Abstract

Wavelength selective coatings are of common use in order to enhance the efficiency of devices heated by radiation such as solar thermal collectors. The use of suitable materials and the optimization of coating layer thicknesses are advisable ways to maximize the absorption. Further improvement is achievable by embedding particles in certain layers in order to modify material properties. We focus on optimizing the absorption behavior of a solar collector setup using copper as substrate, a layer of amorphous hydrogenated carbon with embedded titanium carbide particles (a-C:H/TiC), and an antireflection coating of amorphous silicon dioxide (aSiO2). For the setup utilizing homogeneous particle distribution, a relative absorption of 90.98% was found, while inhomogeneous particle embedding yielded 98.29%. These results are particularly interesting since until now, absorption of more than 95% was found only by using embedded Cr but not by using the more biocompatible Ti.

© 2009 Optical Society of America

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  1. D. P. Gruber, G. Meinhardt, and W. Papousek, “Modelling the light absorption in organic photovoltaic devices,” Solar Energy Mater. Sol. Cells 87, 215-223 (2005).
    [CrossRef]
  2. P. Oelhafen and A. Schüler, “Nanostructured materials for solar energy conversion,” Solar Energy 79, 110-121 (2005).
    [CrossRef]
  3. G. A. Niklasson and C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co-Al2O3 composite films,” J. Appl. Phys. 55, 3382-3410 (1984).
    [CrossRef]
  4. M. Lazarov, P. Raths, H. Metzger, and W. Spirkl, “Optical constants and film density of TiNxOy solar selective absorbers,” J. Appl. Phys. 77, 2133-2137 (1995).
    [CrossRef]
  5. W. Graf, F. Brucker, M. Köhl, T. Troscher, V. Wittwer, and L. Herlitze, “Development of large area sputtered solar absorber coatings,” J. Non-Cryst. Solids 218, 380-387 (1997).
    [CrossRef]
  6. R. Gampp, P. Oelhafen, P. Gantenbein, S. Brunold, and U. Frei, “Accelerated aging test of chromium containing amorphous hydrogenated carbon coatings for solar collectors,” Solar Energy Mater. Sol. Cells 54, 369-377 (1998).
    [CrossRef]
  7. A. Schüler, R. Gampp, and P. Oelhafen, “In situ photoelectron spectroscopy of titanium containing amorphous hydrogenated carbon films,” Phys. Rev. B 60, 16164-16169 (1999).
    [CrossRef]
  8. A. Schüler, J. Geng, P. Oelhafen, S. Brunold, P. Gantenbein, and U. Frei, “Application of titanium containing amorphous hydrogenated carbon films (a-C:H/Ti) as optical selective solar absorber coatings,” Solar Energy Mater. Sol. Cells 60, 295-307 (2000).
    [CrossRef]
  9. C. G. Granqvist and V. Wittwer, “Materials for solar energy conversion: an overview,” Solar Energy Mater. Sol. Cells 54, 39-48 (1998).
    [CrossRef]
  10. A. Schüler, C. Ellenberger, P. Oelhafen, C. Haug, and R. Brenn, “Optical properties of titanium containing amorphous hydrogenated carbon films a-C:H/Ti,” J. Appl. Phys. 87, 4285-4292 (2000).
    [CrossRef]
  11. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).
  12. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
    [CrossRef] [PubMed]
  13. S. Kirkpatrick, “Optimization by simulated annealing: quantitative studies,” J. Stat. Phys. 34, 975-986 (1984).
    [CrossRef]
  14. J. A. Nelder and R. A. Mead, “A simplex method for function minimization,” Comput. J. (Cambridge) 7, 308-313 (1965).
  15. J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London Ser. A 203, 385-420 (1904).
    [CrossRef]
  16. D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. (Leipzig) 416, 665-679 (1935).
    [CrossRef]
  17. P. Sheng, “Theory for the dielectric function of granular composite media,” Phys. Rev. Lett. 45, 60-63 (1980).
    [CrossRef]
  18. U. J. Gibson and R. A. Buhrman, “Optical response of Cermet composite films in the microstructural transition region,” Phys. Rev. B 27, 5046-5051 (1983).
    [CrossRef]
  19. D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292-3302(1979).
    [CrossRef]
  20. G. A. Niklasson, “Optical properties and solar selectivity of inhomogeneous metal-insulator coatings,” Ph.D. dissertation (Chalmers University of Technology, 1982).
  21. C. G. Granqvist, D. Le Bellac, and G. A. Niklasson, “Angular selective window coatings: effective medium theory and experimental data on sputter-deposited films, renewable energy,” in World Renewable Energy Congress IV (Pergamon), pp.530-539.
  22. L. Kolokolova and B. A. S. Gustafson, “Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theories,” J. Quant. Spectrosc. Radiat. Transfer 70, 611-625 (2001).
    [CrossRef]
  23. D. P. Gruber, “Modelling of optical properties of polymeric nanocomposites in single- and multilayer arrangements by utilizing effective medium theories,” PCCL Report, WEMT-III (PCCL, 2004).
  24. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, 1994), pp. 444-455.
  25. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087-1092(1953).
    [CrossRef]
  26. http://rredc.nrel.gov/solar/spectra/am1.5/.

