Clean Energy from First Principles

Thermophotovoltaics

Converts thermal radiation from a hot emitter (1000-2500°C) to electricity using narrow-bandgap photovoltaic cells with photon recycling.

Fundamental Principle

Natural Asymmetry Exploited

The temperature difference between a hot emitter (1000-2500°C) and a cool photovoltaic cell (~25-80°C). Hot objects emit electromagnetic radiation with a spectrum determined by their temperature according to Planck's law. A thermophotovoltaic (TPV) cell absorbs this thermal radiation and converts it to electricity via the photovoltaic effect, exactly as a solar cell converts sunlight.

The key insight is that thermal radiation is fundamentally the same phenomenon as sunlight: both are electromagnetic radiation that can excite electrons across a semiconductor bandgap. The difference is spectral: the Sun at 5800K emits primarily in the visible range (peak ~500nm), while practical thermal emitters at 1000-2400°C emit primarily in the near-infrared (peak ~1-3 μm). This shifts the optimal bandgap for TPV cells to lower energies (0.4-1.1 eV) compared to solar cells (1.1-1.4 eV).

Ultimate Source

TPV systems can harvest thermal energy from any high-temperature source:

The application driving current development is thermal batteries for grid-scale energy storage. Excess renewable electricity heats cheap, earth-abundant materials (graphite blocks) to extreme temperatures (1500-2400°C). The heat is stored with minimal losses in heavily insulated containers, then converted back to electricity via TPV when needed. This offers a potential pathway to very low-cost long-duration energy storage.

Key Physics

Planck's law for thermal emission:

B(λ,T)=2hc2λ5⋅1ehc/λkBT−1B(\lambda, T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{e^{hc/\lambda k_B T} - 1}
λpeak=2898 μm\cdotpKT\lambda_{peak} = \frac{2898 \text{ μm·K}}{T}

For emitter temperatures relevant to TPV:

Higher emitter temperatures shift the spectrum toward shorter wavelengths, enabling higher-bandgap cells with better voltage characteristics.

Stefan-Boltzmann law for total radiated power:

P=σT4P = \sigma T^4

where σ = 5.67 × 10⁻⁸ W/m²K⁴. The "fourth power" in the company name Fourth Power refers to this relationship: radiated power increases dramatically with temperature, enabling high power densities from compact emitters.

At 2000°C, a blackbody emits ~1.5 MW/m². This is ~1500× the power density of unconcentrated sunlight, enabling extremely compact power generation.

Photovoltaic conversion:

The TPV cell operates identically to a solar cell. Photons with energy hν > E_g excite electrons across the bandgap, creating electron-hole pairs that are separated by the built-in field of a p-n junction. The key differences from solar PV are:

  1. Lower optimal bandgap (0.4-1.1 eV vs 1.1-1.4 eV)
  2. Different semiconductor materials (III-V compounds vs silicon)
  3. Opportunity for photon recycling (sub-bandgap photons can be reflected back to the emitter)

Photon recycling:

A critical efficiency enhancement unique to TPV. Photons with energy below the bandgap cannot generate electron-hole pairs and would normally be wasted as heat in the cell. In TPV, a highly reflective back-surface reflector (BSR) can return these photons to the emitter, where they are reabsorbed and re-emitted. With 97-99% reflectance, this photon recycling dramatically improves system efficiency by giving sub-bandgap photons multiple chances to be emitted at useful energies.

Air-bridge cell designs achieve near-unity reflectance by incorporating a thin air gap between the active semiconductor and a gold mirror, exploiting the refractive index contrast to enhance reflection.

Conversion Mechanism

Energy Capture and Conversion

TPV converts thermal radiation directly to electricity with no moving parts, no working fluid, and no intermediate mechanical stage. It is a solid-state heat engine. The conversion chain is:

$$\text{Heat} \rightarrow \text{Thermal radiation} \rightarrow \text{Photon absorption} \rightarrow \text{Electron-hole pairs} \rightarrow \text{DC electricity}$$

This solid-state nature offers significant advantages over turbines and other mechanical heat engines: no moving parts to wear, no fluids to manage, silent operation, rapid response, and potential for very high operating temperatures unconstrained by material fatigue limits.

Physical Processes

1. Thermal emission from hot emitter

The emitter, heated to 1000-2500°C, radiates according to its emissivity spectrum ε(λ). A blackbody has ε = 1 at all wavelengths. Real materials have wavelength-dependent emissivity that can be engineered:

Selective emitters can improve efficiency by reducing useless sub-bandgap emission, but add complexity and may degrade at high temperatures. Most practical systems use broadband emitters with photon recycling instead.

2. Radiative heat transfer to TPV cell

Thermal radiation propagates from emitter to cell across a gap (typically a few mm to cm). The view factor F determines what fraction of emitted radiation reaches the cell. Planar geometries with small gaps achieve F approaching unity.

