Abstract

The electronic structure of porous silicon (PS) has been characterized by optical reflectance spectra analyses. Using a Cary-500 spectrometer, the reflectance spectra of PS are measured in the photon energy range of 0.4–6 eV. The spectral responses of optical constants are calculated for PS and Si by Kramers–Kronig analysis. The analysis clarified strong evidence for widening and direct bandgaps for PS samples. Also, the optical constants of PS layers as a function of porosity have been studied. Our results indicate that PS retains some of the characteristic optical features of crystalline Si. However, in the visible region, PS shows that the imaginary part of the complex refractive index increases, and the real part decreases as porosity increases. This feature could be related to the surface roughness of PS and its role in surface absorption and scattering.

© 2007 Optical Society of America

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  1. G. Bomchil, A. Halimaoui, and R. Herino, "Porous silicon: the material and its applications to SOI technologies," Microelectron. Eng. 8, 293-310 (1988).
    [CrossRef]
  2. L. T. Canham, "Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers," Appl. Phys. Lett. 57, 1046-1048 (1990).
    [CrossRef]
  3. S. F. Chuang, S. D. Collins, and R. L. Smith, "Porous silicon microstructure as studied by transmission electron microscopy," Appl. Phys. Lett. 55, 1540-1542 (1989).
    [CrossRef]
  4. D. A. G. Bruggeman, "Berechnung verschidener physikalischer konstanten von heterogenen substanzen," Ann. Phys. 24, 636-679 (1935).
    [CrossRef]
  5. M. G. Berger, C. Dieker, M. Thonissen, L. Vescan, H. Luth, and H. Munder, "Porosity superlattices: a new class of Si heterostructures," J. Phys. D 27, 1333-1336 (1994).
    [CrossRef]
  6. R. J. Martin-Palma, P. Herrero, R. Guerrero-Lemus, J. D. Moreno, and J. M. Martinez-Duart, "Cross-section TEM and optical characterization of porous silicon multilayer stacks," J. Mater. Sci. Lett. 17, 845-847 (1998).
    [CrossRef]
  7. V. Lucarini, J. J. Saarinen, K. E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).
  8. V. Lucarini, F. Bassani, K. E. Peiponen, and J. J. Saarinen, "Dispersion theory and sum rules in linear and nonlinear optics," Riv. Nuovo Cimento 26, 1-120 (2003).
  9. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1997).
  10. T. S. Robinson, "Optical constants by reflection," Proc. Phys. Soc. London Sect. B 65, 910-911 (1952).
    [CrossRef]
  11. G. A. Nevill Connell, "Optical properties of amorphous metals using a ratio reflectance method," Appl. Opt. 29, 4560-4562 (1990).
    [CrossRef] [PubMed]
  12. H. R. Philipp and E. A. Taft, "Optical constants of silicon in the region 1 to 10 eV," Phys. Rev. 120, 37-38 (1960).
    [CrossRef]
  13. P. Menna, G. Francia, and V. La Ferra, "Porous silicon in solar cells: a review and a description of its application as an AR coating," Sol. Energy Mater. Sol. Cells 37, 13-24 (1995).
    [CrossRef]
  14. W. Theib, "Optical properties of porous silicon," Surf. Sci. Rep. 29, 91-192 (1997).
    [CrossRef]
  15. S. Hilbrich, R. Arens-Fischer, L. Küpper, W. Theiss, M. G. Berger, M. Krüger, and M. Thönissen, "The application of porous silicon interference filters in optical sensors," Thin Solid Films 297, 250-253 (1997).
    [CrossRef]
  16. S. M. Vernon, N. M. Kalkhoran, H. P. Maruska, and W. D. Halverson, "High performance porous silicon solar cell development," in Proceedings of the First World Conference on Photovoltaic Energy Conversion (IEEE, 1994), pp. 1583-1586.
  17. V. Y. Yerokhov and I. I. Melnyk, "Porous silicon in solar cell structures: a review of achievements and modern directions of further use," Renewable Sustainable Energy Rev. 3, 291-322 (1999).
    [CrossRef]
  18. C. Pickering, M. J. Beale, D. J. Robbins, P. J. Pearson, and R. Greef, "Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon," J. Phys. C 17, 6535-6552 (1984).
    [CrossRef]
  19. N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
    [CrossRef]
  20. L. Wang and A. Zunger, "Dielectric constants of silicon quantum dots," Phys. Rev. Lett. 73, 1039-1042 (1994).
    [CrossRef] [PubMed]
  21. G. Sanders and Y. Chang, "Theory of optical properties of quantum wires in porous silicon," Phys. Rev. B 45, 9202-9213 (1992).
    [CrossRef]
  22. D. T. Pierce and W. E. Spicer, "Electronic structure of amorphous Si from photoemission and optical studies," Phys. Rev. B 5, 3017-3029 (1972).
    [CrossRef]
  23. K. Barla, R. Herino, G. Bomchil, J. C. Pfister, and A. Freund, "Determination of lattice parameter and elastic properties of porous silicon by x-ray diffraction," J. Cryst. Growth 63, 727-732 (1984).
    [CrossRef]
  24. V. Lucarini, Y. Ino, K. E. Peiponen, and M. Kuwata-Gonokami, "Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations," Phys. Rev. B 72, 125107 (2005).
    [CrossRef]