2005

D. P. Gruber, G. Meinhardt, and W. Papousek, “Modelling the light absorption in organic photovoltaic devices,” Solar Energy Mater. Sol. Cells 87, 215-223 (2005).
[CrossRef]

P. Oelhafen and A. Schüler, “Nanostructured materials for solar energy conversion,” Solar Energy 79, 110-121 (2005).
[CrossRef]

2001

L. Kolokolova and B. A. S. Gustafson, “Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theories,” J. Quant. Spectrosc. Radiat. Transfer 70, 611-625 (2001).
[CrossRef]

2000

A. Schüler, J. Geng, P. Oelhafen, S. Brunold, P. Gantenbein, and U. Frei, “Application of titanium containing amorphous hydrogenated carbon films (a-C:H/Ti) as optical selective solar absorber coatings,” Solar Energy Mater. Sol. Cells 60, 295-307 (2000).
[CrossRef]

A. Schüler, C. Ellenberger, P. Oelhafen, C. Haug, and R. Brenn, “Optical properties of titanium containing amorphous hydrogenated carbon films a-C:H/Ti,” J. Appl. Phys. 87, 4285-4292 (2000).
[CrossRef]

1999

A. Schüler, R. Gampp, and P. Oelhafen, “In situ photoelectron spectroscopy of titanium containing amorphous hydrogenated carbon films,” Phys. Rev. B 60, 16164-16169 (1999).
[CrossRef]

1998

R. Gampp, P. Oelhafen, P. Gantenbein, S. Brunold, and U. Frei, “Accelerated aging test of chromium containing amorphous hydrogenated carbon coatings for solar collectors,” Solar Energy Mater. Sol. Cells 54, 369-377 (1998).
[CrossRef]

C. G. Granqvist and V. Wittwer, “Materials for solar energy conversion: an overview,” Solar Energy Mater. Sol. Cells 54, 39-48 (1998).
[CrossRef]

1997

W. Graf, F. Brucker, M. Köhl, T. Troscher, V. Wittwer, and L. Herlitze, “Development of large area sputtered solar absorber coatings,” J. Non-Cryst. Solids 218, 380-387 (1997).
[CrossRef]

1995

M. Lazarov, P. Raths, H. Metzger, and W. Spirkl, “Optical constants and film density of TiNxOy solar selective absorbers,” J. Appl. Phys. 77, 2133-2137 (1995).
[CrossRef]

1984

G. A. Niklasson and C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co-Al2O3 composite films,” J. Appl. Phys. 55, 3382-3410 (1984).
[CrossRef]

S. Kirkpatrick, “Optimization by simulated annealing: quantitative studies,” J. Stat. Phys. 34, 975-986 (1984).
[CrossRef]