The cell must be actively cooled to maintain operating temperature ~25-80°C. At higher cell temperatures, dark current increases and efficiency drops. Heat rejection is a significant engineering challenge given the high incident power densities.

3. Photon absorption and carrier generation

Photons with hν > E_g are absorbed in the semiconductor, exciting electrons from valence to conduction band. The quantum efficiency (fraction of above-bandgap photons generating collected carriers) approaches 90-95% in well-designed III-V cells.

Photons with hν >> E_g lose excess energy to thermalisation, just as in solar cells. This loss is less severe in TPV because thermal spectra are narrower than the solar spectrum relative to optimal bandgaps.

4. Charge separation and current extraction

The p-n junction separates electrons and holes. External circuit extracts current at a voltage approaching (but always less than) E_g/q. Fill factors of 70-85% are typical for high-quality TPV cells.

5. Sub-bandgap photon recycling

Photons with hν < E_g pass through the semiconductor. A back-surface reflector returns them toward the emitter with >95% reflectance. These photons are reabsorbed by the emitter, contributing to its thermal energy and eventually being re-emitted at possibly useful wavelengths.

This recycling is the key to high TPV efficiency. Without it, more than half of the emitted power would be lost. With 97%+ reflectance (achieved by air-bridge designs), the effective emitter spectrum seen by the cell approaches an ideal step function at the bandgap energy.

Cell Architectures

Single-junction cells:

Tandem (multi-junction) cells:

Air-bridge cells:

Theoretical Limits

Primary Efficiency Limit

The theoretical efficiency of TPV conversion depends on emitter temperature, cell bandgap, and the degree of spectral control:

Single-junction, blackbody emitter, no photon recycling:

  • Efficiency limited by Shockley-Queisser analog
  • At 2000°C with optimal bandgap (~0.7 eV): ~25-30%
  • Losses from thermalisation and sub-bandgap transmission

Single-junction, blackbody emitter, perfect photon recycling:

  • Sub-bandgap photons returned to emitter
  • Theoretical limit ~50-55% at optimal conditions
  • 2024 air-bridge cells approaching this limit (44% demonstrated)

Ideal selective emitter (emission only at E > E_g):

  • Eliminates sub-bandgap emission entirely
  • Single-junction limit: ~54% (at 0.92 eV bandgap)
  • Multi-junction with concentration: up to 85%

Tandem cells with photon recycling:

  • Multiple bandgaps capture spectrum more efficiently
  • Theoretical limit >50% with practical designs
  • Ultimate thermodynamic limit approaches ~85% with infinite junctions

Origin of the Limit

The efficiency limits arise from the same physics as the Shockley-Queisser limit for solar cells, modified for thermal spectra:

  1. Thermalisation losses: Photons with hν >> E_g create carriers that thermalise to band edges, losing excess energy as heat. This is less severe than for solar spectra because thermal emission from finite-temperature sources is spectrally narrower.

  2. Sub-bandgap losses: Photons with hν < E_g cannot generate carriers. Unlike solar cells (where these photons are simply lost), TPV can recycle them back to the emitter with high-reflectance back surfaces.

  3. Radiative recombination: Fundamental requirement that any absorber must also emit. Sets minimum dark current.

  4. Voltage factor: Operating voltage is always less than E_g/q due to entropy generation.

  5. Carnot considerations: TPV is not a Carnot engine (it doesn't operate between two thermal reservoirs in the traditional sense), but thermodynamic limits still apply. The theoretical maximum efficiency for any heat-to-work conversion at emitter temperature T_H and sink temperature T_C approaches the Carnot limit η = 1 - T_C/T_H only with infinite stages of conversion.

Optimal Operating Conditions

The efficiency-maximising conditions involve trade-offs:

Emitter temperature:

Cell bandgap:

Photon recycling reflectance:

Practical Limitations

Material Constraints

TPV cell materials:

TPV requires narrow-bandgap semiconductors with high-quality p-n junctions. The dominant materials are III-V compounds:

Material Bandgap (eV) Optimal emitter T Notes
InGaAsSb 0.50-0.55 1000-1500°C Quaternary, tunable, complex growth
InGaAs 0.60-0.74 1200-1800°C Ternary, mature technology
GaSb 0.72 1500-2000°C Binary, well-developed
Ge 0.66 1200-1800°C Elemental, cheaper, lower efficiency
InGaAsP 0.74-1.1 1400-2400°C Used in air-bridge cells

Silicon (E_g = 1.1 eV) can work with very high temperature emitters (>2200°C) but requires materials that are stable at such extreme temperatures.

