What Photocurrent Versus Effective Voltage Tells Us About Charge Generation in Organic Solar Cells

Technical Summary: What Photocurrent Versus Effective Voltage Tells Us About Charge Generation in Organic Solar Cells

Problem Statement
In the field of organic solar cells (OSCs), a widely adopted diagnostic procedure involves plotting the photocurrent ($J_{ph}$) against the effective voltage ($V_{eff} = V_0 - V$). This method, often referred to as the $J_{ph}$–$V_{eff}$ procedure, is routinely used to extract an "exciton dissociation probability" ($P_{diss}$) and, by extension, a free-charge generation efficiency. The standard metric defines $P_{diss}$ as the ratio of the photocurrent at short circuit to the saturation current estimated at high reverse bias ($P_{diss} = J_{ph}(V=0) / J_{sat}$).

The authors argue that this interpretation is fundamentally flawed. While the procedure is intended to separate charge generation from charge collection, the paper posits that the extracted $P_{diss}$ measures neither the exciton dissociation yield nor the free-charge generation efficiency. Instead, the authors demonstrate that this metric is actually a proxy for the short-circuit charge collection efficiency, which is intrinsically linked to the fill factor. Consequently, using this method to compare generation efficiencies across different material systems (particularly modern non-fullerene acceptor systems) yields misleading conclusions.

Methodology
To rigorously test the validity of the $J_{ph}$–$V_{eff}$ procedure, the authors employed a two-pronged approach combining numerical simulation and experimental verification:

1. Numerical Drift-Diffusion Modeling:
   The authors constructed a one-dimensional drift-diffusion model solving coupled Poisson and continuity equations. Crucially, in these simulations, the free-charge generation efficiency was prescribed rather than inferred.

   • Ideal Case: Simulations were run with unity charge generation efficiency ($P_{gen} = 1$) and no field dependence. Any deficit in the extracted $P_{diss}$ in this scenario must therefore be attributed solely to collection losses.
   • Field-Dependent Case: The model was extended to include field-dependent generation using the Onsager–Braun yield function to simulate scenarios where generation is not unity.
   • Parameter Variation: The simulations systematically varied carrier mobilities, bimolecular recombination strengths (via a reduction factor $\gamma$), and injection barrier heights to observe how these transport properties influence the apparent $P_{diss}$.

2. Experimental Verification:
   The authors applied the standard $J_{ph}$–$V_{eff}$ procedure to four distinct organic semiconductor blends:

   • High-Efficiency Systems: PM6:Y6 and PM6:BTP-eC9 (non-fullerene blends with near-unity, field-independent generation).
   • Lower-Efficiency Systems: PM6:ITIC and PBDB-T:EH-IDTBR (blends with significant geminate recombination losses).
   • Ground Truth: For all four systems, the true free-charge generation efficiencies ($P_{gen}$) were known independently, having been determined via temperature-dependent internal quantum efficiency (IQE) spectroscopy. This allowed for a direct comparison between the "apparent" $P_{diss}$ derived from the $J_{ph}$–$V_{eff}$ plot and the "true" generation yield.

Key Results

• $P_{diss}$ is a Measure of Collection, Not Generation:
  In simulations where charge generation was set to 100% and field-independent, the $J_{ph}$–$V_{eff}$ procedure still returned an apparent $P_{diss}$ well below unity (e.g., 0.87). This deficit was shown to be entirely due to losses in free carrier collection (bimolecular recombination and recombination with injected charges). The extracted value was found to be a single-valued function of the fill factor and numerically equivalent to the short-circuit collection efficiency.

• The First-Order Ceiling:
  Even in the limit of ideal transport (arbitrarily high mobility) and negligible bimolecular recombination, the apparent $P_{diss}$ does not approach unity. Instead, it saturates at a first-order limit determined by the recombination of photogenerated carriers with injected equilibrium charges at the electrodes. This loss mechanism is intensity-independent and is fixed by the injection barriers and the built-in field.

• Decoupling from Generation Yield:
  When the procedure was applied to systems with varying true generation yields (from 0.65 to 0.995), the apparent $P_{diss}$ did not track the generation yield.

  • For systems with poor collection (low fill factor), the apparent $P_{diss}$ was low regardless of whether the true generation yield was high or low.
  • For high-fill-factor systems, the apparent $P_{diss}$ approached the collection ceiling, often overestimating the generation yield in systems with significant geminate losses (e.g., reporting ~0.97 for a system with a true yield of 0.85).
  • The data points for apparent $P_{diss}$ versus true $P_{gen}$ deviated significantly from the line of unit slope, confirming that the metric reports collection efficiency modulated by generation, rather than generation yield itself.

• Impact of Field Dependence:
  Introducing field-dependent generation (via the Onsager–Braun model) into the simulations did not resolve the issue. The extracted $P_{diss}$ remained a product of the short-circuit generation yield and the transport-set collection efficiency, failing to isolate the generation component.

Significance and Claims
The paper concludes that the $J_{ph}$–$V_{eff}$ procedure, as currently practiced, provides no additional insight into charge generation mechanisms beyond what is already revealed by the fill factor. The authors assert that:

1. Misinterpretation of Data: Reporting an apparent $P_{diss}$ near unity as evidence of efficient free-charge generation is physically unjustified, as the value is capped by transport limitations and electrode recombination, not just generation efficiency.
2. Invalid Comparisons: Comparisons of exciton dissociation efficiencies between different material systems using this method are effectively disguised comparisons of fill factors and collection efficiencies.
3. Recommendation: The authors suggest that this construction should not be used to quantify charge generation, particularly in state-of-the-art non-fullerene acceptor systems where generation is already known to be highly efficient.
4. Correct Methodology: To truly quantify free-charge generation yield, techniques that probe the generation current ($J_G$) independently of the steady-state current-voltage curve are required. The authors cite time-delayed collection field measurements and temperature-dependent IQE spectroscopy as appropriate methods, arguing that collection efficiency should be normalized against an independently measured $J_G$, not against the saturated photocurrent.

In summary, the paper argues that the widespread use of the $J_{ph}$–$V_{eff}$ ratio to claim improvements in charge generation is a methodological error that conflates transport losses with generation physics.