1983

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

U. J. Gibson and R. A. Buhrman, “Optical response of Cermet composite films in the microstructural transition region,” Phys. Rev. B 27, 5046-5051 (1983).
[CrossRef]

1980

P. Sheng, “Theory for the dielectric function of granular composite media,” Phys. Rev. Lett. 45, 60-63 (1980).
[CrossRef]

1979

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292-3302(1979).
[CrossRef]

1965

J. A. Nelder and R. A. Mead, “A simplex method for function minimization,” Comput. J. (Cambridge) 7, 308-313 (1965).

1953

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087-1092(1953).
[CrossRef]

1935

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. (Leipzig) 416, 665-679 (1935).
[CrossRef]

1904

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London Ser. A 203, 385-420 (1904).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292-3302(1979).
[CrossRef]

Bellac, D. Le

C. G. Granqvist, D. Le Bellac, and G. A. Niklasson, “Angular selective window coatings: effective medium theory and experimental data on sputter-deposited films, renewable energy,” in World Renewable Energy Congress IV (Pergamon), pp.530-539.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Brenn, R.

A. Schüler, C. Ellenberger, P. Oelhafen, C. Haug, and R. Brenn, “Optical properties of titanium containing amorphous hydrogenated carbon films a-C:H/Ti,” J. Appl. Phys. 87, 4285-4292 (2000).
[CrossRef]

Brucker, F.

W. Graf, F. Brucker, M. Köhl, T. Troscher, V. Wittwer, and L. Herlitze, “Development of large area sputtered solar absorber coatings,” J. Non-Cryst. Solids 218, 380-387 (1997).
[CrossRef]

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. (Leipzig) 416, 665-679 (1935).
[CrossRef]

Brunold, S.

A. Schüler, J. Geng, P. Oelhafen, S. Brunold, P. Gantenbein, and U. Frei, “Application of titanium containing amorphous hydrogenated carbon films (a-C:H/Ti) as optical selective solar absorber coatings,” Solar Energy Mater. Sol. Cells 60, 295-307 (2000).
[CrossRef]

R. Gampp, P. Oelhafen, P. Gantenbein, S. Brunold, and U. Frei, “Accelerated aging test of chromium containing amorphous hydrogenated carbon coatings for solar collectors,” Solar Energy Mater. Sol. Cells 54, 369-377 (1998).
[CrossRef]

Buhrman, R. A.

U. J. Gibson and R. A. Buhrman, “Optical response of Cermet composite films in the microstructural transition region,” Phys. Rev. B 27, 5046-5051 (1983).
[CrossRef]

Ellenberger, C.

A. Schüler, C. Ellenberger, P. Oelhafen, C. Haug, and R. Brenn, “Optical properties of titanium containing amorphous hydrogenated carbon films a-C:H/Ti,” J. Appl. Phys. 87, 4285-4292 (2000).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, 1994), pp. 444-455.

Frei, U.

A. Schüler, J. Geng, P. Oelhafen, S. Brunold, P. Gantenbein, and U. Frei, “Application of titanium containing amorphous hydrogenated carbon films (a-C:H/Ti) as optical selective solar absorber coatings,” Solar Energy Mater. Sol. Cells 60, 295-307 (2000).
[CrossRef]

R. Gampp, P. Oelhafen, P. Gantenbein, S. Brunold, and U. Frei, “Accelerated aging test of chromium containing amorphous hydrogenated carbon coatings for solar collectors,” Solar Energy Mater. Sol. Cells 54, 369-377 (1998).
[CrossRef]

Gampp, R.

A. Schüler, R. Gampp, and P. Oelhafen, “In situ photoelectron spectroscopy of titanium containing amorphous hydrogenated carbon films,” Phys. Rev. B 60, 16164-16169 (1999).
[CrossRef]

R. Gampp, P. Oelhafen, P. Gantenbein, S. Brunold, and U. Frei, “Accelerated aging test of chromium containing amorphous hydrogenated carbon coatings for solar collectors,” Solar Energy Mater. Sol. Cells 54, 369-377 (1998).
[CrossRef]

Gantenbein, P.

