Abstract

The limits of selective surface performance are evaluated using net power gain as a comparison variable. It is found that a model selective surface based on the optical constants of c-Ge will approach the power gain of an ideal thermally broadened selective surface within 10% for fixed collectors at 300°C, seasonally adjusted collectors at 500°C, and conventional linear tracking parabolic collectors at 700°C. Previous loss limits of performance in the literature were pessimistic primarily due to incorrect absorption edge placement in the energy spectrum and insufficiently effective methods of emittance reduction. Novel emittance reduction methods are suggested.

© 1985 Optical Society of America

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References

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  1. D. M. Trotter, A. J. Sievers, “Thermal Emissivity of Selective Surfaces: New Lower Limits,” Appl. Phys. Lett. 35, 374 (1979).
    [Crossref]
  2. D. M. Trotter, A. J. Sievers, “Spectral Selectivity of High-Temeprature Solar Absorbers,” Appl. Opt. 19, 711 (1980).
    [Crossref] [PubMed]
  3. D. R. Mills, L. C. Botten, “Laser Emissivity Limits Indicated for High Temperature Selectivity Surfaces,” Appl. Opt. 22, 3182 (1983).
    [Crossref] [PubMed]
  4. F. Kreith, J. F. Kreider, Principles of Solar Engineering (McGraw-Hill, New York, 1978), p. 152.
  5. D. R. Mills “Periodically Adjusted Solar Collectors for Medium Temperature Applications,” in Proceedings, ISES Conference, ANZ Branch, Auckland, N.Z. (Aug.1984).
  6. Ref. 4, pp. 653–657.
  7. A. J. Sievers, Solar Energy Conversion, Solid State Physics Aspects (Springer-Verlag, New York, 1979), p. 84.
  8. D. E. Aspes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985 (1983).
    [Crossref]
  9. W. C. Dash, R. Newman, “Intrinsic Optical Absorption in Single-Crystal Germanium and Silicon at 77°K and 300°K,” Phys. Rev. 99, 1151 (1955).
    [Crossref]
  10. R. P. Edwin, M. T. Dudermel, M. Lamare, “Refractive Index Measurements of Ten Germanium Samples,” Appl. Opt. 21, 878 (1982).
    [Crossref] [PubMed]
  11. G. G. Macfarlane, V. Roberts, “Infrared Adsorption of Germanium Near the Lattice Edge,” Phys. Rev. 97, 1715 (1955).
    [Crossref]
  12. R. Hulthén, “Kramers-Kronig Relations Generalized on Dispersion Relations for Finite Frequency Intervals. A Spectrum-Restoring Filter,” J. Opt. Soc. Am. 72, 794 (1982).
    [Crossref]
  13. R. Braunstein, A. R. Moore, F. Herman, “Intrinsic Optical Absorption in Germanium-Silicon Alloys,” Phys. Rev. 109, 695 (1957).
    [Crossref]
  14. D. R. Mills, E. Harting, J. E. Giutronich, “Simple High Efficiency Nontracking Thermal Concentrator for Temperatures up to 250°C,” in Proceedings, ISES Congress, Brighton (1981).
  15. D. R. Mills, “Relative Cost-Effectiveness of Periodically Adjusted, Solar Collectors Using Evacuated Absorber Tubes,” accepted for publication by Sol. Energy.
  16. M. Sikkens, “Physical Background of Spectral Selectivity,” Sol. Energy Mater. 5, 55 (1981).
    [Crossref]
  17. D. M. Trotter, A. J. Sievers, “Spectral Selectivity of High Temperature Solar Absorbers. II: Effects of Interference,” Sol. Energy Mater. 7, 281 (1982).
    [Crossref]

1983 (2)

D. R. Mills, L. C. Botten, “Laser Emissivity Limits Indicated for High Temperature Selectivity Surfaces,” Appl. Opt. 22, 3182 (1983).
[Crossref] [PubMed]

D. E. Aspes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985 (1983).
[Crossref]

1982 (3)

1981 (1)

M. Sikkens, “Physical Background of Spectral Selectivity,” Sol. Energy Mater. 5, 55 (1981).
[Crossref]

1980 (1)

1979 (1)

D. M. Trotter, A. J. Sievers, “Thermal Emissivity of Selective Surfaces: New Lower Limits,” Appl. Phys. Lett. 35, 374 (1979).
[Crossref]

1957 (1)

R. Braunstein, A. R. Moore, F. Herman, “Intrinsic Optical Absorption in Germanium-Silicon Alloys,” Phys. Rev. 109, 695 (1957).
[Crossref]

1955 (2)

G. G. Macfarlane, V. Roberts, “Infrared Adsorption of Germanium Near the Lattice Edge,” Phys. Rev. 97, 1715 (1955).
[Crossref]

W. C. Dash, R. Newman, “Intrinsic Optical Absorption in Single-Crystal Germanium and Silicon at 77°K and 300°K,” Phys. Rev. 99, 1151 (1955).
[Crossref]

Aspes, D. E.

