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Modeling efficiency penalties of narrow-bandgap perovskites in Si-based tandem solar cells: Incorporating luminescent coupling at non-ideal absorption

This study presents a detailed balance model incorporating luminescent coupling to demonstrate that narrow-bandgap perovskites (~1.57 eV) incur surprisingly small efficiency penalties in silicon-based tandem solar cells compared to optimal bandgap counterparts, suggesting their potential relevance is underestimated due to significant gains in stability and material savings.

Original authors: Rolf Brendel

Published 2026-08-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Rolf Brendel

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Solar cells are the workhorses of the renewable energy transition, turning sunlight directly into electricity. For decades, scientists have known that a single layer of material cannot capture all the energy in sunlight efficiently; some colors of light pass right through, while others are absorbed too quickly, wasting their energy as heat. To solve this, researchers stack two different types of solar cells on top of each other, creating a tandem device. The top layer is designed to catch the high-energy, blue light, while letting the lower-energy, red light pass through to a silicon layer underneath to be harvested. This pairing has the potential to push solar efficiency far beyond what single-layer cells can achieve. However, finding the perfect material for that top layer is a delicate balancing act. If the top layer is tuned to absorb the wrong range of colors, it might generate too much electricity for the bottom layer to handle, or it might be too thick, making the device expensive and unstable.

A researcher at Leibniz University Hannover and the Institute for Solar Energy Research Hamelin has developed a new way to model these stacked cells to see if a slightly different material choice might actually be better than the current favorite. They focused on a specific type of material called a perovskite, which is a crystal structure that can be tuned to absorb different colors of light. While the scientific community has generally agreed that the ideal top layer should have a band gap of about 1.7 electron volts to maximize power, the researcher wanted to know what happens if the material is slightly different, with a band gap of 1.57 electron volts. This narrower gap means the material absorbs more of the solar spectrum, but it also creates a surplus of energy that needs to be managed. The key to their investigation was a phenomenon called luminescent coupling, a process where the top cell, after absorbing light, re-emits some of that energy as light that travels down into the bottom silicon cell to be used again.

Using a detailed computer model based on fundamental physics, the researcher simulated how these tandem cells behave under standard sunlight. They accounted for the thickness of the top layer and how light bounces and travels through the device, rather than relying on simplified assumptions that ignore these optical details. Their simulations revealed a surprising result: the efficiency penalty for using the narrower-gap material is much smaller than previously thought. When the top cell is tuned to the ideal 1.7 electron volts, the device reaches a peak efficiency of about 41.8 percent. When the top cell is made of the narrower-gap material, the efficiency drops to roughly 39.9 percent. This represents a relative loss of only about 5 percent. In the world of solar energy, where every fraction of a percent is fiercely contested, this is a remarkably small price to pay.

The reason this small loss is so significant lies in the thickness of the materials required. To reach that peak efficiency with the ideal 1.7 electron-volt material, the top layer needs to be quite thick, around 1500 nanometers. However, the researcher found that the narrower-gap material reaches its best performance at a thickness of just 733 nanometers. This means that by accepting a tiny drop in theoretical efficiency, manufacturers could cut the amount of material needed for the top cell by more than half. This reduction is not just about saving money on raw materials; it also speeds up the manufacturing process, as depositing thinner layers takes less time, and it reduces the amount of toxic lead contained in each square meter of the panel.

The study also explored how these findings hold up in different configurations. In a setup where the two cells are connected electrically in a single circuit, the 5 percent penalty remains consistent. However, if the cells are wired separately, allowing them to operate independently, the efficiency gap shrinks even further to just 2 percent. This suggests that the narrower-gap material is highly versatile. The researcher noted that while the ideal gap material is the theoretical maximum, the narrower-gap option offers a compelling trade-off. If the narrower-gap material proves to be more stable over time or cheaper to produce, it could ultimately deliver more electricity over the lifetime of a solar farm than the theoretically perfect but more fragile alternative.

By rigorously calculating how light moves and couples between the layers, this work challenges the assumption that the optimal band gap is the only path forward. It suggests that the narrow-gap perovskite, which has been somewhat overlooked in favor of the theoretical ideal, may be a more practical choice for real-world solar panels. The findings provide a data-driven way to weigh the trade-offs between raw efficiency and factors like stability, cost, and material usage. For the future of solar power, this means that the search for the perfect solar cell might not require chasing a single theoretical number, but rather finding the right balance between performance and practicality.

Technical Summary: Modeling Efficiency Penalties of Narrow-Bandgap Perovskites in Si-Based Tandem Solar Cells

Problem Statement
Accurate prediction of the efficiency potential for perovskite (Pk) top cells in silicon (Si)-based tandem devices depends critically on quantifying luminescent coupling (LC). While the optimal band gap for a Pk top cell is generally accepted to be approximately 1.7 eV, materials with narrower band gaps (~1.57 eV) offer potential advantages in stability, reduced material usage, and lower toxicity. However, previous modeling approaches have struggled to reliably quantify the efficiency penalty associated with these sub-optimal band gaps. Existing models often relied on simplifying assumptions, such as abrupt absorption onsets, unity absorption for all photons above the band gap, or empirical LC values that failed to capture the intrinsic dependence of LC on band gap and absorber thickness. Crucially, no prior approach rigorously derived LC from first principles for non-ideal (non-black) top cells, leading to potential overestimations of efficiency losses for narrow-bandgap materials.