A. Schüler, J. Geng, P. Oelhafen, S. Brunold, P. Gantenbein, and U. Frei, “Application of titanium containing amorphous hydrogenated carbon films (a-C:H/Ti) as optical selective solar absorber coatings,” Solar Energy Mater. Sol. Cells 60, 295-307 (2000).
[CrossRef]

R. Gampp, P. Oelhafen, P. Gantenbein, S. Brunold, and U. Frei, “Accelerated aging test of chromium containing amorphous hydrogenated carbon coatings for solar collectors,” Solar Energy Mater. Sol. Cells 54, 369-377 (1998).
[CrossRef]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Geng, J.

A. Schüler, J. Geng, P. Oelhafen, S. Brunold, P. Gantenbein, and U. Frei, “Application of titanium containing amorphous hydrogenated carbon films (a-C:H/Ti) as optical selective solar absorber coatings,” Solar Energy Mater. Sol. Cells 60, 295-307 (2000).
[CrossRef]

Gibson, U. J.

U. J. Gibson and R. A. Buhrman, “Optical response of Cermet composite films in the microstructural transition region,” Phys. Rev. B 27, 5046-5051 (1983).
[CrossRef]

Graf, W.

W. Graf, F. Brucker, M. Köhl, T. Troscher, V. Wittwer, and L. Herlitze, “Development of large area sputtered solar absorber coatings,” J. Non-Cryst. Solids 218, 380-387 (1997).
[CrossRef]

Granqvist, C. G.

C. G. Granqvist and V. Wittwer, “Materials for solar energy conversion: an overview,” Solar Energy Mater. Sol. Cells 54, 39-48 (1998).
[CrossRef]

G. A. Niklasson and C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co-Al2O3 composite films,” J. Appl. Phys. 55, 3382-3410 (1984).
[CrossRef]

C. G. Granqvist, D. Le Bellac, and G. A. Niklasson, “Angular selective window coatings: effective medium theory and experimental data on sputter-deposited films, renewable energy,” in World Renewable Energy Congress IV (Pergamon), pp.530-539.

Gruber, D. P.

D. P. Gruber, G. Meinhardt, and W. Papousek, “Modelling the light absorption in organic photovoltaic devices,” Solar Energy Mater. Sol. Cells 87, 215-223 (2005).
[CrossRef]

D. P. Gruber, “Modelling of optical properties of polymeric nanocomposites in single- and multilayer arrangements by utilizing effective medium theories,” PCCL Report, WEMT-III (PCCL, 2004).

Gustafson, B. A. S.

L. Kolokolova and B. A. S. Gustafson, “Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theories,” J. Quant. Spectrosc. Radiat. Transfer 70, 611-625 (2001).
[CrossRef]

Haug, C.

A. Schüler, C. Ellenberger, P. Oelhafen, C. Haug, and R. Brenn, “Optical properties of titanium containing amorphous hydrogenated carbon films a-C:H/Ti,” J. Appl. Phys. 87, 4285-4292 (2000).
[CrossRef]

Herlitze, L.

W. Graf, F. Brucker, M. Köhl, T. Troscher, V. Wittwer, and L. Herlitze, “Development of large area sputtered solar absorber coatings,” J. Non-Cryst. Solids 218, 380-387 (1997).
[CrossRef]

Hottier, F.

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292-3302(1979).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, “Optimization by simulated annealing: quantitative studies,” J. Stat. Phys. 34, 975-986 (1984).
[CrossRef]

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Köhl, M.

W. Graf, F. Brucker, M. Köhl, T. Troscher, V. Wittwer, and L. Herlitze, “Development of large area sputtered solar absorber coatings,” J. Non-Cryst. Solids 218, 380-387 (1997).
[CrossRef]

Kolokolova, L.

L. Kolokolova and B. A. S. Gustafson, “Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theories,” J. Quant. Spectrosc. Radiat. Transfer 70, 611-625 (2001).
[CrossRef]

Lazarov, M.

