Thermophotovoltaic

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Thermophotovoltaic (TPV) energy conversion is a direct conversion process from heat to electricity via photons. A basic thermophotovoltaic system consists of a thermal emitter and a photovoltaic diode cell.

The temperature of the thermal emitter varies between different systems from about 900 °C to about 1300 °C, although in principle TPV devices can extract energy from any emitter with temperature elevated above that of the photovoltaic device (forming an optical heat engine). The emitter can be a piece of solid material or a specially engineered structure.Thermal emission is the spontaneous emission of photons due to thermal motion of charges in the material. For these TPV temperatures, this radiation is mostly at near infrared and infrared frequencies. The photovoltaic diodes absorbs some of these radiated photons and converts them into electricity.

Thermophotovoltaic systems have few to no moving parts and are therefore quiet and require little maintenance. These properties make thermophotovoltaic systems suitable for remote-site and portable electricity-generating applications. Their efficiency-cost properties, however, are often poor compared to other electricity-generating technologies. Current research in the area aims at increasing system efficiencies while keeping the system cost low.

TPV systems usually attempt to match the optical properties of thermal emission (wavelength, polarization, direction) with the most efficient absorption characteristics of the photovoltaic cell, since unconverted thermal emission is a major source of inefficiency. Most groups focus on gallium antimonide (GaSb) cells. Germanium (Ge) is also suitable.[1] Much research and development concerns methods for controlling the emitter's properties.

TPV cells have been proposed as auxiliary power conversion devices for capture of otherwise lost heat in other power generation systems, such as steam turbine systems or solar cells.

A prototype TPV hybrid car was built, the "Viking 29"[2] (TPV) powered automobile, designed and built by the Vehicle Research Institute (VRI) at Western Washington University.

TPV research is an active area. Among others, the University of Houston TPV Radioisotope Power Conversion Technology development effort is attempting to combine a thermophotovoltaic cell with thermocouples to provide a 3 to 4-fold improvement in system efficiency over current radioisotope thermoelectric generators.

History[edit]

Henry Kolm had constructed an elementary TPV system at MIT in 1956. However, Pierre Aigrain is widely cited as the inventor based on the content of lectures he gave at MIT between 1960–1961 which, unlike Kolm's system, led to research and development.[3]

Background[edit]

Thermophotovoltaics (TPVs) are a class of power generating system that convert thermal energy into electrical energy. They consist of, at a minimum, an emitter and a photovoltaic power converter. Most TPV systems include additional components such as concentrators, filters and reflectors.

The basic principle is similar to that of traditional photovoltaics (PV) where a p-n junction is used to absorb optical energy, generate and separate electron/hole pairs, and in doing so convert that energy into electricity. The difference is that the optical energy is not directly generated by the Sun, but instead by a material at high temperature (termed the emitter), that causes it to emit light. In this way thermal energy is converted to electrical energy.

The emitter can be heated by sunlight or other techniques. In this sense, TPVs provide a great deal of versatility in potential fuels. In the case of solar TPVs, large concentrators are needed to provide reasonable temperatures for efficient operation.

Improvements can take advantage of filters or selective emitters to create emissions in a wavelength range that is optimized for a specific photovoltaic (PV) converter. In this way TPVs can overcome a fundamental challenge for traditional PVs, making efficient use of the entire solar spectrum. For black body emitters, photons with energy less than the bandgap of the converter cannot be absorbed and are either reflected and lost or pass through the cell. Photons with energy above the bandgap can be absorbed, but the excess energy, , is again lost, generating undesirable heating in the cell. In the case of TPVs, similar issues can exist, but the use of either selective emitters (emissivity over a specific wavelength range), or optical filters that only pass a narrow range of wavelengths and reflect all others, can be used to generate emission spectra that can be optimally converted by the PV device.

To maximize efficiency, all photons should be converted. A process often termed photon recycling can be used to approach this. Reflectors are placed behind the converter and anywhere else in the system that photons might not be efficiently directed to the collector. These photons are directed back to the concentrator where they can be converted, or back to the emitter, where they can be reabsorbed to generate heat and additional photons. An optimal TPV system would use photon recycling and selective emission to convert all photons into electricity.