Methodology
The author presents a comprehensive detailed balance (DB) model that derives luminescent coupling from basic physical principles, specifically accounting for wavelength-dependent absorption in non-ideal top cells. The model integrates and extends previous frameworks to ensure full compatibility with established DB modeling for single-junction crystalline Si cells.

Key features of the modeling framework include:

Physical Rigor: The model calculates LC by solving an equation system for interface intensities, considering both specular and diffuse light fluxes. It explicitly accounts for the density of photon states in air versus the bottom cell, avoiding the assumption that a "black" cell emits equally in all directions.
Optical and Electronic Parameters: The simulation incorporates the AM1.5G solar spectrum, wavelength-dependent optical constants derived from Kramers-Kronig conform dielectric functions (using Tauc-Lorenz models for MAPbI3), ideal anti-reflection, a Lambertian back reflector, and Auger recombination in the Si bottom cell.
ALIAS Approach: The core of the method involves calculating the probability of luminescence from the top cell being absorbed in the bottom cell ( $\Lambda_{1\to2}$ ) versus escaping or being parasitically absorbed. This allows for the calculation of the recombination current and short-circuit current without relying on empirical coupling constants.
Configurations: The model is applied to two-terminal (2T), three-terminal (3T), and four-terminal (4T) configurations, varying the perovskite thickness ( $W_1$ ) and band gap ( $E_{g1}$ ).

Key Contributions

First-Principles LC Derivation: The paper provides the first rigorous derivation of luminescent coupling for non-black cells, demonstrating that LC is sensitive to both the band gap and the thickness of the top cell.
Quantification of Efficiency Penalties: The study quantifies the relative efficiency penalty of narrow-bandgap perovskites (~~1.57 eV) compared to the optimal band gap (~~1.7 eV).
Thickness Optimization: The model reveals that narrow-bandgap materials allow for significantly thinner absorber layers while maintaining current matching, a factor previously underutilized in efficiency trade-off analyses.

Results
The simulations yield the following primary findings:

Efficiency Penalty: For a 2T configuration, the relative efficiency penalty for a 1.57 eV perovskite compared to the optimal 1.7 eV gap is approximately 4.7% to 5%. This is significantly lower than previous estimates (up to 25%) that neglected LC or used less rigorous models. In 4T configurations, the penalty drops further to roughly 2%.
Thickness Savings: The optimal thickness for the narrow-bandgap (1.57 eV) top cell is reduced by more than 50% compared to the optimal gap case. For instance, in the reference 2T case, the optimal thickness for 1.57 eV is ~733 nm, whereas the optimal gap requires ~1500 nm.
Luminescent Coupling Magnitude: The LC current density ( $J_{1\to2}$ ) increases steeply with thickness for narrow band gaps, reaching 4.37 mA/cm² at 1500 nm. This coupling is essential for current matching in 2T devices with narrow-bandgap top cells.
Robustness: The ~5% penalty and >50% thickness savings remain consistent across various assumptions, including reduced internal luminescent efficiency ( $Q_i = 0.7$ ), the inclusion of front surface light trapping, and the addition of non-radiative recombination in the Si cell.
Configuration Dependence: In 3T and 4T configurations, the efficiency penalty remains low (~2-5%), but the advantage in optimal thickness disappears as current matching constraints are relaxed.

Significance and Claims
The paper argues that the modest efficiency losses associated with narrow-bandgap perovskites (~1.57 eV) may have been previously underestimated due to the lack of rigorous LC modeling. The author claims that these materials possess a "previously underestimated relevance" for tandem photovoltaics.

The significance lies in the potential trade-off: the ~5% relative efficiency loss in 2T configurations is offset by:

Material Savings: A reduction in absorber thickness by more than half, which is critical for vacuum deposition techniques and cost reduction.
Stability: Narrow-bandgap materials often exhibit voltages closer to their radiative limits and suffer less from phase segregation and compositional inhomogeneities compared to wide-bandgap counterparts.
Toxicity: Thinner films reduce the total lead (Pb) content per module area.
Versatility: These materials are suitable for high-efficiency single-junction modules (in 4T setups) and space applications due to superior radiation tolerance.

The author concludes that their model enables a data-driven selection of band-gap materials, allowing performance considerations to be balanced against stability and manufacturing criteria, potentially motivating a strategic reassessment of developing Pk-Si tandems with lower-bandgap absorbers.

Technical Summary: Modeling Efficiency Penalties of Narrow-Bandgap Perovskites in Si-Based Tandem Solar Cells

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