M. Lazarov, P. Raths, H. Metzger, and W. Spirkl, “Optical constants and film density of TiNxOy solar selective absorbers,” J. Appl. Phys. 77, 2133-2137 (1995).
[CrossRef]

Maxwell-Garnett, J. C.

J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London Ser. A 203, 385-420 (1904).
[CrossRef]

Mead, R. A.

J. A. Nelder and R. A. Mead, “A simplex method for function minimization,” Comput. J. (Cambridge) 7, 308-313 (1965).

Meinhardt, G.

D. P. Gruber, G. Meinhardt, and W. Papousek, “Modelling the light absorption in organic photovoltaic devices,” Solar Energy Mater. Sol. Cells 87, 215-223 (2005).
[CrossRef]

Metropolis, N.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087-1092(1953).
[CrossRef]

Metzger, H.

M. Lazarov, P. Raths, H. Metzger, and W. Spirkl, “Optical constants and film density of TiNxOy solar selective absorbers,” J. Appl. Phys. 77, 2133-2137 (1995).
[CrossRef]

Nelder, J. A.

J. A. Nelder and R. A. Mead, “A simplex method for function minimization,” Comput. J. (Cambridge) 7, 308-313 (1965).

Niklasson, G. A.

G. A. Niklasson and C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co-Al2O3 composite films,” J. Appl. Phys. 55, 3382-3410 (1984).
[CrossRef]

G. A. Niklasson, “Optical properties and solar selectivity of inhomogeneous metal-insulator coatings,” Ph.D. dissertation (Chalmers University of Technology, 1982).

C. G. Granqvist, D. Le Bellac, and G. A. Niklasson, “Angular selective window coatings: effective medium theory and experimental data on sputter-deposited films, renewable energy,” in World Renewable Energy Congress IV (Pergamon), pp.530-539.

Oelhafen, P.

P. Oelhafen and A. Schüler, “Nanostructured materials for solar energy conversion,” Solar Energy 79, 110-121 (2005).
[CrossRef]

A. Schüler, C. Ellenberger, P. Oelhafen, C. Haug, and R. Brenn, “Optical properties of titanium containing amorphous hydrogenated carbon films a-C:H/Ti,” J. Appl. Phys. 87, 4285-4292 (2000).
[CrossRef]

A. Schüler, J. Geng, P. Oelhafen, S. Brunold, P. Gantenbein, and U. Frei, “Application of titanium containing amorphous hydrogenated carbon films (a-C:H/Ti) as optical selective solar absorber coatings,” Solar Energy Mater. Sol. Cells 60, 295-307 (2000).
[CrossRef]

A. Schüler, R. Gampp, and P. Oelhafen, “In situ photoelectron spectroscopy of titanium containing amorphous hydrogenated carbon films,” Phys. Rev. B 60, 16164-16169 (1999).
[CrossRef]

R. Gampp, P. Oelhafen, P. Gantenbein, S. Brunold, and U. Frei, “Accelerated aging test of chromium containing amorphous hydrogenated carbon coatings for solar collectors,” Solar Energy Mater. Sol. Cells 54, 369-377 (1998).
[CrossRef]

Papousek, W.

D. P. Gruber, G. Meinhardt, and W. Papousek, “Modelling the light absorption in organic photovoltaic devices,” Solar Energy Mater. Sol. Cells 87, 215-223 (2005).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, 1994), pp. 444-455.

Raths, P.

M. Lazarov, P. Raths, H. Metzger, and W. Spirkl, “Optical constants and film density of TiNxOy solar selective absorbers,” J. Appl. Phys. 77, 2133-2137 (1995).
[CrossRef]

Rosenbluth, A. W.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087-1092(1953).
[CrossRef]

Rosenbluth, M. N.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087-1092(1953).
[CrossRef]

Schüler, A.