Efficiency[edit]

The upper limit for efficiency in TPVs (and all systems that convert heat energy to work) is the Carnot efficiency, that of an ideal heat engine. This efficiency is given by:

where Tcell is the temperature of the PV converter. For the best reasonable values in a practical system, Tcell~300K and Temit~1800, giving a maximum efficiency of ~83%. This limit sets the upper limit for the system efficiency. At 83% efficiency, all heat energy is converted to radiation by the emitter which is then converted by the PV into electrical energy without losses, such as thermalization or Joule heating. Maximum efficiency presumes no entropy change, which is only possible if the emitter and cell are at the same temperature. More accurate models are quite complicated.

Emitters[edit]

Deviations from perfect absorption and perfect black body behavior lead to light losses. For selective emitters, any light emitted at wavelengths not matched to the bandgap energy of the photovoltaic may not be efficiently converted (for reasons discussed above) and leads to reduced efficiency. In particular, emissions associated with phonon resonances are difficult to avoid for wavelengths in the deep infrared, which cannot be practically converted. Ideal emitters produce no infrared.

Filters[edit]

For black body emitters or imperfect selective emitters, filters reflect non-ideal wavelengths back to the emitter. These filters are imperfect. Any light that is absorbed or scattered and not redirected to the emitter or the converter is lost, generally as heat. Conversely, practical filters often reflect a small percentage of light in desired wavelength ranges. Both are inefficiencies.

Converters[edit]

Even for systems where only light of optimal wavelengths is passed to the converter, inefficiencies associated with non-radiative recombination and ohmic losses exist. Since these losses can depend on the light intensity incident on the cell, real systems must consider the intensity produced by a given set of conditions (emitter material, filter, operating temperature).

Geometry[edit]

In an ideal system, the emitter would be surrounded by converters so no light is lost. However, realistically, geometries must accommodate the input energy (fuel injection or input light) used to heat the emitter. Additionally, costs prohibit the placement of converters everywhere. When the emitter reemits light, anything that does not travel to the converters is lost. Mirrors can be used to redirect some of this light back to the emitter; however, the mirrors may have their own losses.

Black body radiation[edit]

For black body emitters where photon recirculation is achieved via filters, Planck's law states that a black body emits light with a spectrum given by:

where I' is the flux of light of a specific wavelength, λ, given in units of 1/m3/s. h is Planck's constant, k is Boltzmann's constant, c is the speed of light, and Temit is the emitter temperature. Thus, the light flux with wavelengths in a specific range can be found by integrating over the range. The peak wavelength is determined by the temperature, Temit based on Wien's displacement law:

where b is Wien's displacement constant. For most materials, the maximum temperature an emitter can stably operate at is about 1800 °C. This corresponds to an intensity that peaks at λ~1600 nm or an energy of ~0.75 eV. For more reasonable operating temperatures of 1200 °C, this drops to ~0.5 eV. These energies dictate the range of bandgaps that are needed for practical TPV converters (though the peak spectral power is slightly higher). Traditional PV materials such as Si (1.1 eV) and GaAs (1.4 eV) are substantially less practical for TPV systems, as the intensity of the black body spectrum is extremely low at these energies for emitters at realistic temperatures.

Active components and materials selection[edit]

Emitters[edit]

Efficiency, temperature resistance and cost are the three major factors for choosing a TPV radiator. Efficiency is determined by energy absorbed relative to total incoming radiation. High temperature operation is a crucial factor because efficiency increases with operating temperature. As emitter temperature increases, black body radiation shifts to shorter wavelengths, allowing for more efficient absorption by photovoltaic cells. Cost is another major commercialization issue.

Polycrystalline silicon carbide[edit]

Polycrystalline silicon carbide (SiC) is the most commonly used emitter for burner TPVs. SiC is thermally stable to ~1700 °C. However, SiC radiates much of its energy in the long wavelength regime, far lower in energy than even the narrowest bandgap photovoltaic. This radiation is not converted into electrical energy. However, non-absorbing selective filters in front of the PV,[4] or mirrors deposited on the back side of the PV[5] can be used to reflect the long wavelengths back to the emitter, thereby recycling the unconverted energy. In addition, polycrystalline SiC is cheap to manufacture.

Tungsten[edit]

Refractory metals can be used as selective emitters for burner TPVs. Tungsten is the most common choice. It has higher emissivity in the visible and near-IR range of 0.45 to 0.47 and a low emissivity of 0.1 to 0.2 in the IR region.[6] The emitter is usually in the shape of a cylinder with a sealed bottom, which can be considered a cavity. The emitter is attached to the back of a thermal absorber such as SiC and maintains the same temperature. Emission occurs in the visible and near IR range, which can be readily converted by the PV to electrical energy.

