Open-circuit voltage of organic solar cells: interfacial roughness makes the difference

The study addresses why organic solar cells suffer significant open-circuit voltage (VOC) losses and how interfacial energetics and morphology control VOC. Organic solar cells convert strongly bound excitons into charge-transfer (CT) states at donor–acceptor interfaces, which then dissociate into free carriers. Early optimization sought small optical gaps and large photovoltaic gaps (|IED − EAA|), but this proved oversimplified due to density-of-states broadening and transport/recombination effects. Recent advances in non-fullerene acceptors and recognition of long-range electrostatics from molecular quadrupoles show that interfacial electrostatics critically shape ionization energies (IE), electron affinities (EA), CT energies, and VOC. The central hypothesis is that an electrostatic interfacial bias arising from molecular quadrupoles and interfacial roughness modulates the photovoltaic gap and CT energy, thereby controlling VOC; tuning the interfacial morphology can mitigate adverse electrostatic effects and improve VOC.

- Progress in organic photovoltaics has pushed single-junction PCEs near 19%, driven by non-fullerene acceptors and materials/process innovations (e.g., refs. 4–17). - Traditional donor design rules based on maximizing photovoltaic gap and minimizing optical gap are insufficient due to energetic disorder and density-of-states tails (refs. 19–23). - Device-scale models underscore the importance of mobility, recombination, and thickness optimization for current and fill factor (refs. 24–27). - Long-range electrostatics from molecular quadrupoles significantly impact IE, EA, CT energetics, charge separation, and VOC (refs. 28–33). Quadrupole-induced crystal fields shift energy levels and can both aid CT dissociation and reduce the photovoltaic gap, necessitating careful balance (refs. 28–34, 35–37). - Prior work related VOC to CT energetics and interfacial properties and established low-temperature VOC ≈ ECT limits (refs. 38–39). Kinetically limited phase separation and morphology control during growth are documented and relevant to interfacial roughness (ref. 40, 41).

- Electrostatic modeling and simulations: Atomistic models of mixed ZnPc:F4ZnPc and ZnPc:FZnPc donor films (10 nm thickness; 17×6 molecules; edge-on orientation per XRD) were constructed with random intermixing at ZnPc fraction c. Long-range embedding with periodic boundary conditions in-plane was used to compute solid-state corrections to site energies (ΔE) and resultant ionization energies IE = IEg + ΔE. Interfacial electrostatic bias terms for holes and electrons (Bh, Be) are defined from solid-state contributions when molecules are embedded in the opposite mesophase and approximated using bulk Δ values at the interface. CT state energy modeled as ECT(c) = ϵ(c) − Δeh + χ(c,ρ), with Δeh ≈ 0.5 eV and χ capturing interfacial push-out/bias modulated by nanoscale roughness ρ = 2h/δ (h: intermixed depth; δ: interlayer spacing). Analytical relations link photovoltaic gap I(c), interfacial bias B(c), CT energy, and VOC via chemical potentials including disorder terms and carrier densities. - Device fabrication: Planar heterojunction small-molecule devices (ITO/BPAPF:NDP9/Donor[/Interlayer]/C60/BPhen/Al). Donors: ZnPc mixed with FZnPc or F4ZnPc in varying ratios in a 10 nm donor layer; acceptor: 40 nm C60. Some devices include a co-deposited interlayer of ZnPc:C60 (1:1) with variable thickness (0–10 nm) between pure ZnPc and C60 to tune interface roughness. Materials purified by thermal sublimation; vacuum thermal evaporation at <1e-7 mbar. Encapsulation to avoid ambient exposure. - Electrical and spectroscopic characterization: J–V under AM1.5G with calibrated intensity; dark J–V. Sensitive EQEPY: chopped halogen lamp + monochromator, lock-in detection; EL with calibrated spectrometers. CT energies ECT, reorganization energy λ, and oscillator strength f extracted by fitting EQEPY low-energy tail with Marcus lineshape; when overlapping with donor optical transition, ECT from EL high-energy tail fits. Summary device data compiled (JSC, VOC, FF, PCE, ECT, λ, f) across compositions and interlayer thicknesses. - Data analysis: Compare composition dependence of simulated IE and measured UPS, compute interfacial bias B(c), and fit ECT(c) and VOC(c) vs c using roughness parameter ρ. Independently vary interlayer thickness h to experimentally modulate ρ and validate predicted trends of ECT and VOC vs roughness. All simulations performed with VOTCA.