2005

V. Lucarini, Y. Ino, K. E. Peiponen, and M. Kuwata-Gonokami, "Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations," Phys. Rev. B 72, 125107 (2005).
[CrossRef]

2003

V. Lucarini, F. Bassani, K. E. Peiponen, and J. J. Saarinen, "Dispersion theory and sum rules in linear and nonlinear optics," Riv. Nuovo Cimento 26, 1-120 (2003).

1999

V. Y. Yerokhov and I. I. Melnyk, "Porous silicon in solar cell structures: a review of achievements and modern directions of further use," Renewable Sustainable Energy Rev. 3, 291-322 (1999).
[CrossRef]

1998

R. J. Martin-Palma, P. Herrero, R. Guerrero-Lemus, J. D. Moreno, and J. M. Martinez-Duart, "Cross-section TEM and optical characterization of porous silicon multilayer stacks," J. Mater. Sci. Lett. 17, 845-847 (1998).
[CrossRef]

1997

W. Theib, "Optical properties of porous silicon," Surf. Sci. Rep. 29, 91-192 (1997).
[CrossRef]

S. Hilbrich, R. Arens-Fischer, L. Küpper, W. Theiss, M. G. Berger, M. Krüger, and M. Thönissen, "The application of porous silicon interference filters in optical sensors," Thin Solid Films 297, 250-253 (1997).
[CrossRef]

1995

P. Menna, G. Francia, and V. La Ferra, "Porous silicon in solar cells: a review and a description of its application as an AR coating," Sol. Energy Mater. Sol. Cells 37, 13-24 (1995).
[CrossRef]

1994

L. Wang and A. Zunger, "Dielectric constants of silicon quantum dots," Phys. Rev. Lett. 73, 1039-1042 (1994).
[CrossRef] [PubMed]

M. G. Berger, C. Dieker, M. Thonissen, L. Vescan, H. Luth, and H. Munder, "Porosity superlattices: a new class of Si heterostructures," J. Phys. D 27, 1333-1336 (1994).
[CrossRef]

1993

N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
[CrossRef]

1992

G. Sanders and Y. Chang, "Theory of optical properties of quantum wires in porous silicon," Phys. Rev. B 45, 9202-9213 (1992).
[CrossRef]

1990

L. T. Canham, "Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers," Appl. Phys. Lett. 57, 1046-1048 (1990).
[CrossRef]

G. A. Nevill Connell, "Optical properties of amorphous metals using a ratio reflectance method," Appl. Opt. 29, 4560-4562 (1990).
[CrossRef] [PubMed]

1989

S. F. Chuang, S. D. Collins, and R. L. Smith, "Porous silicon microstructure as studied by transmission electron microscopy," Appl. Phys. Lett. 55, 1540-1542 (1989).
[CrossRef]

1988

G. Bomchil, A. Halimaoui, and R. Herino, "Porous silicon: the material and its applications to SOI technologies," Microelectron. Eng. 8, 293-310 (1988).
[CrossRef]