Rare-earth oxides[edit]

Rare-earth oxides such as ytterbium oxide (Yb2O3) and erbium oxide (Er2O3) are the most commonly used selective emitters for TPVs. These oxides emit a narrow band of wavelengths in the near-infrared region, allowing the tailoring of the emission spectra to better fit the absorbance characteristics of a particular PV cell. The peak of the emission spectrum occurs at 1.29 eV for Yb2O3 and 0.827 eV for Er2O3. As a result, Yb2O3 can be used a selective emitter for Si PV cells and Er2O3, for GaSb or InGaAs. However, the slight mismatch between the emission peaks and band gap of the absorber results in a significant loss of efficiency. Selective emission only becomes significant at 1100 °C and increases with temperature, per Planck's Law. At operating temperatures below 1700 °C, selective emission of rare-earth oxides is fairly low, resulting in a further decrease in efficiency. Currently, 13% efficiency has been achieved with Yb2O3 and silicon PV cells. In general selective emitters have had limited success. More often filters are used with black body emitters to pass wavelengths matched to the bandgap of the PV and reflect mismatched wavelengths back to the emitter.

Photonic crystals[edit]

Photonic crystals are a class of periodic materials that allow the precise control of electromagnetic wave properties. These materials give rise to the photonic bandgap (PBG). In the spectral range of the PBG, electromagnetic waves cannot propagate. The engineering of these materials allows some ability to tailor their emission and absorption properties, allowing for more effective design of selective emitters. Selective emitters with peaks at higher energy than the black body peak (for practical TPV temperatures) allow for wider bandgap converters. These converters are traditionally cheaper to manufacture and less temperature sensitive. Researchers at Sandia Labs demonstrated a high-efficiency (34% of light emitted from PBG selective emitter can be converted to electricity) TPV emitter using tungsten photonic crystals.[7] However, manufacturing of these devices is difficult and not commercially feasible.

Photovoltaic cells[edit]

Silicon[edit]

Early work in TPVs focused on the use of Si PVs. Silicon's commercial availability, extremely low cost, scalability and ease of manufacture makes this material an appealing candidate. However, the relatively wide bandgap of Si (1.1eV) is not ideal for use with a black body emitter at lower operating temperatures. Calculations using Planck's law, which describes the black body spectrum as a function of temperature, indicates that Si PVs would only be feasible at temperatures much higher than 2000 K. No emitter has been demonstrated that can operate at these temperatures. These engineering difficulties led to the pursuit of lower-bandgap semiconductor PVs.

Using selective radiators with Si PVs is still a possibility. Selective radiators would eliminate high and low energy photons, reducing heat generated. Ideally, selective radiators would emit no radiation beyond the band edge of the PV converter, increasing conversion efficiency significantly. No efficient TPVs have been realized using Si PVs.

Germanium[edit]

Early investigations into low bandgap semiconductors focused on germanium (Ge). Ge has a bandgap of 0.66 eV, allowing for conversion of a much higher fraction of incoming radiation. However, poor performance was observed due the extremely high effective electron mass of Ge. Compared to III-V semiconductors, Ge's high electron effective mass leads to a high density of states in the conduction band and therefore a high intrinsic carrier concentration. As a result, Ge diodes have fast decaying "dark" current and therefore, a low open-circuit voltage. In addition, surface passivation of germanium has proven extremely difficult.

Gallium antimonide[edit]

The gallium antimonide (GaSb) PV cell, invented in 1989,[8] is the basis of most PV cells in modern TPV systems. GaSb is a III-V semiconductor with the zinc blende crystal structure. The GaSb cell is a key development owing to its narrow bandgap of 0.72 eV. This allows GaSb to respond to light at longer wavelengths than silicon solar cell, enabling higher power densities in conjunction with manmade emission sources. A solar cell with 35% efficiency was demonstrated using a bilayer PV with GaAs and GaSb,[8] setting the solar cell efficiency record.

