Absorption to reflection transition in selective solar coatings

Kyle D. Olson; Joseph J. Talghader

doi:10.1364/OE.20.00A554

Optics Express
Vol. 20,
Issue S4,
pp. A554-A559
(2012)
•https://doi.org/10.1364/OE.20.00A554

Absorption to reflection transition in selective solar coatings

Kyle D. Olson and Joseph J. Talghader

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Kyle D. Olson and Joseph J. Talghader, "Absorption to reflection transition in selective solar coatings," Opt. Express 20, A554-A559 (2012)

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Abstract

The optimum transition wavelength between high absorption and low emissivity for selective solar absorbers has been calculated in several prior treatises for an ideal system, where the emissivity is exactly zero in the infrared. However, no real coating can achieve such a low emissivity across the entire infrared with simultaneously high absorption in the visible. An emissivity of even a few percent radically changes the optimum wavelength separating the high and low absorption spectral bands. This behavior is described and calculated for AM0 and AM1.5 solar spectra with an infrared emissivity varying between 0 and 5%. With an emissivity of 5%, solar concentration of 10 times the AM1.5 spectrum the optimum transition wavelength is found to be 1.28µm and have a 957K equilibrium temperature. To demonstrate typical absorptions in optimized solar selective coatings, a four-layer sputtered Mo and SiO₂ coating with absorption of 5% across the infrared is described experimentally and theoretically.

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Corrections

Kyle D. Olson and Joseph J. Talghader, "Absorption to reflection transition in selective solar coatings: errata," Opt. Express 20, 26744-26745 (2012)
https://opg.optica.org/oe/abstract.cfm?uri=oe-20-24-26744

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Fig. 1 Solar radiation and the thermal blackbody emission spectrums. AM0 is the solar spectrum outside of earth’s atmosphere, AM1.5 is the standard spectrum used for terrestrial solar energy applications. Notice that even though the sun is at an effective emission temperature of 5778K, the peak is comparable to a 700K blackbody because of the great distance between the earth and sun.

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Fig. 2 Calculated and measured reflectivity of an alternating 4 layer structure of Mo and SiO₂ on a Si wafer as a function of wavelength on a log scale. Also a non-ideal step reflectivity used in further simulations. We assume no transmission so the absorption and emission are calculated as 100-R [%]. The actual reflectivity doesn’t reach 100% because we used a gold reference reflector in the FTIR measurement. The dip in reflectivity around 8µm is from the high NA of the FTIR resulting in an average reflectivity over a large angle, and at large angles some light is absorbed due to the SiO₂ IR absorption peak.

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Fig. 3 (a) The ideal thermal equilibrium temperature between a selective absorber and the sun with no concentration (C = 1) as a function of transition wavelength. As the emissivity increases notice that the optimum transition wavelength for a certain operating temperature is shifted to shorter wavelengths. AM0 will have a very similar result to this case.

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Fig. 4 Thermal equilibrium temperature as a function of transition wavelength and emissivity for the AM1.5 solar spectrum with no concentration (C = 1)

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Fig. 5 Thermal equilibrium temperature as a function of transition wavelength for a selective absorber with an emissivity of 5% under AM1.5 illumination at different concentrations. The optimal transition wavelength is highly dependent on the concentration of incoming radiation.

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Equations (5)

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u_{λ}^{d e v i c e} (T) = \frac{2 h c^{2}}{λ^{5}} \frac{1}{[\exp (h c / λ k_{B} T) - 1]}

u_{λ}^{s o l a r} (T) = \frac{2 h c^{2}}{λ^{5}} \frac{1}{[\exp (h c / λ k_{B} T) - 1]} \frac{r^{2}}{R^{2}}

\int_{0}^{\infty} u_{λ}^{d e v i c e} (700 K) \partial λ ≫ \int_{0}^{\infty} u_{λ}^{s o l a r} (5778 K) \partial λ

P_{i n} = C (\int_{0}^{λ_{s}} α u_{λ}^{s o l a r} (T_{s u n}) d λ + \int_{λ_{s}}^{\infty} ε u_{λ}^{s o l a r} (T_{s u n}) d λ)

\begin{matrix} P_{o u t} = \int_{0}^{2 π} \int_{0}^{\frac{π}{2}} (\int_{0}^{λ_{s}} α u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ + \int_{λ_{s}}^{\infty} ε u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ) \sin (θ) \cos (θ) d θ d φ \\ P_{o u t} = π (\int_{0}^{λ_{s}} α u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ + \int_{λ_{s}}^{\infty} ε u_{λ}^{d e v i c e} (T_{d e v i c e}) d λ) \end{matrix}

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Equations (5)

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