits of OSCs.⁶ Plasmonics, which harnesses the resonant interaction of light with collective electron oscillations in metallic nanostructures, has emerged as a particularly powerful approach for enhancing light–matter interactions.^7,8 However, the field has been overwhelmingly dominated by noble metals like gold (Au) and silver (Ag), whose prohibitive cost and scarcity fundamentally challenge the low-cost premise of organic photovoltaics, creating a critical need to identify and understand earth-abundant plasmonic alternatives.^7,9

Aluminium has emerged as a particularly compelling candidate, with a growing body of experimental work demonstrating its multifaceted benefits. Seminal studies showed that incorporating Al nanoparticles (NPs) into the active layer could yield superior PCE enhancements compared to noble metals, with early work attributing this to improved spectral overlap and increased charge separation at the donor–acceptor interface.^10,11 Subsequent research has reinforced these findings, showing significant PCE boosts in PTB7:PC₇₁BM systems by leveraging the localized surface plasmon resonance of Al NPs embedded in the anode buffer layer.¹² Critically, beyond just efficiency, the integration of Al NPs has been proven to confer a dramatic advantage in device longevity, extending the operational lifetime of OSCs by up to fivefold by enhancing the structural stability of the active blend and mitigating photo-oxidation.^13,14 Concurrently, theoretical explorations by Bagheri into Fe-core/ZnO-shell nanostructures predicted, via optical simulations, that iron could also achieve competitive absorption enhancement over gold, reinforcing the hypothesis that non-noble metals operate via distinct and potentially more advantageous light-coupling mechanisms.¹⁵ Yet, despite compelling evidence for Al's benefits to efficiency and stability, a deep, unifying physical understanding of why it so effectively couples and redistributes light within the solar cell cavity has remained elusive.

A significant hurdle in accurately assessing and comparing these plasmonic enhancers has also been methodological. Many computational studies rely on metrics that conflate useful photon absorption within the active layer with parasitic absorption within the metallic nanostructures themselves, leading to potentially inflated performance predictions. Furthermore, beyond direct optical enhancement, plasmon decay is a quantum process that generates energetic “hot” carriers within the metal. This offers a parallel pathway to boost photocurrent, and the fundamental science and application of hot carrier dynamics remains a topic of intense current investigation in fields from photocatalysis to photodetectors.^16–19

This study confronts these challenges through a comprehensive multiphysics investigation that bridges the gap between prior experimental observations and fundamental plasmonic theory. We introduce and validate a rigorous “four core” simulation workflow that employs spatial masking to accurately calculate direct optical generation (G_{opt_direct}) and a phenomenological model to estimate hot carrier contributions (G_{hot_carrier}). Applying this methodology, we uncover a novel, material-dependent light coupling mechanism, which we term “plasmonic vortex-coupled forward emission” (PVCFE). Phase-resolved electromagnetic field analysis reveals that this mechanism, prominent in Al, involves the synchronous coupling of a vortical near-field with a directional energy channeling component, which “pumps” optical energy deep into the active layer. This is fundamentally different from the asynchronous, near-surface enhancement of noble metals. Harnessing this discovery, our simulations establish aluminium as optically superior to silver and gold in the studied OSC architectures. Finally, we leverage these insights to design and optimize a high-performance, cost-effective inverted OSC—ITO/AZO/PTB7:PC₇₁BM (with Al–Al₂O₃ NPs)/PEDOT:PSS/graphite—that fully exploits the PVCFE. The final simulated device is predicted to achieve a power conversion efficiency of 9.34%, a remarkable 57% relative enhancement over its intrinsic baseline, driven by a massive increase in short-circuit current from the synergistic action of PVCFE and hot carrier contributions. This work provides a new physical framework for understanding non-noble metal plasmonics and presents a clear design pathway toward ultra-high efficiency, low-cost organic solar cells.

2 Theoretical framework

The performance of the nanostructure-enhanced organic solar cells is analysed through a multiphysics framework that combines classical electromagnetic theory with semiconductor device physics. This section outlines the essential theoretical models for light absorption, carrier generation (including direct optical and plasmon-induced hot carrier pathways), and charge transport.

2.1 Optical modelling of nanostructured media

The interaction of light with the device is modelled by solving Maxwell's equations using the finite-difference time-domain (FDTD) method. The material-specific response at optical wavelengths (λ) is governed by the complex relative permittivity, ε_r(r,λ) = (n(r,λ) + ik(r,λ))², which dictates the local dispersive and absorptive properties.^20,21

The local time-averaged power absorption density, P_abs(r,λ), is derived from the Poynting theorem and is given by:²²

where ε″(r,λ) is the imaginary part of the permittivity, |E(r,λ)|² is the local electric field intensity, c is the speed of light, and ε₀ is the vacuum permittivity. This equation forms the basis for calculating all photon absorption events.

The direct optical carrier generation rate, G_{opt_direct}(r), within the primary semiconductor active layer is calculated assuming each absorbed photon with energy greater than the material's bandgap (E_g,active) generates one electron–hole pair:²³

Here, P_{abs_active}(r,λ) represents the power absorption density occurring exclusively within the semiconductor volume, normalized to the AM1.5G solar spectrum, and h is Planck's constant.

2.2 Plasmon-induced hot carrier generation

In addition to enhancing G_{opt_direct}, the decay of localized surface plasmons in the metallic nanostructures generates energetic “hot” carriers.^16,24 This non-radiative decay creates a non-equilibrium distribution of hot electrons and holes within the metal. Before thermalization, these hot carriers may traverse an ultrathin dielectric shell and inject into the semiconductor, providing a parallel pathway for photocurrent generation.^25,26

The total current density contribution from this mechanism, J_{sc_hot_carrier}, is phenomenologically estimated as:^27,28

where P_{abs_metal_NP} is the total power absorbed by a single metallic core under AM1.5G illumination, E_{avg_photon_hc} is an effective average photon energy, N_{density_NP} is the nanostructure areal density, and η_{hc_conversion} and η_{hc_injection} are the critical internal efficiencies for hot carrier generation in the metal and subsequent injection into the semiconductor, respectively. These efficiencies are estimated based on established literature and account for the metal's electronic structure, interface barrier properties, and shell thickness.^29–31 For device simulation, this J_{sc_hot_carrier} is converted into an equivalent spatially distributed generation profile, G_{hot_carrier}(r), localized at the nanostructure/semiconductor interface.

2.3 Electrical modelling of device performance

The solar cell's electrical characteristics are modelled by solving the coupled semiconductor drift-diffusion equations under steady-state conditions.^32,33 This framework includes the Poisson equation and the electron/hole continuity equations:³⁴

∇·(ε(r)∇ψ(r)) = −q[p(r) − n(r) + N_D⁺(r) − N_A⁻(r) + ρ_trap(r)] (4)

Here, ψ(r) is the electrostatic potential, p(r) and n(r) are the free carrier concentrations, ε(r) is the static permittivity, and U(r) is the net carrier recombination rate. The total generation rate, G_total = G_{opt_direct} + G_{hot_carrier}(r), serves as the source term. The electron (J_n) and hole (J_p) current densities are described by the drift-diffusion model, accounting for carrier motion due to both electric fields and concentration gradients.³²

The net recombination rate, U(r), incorporates contributions from trap-assisted Shockley–Read–Hall (SRH) and bimolecular (Langevin or radiative) recombination processes, which are the dominant loss mechanisms in the organic semiconductors studied.³⁵ Auger recombination is considered a secondary effect and is not included in this model. By solving this system of equations with appropriate boundary conditions at the contacts, the device's current density–voltage (J–V) characteristic is obtained, from which all key performance metrics (J_sc, V_oc, FF, PCE, and EQE) are determined.

3 Computational methods

This section details the numerical simulation methodologies used to implement the theoretical models from Section 2, beginning with the optical FDTD framework and the “four core” data processing workflow used to determine the final carrier generation profiles.

3.1 Optical simulation workflow: FDTD and the “four core” model

3.1.1 FDTD simulation environment. All electromagnetic simulations were performed using the finite-difference time-domain (FDTD) method via Ansys Lumerical FDTD Solutions. A 3D simulation domain modelling a single unit cell of the nanostructure array was used, with periodic boundary conditions on the x- and y-axes and perfectly matched layers (PMLs) on the z-axis. A plane wave source, weighted for the AM1.5G solar spectrum (250–3000 nm), was injected under normal incidence. A non-uniform mesh with high resolution (1–2 × 1–2 × 1–2 nm³) was employed in and around the nanostructures to ensure accurate field representation, with a simulation time (100 fs) and auto-shutoff criteria (1 × 10⁻⁶) set for full field convergence.

To identify the optimal geometric configuration for maximizing device performance, a particle swarm optimization (PSO) algorithm was employed. The algorithm iteratively adjusts a population of candidate solutions (“particles”) within a multi-dimensional parameter space, with each particle's movement influenced by its own best-known position and the best-known position of the entire swarm.^36–38 The objective function for the optimization was the maximization of the J_sc. This automated search was further refined by manual fine-tuning based on the physical insights and trends identified during the optimization process.

