Abstract

Minimum emissivity limits given in the literature for high temperature selective surfaces may be too pessimistic. To reassess these limits, hypothetical bulk absorbing semiconductor–metal (SM) and semiconductor-insulator-metal (SIM) coatings were modeled using plausible high temperature semiconductor optical constants. Careful attention was paid to the positioning of the exponential region of the semiconductor absorption edge. Values of α/∊ near those of an ideal selective surface on copper were obtained with SIM surfaces, which use a dielectric refractive-index mismatch layer to reduce emittance. It is suggested that an ideal selective surface on copper (or silver) be regarded as the approachable limiting performances case for most applications. If favorable but extreme values of refractive index can be utilized, the ideal α/∊ may even be exceeded using interference effects to limit copper emissivity to below vacuum values.

© 1983 Optical Society of America

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References

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  1. D. M. Trotter, A. J. Sievers, Appl. Phys. Lett. 35, 374 (1979).
    [CrossRef]
  2. B. O. Seraphin, in Solar Energy Conversion—Solid State Physics Aspects, B. O. Seraphin, Ed. (Springer, Heidelberg, 1979), pp. 25–32.
  3. J. Tauc, Amorphous and Liquid Semiconductors (Plenum, New York, 1974), Chap. 4.
    [CrossRef]
  4. G. A. N. Connell, in Topics in Applied Physics, Vol. 36 (Springer, New York, 1979), pp. 80–84.
    [CrossRef]
  5. D. M. Trotter, A. J. Sievers, Appl. Opt. 19, 711 (1980).
    [CrossRef] [PubMed]
  6. K. G. Ramanathan, S. H. Yen, J. Opt. Soc. Am. 67, 32 (1977).
    [CrossRef]
  7. I. T. Ritchie, B. Window, Appl. Opt. 16, 1438 (1977).
    [CrossRef] [PubMed]
  8. D. R. Mills, E. Harting, J. E. Giutronich, “Simple High-Efficiency Nontracking Thermal Concentrator or Temperatures up to 250°C,” in Proceedings, ISES Congress, Brighton (1981).
  9. D. R. McKenzie, N. Savvides, L. C. Botten, D. R. Mills, R. C. McPhedran, Sol. Energy Mater. 9, 113 (1983).
    [CrossRef]

1983 (1)

D. R. McKenzie, N. Savvides, L. C. Botten, D. R. Mills, R. C. McPhedran, Sol. Energy Mater. 9, 113 (1983).
[CrossRef]

1980 (1)

1979 (1)

D. M. Trotter, A. J. Sievers, Appl. Phys. Lett. 35, 374 (1979).
[CrossRef]

1977 (2)

Botten, L. C.

D. R. McKenzie, N. Savvides, L. C. Botten, D. R. Mills, R. C. McPhedran, Sol. Energy Mater. 9, 113 (1983).
[CrossRef]

Connell, G. A. N.

G. A. N. Connell, in Topics in Applied Physics, Vol. 36 (Springer, New York, 1979), pp. 80–84.
[CrossRef]

Giutronich, J. E.

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

McKenzie, D. R.

D. R. McKenzie, N. Savvides, L. C. Botten, D. R. Mills, R. C. McPhedran, Sol. Energy Mater. 9, 113 (1983).
[CrossRef]

McPhedran, R. C.

D. R. McKenzie, N. Savvides, L. C. Botten, D. R. Mills, R. C. McPhedran, Sol. Energy Mater. 9, 113 (1983).
[CrossRef]

Mills, D. R.

D. R. McKenzie, N. Savvides, L. C. Botten, D. R. Mills, R. C. McPhedran, Sol. Energy Mater. 9, 113 (1983).
[CrossRef]

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

Ramanathan, K. G.

Ritchie, I. T.

Savvides, N.

D. R. McKenzie, N. Savvides, L. C. Botten, D. R. Mills, R. C. McPhedran, Sol. Energy Mater. 9, 113 (1983).
[CrossRef]

Seraphin, B. O.

B. O. Seraphin, in Solar Energy Conversion—Solid State Physics Aspects, B. O. Seraphin, Ed. (Springer, Heidelberg, 1979), pp. 25–32.