D. E. Aspes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985 (1983).
[Crossref]

Botten, L. C.

Braunstein, R.

R. Braunstein, A. R. Moore, F. Herman, “Intrinsic Optical Absorption in Germanium-Silicon Alloys,” Phys. Rev. 109, 695 (1957).
[Crossref]

Dash, W. C.

W. C. Dash, R. Newman, “Intrinsic Optical Absorption in Single-Crystal Germanium and Silicon at 77°K and 300°K,” Phys. Rev. 99, 1151 (1955).
[Crossref]

Dudermel, M. T.

Edwin, R. P.

Giutronich, J. E.

D. R. Mills, E. Harting, J. E. Giutronich, “Simple High Efficiency Nontracking Thermal Concentrator for Temperatures up to 250°C,” in Proceedings, ISES Congress, Brighton (1981).

Harting, E.

D. R. Mills, E. Harting, J. E. Giutronich, “Simple High Efficiency Nontracking Thermal Concentrator for Temperatures up to 250°C,” in Proceedings, ISES Congress, Brighton (1981).

Herman, F.

R. Braunstein, A. R. Moore, F. Herman, “Intrinsic Optical Absorption in Germanium-Silicon Alloys,” Phys. Rev. 109, 695 (1957).
[Crossref]

Hulthén, R.

Kreider, J. F.

F. Kreith, J. F. Kreider, Principles of Solar Engineering (McGraw-Hill, New York, 1978), p. 152.

Kreith, F.

F. Kreith, J. F. Kreider, Principles of Solar Engineering (McGraw-Hill, New York, 1978), p. 152.

Lamare, M.

Macfarlane, G. G.

G. G. Macfarlane, V. Roberts, “Infrared Adsorption of Germanium Near the Lattice Edge,” Phys. Rev. 97, 1715 (1955).
[Crossref]

Mills, D. R.

D. R. Mills, L. C. Botten, “Laser Emissivity Limits Indicated for High Temperature Selectivity Surfaces,” Appl. Opt. 22, 3182 (1983).
[Crossref] [PubMed]

D. R. Mills, E. Harting, J. E. Giutronich, “Simple High Efficiency Nontracking Thermal Concentrator for Temperatures up to 250°C,” in Proceedings, ISES Congress, Brighton (1981).

D. R. Mills, “Relative Cost-Effectiveness of Periodically Adjusted, Solar Collectors Using Evacuated Absorber Tubes,” accepted for publication by Sol. Energy.

D. R. Mills “Periodically Adjusted Solar Collectors for Medium Temperature Applications,” in Proceedings, ISES Conference, ANZ Branch, Auckland, N.Z. (Aug.1984).

Moore, A. R.

R. Braunstein, A. R. Moore, F. Herman, “Intrinsic Optical Absorption in Germanium-Silicon Alloys,” Phys. Rev. 109, 695 (1957).
[Crossref]

Newman, R.

W. C. Dash, R. Newman, “Intrinsic Optical Absorption in Single-Crystal Germanium and Silicon at 77°K and 300°K,” Phys. Rev. 99, 1151 (1955).
[Crossref]

Roberts, V.

G. G. Macfarlane, V. Roberts, “Infrared Adsorption of Germanium Near the Lattice Edge,” Phys. Rev. 97, 1715 (1955).
[Crossref]

Sievers, A. J.

D. M. Trotter, A. J. Sievers, “Spectral Selectivity of High Temperature Solar Absorbers. II: Effects of Interference,” Sol. Energy Mater. 7, 281 (1982).
[Crossref]

D. M. Trotter, A. J. Sievers, “Spectral Selectivity of High-Temeprature Solar Absorbers,” Appl. Opt. 19, 711 (1980).
[Crossref] [PubMed]

D. M. Trotter, A. J. Sievers, “Thermal Emissivity of Selective Surfaces: New Lower Limits,” Appl. Phys. Lett. 35, 374 (1979).
[Crossref]

A. J. Sievers, Solar Energy Conversion, Solid State Physics Aspects (Springer-Verlag, New York, 1979), p. 84.

Sikkens, M.

M. Sikkens, “Physical Background of Spectral Selectivity,” Sol. Energy Mater. 5, 55 (1981).
[Crossref]

Studna, A. A.

D. E. Aspes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985 (1983).
[Crossref]

Trotter, D. M.

