🔬 mesoscale physics

Improving photovoltaics by adding extra terminals to extract hot carriers

The paper predicts that adding extra terminals to photovoltaic cells to selectively extract "hot" carriers before they relax can boost power output by 20–40% compared to optimal two-terminal designs, a principle also applicable to multi-terminal thermoelectrics.

Original authors: Bruno Bertin-Johannet, Thibaut Thuégaz, Janine Splettstoesser, Robert S. Whitney

Published 2026-06-29

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CC BY 4.0

Original authors: Bruno Bertin-Johannet, Thibaut Thuégaz, Janine Splettstoesser, Robert S. Whitney

Original paper licensed under CC BY 4.0 (http://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

Imagine a solar panel as a busy train station where sunlight acts as the ticket agent, handing out "energy tickets" to passengers (electrons and holes) so they can travel to a destination to do work.

The Problem: The Rush to the Exit
In a standard solar panel (a "two-terminal" system), there are only two exits: one for passengers going left and one for passengers going right.

The Hot Passengers: When the sun hits the panel, it creates some passengers who are incredibly energetic ("hot"). They are vibrating with the same high energy as the sun itself (about 6,000 degrees).
The Cooling Effect: Unfortunately, the station floor is warm (about 300 degrees). As these hot passengers rush toward the exit, they bump into the floor and quickly lose their extra energy, cooling down to the temperature of the station before they can leave.
The Dilemma: To capture the most energy, you want to catch the passengers while they are still "hot." But if you build a special gate that only lets the super-hot passengers through, you accidentally block the cooler passengers who arrived later or lost some energy. You get high-quality energy from a few people, but you miss out on the crowd. If you open the gate wide to let everyone through, you catch the crowd, but they are all too cool to do much work.

The Solution: Adding More Gates (Terminals)
The researchers propose a simple but clever fix: Add more exits. Instead of just two gates, imagine building a four-gate system.

Gate A (The VIP Exit): This gate has a special filter that only lets the super-hot, high-energy passengers through. Because they are so energetic, they can push against a heavy load (like a heavy door) and generate a lot of power.
Gate B (The Economy Exit): This gate is designed for the passengers who have cooled down a bit. They aren't as strong, so they push against a lighter load, but because the gate is open to them, they can still generate a decent amount of power.

By splitting the crowd, the solar panel gets the best of both worlds: it harvests the high energy from the "VIPs" and the steady flow from the "economy" passengers.

The Results: A Bigger Payday
The paper uses computer models to test this idea:

The Ideal Scenario: In a perfect world where passengers don't lose energy until they hit the gate, adding these extra terminals boosts the power output by about 40% compared to the old two-gate system.
The Realistic Scenario: In the real world, passengers do lose some energy while running through the station. Even with this "friction," the four-gate system still outperforms the two-gate system by 20% to 40%.

The "Infinite" Idea
The researchers also asked, "What if we had a gate for every energy level?" They found that if you could build a system with an infinite number of tiny gates, each tuned to a specific energy level, you could capture 80% of the sun's heat energy. However, the biggest jump in efficiency happens just by going from two gates to four. Adding more than that helps, but the gains get smaller and smaller.

Why This Matters
For 40 years, scientists have tried to build "hot carrier" solar cells (which catch the hot passengers) but struggled because it's hard to catch them before they cool down. This paper suggests that instead of trying to catch everyone with one perfect gate, we should just build more gates with different settings. This allows us to harvest energy from both the hot and the cool passengers simultaneously, making solar cells significantly more powerful without needing to solve the difficult problem of stopping the passengers from cooling down entirely.

The authors suggest this idea could also work for other devices that turn heat into electricity, not just solar panels, and point to nanowires as a promising way to physically build these multi-gate systems.

Technical Summary: Improving Photovoltaics by Adding Extra Terminals to Extract Hot Carriers

Problem Statement
Conventional photovoltaic (PV) cells typically utilize two terminals to collect electrons and holes. A fundamental limitation in these devices is the loss of useful energy via carrier-phonon relaxation. When solar photons excite carriers to energies well above the semiconductor band gap, these "hot" carriers rapidly lose excess energy to the substrate's phonons (thermalizing to ~300 K) before they can be collected. This relaxation converts a significant portion of the photon's energy into heat rather than electrical power.