3.1.2 The “four core” generation profile workflow. A central contribution of this work is an advanced computational workflow, termed the “four core script model,” used to derive an accurate total carrier generation profile, G_total(r), for subsequent electrical device simulation. This workflow, executed via coupled Lumerical and Python/MATLAB scripts, is visually mapped onto the device architecture in Fig. 1 and detailed below as a step-by-step process:

Fig. 1 Schematic of the multiphysics simulation workflow. The “four core” model is mapped onto the physical device structure. Core 1 calculates raw absorption including parasitic losses in the nanostructure. Core 2 applies a spatial mask to isolate the useful direct optical generation (G_{opt_direct}) in the semiconductor. Core 3 estimates the hot carrier generation (G_{hot_carrier}) from power absorbed in the metal core. Core 4 superimposes these profiles to create the final total generation rate (G_total) for electrical simulation.

Core 1 raw optical absorption calculation: a 3D frequency-domain monitor is used to record the electric fields and material indices throughout the geometric domain of the active layer. From this, the raw, spectrally-resolved power absorption density, P_abs(r,λ), is calculated based on eqn (1). This is then converted to an AM1.5G-normalized raw optical generation rate, G_{opt_raw}, which at this stage includes contributions from all materials within the monitor (semiconductor, metal, shell).

Core 2 spatial masking for G_{opt_direct}: the G_{opt_raw}(r) data is processed by applying a 3D spatial mask based on the precise geometry of the nanostructures. Generation rate values within the volumes of the non-semiconducting metallic cores and dielectric shells are rigorously set to zero. The result is the direct optical generation profile, G_{opt_direct_semiconductor}eqn (2), which accurately represents carrier generation occurring only within the primary semiconductor absorber.

Core 3 G_{hot_carrier} estimation & superposition: first, the total AM1.5G-normalized power absorbed solely within the metallic core of a single nanostructure, P_{abs_metal_NP} (Watts), is calculated using a separate, tightly-bound FDTD monitor. This value serves as the input to the phenomenological hot carrier model (eqn (3)), which estimates the device-level hot carrier current density, J_{sc_hot_carrier}, based on the efficiencies (η) specified in Section 3.3. This J_sc is then converted into a uniform volumetric generation rate, G_{hot_carrier_local}, and spatially distributed within the previously defined nanostructure mask volume.

Core 4 G_total superposition & final processing: the final total generation rate is computed by superimposing the two distinct generation profiles:

G_total(r) = G_{opt_direct_semiconductor}(r) + G_{hot_carrier_local}(r) (6)

For simulations of asymmetric nanostructures under unpolarized light, this entire workflow (cores 1–4) is performed independently for two orthogonal polarizations (e.g., transverse electric, TE, and transverse magnetic, TM). The final generation rate is then taken as the average:

Finally, the 3D G_total(r) profile is laterally averaged to produce the 1D G_total(z) profile required for device simulation.

3.2 Materials optical database (n, k data)

The complex refractive indices (n and k) as a function of wavelength (λ) for all materials used in the optical simulations were obtained from experimental literature or established databases. Fig. 2 graphically presents the n(λ) and k(λ) spectra for the key semiconductor and transparent conductive oxide (TCO) layers (a) and (b), and the metallic components (c) and (d). Specifically: the material stack includes an indium tin oxide (ITO) anode,³⁹ a poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) HTL,⁴⁰ and two active semiconductor layers: poly(3-hexylthiophene-2,5-diyl):[6,6]-phenyl-C61 butyric acid methyl ester blend (P3HT:PCBM),⁴¹ 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]]:phenyl-C₇₁-butyric acid methyl ester blend (PTB7:PC₇₁BM).⁴¹ The ETLs studied were zinc oxide (ZnO)⁴² and aluminium-doped zinc oxide (AZO).⁴³ The refractive indices for the metals iron (Fe),⁴⁴ gold (Au),⁴⁵ silver (Ag),⁴⁴ aluminium (Al),⁴⁶ copper (Cu),⁴⁵ and platinum (Pt)⁴⁷ were sourced from the cited literature. Data for aluminum oxide Al₂O₃ shell and glass (SiO₂) were modelled using Palik²¹ from the Lumerical material database, while data for graphite was taken from ref. 48.

Fig. 2 Optical constants used in the FDTD simulations. Real (n) and imaginary (k) parts of the complex refractive index as a function of wavelength for: (a) and (b) key semiconductor and transparent conductive layers, and (c) and (d) metallic components. Data sourced from the references cited in Section 3.2.

3.3 Hot carrier generation estimation parameters

The injection efficiency (η_{hc_injection}) depends critically on the ultrathin dielectric shell, which serves to prevent charge recombination at the metal surface while allowing for hot carrier tunnelling. For this study, a 2 nm shell is used. We model a self-passivating Al₂O₃ shell for aluminium nanoparticles, which is known to form naturally. For all other metals, zinc oxide (ZnO) is chosen as a representative, stable, and wide-bandgap dielectric shell, consistent with previous theoretical explorations and its common use as an electron transport layer.

The phenomenological model for estimating the hot carrier current density contribution (J_{sc_hot_carrier}, eqn (3)) requires several key parameters. The total AM1.5G-normalized power absorbed within a single metallic core (P_{abs_metal_NP}) is directly calculated from the FDTD simulations (Section 3.1.2), and the nanostructure areal density (N_{density_NP}) is defined by the simulated array periodicity. The critical efficiency parameters η_{hc_conversion} (internal plasmon-to-energetic-carrier conversion) and η_{hc_injection} (injection through the dielectric shell) are estimated based on a careful review of foundational theoretical and experimental literature. It is emphasized that these efficiencies are highly sensitive to nanoscale geometry, interface chemistry, and material quality; therefore, the values used represent reasoned estimates for an optimized system, intended to explore the relative potential impact of the hot carrier pathway for different materials. An effective average photon energy of E_{avg_photon_hc} ≈ 1.7–2.0 eV is assumed, representing the energetic portion of the solar spectrum that drives plasmon excitation.^24,25,27 The specific efficiencies for each metal, detailed in Table 1, are justified as follows:

Table 1 Estimated hot carrier efficiency parameters used in the phenomenological model (eqn (3))

Metal	η hc_conversion	η hc_injection	E avg_photon_hc (eV)
Fe	0.30	0.20	2.0
Au	0.20	0.10	2.0
Al	0.30	0.20	1.7
Cu	0.15	0.10	2.0
Ag	0.40	0.10	2.0
Pt	0.20	0.15	2.0

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The efficiency of generating energetic hot carriers (η_{hc_conversion}) is fundamentally dictated by the metal's electronic density of states (EDOS) near the Fermi level.²⁹ For Ag, strong intraband transitions in the visible spectrum make it the most efficient generator of energetic hot electrons, justifying a high η_{hc_conversion} of 0.40.^29,30 In contrast, Au and Cu are dominated by d-band interband transitions for much of the visible spectrum, a process that primarily yields energetic hot holes but low-energy hot electrons. Consequently, their η_{hc_conversion} for generating useful hot electrons is estimated to be very low, whereas for hot holes, a more moderate value of 0.20–0.15 is used.^29,30 Aluminium, with its more free-electron-like EDOS, can support energetic carrier generation via both intraband and interband (>1.5 eV) transitions, warranting a high estimated efficiency of 0.30.²⁹ Transition metals with complex d-bands, Fe and Pt, are predicted to generate both energetic electrons and holes under broadband solar illumination;²⁹ their efficiencies are estimated at 0.30 and 0.20 respectively, reflecting this potential balanced against increased scattering pathways common in d-band metals.^16,17,49

The injection efficiency (η_{hc_injection}) depends critically on the ∼2 nm dielectric shell (Al₂O₃ for Al, ZnO for others). Based on theoretical models of tunnelling across such thin barriers and the quality of self-passivated interfaces,³¹ Al is assigned a high potential η_{hc_injection} of 0.20. Fe and Pt, given their potential for favorable interface energetics with ZnO, are assigned a strong η_{hc_injection} of 0.20 and 0.15, respectively (with platinum's value being slightly lower because its dominant injection pathway is hot holes, which are less efficiently extracted when injected into the n-type ETL, whereas iron and aluminium are highly efficient injectors of both electrons and holes²⁹). For Au and Cu, a more conservative 0.10 is used, informed by experimental work showing low overall device efficiencies for Au/TiO₂ systems.³⁰ Silver's injection efficiency is estimated conservatively at 0.10, as experimental work suggests that injection can be a significant bottleneck despite the high energy of its hot electrons.^30,31

To address the inherent uncertainty in these literature-derived efficiency parameters, a comprehensive parametric sensitivity analysis was performed. The results, presented in the SI (Fig. 6), demonstrate how the estimated hot carrier J_sc varies with the total conversion and injection efficiency. This analysis confirms that the relative performance ranking of the materials is robust and primarily dictated by their intrinsic optical absorption properties.