D. M. Trotter, A. J. Sievers, “Spectral Selectivity of High Temperature Solar Absorbers. II: Effects of Interference,” Sol. Energy Mater. 7, 281 (1982).
[Crossref]

D. M. Trotter, A. J. Sievers, “Spectral Selectivity of High-Temeprature Solar Absorbers,” Appl. Opt. 19, 711 (1980).
[Crossref] [PubMed]

D. M. Trotter, A. J. Sievers, “Thermal Emissivity of Selective Surfaces: New Lower Limits,” Appl. Phys. Lett. 35, 374 (1979).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

D. M. Trotter, A. J. Sievers, “Thermal Emissivity of Selective Surfaces: New Lower Limits,” Appl. Phys. Lett. 35, 374 (1979).
[Crossref]

J. Opt. Soc. Am. (1)

Phys. Rev. (3)

R. Braunstein, A. R. Moore, F. Herman, “Intrinsic Optical Absorption in Germanium-Silicon Alloys,” Phys. Rev. 109, 695 (1957).
[Crossref]

W. C. Dash, R. Newman, “Intrinsic Optical Absorption in Single-Crystal Germanium and Silicon at 77°K and 300°K,” Phys. Rev. 99, 1151 (1955).
[Crossref]

G. G. Macfarlane, V. Roberts, “Infrared Adsorption of Germanium Near the Lattice Edge,” Phys. Rev. 97, 1715 (1955).
[Crossref]

Phys. Rev. B (1)

D. E. Aspes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27, 985 (1983).
[Crossref]

Sol. Energy Mater. (2)

M. Sikkens, “Physical Background of Spectral Selectivity,” Sol. Energy Mater. 5, 55 (1981).
[Crossref]

D. M. Trotter, A. J. Sievers, “Spectral Selectivity of High Temperature Solar Absorbers. II: Effects of Interference,” Sol. Energy Mater. 7, 281 (1982).
[Crossref]

Other (6)

D. R. Mills, E. Harting, J. E. Giutronich, “Simple High Efficiency Nontracking Thermal Concentrator for Temperatures up to 250°C,” in Proceedings, ISES Congress, Brighton (1981).

D. R. Mills, “Relative Cost-Effectiveness of Periodically Adjusted, Solar Collectors Using Evacuated Absorber Tubes,” accepted for publication by Sol. Energy.

F. Kreith, J. F. Kreider, Principles of Solar Engineering (McGraw-Hill, New York, 1978), p. 152.

D. R. Mills “Periodically Adjusted Solar Collectors for Medium Temperature Applications,” in Proceedings, ISES Conference, ANZ Branch, Auckland, N.Z. (Aug.1984).

Ref. 4, pp. 653–657.

A. J. Sievers, Solar Energy Conversion, Solid State Physics Aspects (Springer-Verlag, New York, 1979), p. 84.

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Figures (9)

Fig. 1
Fig. 1

Absorptance profile of an ideal selective surface showing the edge position λe.

Fig. 2
Fig. 2

Optional edge position vs logCK for three temperatures. The range of CK corresponding to various classes of solar concentrator is also shown.

Fig. 3
Fig. 3

PN/PI, where PI is the input power at the selective surface vs λe for values of CK = 1, 10, and 100. Both ideal and ideal thermally broadened (ITB) surfaces are shown for temperatures of 27, 30, 500, ad 700°C.

Fig. 4
Fig. 4

Minimum possible thermal broadening in ITB surfaces of λe = 1.5, 1.8, and 2.0 μm. Note that the IR tail is considerably less severe for lower values of λe. A modeled edge for room temperature c-Ge on copper is shown for comparison.

Fig. 5
Fig. 5

Effect of thermal broadening on the absorption coefficient in modeled pseudo-Ge material. The value of Eg is kept constant at 0.8 eV but would shift to lower energies in real c-Ge.

Fig. 6
Fig. 6

Optical constants n and k for c-Ge at room temperature.

Fig. 7
Fig. 7

Structure of (a) SIM and (b) SISIM selective surfaces modeled.

Fig. 8
Fig. 8

Hemispherical aborptance and emittance of a modeled SIM surface at four temperatures. Transparent layer thickneses used were 1.9, 0.9, 0.8, and 0.5 μm for surfaces at 7, 300, 50, and 700°C, respectively.

Fig. 9
Fig. 9

Hemispherical emittance of a SISIM surface at 500°C compared with the results for completely transparent high index layers of n = 4.0. The dotted lines indicate the result for an IIIIM surface with an ungraded transparent top layer, the dashed lines for an IIIIM surface with a graded top transparent layer, and the solid lines a graded SISIM surface using pseudo-Ge.

Equations (9)

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P N = λ= 0 [ K E 0 ( λ ) 1 C E ( λ, T ) ] A α ( λ ) d λ ,
P N = λ= 0 λ e [ K E 0 ( λ ) 1 C E ( λ, T ) ] A ( λ ) d λ .
d P N d λ e = 0 ,
C K E 0 ( λ 0 ) = E ( λ 0 , T ) ,
E ( λ 0 , T ) = ( 374 . 15 × 10 6 ) × [ exp ( 14387 . 9 / λ 0 T ) 1 ] 1 W · m 2 · μ m ,
A = A 0 exp [ ћ ( ω ω e ) / k B T ] { exp [ ћ ( ω ω e ) / k B T ] + 1 } 1 ,
P N = K I e A α S ( λ e ) A C σ T 4 T ( λ e ) ,
α ( h ω , T ) = A [ ( ћ ω E g k θ 2 ) 1 exp ( θ / T ) + ( ћ ω E g + k θ ) 2 exp ( θ / T ) 1 ] ,
n ( ω ) = 2 π P 0 ω k ( ω ) ω 2 ω e 2 d ω

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