1984

C. Pickering, M. J. Beale, D. J. Robbins, P. J. Pearson, and R. Greef, "Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon," J. Phys. C 17, 6535-6552 (1984).
[CrossRef]

K. Barla, R. Herino, G. Bomchil, J. C. Pfister, and A. Freund, "Determination of lattice parameter and elastic properties of porous silicon by x-ray diffraction," J. Cryst. Growth 63, 727-732 (1984).
[CrossRef]

1972

D. T. Pierce and W. E. Spicer, "Electronic structure of amorphous Si from photoemission and optical studies," Phys. Rev. B 5, 3017-3029 (1972).
[CrossRef]

1960

H. R. Philipp and E. A. Taft, "Optical constants of silicon in the region 1 to 10 eV," Phys. Rev. 120, 37-38 (1960).
[CrossRef]

1952

T. S. Robinson, "Optical constants by reflection," Proc. Phys. Soc. London Sect. B 65, 910-911 (1952).
[CrossRef]

1935

D. A. G. Bruggeman, "Berechnung verschidener physikalischer konstanten von heterogenen substanzen," Ann. Phys. 24, 636-679 (1935).
[CrossRef]

Araki, M.

N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
[CrossRef]

Arens-Fischer, R.

S. Hilbrich, R. Arens-Fischer, L. Küpper, W. Theiss, M. G. Berger, M. Krüger, and M. Thönissen, "The application of porous silicon interference filters in optical sensors," Thin Solid Films 297, 250-253 (1997).
[CrossRef]

Barla, K.

K. Barla, R. Herino, G. Bomchil, J. C. Pfister, and A. Freund, "Determination of lattice parameter and elastic properties of porous silicon by x-ray diffraction," J. Cryst. Growth 63, 727-732 (1984).
[CrossRef]

Bassani, F.

V. Lucarini, F. Bassani, K. E. Peiponen, and J. J. Saarinen, "Dispersion theory and sum rules in linear and nonlinear optics," Riv. Nuovo Cimento 26, 1-120 (2003).

Beale, M. J.

C. Pickering, M. J. Beale, D. J. Robbins, P. J. Pearson, and R. Greef, "Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon," J. Phys. C 17, 6535-6552 (1984).
[CrossRef]

Berger, M. G.

S. Hilbrich, R. Arens-Fischer, L. Küpper, W. Theiss, M. G. Berger, M. Krüger, and M. Thönissen, "The application of porous silicon interference filters in optical sensors," Thin Solid Films 297, 250-253 (1997).
[CrossRef]

M. G. Berger, C. Dieker, M. Thonissen, L. Vescan, H. Luth, and H. Munder, "Porosity superlattices: a new class of Si heterostructures," J. Phys. D 27, 1333-1336 (1994).
[CrossRef]

Bomchil, G.

G. Bomchil, A. Halimaoui, and R. Herino, "Porous silicon: the material and its applications to SOI technologies," Microelectron. Eng. 8, 293-310 (1988).
[CrossRef]

K. Barla, R. Herino, G. Bomchil, J. C. Pfister, and A. Freund, "Determination of lattice parameter and elastic properties of porous silicon by x-ray diffraction," J. Cryst. Growth 63, 727-732 (1984).
[CrossRef]

Bruggeman, D. A. G.

D. A. G. Bruggeman, "Berechnung verschidener physikalischer konstanten von heterogenen substanzen," Ann. Phys. 24, 636-679 (1935).
[CrossRef]

Canham, L. T.

L. T. Canham, "Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers," Appl. Phys. Lett. 57, 1046-1048 (1990).
[CrossRef]

Chang, Y.

G. Sanders and Y. Chang, "Theory of optical properties of quantum wires in porous silicon," Phys. Rev. B 45, 9202-9213 (1992).
[CrossRef]

Chuang, S. F.

S. F. Chuang, S. D. Collins, and R. L. Smith, "Porous silicon microstructure as studied by transmission electron microscopy," Appl. Phys. Lett. 55, 1540-1542 (1989).
[CrossRef]

Collins, S. D.