- Electrostatic quadrupole fields in mixed donor phases linearly tune donor IE and acceptor EA with composition, yielding a linear composition dependence of the photovoltaic gap I(c) and interfacial bias B(c). - Interfacial electrostatic bias B can be positive (push-out) or negative (pull-in), depending on donor composition and quadrupole component Q20. In ZnPc:F4ZnPc, B becomes negative around c ≈ 0.3, correlating with deteriorating fill factor; in ZnPc:FZnPc, B remains positive and devices perform better. - Interface roughness, quantified by ρ = 2h/δ, modulates how much the interfacial bias affects CT energies: ECT(c,ρ) shifts upward (B>0) or downward (B<0) with increasing roughness. Best fits to composition-dependent ECT and VOC trends are achieved with ρ ≈ 1, corresponding to roughly two intermixed molecular layers. - Composition-dependent measurements (planar junctions with C60): As ZnPc fraction increases in ZnPc:F4ZnPc/C60 and ZnPc:FZnPc/C60, both ECT and VOC change with slopes reproduced by the model using ρ = 1 and Δeh ≈ 0.5 eV. Example data (Table 1): ZnPc:F4ZnPc (1:1)/C60 yields VOC = 0.61 V, ECT = 1.19 eV; F4ZnPc/C60 yields high VOC = 0.89 V but low FF = 36.9% and PCE = 0.59%. - Interlayer-induced roughness tuning (ZnPc/ZnPc:C60(1:1)/C60): Increasing interlayer thickness h from 2 to 10 nm increases ECT from ~1.10 to ~1.17 eV and VOC from ~0.47 to ~0.52–0.53 V; JSC and PCE also increase (e.g., PCE from 1.11% at h=2 nm to 1.91% at h=10 nm). Fitted parameters (ECT,0 = 0.92 eV, χ0 = 0.27 eV, δ ≈ 1.43 nm, h0 ≈ 1.43 nm) agree with simulations and composition-derived roughness. - Analytical relation connects VOC to carrier chemical potentials with disorder and a term αkBT ln(np); at low temperature, VOC ≈ ECT (α≈1), preserving VOC–ECT correlation. - Two regimes: (i) flat interfaces (ρ≈0): ΔVOC follows ΔI (photovoltaic gap). (ii) rough interfaces (ρ≫1): ΔI can be compensated by changes in carrier density via push-out energies, keeping VOC approximately constant. - Practical implication: For systems with B>0 (e.g., ZnPc/C60, FZnPc/C60), roughness enhances VOC and suppresses recombination; for B<0 (e.g., F4ZnPc/C60), roughness is detrimental to VOC and performance.

The results demonstrate that long-range electrostatics from molecular quadrupoles, coupled with interfacial morphology, govern the photovoltaic gap, CT energy, and VOC in organic solar cells. By formulating an interfacial bias B and a roughness parameter ρ, the study quantitatively links the composition-dependent energetics to measurable device outputs. The model explains when VOC tracks the photovoltaic gap (flat interfaces) and when morphology-induced push-out of carriers compensates gap changes (rough interfaces), maintaining VOC. Experimental validation using tailored ZnPc:F4ZnPc and ZnPc:FZnPc donors with C60 acceptor confirms predicted linear composition trends and the beneficial/harmful role of roughness depending on the sign of B. The anticorrelation of VOC and JSC observed with composition and roughness arises from reduced driving force for exciton-to-CT conversion as ECT increases. These insights offer clear design rules: tune donor quadrupole moments and control interfacial roughness to optimize VOC while managing trade-offs in current and recombination.

This work introduces and validates an electrostatic model that captures how interfacial bias and nanoscale roughness regulate the photovoltaic gap, CT energy, and open-circuit voltage in organic solar cells. By adjusting donor composition (controlling quadrupolar fields) and engineering interfacial roughness (e.g., via mixed interlayers), VOC can be increased or safeguarded against reductions in the photovoltaic gap. The model preserves the empirical VOC–ECT correlation, predicts low-temperature limits, and distinguishes regimes where VOC follows the gap versus being stabilized by push-out effects. Future research should: (i) extend the approach to non-fullerene acceptors and bulk-heterojunction morphologies; (ii) integrate kinetic/transport models to co-optimize JSC, FF, and PCE alongside VOC; (iii) develop processing routes to precisely control interfacial roughness and molecular orientation; and (iv) explore broader chemical space to tailor quadrupole moments for targeted interfacial biases.

- The interfacial solid-state contributions are approximated by bulk Δh and Δe values at the interface, neglecting detailed interfacial mixing configurations. - The model assumes long-range quadrupole interactions dominate and uses linear composition dependences; short-range specific interactions are not explicitly treated. - CT binding energy Δeh is taken as constant (~0.5 eV) independent of composition and morphology. - Energetic disorder in the acceptor (C60) is assumed negligible; results may not generalize to acceptors with significant disorder. - Roughness is reduced to a single parameter ρ = 2h/δ; real interfaces may have more complex topographies and correlations. - Device set focuses on small-molecule planar heterojunctions with C60; extrapolation to bulk heterojunctions and NFA systems requires further validation. - Carrier densities n0, p0 are assumed based on well-functioning systems under AM1.5G; illumination and recombination kinetics are not fully modeled.