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May 30, 2022

I once researched a thermoelectric device for energy recovery of the waste heat of aircraft turbine engines. Prior to that, I had never been interested in thermoelectric devices because of their low efficiency. I was also annoyed that even modest increases in their efficiency were praised in press releases for no reason other than as a way of generating more research funding. Thermoelectrics were only useful in my particular application because of the large temperature gradient involved. Turbine engines run really hot, and the temperature difference to a coolant, such as air, is huge. I wrote about thermoelectrics in an earlier article (Thermoelectrics, October 26, 2020).

A simple thermoelectric generator, as shown in the figure, operates by the Seebeck effect, named after Thomas Seebeck (1770-1831). Seebeck demonstrated that dissimilar conductors will generate electricity when a temperature gradient is applied. The principle is that the heat flow in a conductor caused by a temperature gradient results in a diffusion of charge carriers, and this becomes a voltage difference. Thermocouples, useful to temperature measurement, are devices that use metal pairs of alloys such as chromel-alumel (Type K thermocouple). Shown in the figure is a Seekbeck device that operates by electron and hole transport in semiconductors.

Thermoelectric cell of n- and p-doped semiconductor.

A thermoelectric cell of n- and p-doped semiconductor.

A series connection of many such cells offer a means to extract useful electrical power from sources of waste heat, such as automobile exhaust gas.

(Click for larger image.)

Since electrons contribute to both thermal conductivity and electrical conductivity, it's difficult maintaining a large thermal gradient in thermoelectric materials. However, certain semiconductors have a high ratio of electrical conductivity to thermal conductivity. Junctions of n- and p-doped bismuth telluride (Bi2Te3) are typically used in thermoelectric cells, and there are nanotechnology techniques to further increase thermoelectric efficiency.

Good thermoelectric performance is identified by a high Seebeck coefficient (S, volts/kelvin), and low thermal conductivity (κ, watts/(meter-kelvin)); so, these are combined into a thermoelectric figure of merit, commonly denoted as zT, as follows:
Thermoelectric figure of merit equation

In this equation, σ is the electrical conductivity. Somewhat confusingly, zT, is used as the figure of merit, since multiplication by temperature gives a dimensionless number. That's why we don't just cancel the temperature term from both sides of the equation. The highest figures of merit were stalled at just slightly above 1.0 with no great advances over the years. However, the figure of merit has approach 2.0 in decades of research, and it's now possible to get an energy conversion efficiency of nearly 10%.

Research continues on thermoelectric materials, since there are so many applications for thermoelectric recovery of waste heat in today's energy-conscious world. As I write this, my desktop computer is blowing heated air into my office, which is a benefit on cold winter nights, but a thermoelectric generator could reduce my carbon footprint on hot summer days.

Thermoelectric efficiency is still too low, so it was refreshing to read that a research team from MIT and the National Renewable Energy Laboratory (NREL) has enhanced the efficiency of a different device for conversion of heat to electricity. Their thermophotovoltaic (TPV) cell captures high-energy photons from a white-hot heat source and converts that light to electricity, just as a photovoltaic solar cell converts sunlight into electricity.[1-3] This device operates best with a very high temperature source, around 2000 °C. It would have been more useful in my turbine engine application than a thermoelectric generator, but it won't be useful for general waste heat recovery from the most common sources. It's intended as a means of storing energy by heating a material such as graphite to recover the energy at a later time.[1-3]

A thermophotovoltaic cell

The MIT thermophotovoltaic cell.

This 1 cm x 1 cm cell is mounted on a heatsink for an efficiency measurement.

(MIT image by Felice Frankel, licensed under a Creative Commons Attribution Non-Commercial No Derivatives license.[2] Click for larger image.)