Manufacturing a GaSb PV cell is quite simple. Czochralski Te-doped n-type GaSb wafers are commercially available. Vapor-based Zn diffusion is carried out at elevated temperatures ~450 °C to allow for p-type doping. Front and back electrical contacts are patterned using traditional photolithography techniques and an anti-reflective coating is deposited. Current efficiencies are estimated at ~20% using a 1000 °C black body spectrum.[9] The radiative limit for efficiency of the GaSb cell in this setup is 52%, so vast improvements can still be made.

Indium gallium arsenide antimonide[edit]

Indium gallium arsenide antimonide (InGaAsSb) is a compound III-V semiconductor. (InxGa1−xAsySb1−y) The addition of GaAs allows for a narrower bandgap (0.5 to 0.6 eV), and therefore better absorption of long wavelengths. Specifically, the bandgap was engineered to 0.55 eV. With this bandgap, the compound achieved a photon-weighted internal quantum efficiency of 79% with a fill factor of 65% for a black body at 1100 °C.[10] This was for a device grown on a GaSb substrate by organometallic vapour phase epitaxy (OMVPE). Devices have been grown by molecular beam epitaxy (MBE) and liquid phase epitaxy (LPE). The internal quantum efficiencies (IQE) of these devices are approaching 90%, while devices grown by the other two techniques exceed 95%.[11] The largest problem with InGaAsSb cells is phase separation. Compositional inconsistencies throughout the device degrade its performance. When phase separation can be avoided, the IQE and fill factor of InGaAsSb approach theoretical limits in wavelength ranges near the bandgap energy. However, the Voc/Eg ratio is far from the ideal.[11] Current methods to manufacture InGaAsSb PVs are expensive and not commercially viable.

Indium gallium arsenide[edit]

Indium gallium arsenide (InGaAs) is a compound III-V semiconductor. It can be applied in two ways for use in TPVs. When lattice-matched to an InP substrate, InGaAs has a bandgap of 0.74 eV, no better than GaSb. Devices of this configuration have been produced with a fill factor of 69% and an efficiency of 15%.[12] However, to absorb higher wavelength photons, the bandgap may be engineered by changing the ratio of In to Ga. The range of bandgaps for this system is from about 0.4 to 1.4 eV. However, these different structures cause strain with the InP substrate. This can be controlled with graded layers of InGaAs with different compositions. This was done to develop of device with a quantum efficiency of 68% and a fill factor of 68%, grown by MBE.[10] This device had a bandgap of 0.55 eV, achieved in the compound In0.68Ga0.33As. n has the advantage of being a well-developed material. InGaAs can be made to lattice match perfectly with Ge resulting in low defect densities. Ge as a substrate is a significant advantage over more expensive or harder-to-produce substrates.

Indium phosphide arsenide antimonide[edit]

The InPAsSb quaternary alloy has been grown by both OMVPE and LPE. When lattice-matched to InAs, it has a bandgap in the range 0.3–0.55 eV. The benefits of a TPV system with such a low band gap have not been studied in depth. Therefore, cells incorporating InPAsSb have not been optimized and do not yet have competitive performance. The longest spectral response from an InPAsSb cell studied was 4.3 μm with a maximum response at 3 μm.[11] While this is a promising material, it has yet to be developed. For this and other low-bandgap materials, high IQE for long wavelengths is hard to achieve due to an increase in Auger recombination.

Applications[edit]

TPVs promise efficient and economically viable power systems for both military and commercial applications. Compared to traditional nonrenewable energy sources, burner TPVs have little NOx emissions and are virtually silent. Solar TPVs are a source of emission-free renewable energy. TPVs can be more efficient than PV systems owing to recycling of unabsorbed photons. However, TPVs are more complex and losses at each energy conversion step can lower efficiency. Further developments must be made to the absorber/emitter and PV cell. When TPVs are used with a burner source, they provide on-demand energy. As a result, energy storage is not needed. In addition, owing to the PV's proximity to the radiative source, TPVs can generate current densities 300 times that of conventional PVs.

Man-portable power[edit]

Battlefield dymamics require portable power. Conventional diesel generators are too heavy for use in the field. Scalability allows TPVs to be smaller and lighter than conventional generators. Also, TPVs have few emissions and are silent. Multifuel operation is another potential benefit.