P. Oelhafen and A. Schüler, “Nanostructured materials for solar energy conversion,” Solar Energy 79, 110-121 (2005).
[CrossRef]

A. Schüler, C. Ellenberger, P. Oelhafen, C. Haug, and R. Brenn, “Optical properties of titanium containing amorphous hydrogenated carbon films a-C:H/Ti,” J. Appl. Phys. 87, 4285-4292 (2000).
[CrossRef]

A. Schüler, J. Geng, P. Oelhafen, S. Brunold, P. Gantenbein, and U. Frei, “Application of titanium containing amorphous hydrogenated carbon films (a-C:H/Ti) as optical selective solar absorber coatings,” Solar Energy Mater. Sol. Cells 60, 295-307 (2000).
[CrossRef]

A. Schüler, R. Gampp, and P. Oelhafen, “In situ photoelectron spectroscopy of titanium containing amorphous hydrogenated carbon films,” Phys. Rev. B 60, 16164-16169 (1999).
[CrossRef]

Sheng, P.

P. Sheng, “Theory for the dielectric function of granular composite media,” Phys. Rev. Lett. 45, 60-63 (1980).
[CrossRef]

Spirkl, W.

M. Lazarov, P. Raths, H. Metzger, and W. Spirkl, “Optical constants and film density of TiNxOy solar selective absorbers,” J. Appl. Phys. 77, 2133-2137 (1995).
[CrossRef]

Teller, A. H.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087-1092(1953).
[CrossRef]

Teller, E.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087-1092(1953).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, 1994), pp. 444-455.

Theeten, J. B.

D. E. Aspnes, J. B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292-3302(1979).
[CrossRef]

Troscher, T.

W. Graf, F. Brucker, M. Köhl, T. Troscher, V. Wittwer, and L. Herlitze, “Development of large area sputtered solar absorber coatings,” J. Non-Cryst. Solids 218, 380-387 (1997).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, 1994), pp. 444-455.

Wittwer, V.

C. G. Granqvist and V. Wittwer, “Materials for solar energy conversion: an overview,” Solar Energy Mater. Sol. Cells 54, 39-48 (1998).
[CrossRef]

W. Graf, F. Brucker, M. Köhl, T. Troscher, V. Wittwer, and L. Herlitze, “Development of large area sputtered solar absorber coatings,” J. Non-Cryst. Solids 218, 380-387 (1997).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Ann. Phys. (Leipzig)

D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. (Leipzig) 416, 665-679 (1935).
[CrossRef]

Comput. J. (Cambridge)

J. A. Nelder and R. A. Mead, “A simplex method for function minimization,” Comput. J. (Cambridge) 7, 308-313 (1965).

J. Appl. Phys.

A. Schüler, C. Ellenberger, P. Oelhafen, C. Haug, and R. Brenn, “Optical properties of titanium containing amorphous hydrogenated carbon films a-C:H/Ti,” J. Appl. Phys. 87, 4285-4292 (2000).
[CrossRef]

G. A. Niklasson and C. G. Granqvist, “Optical properties and solar selectivity of coevaporated Co-Al2O3 composite films,” J. Appl. Phys. 55, 3382-3410 (1984).
[CrossRef]

M. Lazarov, P. Raths, H. Metzger, and W. Spirkl, “Optical constants and film density of TiNxOy solar selective absorbers,” J. Appl. Phys. 77, 2133-2137 (1995).
[CrossRef]

J. Chem. Phys.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087-1092(1953).
[CrossRef]

J. Non-Cryst. Solids

W. Graf, F. Brucker, M. Köhl, T. Troscher, V. Wittwer, and L. Herlitze, “Development of large area sputtered solar absorber coatings,” J. Non-Cryst. Solids 218, 380-387 (1997).
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http://rredc.nrel.gov/solar/spectra/am1.5/.

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Figures (6)

Fig. 1
Fig. 1

Setup of the simulated multilayer. Amorphous hydrogenated carbon with embedded titanium carbide particles ( a - C : H / TiC ) on a copper substrate. At the top, amorphous silicon dioxide ( a SiO 2 ).