The device, which generates electrical power from a heat source of between 2,900 to 2,400 degrees Celsius, has more than a 40% efficiency.[2] This efficiency is about that of steam turbine generator, which is in the range 33-48%.[2] Thermodynamics places an upper efficiency limit on steam conversion at 60%.[2] Presently, more than 90 percent of global electricity derives from heat sources such as coal, natural gas, nuclear energy, and concentrated solar energy, with the conversion of heat to electricity via steam turbine generators.[2] This device, which operates as a heat converter with no moving parts, can work at higher temperatures and at a potentially higher efficiency. Says the paper's corresponding author, Asegun Henry of the MIT Department of Mechanical Engineering,
"One of the advantages of solid-state energy converters are that they can operate at higher temperatures with lower maintenance costs because they have no moving parts... They just sit there and reliably generate electricity."[2]

Thermophotovoltaic devices with just a few percent efficiency were first fabricated in the 1960s, but the efficiency increased to a record 32% in 1980 and plateaued.[2-3] The reason for lack of progress is that heat radiation, idealized as blackbody radiation, extends over a wide range of wavelengths, while photovoltaics are optimized for photon conversion in a narrow range of wavelengths, and some of the light energy is wasted.[3] This new thermophotovoltaic device captures more of the light spectrum through use of wide-bandgap semiconductors stacked in layers that allow photon absorption over an extended range of wavelengths.[2]

Planck's law Blackbody Spectra

blackbody radiation curves.

Higher temperatures are characterized by greater energy and a shift to lower wavelengths.

(Modified Wikimedia Commons image by Darth Kule. Click for larger image.)

To achieve such high efficiency, the thermophotovoltaic device was built from more than twenty layers of materials such as GaAs, (Al,Ga)As, (Ga,In)P, (Ga,In)As, (Al,Ga,In)As, and Ga(As,Sb).[1] This created two separate photovoltaic cells, stacked one on top of the other, in which the top cell is an absorber of mostly visible and ultraviolet light, while the lower cell handles the infrared.[2-3] There's a gold layer at the bottom that reflects the low-energy photons not absorbed by these two cells, so the energy can be reabsorbed by the heat source.[2-3]

Device testing was accomplished by exposure to concentrated light from a high temperature lamp.[2] By changing the voltage, they changed the lamp's temperature; and the thermophotovoltaic device maintained an efficiency of near 40 percent from 2,400-2,900 degrees Celsius with a maximum efficiency of 41.1% for a 2400 °C tungsten filament.[2-3] The thermophotovoltaic cell in this study had an area of a square centimeter.[2] A grid-scale thermal battery system would require 20,000 square feet (about a quarter the area of a football field).[2]

It's estimated that even a 35% efficiency in heat-to-electricity conversion would make this thermal battery approach to energy storage economically viable.[3] Such a system would use renewable energy to heat a liquid metal bath, or graphite, to the required high temperature.[2-3] A mirror capable of reflecting nearly 99% of unabsorbed infrared light back into the heat source was developed previously, and this would boost the device efficiency to a 50% level.[3-4] A venture has been launched to commercialize this technology, and it's estimated that the capital requirement for a viable system would be about $10 perkilowatt-hour of capacity, less than a tenth the cost of grid-scale lithium ion batteries.[3] This research was partially supported by the United States Department of Energy.[2]


  1. Alina LaPotin, Kevin L. Schulte, Myles A. Steiner, Kyle Buznitsky, Colin C. Kelsall, Daniel J. Friedman, Eric J. Tervo, Ryan M. France, Michelle R. Young, Andrew Rohskopf, Shomik Verma, Evelyn N. Wang & Asegun Henry, "Thermophotovoltaic efficiency of 40%," Nature, vol. 604 (April 13, 2022), pp.287-291, https://doi.org/10.1038/s41586-022-04473-y. This is an open access article with a PDF file here.
  2. Jennifer Chu, "A new heat engine with no moving parts is as efficient as a steam turbine," MIT Press Release, April 13, 2022.
  3. Robert F. Service, "'Thermal batteries' could efficiently store wind and solar power in a renewable grid," Science, vol. 376, no. 6590 (April 15, 2022), p. 230.
  4. Dejiu Fan, Tobias Burger, Sean McSherry, Byungjun Lee, Andrej Lenert, & Stephen R. Forrest, "Near-perfect photon utilization in an air-bridge thermophotovoltaic cell," Nature, vol, 586 (September 21, 2020), pp.237-241, https://doi.org/10.1038/s41586-020-2717-7.

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