S. F. Chuang, S. D. Collins, and R. L. Smith, "Porous silicon microstructure as studied by transmission electron microscopy," Appl. Phys. Lett. 55, 1540-1542 (1989).
[CrossRef]

Connell, G. A. Nevill

Dieker, C.

M. G. Berger, C. Dieker, M. Thonissen, L. Vescan, H. Luth, and H. Munder, "Porosity superlattices: a new class of Si heterostructures," J. Phys. D 27, 1333-1336 (1994).
[CrossRef]

Francia, G.

P. Menna, G. Francia, and V. La Ferra, "Porous silicon in solar cells: a review and a description of its application as an AR coating," Sol. Energy Mater. Sol. Cells 37, 13-24 (1995).
[CrossRef]

Freund, A.

K. Barla, R. Herino, G. Bomchil, J. C. Pfister, and A. Freund, "Determination of lattice parameter and elastic properties of porous silicon by x-ray diffraction," J. Cryst. Growth 63, 727-732 (1984).
[CrossRef]

Greef, R.

C. Pickering, M. J. Beale, D. J. Robbins, P. J. Pearson, and R. Greef, "Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon," J. Phys. C 17, 6535-6552 (1984).
[CrossRef]

Guerrero-Lemus, R.

R. J. Martin-Palma, P. Herrero, R. Guerrero-Lemus, J. D. Moreno, and J. M. Martinez-Duart, "Cross-section TEM and optical characterization of porous silicon multilayer stacks," J. Mater. Sci. Lett. 17, 845-847 (1998).
[CrossRef]

Halimaoui, A.

G. Bomchil, A. Halimaoui, and R. Herino, "Porous silicon: the material and its applications to SOI technologies," Microelectron. Eng. 8, 293-310 (1988).
[CrossRef]

Halverson, W. D.

S. M. Vernon, N. M. Kalkhoran, H. P. Maruska, and W. D. Halverson, "High performance porous silicon solar cell development," in Proceedings of the First World Conference on Photovoltaic Energy Conversion (IEEE, 1994), pp. 1583-1586.

Herino, R.

G. Bomchil, A. Halimaoui, and R. Herino, "Porous silicon: the material and its applications to SOI technologies," Microelectron. Eng. 8, 293-310 (1988).
[CrossRef]

K. Barla, R. Herino, G. Bomchil, J. C. Pfister, and A. Freund, "Determination of lattice parameter and elastic properties of porous silicon by x-ray diffraction," J. Cryst. Growth 63, 727-732 (1984).
[CrossRef]

Herrero, P.

R. J. Martin-Palma, P. Herrero, R. Guerrero-Lemus, J. D. Moreno, and J. M. Martinez-Duart, "Cross-section TEM and optical characterization of porous silicon multilayer stacks," J. Mater. Sci. Lett. 17, 845-847 (1998).
[CrossRef]

Hilbrich, S.

S. Hilbrich, R. Arens-Fischer, L. Küpper, W. Theiss, M. G. Berger, M. Krüger, and M. Thönissen, "The application of porous silicon interference filters in optical sensors," Thin Solid Films 297, 250-253 (1997).
[CrossRef]

Ino, Y.

V. Lucarini, Y. Ino, K. E. Peiponen, and M. Kuwata-Gonokami, "Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations," Phys. Rev. B 72, 125107 (2005).
[CrossRef]

Kalkhoran, N. M.

S. M. Vernon, N. M. Kalkhoran, H. P. Maruska, and W. D. Halverson, "High performance porous silicon solar cell development," in Proceedings of the First World Conference on Photovoltaic Energy Conversion (IEEE, 1994), pp. 1583-1586.

Koshida, N.

N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
[CrossRef]

Koyama, H.

N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
[CrossRef]

Krüger, M.

S. Hilbrich, R. Arens-Fischer, L. Küpper, W. Theiss, M. G. Berger, M. Krüger, and M. Thönissen, "The application of porous silicon interference filters in optical sensors," Thin Solid Films 297, 250-253 (1997).
[CrossRef]

Küpper, L.

S. Hilbrich, R. Arens-Fischer, L. Küpper, W. Theiss, M. G. Berger, M. Krüger, and M. Thönissen, "The application of porous silicon interference filters in optical sensors," Thin Solid Films 297, 250-253 (1997).
[CrossRef]

Kuwata-Gonokami, M.