These III-V materials are grown by molecular beam epitaxy (MBE) or metal-organic chemical vapour deposition (MOCVD), which are expensive batch processes. Manufacturing cost is a primary barrier to deployment.

Emitter materials:

Must withstand extreme temperatures (1500-2500°C) with stable optical properties:

For thermal battery applications, graphite is strongly favoured due to its extreme thermal stability, high thermal conductivity (enabling fast charging), and very low cost (~$1-5/kg).

Insulation:

Containing heat at 1500-2500°C requires excellent insulation:

Thermal losses determine storage efficiency. State-of-the-art designs lose ~1% of stored energy per day.

Manufacturing Constraints

III-V TPV cell fabrication uses the same epitaxial growth techniques as multi-junction solar cells and high-performance LEDs. These processes are:

  • Capital-intensive (MOCVD reactors cost $1-10M each)
  • Slow (epitaxial growth is a batch process)
  • Require high-purity precursors
  • Have significant yield losses

As of 2024, Antora Energy operates the world's first dedicated TPV manufacturing line with 2 MW/year capacity. Scaling to GW-scale production will require substantial investment and manufacturing learning curves similar to those that drove down solar PV costs.

Thermal Management

The TPV cell must reject all incident radiation that isn't converted to electricity. At 40% efficiency with 1 MW/m² incident power, this means rejecting 600 kW/m² of heat while maintaining cell temperature below ~80°C.

This requires:

Heat rejection is a significant fraction of system complexity and cost, particularly for high-power-density designs.

System Integration

Complete TPV systems require:

The system complexity is substantial but involves no moving parts in the core power conversion, which is the key advantage over turbines.

Scaling Characteristics

Output Scaling Behaviour

TPV power output scales with cell area. Like photovoltaics, this is essentially linear: twice the cell area produces twice the power (given adequate emitter area and thermal management).

Power density depends on:

At 2000°C emitter temperature with ~40% efficiency, power densities of 50-100 W/cm² are achievable. A living-room-sized array (~20 m²) could produce ~1 MW. This is far more compact than any other form of renewable electricity generation.

Viable Scale Range

Minimum scale:

Target scale for grid storage:

Maximum scale:

Cost Scaling

The dominant cost driver is TPV cell manufacturing. Current cells are expensive due to:

Cost reduction pathways:

Thermal storage medium (graphite) is already very cheap. Balance of system costs should follow conventional industrial equipment learning curves.

Target economics for thermal batteries:

Current Status

Technology Readiness Level

Technology TRL Status
III-V TPV cells (GaSb, InGaAs) 7-8 Demonstrated in systems, early manufacturing
Tandem TPV cells 6-7 Lab records, pilot production starting
Air-bridge TPV cells 5-6 Lab demonstration, manufacturing development
Thermal battery + TPV systems 6-7 First commercial-scale demonstration (Antora)
Radioisotope TPV 8-9 Flight heritage (space applications)
Combustion TPV 5-6 Demonstrated, limited commercial traction

TPV for thermal batteries is the application driving current development. The technology has advanced rapidly since 2020, with efficiency records broken multiple times and the first commercial manufacturing now operational.

Efficiency Records

Configuration Efficiency Emitter T Year Organisation
Single-junction air-bridge 44% 1435°C 2024 University of Michigan
Tandem III-V 41.1% 2400°C 2022 MIT/NREL
Single-junction (previous) 32% Various 2020 Various
Commercial target >40% 1500-2000°C 2024 Antora Energy

The jump from ~32% to >40% represents a fundamental breakthrough enabling thermal batteries to compete with turbines on efficiency while offering solid-state simplicity.

Commercial Development

Antora Energy (Sunnyvale, CA):

Fourth Power (Boston):

Other players:

Research Frontiers

Higher efficiency cells:

Lower-cost manufacturing:

System integration:

Alternative applications:

Potential Impact

If thermal battery + TPV systems achieve their cost targets (<$25/kWh, >40% round-trip efficiency), they could address critical gaps in the clean energy transition:

Long-duration storage:

  • Lithium-ion batteries are economical for ~4 hours
  • Thermal batteries could be economical for 10-500 hours
  • Enables very high renewable penetration (approaching 100%)

Industrial decarbonisation:

  • Industry accounts for ~30% of global emissions
  • Much of this is high-temperature heat (>400°C)
  • Thermal batteries can deliver heat at any temperature up to 1500°C+
  • First practical pathway to decarbonise steel, cement, glass, chemicals

Grid flexibility:

  • Solid-state, no moving parts
  • Fast response (seconds)
  • No geographic constraints (unlike pumped hydro)
  • Uses abundant, non-toxic materials (graphite, tin)

The combination of TPV and thermal storage represents one of the most significant recent developments in energy technology, potentially unlocking both long-duration grid storage and industrial heat decarbonisation with a single system architecture.