3.4 Electrical device simulation

The final electrical performance of the solar cell was simulated using the SCAPS-1D device simulator (v.3.3.07, University of Gent),⁵⁰ which numerically solves the fundamental semiconductor device equations. The one-dimensional total generation profile, G_total(z), derived from our comprehensive “four core” workflow, was imported to model the creation of charge carriers. The simulation solves the coupled Poisson, continuity, and drift-diffusion equations (eqn (4) and (5)) to generate the device's current density–voltage (J–V) characteristics under steady-state AM1.5G illumination (1000 W m⁻²) at 300 K.

This work focuses on a high-performance inverted architecture: ITO/AZO/PTB7:PC₇₁BM (with Al/Al₂O₃ NPs)/PEDOT:PSS/graphite. Table 2 details the full set of material and electrical parameters used to model each layer in this stack. These parameters were carefully selected and optimized based on extensive review of established experimental literature to construct a model that is both physically realistic and representative of a high-quality device.⁵¹ Standard series (1 Ω cm²) and shunt (5000 Ω cm²) resistances were used.

Table 2 Material and electrical parameters for the SCAPS-1D simulation of the final inverted PTB7:PC₇₁BM solar cell

Parameter	Unit	ITO (cathode)	AZO (ETL)	PTB7:PC71BM (active)	PEDOT:PSS (HTL)	Graphite (anode)
Global parameters: thermal velocity for all e^−/h^+ = 1 × 10^7 cm s^−1; interface defect capture cross-sections for all = 1 × 10^−19 cm^2.
Thickness	nm	80	20	130	40	(Contact)
Bandgap (Eg)	eV	3.7^39,51	3.2^52	1.65^53	1.77^54	N/A
Electron affinity (χ)	eV	4.5^39	4.3^52	3.70^53	3.3^54	N/A
Rel. permittivity (εr_static)		9.0^39	9.0^52	3.8^53	3.5^54	N/A
Effective DoS (Nc)	cm^−3	2.2 × 10^18	2.2 × 10^18	2.5 × 10^19	2.5 × 10^19	N/A
Effective DoS (Nv)	cm^−3	1.8 × 10^19	1.8 × 10^19	2.5 × 10^19	2.5 × 10^19	N/A
Mobility (μn/μp)	cm^2 V^−1 s^−1	30/10	1/0.1	2 × 10^−3/4 × 10^−4	1 × 10^−4/5 × 10^−3	N/A
Doping (ND/NA)	cm^−3	1 × 10^20 (ND)	1 × 10^19 (ND)	1.7 × 10^16 (NA)	1 × 10^19 (NA)	N/A
Defect density (Nt)	cm^−3	1 × 10^14	1 × 10^14	1 × 10^14	1 × 10^14	N/A
Contact work function	eV	4.5^39	N/A	N/A	N/A	4.8^55
Interface defects (AZO/active)	cm^−2	—	—	1 × 10^12	—	—
Interface defects (active/HTL)	cm^−2	—	—	—	5 × 10^12	—
Interface defects (ITO/AZO)	cm^−2	5 × 10^11	—	—	—	—

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The parameters in Table 2 were chosen to create a realistic model of a high-performance inverted organic solar cell. The inverted p–i–n architecture (ITO/ETL/active/HTL/anode) was selected for its proven high efficiency and operational stability with modern organic blends.⁵⁶

Active layer (PTB7:PC₇₁BM): we employ an experimentally verified optical bandgap of 1.65 eV.⁵³ A crucial aspect of this model is treating the active layer not as purely intrinsic, but as a lightly p-doped semiconductor with a shallow acceptor density of N_A = 1.7 × 10¹⁶ cm⁻³. This approach models the real-world characteristics of a polymer blend where unintentional doping and small internal gradients exist, allowing for a more accurate prediction of device physics. The charge carrier mobilities of μ_n = 2 × 10⁻³ cm² V⁻¹ s⁻¹ and μ_p = 4 × 10⁻⁴ cm² V⁻¹ s⁻¹ were chosen to be representative of well-optimized blend morphologies known to facilitate high performance.⁵⁷

Charge transport layers: an aluminium-doped zinc oxide (AZO) layer serves as the electron transport layer (ETL). The parameters for AZO (E_g = 3.2 eV, χ = 4.3 eV) are chosen to reflect a conductive, n-type TCO that forms an efficient electron-selective contact with a favorable energy cascade from the active layer's LUMO (∼−3.7 eV).⁵⁸ On the anode side, a heavily p-doped PEDOT:PSS is used as the hole transport layer (HTL). Critically, an experimentally validated electronic bandgap of 1.77 eV was used,⁵⁴ which, combined with its electron affinity of 3.3 eV, creates a HOMO level of ∼−5.07 eV, providing an excellent energetic match for hole extraction from PTB7's HOMO.

Contacts and interfaces: a cost-effective graphite back contact is used as the anode. Its work function of 4.8 eV forms a near-ohmic contact with the PEDOT:PSS HTL, ensuring a minimal barrier for hole extraction.⁵³ The ITO front contact (cathode) has a work function of 4.5 eV, well-aligned with the AZO ETL for electron collection.^39,50,51 To create a realistic model that accounts for primary loss mechanisms, recombination at interfaces was included. Significant defect densities (N_it) were introduced at the critical AZO/active layer (1 × 10¹² cm⁻²) and active layer/HTL (5 × 10¹² cm⁻²) interfaces to account for potential chemical and morphological imperfections that are common in solution-processed devices.⁵⁹

This comprehensive and physically grounded set of parameters establishes a robust baseline for investigating the impact of plasmonic enhancement on a realistically modelled, high-performance OSC.

4 Results and discussions

4.1 Foundational investigation: a refined analysis of plasmonic enhancement in P3HT:PCBM organic solar cells

Our investigation commences by applying our advanced multiphysics modelling workflow to a P3HT:PCBM based organic solar cell, an architecture that has been instrumental in foundational plasmonics research. This serves to validate our methodology against established systems and to uncover the nuanced physical mechanisms that govern the performance of cost-effective plasmonic materials like Al and Fe. The device architecture, nanostructure dimensions, and material properties are based on the optimized design previously reported by Bagheri,¹⁵ with updated, high-accuracy optical constants for all materials.

4.1.1 Quantitative evaluation of enhancement mechanisms via the “four core script model”. To quantitatively dissect the performance of various plasmonic materials, the results from our “four core” simulation workflow are summarized in Table 3. The table is categorized by the progressive application of the analysis cores: an initial unmasked calculation (core 1), followed by a rigorously masked evaluation of direct optical generation (core 2), and finally, the inclusion of estimated hot carrier contributions (core 3) which are then combined with the direct generation via core 4 to yield the final total performance. The intrinsic reference device, a planar P3HT:PCBM cell with an Al back cathode, yields a calculated J_{sc_opt_direct} of 10.14 mA cm⁻², serving as the primary benchmark.

Table 3 Quantitative breakdown of short-circuit current density (J_sc) contributions for the P3HT:PCBM device, calculated using the “four core” workflow. C1: unmasked raw generation. C2: masked direct optical generation. C3/C4: masked optical generation plus estimated hot carrier contribution, combined to produce the final total