Early investigations into TPVs in the 1970s failed due to PV limitations. However, with the realization of the GaSb photocell, a renewed effort in the 1990s improved results. In early 2001, JX Crystals delivered a TPV based battery charger to the Army that produced an output of 230 W with propane. This prototype utilized an SiC emitter operating at 1250 °C and GaSb photocells and was approximately 0.5 m tall.[13] The power source had an efficiency of 2.5%, calculated by the ratio of the power generated to the thermal energy of the fuel burned. This is too low for practical battlefield use. To increase efficiency, narrow-band emitters must be realized and the temperature of the burner must be raised. Further thermal management steps, such as water cooling or coolant boiling, must be implemented. Although many successful proof-of-concept prototypes wer demonstrated, no portable TPV power sources have reached troop testing or battlefield implementation.

Spacecraft[edit]

For space travel power generation systems must provide consistent and reliable power without large amounts of fuel. As a result, solar and radioisotope fuels (extremely high power density and long lifetime) are ideal sources of energy. TPVs have been proposed for each. In the case of solar energy, orbital spacecraft may be better locations for the large and potentially cumbersome concentrators required for practical TPVs. However, because of weight considerations and inefficiencies associated with the somewhat more complicated design of TPVs, conventional PVs will almost surely be more effective for these applications.

Probably more interesting is the prospect of using TPVs for conversion of radioisotope energy. The output of isotopes is thermal energy. In the past thermoelectricity (direct thermal to electrical conversion with no moving parts) has been used because of TPV efficiency is less than the ~10% of thermoelectric converters.[14] Stirling engines have also been considered, but face reliability concerns, which are unacceptable for space missions, despite improved conversion efficiencies (>20%).[15] However, with the recent advances in small-bandgap PVs, TPVs are becoming more promising candidates. A TPV radioisotope converter with 20% efficiency was demonstrated that uses a tungsten emitter heated to 1350 K, with tandem filters and a 0.6 eV bandgap InGaAs PV converter (cooled to room temperature). About 30% of the lost energy was due to the optical cavity and filters. The remainder was due to the efficiency of the PV converter.[15]

Low-temperature operation of the converter is critical to the efficiency of TPV. Heating PV converters increases their dark current, thereby reducing efficiency. The converter is heated by the radiation from the emitter. In terrestrial systems it is reasonable to dissipate this heat without using additional energy with a heat sink. However, space is an isolated system, where heat sinks are impractical. Therefore, it is critical to develop innovative solutions to efficiently remove that heat, or optimized TPV cells that can operate efficiently with higher temperature converters. Both represent substantial challenges. Despite this, TPVs offer substantial promise for use in future space applications.[14]

Commercial applications[edit]

Off-grid generators[edit]

Many homes are located in remote regions not connected to the power grid. Where available, power line extensions can be impractical. TPVs can provide a continuous supply of power in off-grid homes. Traditional PVs on the other hand, would not provide sufficient power during the winter months and nighttime, while TPVs can utilize alternative fuels to augment solar-only production.

The greatest advantage for TPV generators is cogeneration of heat and power. In cold climates, it can function as both a heater or stove and a power generator. JX Crystals developed a prototype TPV heating stove and generator. It burns natural gas and uses a SiC source emitter operating at 1250 °C and GaSb photocell to output 25,000 BTU/hr simultaneously generating 100 W. However, costs must be significantly reduced to render it commercially viable.

When a furnace is used as a heater and a generator, it is called combined heat and power (CHP). Many TPV CHP scenarios have been theorized, but a generator using boiling coolant was found most cost efficient.[16] The proposed CHP would utilize a SiC IR emitter operating at 1425 °C and GaSb photocells cooled by boiling coolant. The TPV CHP would output 85,000 BTU/hr and generate 1.5 kW. The estimated efficiency would be 12.3% and the investment would be 0.08 €/kWh provided that the lifetime of the CHP furnace is 20 years. The estimated cost of other non-TPV CHPs are 0.12 €/kWh for gas engine CHP and 0.16 €/kWh for fuel cell CHP. This proposed furnace has not been commercialized because the market was not thought to be large enough.