Fig. 2
Fig. 2

Electrodynamic behavior of a Cu / a - C : H / a SiO 2 solar collector setup. Incident intensity, reflection, and absorption of the coatings and the substrate are shown dependent on the wavelength. Optimal layer thicknesses are calculated to be d a SiO 2 = 92 nm and d a - C H = 300 nm . The relative integrated absorption with respect to the incident intensity [AM 1.5 (global), 400 nm λ 2500 nm ] was found to be α sol = 75.63 % .

Fig. 3
Fig. 3

Electrodynamic behavior of a Cu / a - C : H . TiC / a SiO 2 solar collector setup with homogeneously embedded particles. Incident intensity, reflection, and absorption of the coatings and the substrate are shown dependent on the wavelength. Optimized layer thicknesses are d a SiO 2 = 92 nm and d a - C H / TiC = 62 nm . The optimized volume fraction is f TiC = 0.42 . The relative integrated absorption with respect to the incident intensity [AM 1.5 (global), 400 nm λ 2500 nm ] was calculated to be α sol = 90.98 % , showing a significant improvement compared to the setup without embedded particles. The corresponding setup is shown in Fig. 1.

Fig. 4
Fig. 4

Linear gradient layer with TiC particles: Linearly increasing volume fraction dependent on the normalized depth of the a - C : H / TiC layer. The gradient layer was approximated by 20 single layers, each with a specific homogeneous particle volume fraction. Parameters were optimized for maximum absorption by simulated-simplex annealing and were found to be d a SiO 2 = 96 nm , d a - C H / TiC = 186 nm , c 0 = 17.55 , and c 1 = 5.849 [see Eq. (3)]. The relative integrated absorption with respect to the incident intensity [AM 1.5 (global), 400 nm λ 2500 nm ] was found to be α sol = 98.29 % . The resulting characteristic of the dielectric permeability of the gradient layer is shown in Fig. 5. The corresponding setup (shown in Fig. 1) exhibits the highest absorption of all simulated multilayers.

Fig. 5
Fig. 5

Optical parameters of the linear gradient layer ( a - C : H / TiC ): (a) real and (b) negative imaginary parts of the dielectric permeability are shown dependent on the wavelength and the normalized depth of the layer. The gradient layer was approximated by 20 single layers, each with homogeneous particle volume fraction. The corresponding volume fraction characteristic is shown in Fig. 4.

Fig. 6
Fig. 6

Electrodynamic behavior of a Cu / a - C : H . TiC / a SiO 2 linear gradient layer solar collector setup. Incident intensity, reflection, and absorption of the coatings and the substrate are shown dependent on the wavelength. Using a a - C : H / TiC layer with a linear TiC particle volume fraction characteristic yielded the highest absorption of the simulated multilayers: α sol = 98.29 % . The corresponding volume fraction characteristic is shown in Fig. 4, and the corresponding setup is demonstrated in Fig. 1.

Tables (1)

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Table 1 Overview of Multilayer Simulation Results, Including Optimized Layer Thicknesses and Corresponding Relative Absorption a

Equations (4)

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v 1 ( ϵ B ϵ eff ) ( ϵ A + 2 ϵ B ) + f A ( 2 ϵ B + ϵ eff ) ( ϵ A ϵ B ) ( ϵ B + 2 ϵ eff ) ( ϵ A + 2 ϵ B ) + 2 f A ( ϵ B ϵ eff ) ( ϵ A ϵ B ) + v 2 ( ϵ A ϵ eff ) ( ϵ B + 2 ϵ A ) + ( 1 f A ) ( 2 ϵ A + ϵ eff ) ( ϵ B ϵ A ) ( ϵ A + 2 ϵ eff ) ( ϵ B + 2 ϵ A ) + 2 ( 1 f A ) ( ϵ A ϵ eff ) ( ϵ B ϵ A ) = 0.
v 1 = ( 1 f A 1 / 3 ) 3 ,
v 2 = ( 1 ( 1 f A ) 1 / 3 ) 3 ,
f ( z ) = max [ 0 , min ( 1 , c 0 + c 1 ( z ) d a - C H / TiC ) ] .

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