Analysis	Structure		J sc_opt_direct (mA cm^−2)	Injected HC (carriers per s per NP)	J sc_hot_carrier (mA cm^−2)		J total (mA cm^−2)
C1:ON	Intrinsic	6.328 × 10^20	10.14	—	—	6.328 × 10^20	10.14
C2:OFF	ZnO	5.675 × 10^20	9.09	—	—	5.675 × 10^20	9.09
C3:OFF	Al–ZnO	9.706 × 10^20	15.55	—	—	9.706 × 10^20	15.55
C4:OFF	Fe–ZnO	1.022 × 10^21	16.38	—	—	1.022 × 10^21	16.38
	Au–ZnO	8.198 × 10^20	13.14	—	—	8.198 × 10^20	13.14
	Ag–ZnO	8.056 × 10^20	12.91	—	—	8.056 × 10^20	12.91
	Cu–ZnO	8.514 × 10^20	13.64	—	—	8.514 × 10^20	13.64
	Pt–ZnO	1.032 × 10^21	16.54	—	—	1.032 × 10^21	16.54
C1:ON	Intrinsic	6.328 × 10^20	10.14	—	—	6.328 × 10^20	10.14
C2:ON	ZnO	5.292 × 10^20	8.48	—	—	5.292 × 10^20	8.48
C3:OFF	Al–ZnO	7.379 × 10^20	11.82	—	—	7.379 × 10^20	11.82
C4:OFF	Fe–ZnO	5.617 × 10^20	9.00	—	—	5.617 × 10^20	9.00
	Au–ZnO	5.743 × 10^20	9.20	—	—	5.743 × 10^20	9.20
	Ag–ZnO	6.665 × 10^20	10.68	—	—	6.665 × 10^20	10.68
	Cu–ZnO	5.649 × 10^20	9.05	—	—	5.649 × 10^20	9.05
	Pt–ZnO	5.997 × 10^20	9.61	—	—	5.997 × 10^20	9.61
C1:ON	Intrinsic	6.328 × 10^20	10.14	—	—	6.328 × 10^20	10.14
C2:ON	ZnO	5.292 × 10^20	8.48	—	—	5.292 × 10^20	8.48
C3:ON	Al–ZnO	7.379 × 10^20	11.82	9.78 × 10^5	0.928	7.958 × 10^20	12.75
C4:ON	Fe–ZnO	5.617 × 10^20	9.00	1.75 × 10^6	1.661	6.654 × 10^20	10.66
	Au–ZnO	5.743 × 10^20	9.20	2.08 × 10^5	0.197	5.867 × 10^20	9.40
	Ag–ZnO	6.665 × 10^20	10.68	7.79 × 10^4	0.074	6.712 × 10^20	10.75
	Cu–ZnO	5.649 × 10^20	9.05	1.82 × 10^5	0.173	5.757 × 10^20	9.22
	Pt–ZnO	5.997 × 10^20	9.61	8.55 × 10^5	0.811	6.504 × 10^20	10.42

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The initial unmasked analysis (“C1” row set) calculates the apparent J_sc by converting all photon absorption within the active layer's geometric domain—including absorption within the metallic nanostructures—into carrier generation. This method, common in preliminary optical studies, yields significantly inflated current densities, particularly for highly absorbing metals like Pt (16.54 mA cm⁻²) and Fe (16.38 mA cm⁻²). While providing an upper limit of total light interaction, this approach fails to distinguish between useful generation in the P3HT:PCBM and parasitic thermal losses in the metal, thereby overestimating the device's true photovoltaic potential and underscoring the necessity for a more refined analytical approach.

Upon applying the “core 2” spatial mask to isolate carrier generation exclusively within the P3HT:PCBM active layer, a physically accurate picture of direct optical enhancement emerges (“C2” row set). The results reveal that aluminium (Al–ZnO) and silver (Ag–ZnO) are the most effective materials for enhancing direct optical generation in this specific P3HT:PCBM architecture, achieving J_{sc_opt_direct} values of 11.82 mA cm⁻² and 10.68 mA cm⁻², respectively. These represent significant improvements over both the bare ZnO nanostructure reference (8.48 mA cm⁻²) and the intrinsic cell. In contrast, Au, Cu, Fe, and Pt nanostructures, in this particular geometric configuration, provide a lower J_{sc_opt_direct} than the intrinsic cell, indicating that their direct optical coupling into the P3HT:PCBM is less efficient than that of Al and Ag.

The final stage of the analysis (“C3/C4:ON” row set) incorporates the “core 3” hot carrier estimation and the “core 4” superposition to evaluate the total potential photocurrent (J_total). Here, the versatility of the different materials becomes evident. Iron (Fe), despite having one of the lowest direct optical contributions (9.00 mA cm⁻²), exhibits the highest estimated hot carrier current (1.66 mA cm⁻²), boosting its J_total to 10.66 mA cm⁻². This substantial hot carrier contribution elevates Fe to be highly competitive with Ag and nearly recovers the performance of the intrinsic cell. Aluminium also shows a strong hot carrier contribution (0.93 mA cm⁻²), cementing its position as the overall top-performing material with a J_total of 12.75 mA cm⁻². Conversely, Ag, while optically efficient, is estimated to have a negligible hot carrier contribution (0.07 mA cm⁻²), and Au's hot carrier potential is also modest (0.20 mA cm⁻²) due to the less favorable energy distribution of its hot electrons generated from visible light, as discussed in the theory.

This tiered analysis reveals a critical insight: aluminium excels in this system due to its superior ability to enhance direct optical generation in the P3HT:PCBM. Iron, while less effective optically, possesses the largest potential for performance gains via hot carrier harvesting. The subsequent sections will now delve into the underlying physical mechanisms that explain these distinct material-dependent behaviours.

4.1.2 Dissecting light coupling mechanisms: analysis of 1D and 2D generation rate profiles. A deeper understanding of the performance values in Table 3 requires a detailed analysis of where and how carrier generation is enhanced within the 120 nm P3HT:PCBM active layer. Fig. 3 presents the laterally-averaged 1D optical generation profiles (G(z)) for all configurations, while Fig. 4 provides corresponding 2D cross-sectional G(x,z) maps for key materials, offering crucial spatial insights.

Fig. 3 Laterally-averaged 1D optical generation profiles (G(z)) in the 120 nm P3HT:PCBM active layer. The profiles compare the intrinsic device with various core–shell nanostructure enhancements, calculated using different stages of the “four core” model. (a) Unmasked raw generation, including parasitic absorption. (b) Masked direct optical generation in the semiconductor only, revealing the true enhancement mechanisms. (c) Total generation including estimated hot carrier contributions.

Fig. 4 Cross-sectional 2D maps of the direct optical generation rate (G(x,z)) within the P3HT:PCBM active layer for the (a) intrinsic cell, and cells enhanced with (b) ZnO, (c) Al–ZnO, (d) Ag–ZnO, (e) Fe–ZnO, (f) Au–ZnO, (g) Pt–ZnO, and (h) Cu–ZnO core–shell nanostructures. The maps reveal distinct spatial patterns of enhancement, from near-surface intensification LSPR (Ag, Au, Cu) to deep, forward-focused generation (Al, Fe, Pt).

4.1.2.1 The intrinsic cell & the influence of the Al cathode. As shown in Fig. 3a–c (green line), the G(z) profile of the intrinsic device is not a simple exponential decay. It exhibits a complex, sinusoidal-like shape with a prominent generation peak near the front of the active layer (z ≈ [100–120 nm]) and a second peak near the back (z ≈ [0–40 nm]). This structure arises from optical cavity effects, but critically, the intense peak near the back is a signature of surface plasmon polaritons (SPPs) being excited on the smooth Al back cathode. The evanescent fields of these SPPs penetrate into the P3HT:PCBM, strongly enhancing absorption in that region. Thus, the Al cathode in this “intrinsic” reference cell is not merely a reflector but an active plasmonic element, and its SPP-field establishes the baseline optical environment into which the nanoparticles are introduced. The 2D map in Fig. 4a visualizes this combined standing wave and SPP-enhanced field pattern.
4.1.2.2 Nanoparticle-induced perturbation of the optical environment. When ZnO nanostructures are introduced (Fig. 3a–c, sky blue line), they replace a portion of the active material and perturb the local refractive index. As a result, they partially disrupt the SPP-enhanced cavity mode, leading to a suppression of the generation peak near the back contact and an overall reduction in J_{sc_opt_direct}, as shown in Fig. 3. This establishes that any enhancement by metallic core–shell nanoparticles must overcome this initial disruption and introduce a more potent light-coupling mechanism. Based on the rigorously masked generation profiles calculated for the various metallic nanoparticles (Fig. 3b), two fundamentally different enhancement pathways are revealed.
4.1.2.3 Case 1: LSPR–SPP mode hybridization (noble metals: Au, Ag, Cu). Noble metal nanoparticles, particularly Au and Ag, are characterized by their strong but spectrally narrower LSPR peaks and relatively moderate broadband absorption. This allows a significant portion of incident sunlight, especially outside their primary LSPR wavelength, to penetrate the active layer and still excite the SPPs on the Al back cathode. The resulting generation profile (e.g., silver line for Ag in Fig. 3b) is therefore a superposition of two effects: strong, localized LSPR-driven enhancement in the P3HT:PCBM immediately surrounding the nanoparticle (z ≈ 0–40 nm), combined with the persistent, broader SPP-driven enhancement from the back contact. This is vividly illustrated in the 2D generation map for Ag (Fig. 4d), which shows intense generation “hot spots” localized on the nanoparticle's surface, coexisting with the broader generation pattern deeper in the cell. In this scenario, the LSPRs on the nanoparticles can also be further enhanced by coupling with the backward-propagating SPP field. Among these materials, Ag demonstrates the most effective near-field coupling, leading to the highest J_{sc_opt_direct} values in this category.
4.1.2.4 Case 2: plasmonic shielding and forward-channeling (non-noble metals: Al, Fe, Pt). A starkly different behaviour is observed for the non-noble metal nanoparticles. Al, Fe, and Pt are potent broadband absorbers. When placed as an array at the front of the active layer, they act as highly effective “plasmonic shields,” intercepting and interacting with the vast majority of incident light. This prevents a significant photon flux from reaching the Al back cathode, leading to a strong suppression of the back-contact SPP mode. Having decoupled the device from the influence of the back-contact SPP, the G(z) profile for these materials is now almost entirely dictated by the intrinsic light-coupling mechanism of the front-side nanoparticles themselves. This mechanism is shown to be a novel form of deep energy deposition. In striking contrast to the noble metals, the generation rate for Al and Fe (purple and black lines, Fig. 3b) is moderate to minimal near the nanoparticle but progressively increases with depth. The 2D G(x,z) map for Al (Fig. 4c) is particularly revealing: instead of hot spots on the NP surface, the dominant feature is a focused, intense “ellipse” of high generation located deep within the active layer, between z ≈ 70–110 nm. This confirms that the Al nanoparticles are actively channelling or “pumping” optical energy to a focal point much deeper than their physical location. Fe and Pt exhibit a similar but weaker deep-generation pumping (Fig. 4e and g).