Recreational vehicles[edit]

TPVs have been proposed for use in recreational vehicles. With the advent of hybrid and other electrically powered vehicles, power generators with electrical outputs have become more interesting. In particular the versatility of TPVs for fuel choice and the ability to use multiple fuel sources makes them interesting as a wider variety of fuels are being with better sustainability are emerging. The silent operation of TPVs allow the generation of electricity when the use of noisy conventional generators is not allowed, and do not disturb others. However, the emitter temperatures required for practical efficiencies make TPVs on this scale unlikely.[17]

References[edit]

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  2. ^ Seal, M.R. "WWU VRI website: Viking 29 – A Thermophotovoltaic Hybrid Vehicle Designed and Built at Western Washington University". Retrieved 2010-11-12. 
  3. ^ Nelson, R.E. (2003). "A brief history of thermophotovoltaic development". Semiconductor Science and Technology. 18 (5): S141–S143. Bibcode:2003SeScT..18S.141N. doi:10.1088/0268-1242/18/5/301. 
  4. ^ Horne E. (2002). Hybrid thermophotovoltaic power systems. Final report by EDTEK Inc. for the California energy commission.
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  8. ^ a b Fraas, L.M., Avery, J.E., Sundaram, V.S., Dinh, V.T., Davenport, T.M. and Yerkes, J.W. (1990). "IEEE Conference on Photovoltaic Specialists": 190. doi:10.1109/PVSC.1990.111616.  |chapter= ignored (help)
  9. ^ Algora, C. & Martin, D. (2003). "Modelling and Manufacturing GaSb TPV". THERMOPHOTOVOLTAIC GENERATION OF ELECTRICITY: Fifth Conference on Thermophotovoltaic Generation of Electricity. AIP Conference Proceedings. 653: 452. Bibcode:2003AIPC..653..452A. doi:10.1063/1.1539400.  |chapter= ignored (help)
  10. ^ a b Charache, G. W.; Egley, J. L.; Depoy, D. M.; Danielson, L. R.; Freeman, M. J.; Dziendziel, R. J.; Moynihan, J. F.; Baldasaro, P. F.; et al. (1998). "Infrared Materials for Thermophotovoltaic Applications". Journal of Electronic Materials. 27 (9): 1038. Bibcode:1998JEMat..27.1038C. doi:10.1007/s11664-998-0160-x. 
  11. ^ a b c Wang, C.A. (2004). "Antimony-based III-V thermophotovoltaic materials and devices". THERMOPHOTOVOLTAIC GENERATION OF ELECTRICITY: Sixth Conference on Thermophotovoltaic Generation of Electricity: TPV6. AIP Conference Proceedings. 738: 255. Bibcode:2004AIPC..738..255W. doi:10.1063/1.1841902.  |chapter= ignored (help)
  12. ^ Karlina, L.B., Kulagina, M.M., Timoshina, N.Kh., Vlasov, A.S. and Andreev, V.M. (2007). "In0.53Ga0.47As/InP conventional and inverted thermophotovoltaic cells with back surface reflector". THERMOPHOTOVOLTAIC GENERATION OF ELECTRICITY: TPV7: Seventh World Conference on Thermophotovoltaic Generation of Electricity. AIP Conference Proceedings. 890: 182. Bibcode:2007AIPC..890..182K. doi:10.1063/1.2711735.  |chapter= ignored (help)
  13. ^ Guazzoni, G. & Matthews, S. (2004). "AIP Conference Proceedings". THERMOPHOTOVOLTAIC GENERATION OF ELECTRICITY: Sixth Conference on Thermophotovoltaic Generation of Electricity: TPV6. AIP Conference Proceedings. 738: 3. Bibcode:2004AIPC..738....3G. doi:10.1063/1.1841874.  |chapter= ignored (help)
  14. ^ a b Teofilo, V.L., Choong, P., Chang, J., Tseng, Y.L., and Ermer, S. (2008). "Thermophotovoltaic Energy Conversion for Space". Journal of Physical Chemistry C. 112 (21): 7841. doi:10.1021/jp711315c. 
  15. ^ a b Wilt, D., Chubb, D., Wolford, D., Magari, P. and Crowley, C. (2007). "AIP Conference Proceedings". THERMOPHOTOVOLTAIC GENERATION OF ELECTRICITY: TPV7: Seventh World Conference on Thermophotovoltaic Generation of Electricity. AIP Conference Proceedings. 890: 335. Bibcode:2007AIPC..890..335W. doi:10.1063/1.2711751.  |chapter= ignored (help)
  16. ^ Palfinger, G., Bitnar, B., Durisch, W., Mayor, J.C., Grützmacher, D. and Gobrecht, J. (2003). "Cost estimate of electricity produced by TPV". Semiconductor Science and Technology. 18 (5): S254. Bibcode:2003SeScT..18S.254P. doi:10.1088/0268-1242/18/5/317. 
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