Hot-carrier photovoltaics aim to mitigate this by collecting carriers while they are still at high energies (near the thermal photon temperature of ~6000 K). However, this approach faces a critical trade-off: to extract high-energy carriers efficiently, energy filters are required to block low-energy carriers. While this maximizes the work extracted per collected carrier, it drastically reduces the total number of carriers collected (specifically those excited by low-energy photons or those that have partially relaxed), often resulting in a lower overall power output compared to optimized two-terminal cells.

Methodology
The authors propose a multi-terminal architecture to resolve the trade-off between carrier energy and collection rate. Instead of coupling the absorber to a single electron-collecting and a single hole-collecting terminal, the model introduces additional terminals (e.g., a four-terminal setup). In this configuration:

Energy Filtering: Different terminals are equipped with energy filters tuned to specific energy intervals. High-energy terminals collect "hot" carriers to generate high voltage, while low-energy terminals collect relaxed carriers to generate additional current.
Independent Loads: Each terminal is coupled to its own load, tuned independently to maximize the total power output.
Modeling Approach: The study employs a scattering-matrix approach to model carrier dynamics.
- Toy-Model: Initially, a thermoelectric toy-model is used where carrier thermalization is absent. Carriers are assumed to follow a thermal distribution at the solar temperature ( $T_{sun} = 6000$ K) and relax only upon re-radiation or collection.
- Full Model: A more realistic model incorporates carrier-carrier thermalization, carrier-phonon thermalization, and electron-hole recombination. These processes are modeled using Büttiker probes, which act as energy-independent relaxation channels. The absorber's carrier distribution is calculated self-consistently as a weighted average of the distributions from the sun, phonons, recombination, and collectors.

Key Contributions and Results

Theoretical Improvement in Power Output:
- Toy-Model Results: In the absence of thermalization, the four-terminal setup achieves a maximum power output approximately 40% higher than the optimal two-terminal setup. Specifically, the four-terminal model converts 48% of the incoming solar heat flow into electrical power, compared to 34% for the two-terminal case.
- Infinite Terminal Limit: The model predicts that adding an infinite number of terminals (with infinitesimally narrow energy filters) could theoretically convert up to 80% of the incoming solar heat flow into electrical power, more than doubling the two-terminal limit. However, the marginal gain diminishes significantly after the first few additional terminals.
Impact of Thermalization (Realistic Conditions):
- The study investigates regimes where carrier-carrier thermalization occurs at rates comparable to other processes.
- In the "hot-carrier limit" (where carrier-carrier thermalization is extremely fast), the two-terminal power output is already high, and adding terminals yields only marginal improvements.
- Crucially, in regimes where thermalization is moderate (a condition often found in experiments), the four-terminal configuration still outperforms the optimal two-terminal device by more than 20%. This suggests that the multi-terminal strategy is most beneficial when experimental conditions do not perfectly isolate the hot-carrier limit.
Robustness to Filter Shape:
- While the theoretical models utilize ideal "boxcar" or step-function energy filters, the authors analyze smoothed filters. They find that filters with a smoothing width ( $w$ ) smaller than half the collector temperature ( $w \lesssim T_{col}/2$ ) yield power outputs nearly identical to those of sharp filters. This implies that experimental realization does not require perfectly sharp energy filters.
Extension to Shockley-Queisser Model:
- The authors apply the multi-terminal concept to the Shockley-Queisser ultimate efficiency model. By adding a pair of terminals to extract carriers before they relax to the band edge, the theoretical efficiency limit increases from ~44% (two-terminal) to ~60% (four-terminal), a 36% relative increase.

Significance and Claims
The paper claims that adding extra terminals to photovoltaic absorbers offers a viable route to significantly improve power output, potentially by 20–40%, without requiring the extreme experimental conditions (ultra-fast carrier-carrier thermalization) that have historically impeded hot-carrier solar cell development.

The authors emphasize that their model captures realistic carrier extraction, including backflow and the impact of extraction on the absorber's non-equilibrium distribution. They assert that while the specific percentage improvements depend on the model parameters, the trend is clear: any model incorporating realistic carrier extraction will show improved power output if extra terminals are added.

The work suggests that this strategy is not limited to photovoltaics but may apply to other nanoscale devices generating work from non-equilibrium distributions, such as thermoelectrics and photoelectrics. The authors point to existing experimental realizations of multi-terminal devices using nanowires as promising platforms for implementing this proposed architecture.

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