Sievers, A. J.

D. M. Trotter, A. J. Sievers, Appl. Opt. 19, 711 (1980).
[CrossRef] [PubMed]

D. M. Trotter, A. J. Sievers, Appl. Phys. Lett. 35, 374 (1979).
[CrossRef]

Tauc, J.

J. Tauc, Amorphous and Liquid Semiconductors (Plenum, New York, 1974), Chap. 4.
[CrossRef]

Trotter, D. M.

D. M. Trotter, A. J. Sievers, Appl. Opt. 19, 711 (1980).
[CrossRef] [PubMed]

D. M. Trotter, A. J. Sievers, Appl. Phys. Lett. 35, 374 (1979).
[CrossRef]

Window, B.

Yen, S. H.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

D. M. Trotter, A. J. Sievers, Appl. Phys. Lett. 35, 374 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

Sol. Energy Mater. (1)

D. R. McKenzie, N. Savvides, L. C. Botten, D. R. Mills, R. C. McPhedran, Sol. Energy Mater. 9, 113 (1983).
[CrossRef]

Other (4)

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

B. O. Seraphin, in Solar Energy Conversion—Solid State Physics Aspects, B. O. Seraphin, Ed. (Springer, Heidelberg, 1979), pp. 25–32.

J. Tauc, Amorphous and Liquid Semiconductors (Plenum, New York, 1974), Chap. 4.
[CrossRef]

G. A. N. Connell, in Topics in Applied Physics, Vol. 36 (Springer, New York, 1979), pp. 80–84.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Typical variation of absorption coefficient as a function of photon energy in an amorphous semiconductor.3 Region BC is the exponential region. Es = Ee(lna/loga).

Fig. 2
Fig. 2

Absorption coefficient vs photon energy profiles for various amorphous materials.3 Also shown is a profile X having 0 = 1.60 eV, Ee = 0.1242 eV, and amax = 6.

Fig. 3
Fig. 3

Modeled structure for (a) SM surfaces and (b) SIM surfaces.

Fig. 4
Fig. 4

Calculated hemispherical emissivity of a bare copper surface using k values from Eq. (3) against an experimental result for various temperatures.6

Fig. 5
Fig. 5

Absorptance to emittance ratio as a function of λB for an ideal selective surface on copper at three temperatures. λB is the location of the step function absorption edge.

Fig. 6
Fig. 6

Variation in hemispherical emittance against dielectric mismatch layer thickness for three different temperatures. In each case, semiconductor parameters are ℏω = 1.60 eV, Ee = 0.1242 eV, amax = 6, and ds = 2 μm. The solid lines show results for the high n(ω) range, while the dashed lines indicate results for low n(ω).

Fig. 7
Fig. 7

Emittance increases for surfaces having perfect lattice absorption for all wavelengths > λL. Semiconductor parameters as for Fig. 4 except dd = 0.5 μm at 700°C and 1.0 μm at 300°C.

Tables (7)

Tables Icon

Table I Values of Semiconductor n and k Used in Selective Surface Optical Calculations as a Function of Wavelengtha

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Table II α/∊ of SM Surface for Different Temperatures and Semiconductor Layer Thicknesses (ds)a

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Table III λ/ of SIM Surface with High ℏω0 and High n(ω)

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Table IV As for Table III but with High ℏω0 and Low n(ω)

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Table V As for Table III but with Low ℏω0 and High n(ω)

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Table VI As for Table III but with Low ℏω0 and Low n(ω)

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Table VII Calculation of Net Energy Gain Using Surfaces in Tables IIIVI on an Absorber of a Perfect Concentrating Systema

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

a ( ω ) ~ exp ( h ω / E e ) ,
a ( ω ) = a max { exp [ h ( ω ω 0 ) / E e ] exp [ h ( ω ω 0 ) / E e ] + 1 } ,
n ( λ , T ) = n ( λ , T 0 ) ( 10 Y ) ,
Y = [ ( T T 0 ) 2 A + ( T T 0 ) B ] ,
F = α H / H ( calculated ) α H / H ( best from Fig . 5 ) ,

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