These G-profiles provide definitive evidence of two competing mechanisms. The choice of nanoparticle material dictates whether the device operates in a hybridized LSPR–SPP mode (with noble metals) or a forward-channelled, nanoparticle-dominated mode (with strongly-absorbing non-noble metals). The subsequent section will use a detailed analysis of local electromagnetic fields to dissect the physical origin of this novel forward-channelling effect.

4.2 A phase-resolved analysis of synchronous and asynchronous plasmon dynamics

The distinct G(z) profiles of noble versus non-noble metals, particularly the “deep energy deposition” characteristic of aluminium, originate from fundamentally different dynamic behaviours of their plasmonic near-fields. To dissect these mechanisms, a phase-resolved analysis of the electric field (E) vectors was performed for the Al–ZnO and Ag–ZnO nanostructures, representing the champions of their respective classes. Fig. 5 showcases key frames from the full dynamic evolution at 580 nm, where P3HT:PCBM exhibits peak absorption.

Fig. 5 Phase-resolved maps of the electric field vector dynamics at 580 nm. The images show the peak resonance frames for (a) the aluminium nanostructure, displaying the synchronous vortical fields and forward energy channelling of the PVCFE mechanism, and (b) the silver nanostructure, showing the intense, near-surface intensification of its LSPR. Full animations showing the complete dynamic evolution are available in the SI.

4.2.1 Silver: an asynchronous, hybridized LSPR–SPP response. For the Ag nanostructure, the enhancement is dominated by a powerful hybridized mode that evolves in two distinct, asynchronous stages. This dynamic behaviour is a direct visualization of the LSPR–SPP coupling identified earlier in the generation profiles. The process begins with the LSPR peak resonance (phase 0–1.05 radians), where the intense localized surface plasmon resonance is excited on the silver nanoparticle itself. As shown in Fig. 5b, this culminates at a peak phase of approximately 1.05 radians. At this point, powerful vortical fields and a classic “hot ellipse” of maximum E-field intensity are formed directly on the nanoparticle's surface, efficiently concentrating energy into the adjacent active material. This corresponds to the initial near-surface enhancement seen in the generation profile. This is followed by a secondary stage of SPP-coupled channelling (decay & echo, phase ∼2.01 radians). After the initial LSPR peak decays, we observe a weaker energy “channelling” effect. This is the physical signature of the surface plasmon polariton (SPP) field, which has travelled from the nanoparticle to the Al back contact and is now reflecting back to interact with the nanoparticle again. This “echo” reaches its maximum strength at a later phase, well after the primary LSPR hot spot has vanished.

This asynchronous dynamic—powerful LSPR first, followed by a delayed SPP-coupled channelling—is definitive proof of two weakly-coupled, out-of-phase processes. The time delay is a direct result of the finite travel time of the SPP to the back contact and back. This hybridized mode, while effective, deposits its energy in two separate steps and primarily at the surface, which is fundamentally less efficient than the unified mechanism we observe in Al.

4.2.2 Aluminium: the synchronous “plasmonic vortex-coupled forward emission” (PVCFE) mechanism. In striking contrast to the noble metals, the plasmonic response of Al, Fe, and Pt is characterized by a powerful, self-contained mechanism that both shields the back of the device and actively channels energy forward. We collectively designate this class of behaviours—prominent in these strongly absorbing metals and linked to their large Im(ε) values (Fig. 2d) when embedded in these types of organic solar cell architectures—as the ‘AzizEl effect’.

Within this class, aluminium's response is exceptionally efficient and exhibits a unique, synchronous dynamic that we formally term plasmonic vortex-coupled forward emission (PVCFE). This mechanism, which we identify as the archetypal example of the AzizEl effect, is directly linked to aluminium's unique optical properties, which combine the high absorption of non-noble metals with a distinctively large negative real permittivity (Fig. 2c). The key stages of the PVCFE in aluminium are as follows. The process begins with a synchronous build-up (phase 0.5–1.76 radians). Unlike Ag, both the vortical field pattern and the directional “flow-through” energy channelling appear simultaneously. As the phase progresses towards its peak, these two components grow in unison with no time delay. This leads to the peak resonance (phase ≈ 1.76 radians), which is significantly phase-lagged compared to Ag. Critically, at this peak intensity (Fig. 5a), both the vortex and the energy channelling are at their maximum strength simultaneously. The local field intensification is not confined to the surface (non-local) of the nanoparticle but is the visible signature of this powerful, unified mechanism. Finally, during the unified decay (phase > 2.2 radians), both the vortex and channelling components of the PVCFE weaken together as the system dephases.

This synchronicity is the defining feature of the PVCFE. It is not an asynchronous, two-stage process like the LSPR–SPP hybridization seen in silver. Instead, the vortex and the energy channelling are two inseparable facets of the same complex, phase-lagged plasmon mode intrinsic to the nanoparticle. This unified mechanism is exceptionally efficient at both concentrating and directionally steering electromagnetic energy, providing the direct physical explanation for the deep “pumping” of the generation profile, as visualized in the 2D map for Al in Fig. 4c. This discovery moves beyond simple LSPR enhancement, revealing a sophisticated, material-dependent dynamic wherein the localized plasmon itself possesses a strong, intrinsic forward-radiating character, enabling advanced light management in nanophotonic devices.

4.2.3 Robustness of hot carrier contributions. The quantitative results in Table 3 highlight the significant potential of hot carrier injection, particularly for materials like iron and aluminium. However, as noted in the methodology, the calculation of this contribution relies on efficiency parameters (η_{hc_conversion}, η_{hc_injection}) that are reasoned estimates based on literature. To directly address this uncertainty and test the robustness of our conclusions, we performed a parametric sensitivity analysis.

The results are presented in Fig. 6. This analysis plots the estimated hot carrier J_sc as a linear function of the total hot carrier efficiency (η_total = η_{hc_conversion} × η_{hc_injection}) for the key plasmonic materials. The slope of each line is a direct measure of a material's intrinsic ability to convert absorbed photon power into injected current, independent of the assumed efficiency. The analysis confirms that the superior potential of Fe and Al is a fundamental consequence of their high optical absorption in this device architecture. While the absolute magnitude of the hot carrier J_sc scales with the assumed efficiencies, the relative performance ranking is robust, solidifying the conclusion that these non-noble metals are exceptional candidates for hot carrier harvesting.

Fig. 6 Parametric sensitivity analysis of the estimated hot carrier short-circuit current density (J_sc) as a function of the total assumed hot carrier efficiency (η_total). The distinct slope for each material is determined by its total absorbed power under AM1.5G illumination. This demonstrates that the high potential of Fe, Al, and Pt for hot carrier generation is an intrinsic property that is robust against variations in the precise efficiency values. Markers indicate the specific efficiency values used to calculate the results in Table 3.

4.3 Proving the dominance of PVCFE in a high-performance PTB7:PC₇₁BM testbed

The foundational analysis in the P3HT:PCBM system not only revealed the novel plasmonic vortex-coupled forward emission (PVCFE) mechanism but also suggested that it represents a more potent light-coupling strategy than conventional noble metal plasmonics. To definitively test this hypothesis and isolate the mechanism's performance from the electrical limitations of P3HT:PCBM, we transitioned to a higher-performance PTB7:PC₇₁BM active layer. This material system serves as a high-fidelity testbed, characterized by superior charge transport that can accurately reflect the true extent of optical generation enhancements.

4.3.1 Rationale for Al–Al₂O₃vs. Ag–Al₂O₃ and thin shell configuration. To create a direct and challenging comparison, we designed a device architecture that should, according to conventional wisdom, heavily favour the noble metal, silver. The thick (8 nm top/bottom) ZnO shell used in the P3HT:PCBM study, while enabling the PVCFE, could act as a significant barrier for the evanescent near-fields of a traditional LSPR. Therefore, in this new testbed, we replaced it with a minimal, uniform 2 nm Al₂O₃ dielectric shell for both the Al and Ag nanoparticles. This thin shell provides necessary passivation while placing the plasmonic core in the most intimate possible contact with the PTB7:PC₇₁BM active layer, a condition under which a powerful LSPR, like that of silver, is expected to thrive. The structure was based on the original conventional Al–cathode design (ITO/PEDOT:PSS/active/ZnO/Al) to allow for a direct assessment of the LSPR–SPP hybridization (for Ag) versus the PVCFE (for Al) under identical, well-defined optical cavity conditions. If the PVCFE is a truly superior mechanism, Al should outperform Ag even under these thin-shell conditions that are optimized for conventional near-field enhancement.