V. Lucarini, Y. Ino, K. E. Peiponen, and M. Kuwata-Gonokami, "Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations," Phys. Rev. B 72, 125107 (2005).
[CrossRef]

La Ferra, V.

P. Menna, G. Francia, and V. La Ferra, "Porous silicon in solar cells: a review and a description of its application as an AR coating," Sol. Energy Mater. Sol. Cells 37, 13-24 (1995).
[CrossRef]

Lucarini, V.

V. Lucarini, Y. Ino, K. E. Peiponen, and M. Kuwata-Gonokami, "Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations," Phys. Rev. B 72, 125107 (2005).
[CrossRef]

V. Lucarini, F. Bassani, K. E. Peiponen, and J. J. Saarinen, "Dispersion theory and sum rules in linear and nonlinear optics," Riv. Nuovo Cimento 26, 1-120 (2003).

V. Lucarini, J. J. Saarinen, K. E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Luth, H.

M. G. Berger, C. Dieker, M. Thonissen, L. Vescan, H. Luth, and H. Munder, "Porosity superlattices: a new class of Si heterostructures," J. Phys. D 27, 1333-1336 (1994).
[CrossRef]

Martinez-Duart, J. M.

R. J. Martin-Palma, P. Herrero, R. Guerrero-Lemus, J. D. Moreno, and J. M. Martinez-Duart, "Cross-section TEM and optical characterization of porous silicon multilayer stacks," J. Mater. Sci. Lett. 17, 845-847 (1998).
[CrossRef]

Martin-Palma, R. J.

R. J. Martin-Palma, P. Herrero, R. Guerrero-Lemus, J. D. Moreno, and J. M. Martinez-Duart, "Cross-section TEM and optical characterization of porous silicon multilayer stacks," J. Mater. Sci. Lett. 17, 845-847 (1998).
[CrossRef]

Maruska, H. P.

S. M. Vernon, N. M. Kalkhoran, H. P. Maruska, and W. D. Halverson, "High performance porous silicon solar cell development," in Proceedings of the First World Conference on Photovoltaic Energy Conversion (IEEE, 1994), pp. 1583-1586.

Melnyk, I. I.

V. Y. Yerokhov and I. I. Melnyk, "Porous silicon in solar cell structures: a review of achievements and modern directions of further use," Renewable Sustainable Energy Rev. 3, 291-322 (1999).
[CrossRef]

Menna, P.

P. Menna, G. Francia, and V. La Ferra, "Porous silicon in solar cells: a review and a description of its application as an AR coating," Sol. Energy Mater. Sol. Cells 37, 13-24 (1995).
[CrossRef]

Moreno, J. D.

R. J. Martin-Palma, P. Herrero, R. Guerrero-Lemus, J. D. Moreno, and J. M. Martinez-Duart, "Cross-section TEM and optical characterization of porous silicon multilayer stacks," J. Mater. Sci. Lett. 17, 845-847 (1998).
[CrossRef]

Munder, H.

M. G. Berger, C. Dieker, M. Thonissen, L. Vescan, H. Luth, and H. Munder, "Porosity superlattices: a new class of Si heterostructures," J. Phys. D 27, 1333-1336 (1994).
[CrossRef]

Palik, E. D.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1997).

Pearson, P. J.

C. Pickering, M. J. Beale, D. J. Robbins, P. J. Pearson, and R. Greef, "Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon," J. Phys. C 17, 6535-6552 (1984).
[CrossRef]

Peiponen, K. E.

V. Lucarini, Y. Ino, K. E. Peiponen, and M. Kuwata-Gonokami, "Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations," Phys. Rev. B 72, 125107 (2005).
[CrossRef]

V. Lucarini, F. Bassani, K. E. Peiponen, and J. J. Saarinen, "Dispersion theory and sum rules in linear and nonlinear optics," Riv. Nuovo Cimento 26, 1-120 (2003).

