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WIREs Energy Environ.
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From steam engine to solar cells: can thermodynamics guide the development of future generations of photovoltaics?

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Thermodynamics has played a singular role in the development of virtually all energy technologies to‐date. This review argues that it also has a role to play in the understanding and design of solar cell operation, particularly looking toward the future, high‐efficiency solar cells. After a historical overview of the key developments in the ‘thermodynamics of light,’ the conversion of a monochromatic light beam is used as a starting point to analyze the conversion process, examine the fundamental losses in terms of irreversible entropy generation, and consider in detail one of the key applications: the Shockley–Queisser detailed balance. We review and compare the principal suggestions for the highest theoretical efficiency of solar energy conversion, and analyze one possible embodiment of such a third‐generation structure: the hot‐carrier solar cell. A somewhat different application of the statistical approach—light trapping—is reviewed at a fundamental level, and the future potential is considered for devices which combine such a ‘thermodynamic squeezing’ of light with latest developments in photonics, leading to a photonic bandgap solar cell. We argue that the widespread use of thermodynamic tools in the current photovoltaics research, especially when combined with the potential benefits to future devices, already indicates that our thinking should not be about if but how thermodynamics can guide us to make better solar cells. WIREs Energy Environ 2016, 5:543–569. doi: 10.1002/wene.204 This article is categorized under: Photovoltaics > Science and Materials Solar Heating and Cooling > Science and Materials
Different facets of the balance and reversibility between absorption and emission of radiation. (a) Kirchhoff's law relating the photon emission rate Φout to the absorptivity a and the photon emission rate Φo(T) of a black body. Kirchhoff's law holds for the total emission as well as for its spectral components. (b) Planck's relation between the emission (εv) and absorption (αv) coefficients at frequency v for a small volume element in the interior of a body. (c) Einstein's relation, linking the photon absorption and emission rates to transitions between quantum levels of the medium. No and Nexc denote the numbers of atoms in the ground and excited states, respectively.
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The internal quantum efficiencies of solar cells with geometric and photonic light trapping, compared with a conventional (thickness 500 µm) and thin (1 µm) crystalline silicon solar cells. BSR indicates Back Surface Reflector (after Ref ).
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Principles of photonic frequency management based on thermodynamics. (a) The fluorescent concentrator/collector, where a photonic bandstop helps to guide emitted light toward a solar cell at the edge. (b) The photonic bandgap solar cell where a photonic bandstop traps assists the trapping of light emitted by the highly absorbing photon management layer inside a poorly absorbing solar cell. (c) The reflectance of the photonic bandstop in (a) and (b) compared with the spectrum of the incident and fluorescent radiation.
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Examples of light trapping schemes in several current types of solar cells. (a) Light trapping in the form of small pyramids etched in the top surface as implemented in, for example, the COMSAT ‘black’ solar cell. (b) A more sophisticated form of surface texturing in the form of inverted pyramids on the UNSW PERL cell. (c) Structure of the dye‐sensitized (Grätzel) cell with light trapping by scattering from titanium oxide nanoparticles.
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The Kirchhoff and Planck relations between the absorption and emission of radiation by a volume dV (to be compared with Figure ).
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The energy densities (a) and photon fluxes (b) at the interface between two media with different refractive indices. (c) The radiation and trapped modes in a medium with a higher refractive index, separated by the ‘escape cone’ with critical angle θc, defined by the Snell's law.
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The thermodynamic parameters of the hot‐carrier solar cell. Red lines correspond to maximum concentration; blue lines to one‐sun illumination. (a) The ratio μH/kBTH of the chemical to thermal energy for the absorber. (b) The temperature TH of the hot absorber. (c) The current–voltage and power characteristics (full and dashed lines, respectively).
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A schematic representation of the modified Ross and Nozik model. Photons absorbed in a hot absorber acquire temperature TH and chemical potential μH. Some photons are emitted and some are converted to electricity in a Carnot engine, with maximum efficiency. Entropy is generated only in the absorption/emission process.
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A schematic representations of the band structure and relevant energies in a hot‐carrier solar cell. In an optimum structure, the bandgap Eg would be close to zero.
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The I‐V characteristic of a two‐level converter as energy efficiency. (a) The energy efficiency (blue line) showing the Carnot energy not available for conversion (shaded by blue) and the loss on account of irreversible entropy generation on account of current extraction. The power efficiency (red line) includes additionally the power loss by photon emission (1 − i)ηe. The inset in (b) shows losses at the maximum power point.
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The efficiencies discussed under the maximum concentration of sunlight in this paper for TS = 6000 K and To = 300 K. PT, Photothermal; ER, Endoreversible (both discussed in the Light Heat and Work section); IT, Infinite tandem; IT‐PC, Infinite tandem with pressure correction; HC, Hot‐carrier (the last three discussed in the Future Directions section). The four efficiencies in the Carnot—Landsberg scheme are linked by dashed gray arrows to indicate the insertion of the fill factor/kinetic entropy generation and by full arrows to show the pressure correction.
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The various energy (a) and power (b) efficiencies considered in this paper as functions of the ratio of the temperatures of the cold and hot reservoirs. The dashed line corresponds to the temperatures TS = 6000 K and To = 300 K.
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The fundamental losses in an ideal single‐junction solar cell. (a) The energy (ηe) and power (ηP) efficiencies (heavy full and dashed lines, respectively) plotted against the normalized current i = I/(in). The dotted vertical dashed line shows the maximum power point. The graph corresponds to the room temperature bandgap 1.12 eV of crystalline silicon. (b) The solar cell conversion efficiency under one‐sun illumination and losses at the maximum power point, plotted against the bandgap Eg of the solar cell material. The colors indicating thermodynamic losses correspond to those in part (a). Spectral coverage losses are equal to 1—scf. The dotted line shows the bandgap used in the graph of energy and power efficiencies in part (a).
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A schematic diagram of the primary photosynthetic energy conversion process (after Refs and ).
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Different heat engines that have, at various times, been considered in the context of solar energy conversion. (a) A schematic diagram of Carnot cycle which will form the starting point for our discussions. The engine absorbs heat Qh from a high‐temperature reservoir at temperature Th and rejects heat Q into a low‐temperature reservoir, assumed throughout this paper to be at the temperature of the surroundings To. (b) A schematic representation of the endoreversible engine (after Ref ). The jagged lines show the heat supply by conduction to and from the Carnot engine, operating between two reservoirs at temperatures Thi and Tli. (c) The general scheme of a solar energy converter where photons are absorbed as high‐temperature heat at temperature Th, rejecting heat at temperature To while emitting photons in a separate channel and performing work. (d) An optical heat pump proposed by Weinstein as a model for electroluminescence. Electrical input (viewed as work) supplemented by the low‐grade heat at temperature To is converted into photon emission, equivalent to high‐temperature heat at temperature Th. (e) An optical heat pump considered by Chukova as a thermodynamic model for a photoluminescence device. (f) Scheme of a light emitting device, serving as a thermodynamic model for a solar cell.
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The Shockley–Queisser ideal efficiency of a single‐junction solar cell as a function of the semiconductor bandgap, together with the bandgaps of a number semiconductor with photovoltaic applications. The incident and emitted light beams have the black‐body spectrum at temperatures 6000 and 300 K, respectively.
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The energy and power efficiencies of the photothermal (a) and endoreversible (b) engines: ηCA denotes the energy efficiency of the Curzon–Ahlborn (endoreversible) engine and ηPT the photothermal power efficiency. Both efficiencies are determined at the point where the engine delivers maximum power. denotes the rate of heat supply to the Carnot engine, with the maximum value .
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