4.3.2 Optical performance comparison: PVCFE outperforms conventional enhancement. The performance of the optimized Al–Al₂O₃ and Ag–Al₂O₃ nanostructures within the PTB7:PC₇₁BM testbed was evaluated using our rigorous “four core” analysis. The comprehensive results are summarized in Table 4, and the 1D generation rates are reported in Fig. 7. The final optimized device architecture is: ITO (100 nm)/PEDOT:PSS (40 nm)/PTB7:PC₇₁BM (130 nm)/ZnO (30 nm)/Al (100 nm). The optimized Al/Al₂O₃ nanoparticles are cuboids with a width of 140 nm (a = 140 nm), and a height (h) of 45 nm with 2 nm shell thickness. They are arranged in a rectangular lattice with a period in the x-direction (d_x) of 154 nm and a significantly larger period in the y-direction (d_y) of 200 nm. This anisotropic periodicity was strategically chosen. The larger y-period ensures that contiguous pathways to the ZnO ETL remain open for charge carriers, mitigating the risk of the nanoparticle array acting as a barrier and thus ensuring more realistic and efficient charge collection in a 3D device context. The nanoparticles are positioned on the ZnO ETL and embedded within the bottom region of the PTB7:PC₇₁BM active layer.

Table 4 Quantitative breakdown of J_sc contributions for the PTB7:PC₇₁BM testbed device with an Al back-cathode. The analysis compares the intrinsic cell with Al–Al₂O₃ and Ag–Al₂O₃ nanostructures

Analysis	Structure		J sc_opt_direct (mA cm^−2)	Injected HC (carriers per s per NP)	J sc_hot_carrier (mA cm^−2)		J total (mA cm^−2)
C1:ON	Intrinsic	8.986 × 10^20	14.40	—	—	8.986 × 10^20	14.40
C2:OFF	Al–Al2O3	1.326 × 10^21	21.25	—	—	1.326 × 10^21	21.25
C3/C4:OFF	Ag–Al2O3	1.216 × 10^21	19.48	—	—	1.216 × 10^21	19.48
C1:ON	Intrinsic	8.986 × 10^20	14.40	—	—	8.986 × 10^20	14.40
C2:ON	Al–Al2O3	1.080 × 10^21	17.30	—	—	1.080 × 10^21	17.30
C3/C4:OFF	Ag–Al2O3	1.061 × 10^21	17.00	—	—	1.061 × 10^21	17.00
C1:ON	Intrinsic	8.986 × 10^20	14.40	—	—	8.986 × 10^20	14.40
C2:ON	Al–Al2O3	1.080 × 10^21	17.30	2.22 × 10^6	1.162	1.152 × 10^21	18.46
C3/C4:ON	Ag–Al2O3	1.061 × 10^21	17.00	7.19 × 10^5	0.376	1.085 × 10^21	17.38

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Fig. 7 Integrated 1D generation rates for the PTB7:PC₇₁BM testbed device, comparing the intrinsic cell with Al–Al₂O₃ and Ag–Al₂O₃ nanostructures. The plot shows results from different stages of the “four core” analysis: unmasked (raw optical generation), masked (direct optical generation only), and total (direct optical + hot carrier contributions). The data clearly shows Al surpassing Ag in both direct optical and total potential current generation.

The intrinsic PTB7:PC₇₁BM device, with its strong SPP enhancement from the Al back cathode, establishes a high baseline J_sc of 14.40 mA cm⁻². When nanostructures are introduced, the unmasked “C1” analysis again highlights the significant parasitic absorption of Al (apparent J_sc = 21.25 mA cm⁻²), while the masked analysis reveals the true useful generation.

The rigorously masked results (“C2”) deliver a decisive verdict. The Ag–Al₂O₃ nanostructures, despite the ideal thin-shell configuration, provide a direct optical J_sc (J_{sc_opt_direct}) of 17.00 mA cm⁻². This is an impressive enhancement, showcasing the power of the hybridized LSPR–SPP coupling mechanism. However, the Al–Al₂O₃ nanostructures surpass them, achieving a J_{sc_opt_direct} of 17.30 mA cm⁻². This confirms that even under conditions tailored for conventional near-field enhancement, the PVCFE is an intrinsically more powerful mechanism for channelling light and generating carriers deep within this high-performance active layer.

This conclusion is further solidified by the inclusion of hot carrier estimations (“C3/C4”). Due to its superior efficiencies, aluminium adds a substantial 1.16 mA cm⁻² of J_{sc_hot_carrier}, for a final J_total of 18.46 mA cm⁻². In contrast, silver's much lower hot carrier potential adds only a negligible 0.38 mA cm⁻² for a total of 17.38 mA cm⁻². This widening performance gap confirms that Al is superior in both primary and secondary enhancement pathways.

4.3.3 Conclusion of comparative analysis and path to an optimized architecture. The direct, thin-shell comparison within the high-performance PTB7:PC₇₁BM platform provides conclusive evidence that the plasmonic vortex-coupled forward emission (PVCFE) mechanism inherent to aluminium is fundamentally more effective than the conventional LSPR enhancement of silver. The analysis of the rigorously masked and hot-carrier-inclusive generation rates (Table 4) and 1D generation profiles (Fig. 7) confirms aluminium's superiority. Its final J_total of 18.46 mA cm⁻² surpasses that of silver (17.38 mA cm⁻²) due to a combination of a more potent direct optical enhancement via PVCFE and a significantly larger estimated hot carrier contribution.

Crucially, the ability of Al to actively channel energy deeper into the active layer represents a mechanism that is robustly independent of precise shell thickness, unlike the highly sensitive evanescent near-fields of noble metals. This finding is in complete alignment with previous work by Bagheri on Fe–ZnO and Au–ZnO nanoparticles, which showed that while Au's enhancement decayed significantly with increasing shell thickness, Fe's enhancement remained constant or even improved.¹⁵

Beyond its superior optoelectronic performance, aluminium offers a profound advantage in terms of manufacturability and cost-effectiveness. A key challenge in plasmonic device fabrication is the creation of a uniform, ultrathin dielectric shell to prevent quenching and mediate hot carrier injection. For silver, achieving a uniform ∼2 nm shell demands costly and technically sophisticated methods, such as atomic layer deposition.⁶⁰ In stark contrast, aluminium nanoparticles naturally form a high-quality, self-passivating Al₂O₃ shell through spontaneous oxidation in ambient conditions. This process requires virtually no additional cost or complex synthesis steps, making the protective and functional oxide shell an integral and economically favourable component of the Al nanoparticle design.^12,61,62

Therefore, aluminium emerges as the unequivocal material of choice, offering a trifecta of benefits: a superior light-coupling mechanism (PVCFE), significant hot carrier potential, and a cost-effective, self-passivating shell. Furthermore, its previously identified “plasmonic shield” quality, which renders the device's optical performance largely independent of the back-contact SPP modes, presents a profound opportunity for radical device redesign. Having unequivocally established the superiority of the PVCFE mechanism and aluminium, we are now positioned to design a final, truly innovative OSC. The subsequent section will leverage this knowledge to create an inverted architecture that replaces the expensive, plasmonically-active metal back contact with a low-cost, inert graphite anode. This final design will not only capitalize on aluminium's exceptional optical performance but will also realize the full cost and stability benefits promised by a complete transition to non-noble plasmonics.

4.4 A novel high-performance architecture: decoupling and dominance of PVCFE in a graphite-anode OSC

The analysis in Section 4.1 revealed a critical insight: the aluminium back cathode in the conventional device is not an inert reflector but an active plasmonic element, exciting surface plasmon polariton (SPP) modes that significantly contribute to the baseline optical generation. This finding implies that the performance of any front-side nanostructure is intrinsically entangled with this back-side SPP enhancement, leading to complex and sometimes competitive optical effects. While the Al–cathode design was instrumental in discovering the PVCFE, it represents a suboptimal architecture. Based on this insight, we propose that a superior device architecture is one that is optically decoupled from the back contact. This is a novel design principle for plasmonic OSCs, enabled by the “plasmonic shield” nature of the optimized Al–NP array. Fig. 9c provides direct evidence for this shielding effect. While the intrinsic device allows a significant fraction of light to pass through the active layer to be absorbed parasitically by the graphite anode, the introduction of the Al–NP array reduces the average transmission across the active spectrum to less than 5%. This near-complete photon harvesting at the front of the cell renders the back contact's reflectivity non-critical.

