A figure-of-merit-based framework to evaluate photovoltaic materials

Technical Summary: A Figure-of-Merit-Based Framework to Evaluate Photovoltaic Materials

Problem Statement
The exploration of new photovoltaic (PV) absorber materials has accelerated due to high-throughput and autonomous research methods. However, the field lacks a robust method to quantify the efficiency potential of new absorbers early in their development, determine which material properties require urgent optimization, and distinguish between promising candidates and those unlikely to yield high efficiencies. Traditional methods, such as the Shockley-Queisser (SQ) limit and its extensions incorporating non-radiative recombination, rely on detailed balance principles. While powerful for predicting open-circuit voltage limits, these methods fail to account for efficiency losses arising from imperfect carrier collection. Such losses, driven by finite carrier mobilities, doping densities, and dielectric constants, significantly impact short-circuit current densities and fill factors but are difficult to model in a unified manner using classic detailed balance approaches. Consequently, existing methods often provide upper bounds that are unrealistically high for real-world PV absorbers.

Methodology
The author proposes a general quantitative framework centered on the $\Gamma_{PV}$ photovoltaic figure of merit (FOM). Unlike deductive methods based on fundamental physics, this approach utilizes an inductive methodology derived from drift-diffusion simulations of over 2,500 hypothetical absorbers.

The $\Gamma_{PV}$ is a unitless function defined by eight bulk properties of the PV absorber:

1. $\alpha$: Spectral average of the absorption coefficient.
2. $\sigma$: Spectral dispersion of the absorption coefficient.
3. $\tau$: Non-radiative recombination lifetime.
4. $\mu$: Carrier mobility.
5. $n$: Carrier concentration.
6. $\epsilon$: Static dielectric constant.
7. $m$: Density-of-states (DOS) effective mass.
8. $E_g$: Band gap.

The framework defines a maximum achievable efficiency, $\eta_{\Gamma}$, for a planar single-junction solar cell under standard AM1.5G conditions. This efficiency is expressed as a function of the $\Gamma_{PV}$ value and the theoretical SQ limit ($\eta_{sq}$) of the material. By normalizing $\eta_{\Gamma}$ against $\eta_{sq}$, the framework creates an "accessible region" of efficiency versus FOM space. This region represents the realistic performance ceiling for a material given its bulk properties, distinguishing it from the "inaccessible region" allowed only by the SQ limit but forbidden by carrier collection losses.

Key Contributions

• Inductive Efficiency Limits: The paper introduces a more stringent set of efficiency limits driven by the $\Gamma_{PV}$ FOM, which explicitly incorporates carrier collection losses (via $\mu$, $n$, and $\epsilon$) that classic detailed balance methods overlook.
• Quantitative Bridge: The framework provides a direct quantitative link between computationally determined material properties and realistic PV efficiency, enabling the evaluation of materials at any development stage, including those not yet synthesized.
• Diagnostic Tool: The framework allows researchers to distinguish whether a material's performance is limited by its intrinsic bulk properties or by device-level factors (interfaces, contacts, architecture).
• Integration with Computational Screening: The author demonstrates that the eight required properties can be estimated via first-principles calculations (Density Functional Theory), including recent advances in estimating carrier capture coefficients and scattering rates, making the framework applicable to purely computational materials discovery.

Results
The framework was applied to 28 experimentally synthesized PV absorbers and 10 computationally modeled absorbers:

• Predictive Power: Analysis of the training set (2,500 hypothetical absorbers) shows that while simpler FOMs like $\alpha\tau$ or $\alpha\tau\mu$ lack general predictive power, $\Gamma_{PV}$ correlates strongly with maximum achievable efficiency, effectively splitting the efficiency space into accessible and inaccessible regions.
• Experimental Validation: All 28 experimental absorbers fall within the accessible region defined by $\Gamma_{PV}$. High-performing materials like GaAs and alloyed perovskites lie near the $\eta_{\Gamma,sq}$ limit, indicating their device architectures are sufficiently optimized relative to their bulk quality.
• Material-Specific Insights:
  • CIGSe and mc-Si: These materials have reached efficiencies close to their FOM-predicted limits, suggesting further gains require bulk property improvements.
  • CdTe, Sn-based perovskites, and Kesterites: These materials show a gap between their current efficiency and their $\Gamma_{PV}$-predicted potential, indicating that device-level optimization (interfaces, contacts) is currently the more urgent priority.
  • Low-FOM Materials: Materials like SnS and the recently proposed Ag$_3$SI exhibit extremely low FOMs. The analysis suggests that even perfect device structures cannot compensate for their poor bulk properties, casting doubt on their viability as high-efficiency absorbers.
  • Early-Stage Materials: The data suggests that in the very early stages of novel PV material development, bulk material quality varies significantly regardless of accumulated research experience. This implies that a strategy of rapid diversification and screening may be more effective than deep investigation of a few candidates initially.
• Computational vs. Experimental: For materials with significant experimental history (e.g., MAPbI$_3$, CdTe), efficiency limits calculated using first-principles properties closely match those derived from experimental data, validating the use of computational screening for $\Gamma_{PV}$.

Significance and Claims
The paper claims that the $\Gamma_{PV}$ framework serves as a general objective function suitable for closed-loop research in autonomous labs. By instantly evaluating a single equation based on eight bulk properties, it offers a quantitative bridge between material science and device engineering. The framework enables researchers to:

1. Track the historical development of PV absorbers and correlate progress with specific technological breakthroughs (e.g., the impact of alkali post-deposition treatments on CIGSe).
2. Quantify the relative urgency of optimizing bulk absorber properties versus device-level engineering.
3. Guide future optimization by identifying which specific material properties (e.g., carrier mobility) are the primary bottlenecks for specific technologies.

The author concludes that this approach provides a credible descriptor for the ultimate performance level of candidate PV absorbers, offering a more realistic assessment than traditional detailed balance limits, particularly for materials where carrier collection is a limiting factor.