4.4.1 Design rationale and stability benefits of the inverted graphite-anode architecture. To capitalize on this, we designed and optimized a novel inverted p–i–n solar cell: ITO/AZO/PTB7:PC₇₁BM (with Al–Al₂O₃ NPs)/PEDOT:PSS/graphite. While graphite anodes have been explored for their low cost and chemical inertness, previous implementations often suffered from reduced PCE due to the very light-loss mechanism our design overcomes.⁶³ Our architecture, therefore, offers multiple compelling advantages:

• Optical decoupling and high efficiency: the PVCFE-driven plasmonic shield ensures maximum light absorption, overcoming the primary limitation of non-reflective anodes. This eliminates LSPR–SPP interference, allowing the intrinsic performance of the front-side nanostructures to be unambiguously harnessed.

• Cost-effectiveness and stability: replacing the conventional vacuum-deposited silver or gold anode with solution-coatable, abundant graphite aligns with the low-cost premise of OSCs. Furthermore, this inverted structure provides significant stability benefits by removing the acidic PEDOT:PSS layer from the vulnerable ITO contact, eliminating a major degradation pathway,⁶⁴ and by using a robust AZO ETL and a chemically inert graphite anode.

4.4.2 Multi-polarization optical performance in the decoupled architecture. To maximize the performance of this novel graphite-anode architecture, a multi-parameter PSO was performed, optimizing layer thicknesses, nanostructure geometry, and array periodicity. Recognizing that unpolarized sunlight comprises orthogonal polarizations and that nanostructure arrays can exhibit polarization sensitivity, all final simulations were performed for both TE (E-field along x-axis) and TM (E-field along y-axis) polarized light, with the final results representing their 50/50 average.

The champion device architecture, illustrated in the 3D schematic in Fig. 8, consists of the following optimized parameters: ITO (80 nm), AZO (20 nm), PTB7:PC₇₁BM (130 nm), PEDOT:PSS (40 nm), and a thick graphite anode (>500 nm). The optimized Al-core/Al₂O₃-shell nanoparticles embedded at the AZO/active layer interface are cuboids with dimensions of 150 × 150 nm (width/length) and a height of 30 nm.

Fig. 8 3D schematic of the final, optimized inverted organic solar cell with a graphite anode. The device architecture is ITO (80 nm)/AZO (20 nm)/PTB7:PC₇₁BM (130 nm)/PEDOT:PSS (40 nm)/graphite. The optimized Al-core/Al₂O₃-shell nanoparticles are cuboids with dimensions 150 × 150 × 30 nm and 2 nm shell thickness. Period of nanoparticles array are 166 nm in x axes and 230 nm in y axes.

Table 5 summarizes the comprehensive “four core” analysis for this optimized graphite-anode design, comparing the intrinsic cell with those enhanced by Al–Al₂O₃ and Ag–Al₂O₃ nanostructures. The results unequivocally demonstrate the success of this new design. The intrinsic graphite-based device, now free from back-contact SPP enhancement, establishes a true optical baseline J_total of 12.11 mA cm⁻². The Ag nanostructures, relying on their conventional LSPR mechanism, provide a substantial enhancement, reaching a final TE/TM-averaged J_total of 16.21 mA cm⁻². This performance is overwhelmingly driven by its strong direct optical generation enhancement (J_{sc_opt_direct} = 15.87 mA cm⁻²), while its hot carrier contribution is modest (∼0.35 mA cm⁻²). The Al nanostructure device emerges as the undisputed champion. In this optically clean environment, the PVCFE mechanism is unleashed. The TE/TM-averaged direct optical J_sc (J_{sc_opt_direct}) reaches an outstanding 17.59 mA cm⁻². Furthermore, aluminium's potent intrinsic absorption and favourable electronic properties lead to a very significant estimated hot carrier contribution of 1.03 mA cm⁻².

Table 5 Comprehensive “four core” analysis for the optimized graphite-anode architecture, showing TE, TM, and averaged results

Structure	Polarization		J sc_opt_direct (mA cm^−2)	J sc_hot_carrier (mA cm^−2)	J total (mA cm^−2)
Intrinsic	TE/TM average	7.560 × 10^20	12.11	—	12.11
Al–Al2O3 (C1–C4:ON)	TE	1.113 × 10^21	17.84	1.116	18.96
	TM	1.082 × 10^21	17.33	0.942	18.27
	TE + TM average	1.097 × 10^21	17.59	1.030	18.62
Ag–Al2O3 (C1–C4:ON)	TE	9.498 × 10^20	15.22	0.328	15.55
	TM	1.031 × 10^21	16.52	0.363	16.88
	TE + TM average	9.906 × 10^20	15.87	0.345	16.21

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Combining these two pathways yields a final, TE/TM-averaged total J_sc for the Al-enhanced device of 18.62 mA cm⁻². This represents a remarkable 53.7% increase over the new intrinsic baseline of the graphite-based cell. This result, achieved in a cost-effective and stable architecture and explained by a novel, fully characterized physical mechanism (PVCFE), highlights the immense potential of non-noble plasmonics. A detailed analysis of the generation profiles that lead to these results is presented in the following section.

4.4.3 Analysis of 1D generation profiles and absorption in the decoupled graphite-anode architecture. The move to a graphite anode provides an optically “clean” environment, free from the influence of back-contact SPP modes, allowing for an unambiguous study of the intrinsic performance of the front-side nanostructures. The laterally averaged 1D generation profiles (G_total(z)), total fractional absorption (A(λ)), and total transmission (T(λ)) for this new architecture are presented in Fig. 9.

Fig. 9 Optical performance of the final graphite-anode device. (a) Laterally-averaged 1D total generation profiles (G_total(z)) for the intrinsic, Ag-enhanced, and Al-enhanced (TE, TM, and average) configurations. The layer positions are indicated at the top. (b) Total fractional absorption (A(λ)) spectra. (c) Total transmission (T(λ)) spectra, demonstrating the “plasmonic shield” effect of the Al–NP array.

4.4.3.1 Decoupled intrinsic and Ag performance. As hypothesized, the G(z) profile for the intrinsic graphite-based cell (Fig. 9a, green line) is now fundamentally different from the one observed with the Al cathode. The strong, SPP-induced generation peak previously seen near the back interface is completely absent. Instead, the profile shows a more conventional absorption behaviour, with a broad peak near the front that decays into the film. This confirms the critical role of the Al cathode's SPPs in the previous architecture and quantifies its contribution: the total J_sc for the intrinsic cell drops from 14.4 mA cm⁻² (with Al cathode) to 12.11 mA cm⁻² (with graphite), indicating the back-contact SPP enhancement was responsible for ∼2.3 mA cm⁻² of current in the original design. Similarly, the performance of the Ag nanostructures is impacted. Without the backward-propagating SPP field to hybridize with, the G(z) profile for Ag (Fig. 9a, crimson line), while still strongly peaked near the front of the active layer due to its powerful LSPR, is suppressed across the board compared to its potential in a coupled system. This results in a final TE/TM-averaged J_sc for Ag of 16.21 mA cm⁻². While this still represents a significant enhancement over the new 12.11 mA cm⁻² intrinsic baseline, it confirms that Ag's performance in the previous architecture, in part, relied on synergistic coupling with the back SPP field.
4.4.3.2 Confirmation of Al as a self-contained “plasmonic shield” and PVCFE engine. The results for the Al nanostructures provide the final and definitive proof of the PVCFE mechanism acting as a powerful, self-contained optical engine. The G(z) profiles for Al under both TE and TM polarizations (Fig. 9a, black line) show that its ability to channel energy and create a deep generation peak (now located near z ≈ 120–150 nm in this stack) is fully preserved and even more prominent in the absence of the competing back-SPP mode. Crucially, the TE/TM-averaged total J_sc for the Al-enhanced cell (18.62 mA cm⁻²) is not diminished by the removal of the optically active Al cathode; its enhancement over the new intrinsic baseline is now even more pronounced. This is clear evidence that the “plasmonic shield” nature of the Al nanoparticle array is so effective that it renders the back contact's optical properties largely irrelevant. As shown in the transmission spectra (Fig. 9c), the PVCFE is powerful enough to manage the incident light entirely on its own, reducing transmission to less than 5%. The total fractional absorption shown in Fig. 9b is also significantly higher for the Al-enhanced cell across the entire active spectrum of PTB7:PC₇₁BM, consistent with its superior J_sc.
4.4.3.3 Conclusion and path to final device analysis. This analysis confirms that Al nanostructures, via the PVCFE mechanism, provide a superior and more robust enhancement strategy than conventional plasmonic materials like Ag. Their “plasmonic shield” quality not only provides exceptional light-trapping but also decouples the device's optical performance from the back contact, enabling the use of low-cost, non-reflective materials like graphite. Given these unequivocal advantages, we now proceed with a full electrical simulation of only the champion Al-enhanced device and the intrinsic baseline to quantify the final power conversion efficiency gains.

4.5 Final device performance: electrical and quantum efficiency analysis

Having established aluminium's superior and novel optical enhancement mechanism (PVCFE) in the optimized graphite-anode architecture, we proceeded to a full electrical device simulation to quantify the final impact on power conversion efficiency (PCE). The one-dimensional total generation profiles (G_total(z)) for the calibrated intrinsic and the champion Al–Al₂O₃ enhanced devices, encompassing both direct optical and estimated hot carrier contributions, were imported into a SCAPS-1D model defined by the realistic device parameters in Table 2. All electrical parameters, including charge mobilities and defect profiles, were held constant between the two simulations to ensure a direct and unambiguous assessment of the plasmonic contribution.

The resulting key photovoltaic parameters are summarized in Table 6, with the corresponding current density–voltage (J–V) and power–voltage (P–V) curves plotted in Fig. 10. The calibrated intrinsic reference device, representing a realistic baseline, is predicted to have a PCE of 5.95%, with a J_sc of 11.61 mA cm⁻², a V_oc of 0.853 V, and a healthy FF of 60.08%. The integration of the optimized Al–Al₂O₃ nanostructures is predicted to yield a transformative improvement in performance. The short-circuit current density (J_sc) leaps by a massive 55.8% to 18.09 mA cm⁻², a direct consequence of the enhanced carrier generation from the synergistic action of the PVCFE mechanism and hot carrier injection. Remarkably, the open-circuit voltage (V_oc) remains stable at 0.852 V, indicating that the well-passivated Al/Al₂O₃ nanostructures do not introduce detrimental recombination pathways.

Table 6 Final simulated photovoltaic performance parameters for the intrinsic and champion Al–Al₂O₃ enhanced graphite-anode devices

Structure	J sc (mA cm^−2)	V oc (V)	FF (%)	PCE (%)	V mpp (V)	J mpp (mA cm^−2)	P max (mW cm^−2)
Intrinsic	11.61	0.853	60.08	5.95	0.651	9.136	5.95
Al–Al2O3 enhanced	18.09	0.852	60.57	9.34	0.625	14.938	9.34

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Fig. 10 Simulated current density–voltage (J–V, solid lines, left axis) and power–voltage (P–V, dashed lines, right axis) characteristics for the intrinsic and Al–Al₂O₃ enhanced graphite-anode devices. The massive increase in J_sc with a maintained fill factor leads to a 57% relative PCE enhancement.

Most significantly, the fill factor (FF) is not only maintained but slightly increases to 60.57%. This is a critical result, demonstrating that the robust inverted device architecture with its highly efficient charge transport layers is capable of extracting the massively increased photocurrent without being limited by space-charge effects or increased recombination losses. The final power conversion efficiency (PCE) for the Al-enhanced device is predicted to reach 9.34%. This constitutes an exceptional 57% relative enhancement over the intrinsic cell, unequivocally demonstrating the success of harnessing the PVCFE mechanism in an electrically optimized architecture.

It is important to contextualize this predicted 57% relative enhancement within the existing experimental landscape. Prior experimental work on Al-based plasmonic OSCs has shown significant, albeit more modest, gains. For instance, notable experimental work from Yang et al.¹¹ and Kakavelakis et al.¹³ reported PCE enhancements of approximately 30%, while Cui et al.¹² demonstrated a 20% improvement. We attribute our significantly higher predicted performance to the holistic design approach that goes beyond simple plasmonic enhancement. Our optimization of the nanostructure array as a functional metasurface is what enables the PVCFE mechanism and the highly effective “plasmonic shield” property. This superior light management, in turn, is what makes the cost-effective and stable graphite anode design viable without compromising efficiency, leading to the large overall performance gain.

Further insight is provided by the simulated external quantum efficiency (EQE) spectra shown in Fig. 11. The intrinsic device exhibits a modest QE whose spectral shape mirrors the natural absorption of the PTB7:PC₇₁BM blend, peaking at ∼680 nm before falling to zero at the bandgap edge. In stark contrast, the Al-enhanced device shows a dramatically boosted QE across the entire 300–750 nm spectrum. Crucially, its peak response is red-shifted to ∼700 nm. This broadband enhancement is a direct result of the PVCFE's superior light coupling. However, the red-shift of the peak is the final, unequivocal evidence of the plasmonic mechanism's dominance. It demonstrates that the enhancement is not merely amplifying the material's inherent absorption; rather, the PVCFE is imprinting its own powerful, lower-energy resonant signature onto the device, fundamentally reshaping its response to light. Thus, our comprehensive opto-electronic model, which synergistically combines the novel PVCFE mechanism for direct optical generation enhancement with a physically-grounded estimation of hot carrier injection, successfully predicts a clear and robust pathway to high-efficiency, stable, and cost-effective organic photovoltaics. The >57% relative improvement in PCE demonstrated herein is a direct result of this multi-faceted enhancement. It is worth noting, however, that the standard drift-diffusion formalism used in the electrical model does not explicitly account for all potential secondary benefits arising from the intense, vortical, and dynamic near-fields characteristic of the PVCFE. Advanced effects, such as field-assisted exciton dissociation or localized carrier ‘steering’ within the organic active layer, could further improve charge collection efficiency. While quantifying these contributions requires advanced quantum transport models beyond the scope of this work, their potential suggests that the experimental realization of this device could yield an even greater performance than the already impressive values predicted by our model. This work therefore not only demonstrates a powerful new plasmonic enhancement strategy but also highlights compelling avenues for future research at the intersection of nanophotonics and advanced device physics. It must be re-emphasized that the hot carrier portion of this enhancement is a theoretical estimate based on the parameters in Table 1. While our sensitivity analysis confirms the robustness of the material ranking, the precise magnitude of this contribution in a real-world device would ultimately require direct experimental calibration.

Fig. 11 Simulated external quantum efficiency (EQE) spectra for the intrinsic and Al–Al₂O₃ enhanced devices. The plasmonic enhancement is broadband, and the red-shift of the peak response confirms that the PVCFE mechanism is fundamentally reshaping the device's optical properties.

5 Conclusions

In this comprehensive theoretical and computational study, we have identified, characterized, and leveraged a novel, material-dependent light coupling mechanism in plasmonic organic solar cells, which we term plasmonic vortex-coupled forward emission (PVCFE). The development of a rigorous “four core” simulation workflow, which precisely separates useful semiconductor generation from parasitic metallic absorption and incorporates hot carrier injection estimations, enabled us to move beyond conventional metrics and reveal a deeper layer of plasmonic device physics. Our simulations establish cost-effective aluminium as a potentially superior material to noble metals, driven by the PVCFE mechanism—a synchronous coupling of a vortical near-field with a directional energy channelling component, confirmed via phase-resolved analysis. By translating these fundamental insights into a holistically designed, stable, and inverted OSC architecture (ITO/AZO/PTB7:PC₇₁BM (Al–NPs)/PEDOT:PSS/graphite), we predict a power conversion efficiency of 9.34%, a ∼57% relative improvement over its 5.95% intrinsic counterpart. This exceptional performance stems from a massive J_sc increase to 18.09 mA cm⁻² while maintaining the fill factor, a result of co-optimizing the novel PVCFE optical engine with a robust electrical design. This work not only presents a validated pathway to high-efficiency, stable, and low-cost organic photovoltaics but also provides a new fundamental mechanism—the PVCFE—as a powerful design principle for nanophotonics, shifting the focus from simple near-field enhancement to the sophisticated engineering of complex, hybridized plasmon modes for directional energy control.

While these simulation results are highly promising, we recognize the challenges and prospects for their experimental validation. A key step would be the synthesis of Al-core/Al₂O₃-shell nanostructures with dimensional control approaching that of the optimized model, likely through advanced colloidal chemistry or physical deposition methods followed by controlled oxidation. Fabricating the proposed inverted device architecture would then allow for direct comparison of experimental J–V and EQE curves against our predictions. Furthermore, advanced spectroscopic techniques could provide direct evidence of the PVCFE mechanism. For instance, near-field scanning optical microscopy (NSOM) could potentially map the non-local field intensification within the active layer, while ultrafast pump–probe spectroscopy might be used to discern the synchronous, phase-lagged dynamics characteristic of the PVCFE, distinguishing it from the asynchronous response of noble metals. We believe this work provides a strong theoretical motivation for pursuing such challenging but potentially rewarding experimental investigations.

Author contributions

M. A. S. Bagheri is the sole author of this manuscript and was responsible for all aspects of the work, including conceptualization, methodology, simulation, analysis, and manuscript preparation.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data underlying the results presented in this paper are available in the supplementary information. The custom computational codes generated during the current study are proprietary and are not publicly available.

Acknowledgements

The author declares that no funds, grants, or other support were received during the preparation of this manuscript.

Notes and references

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