V. Lucarini, J. J. Saarinen, K. E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Pfister, J. C.

K. Barla, R. Herino, G. Bomchil, J. C. Pfister, and A. Freund, "Determination of lattice parameter and elastic properties of porous silicon by x-ray diffraction," J. Cryst. Growth 63, 727-732 (1984).
[CrossRef]

Philipp, H. R.

H. R. Philipp and E. A. Taft, "Optical constants of silicon in the region 1 to 10 eV," Phys. Rev. 120, 37-38 (1960).
[CrossRef]

Pickering, C.

C. Pickering, M. J. Beale, D. J. Robbins, P. J. Pearson, and R. Greef, "Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon," J. Phys. C 17, 6535-6552 (1984).
[CrossRef]

Pierce, D. T.

D. T. Pierce and W. E. Spicer, "Electronic structure of amorphous Si from photoemission and optical studies," Phys. Rev. B 5, 3017-3029 (1972).
[CrossRef]

Robbins, D. J.

C. Pickering, M. J. Beale, D. J. Robbins, P. J. Pearson, and R. Greef, "Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon," J. Phys. C 17, 6535-6552 (1984).
[CrossRef]

Robinson, T. S.

T. S. Robinson, "Optical constants by reflection," Proc. Phys. Soc. London Sect. B 65, 910-911 (1952).
[CrossRef]

Saarinen, J. J.

V. Lucarini, F. Bassani, K. E. Peiponen, and J. J. Saarinen, "Dispersion theory and sum rules in linear and nonlinear optics," Riv. Nuovo Cimento 26, 1-120 (2003).

V. Lucarini, J. J. Saarinen, K. E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Saito, T.

N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
[CrossRef]

Sanders, G.

G. Sanders and Y. Chang, "Theory of optical properties of quantum wires in porous silicon," Phys. Rev. B 45, 9202-9213 (1992).
[CrossRef]

Sato, K.

N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
[CrossRef]

Sato, N.

N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
[CrossRef]

Shin, S.

N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
[CrossRef]

Smith, R. L.

S. F. Chuang, S. D. Collins, and R. L. Smith, "Porous silicon microstructure as studied by transmission electron microscopy," Appl. Phys. Lett. 55, 1540-1542 (1989).
[CrossRef]

Spicer, W. E.

D. T. Pierce and W. E. Spicer, "Electronic structure of amorphous Si from photoemission and optical studies," Phys. Rev. B 5, 3017-3029 (1972).
[CrossRef]

Suda, Y.

N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
[CrossRef]

Taft, E. A.

H. R. Philipp and E. A. Taft, "Optical constants of silicon in the region 1 to 10 eV," Phys. Rev. 120, 37-38 (1960).
[CrossRef]

Theib, W.

W. Theib, "Optical properties of porous silicon," Surf. Sci. Rep. 29, 91-192 (1997).
[CrossRef]

Theiss, W.

S. Hilbrich, R. Arens-Fischer, L. Küpper, W. Theiss, M. G. Berger, M. Krüger, and M. Thönissen, "The application of porous silicon interference filters in optical sensors," Thin Solid Films 297, 250-253 (1997).
[CrossRef]

Thonissen, M.

M. G. Berger, C. Dieker, M. Thonissen, L. Vescan, H. Luth, and H. Munder, "Porosity superlattices: a new class of Si heterostructures," J. Phys. D 27, 1333-1336 (1994).
[CrossRef]

Thönissen, M.

S. Hilbrich, R. Arens-Fischer, L. Küpper, W. Theiss, M. G. Berger, M. Krüger, and M. Thönissen, "The application of porous silicon interference filters in optical sensors," Thin Solid Films 297, 250-253 (1997).
[CrossRef]

Vartiainen, E. M.

V. Lucarini, J. J. Saarinen, K. E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Vernon, S. M.

S. M. Vernon, N. M. Kalkhoran, H. P. Maruska, and W. D. Halverson, "High performance porous silicon solar cell development," in Proceedings of the First World Conference on Photovoltaic Energy Conversion (IEEE, 1994), pp. 1583-1586.

Vescan, L.

M. G. Berger, C. Dieker, M. Thonissen, L. Vescan, H. Luth, and H. Munder, "Porosity superlattices: a new class of Si heterostructures," J. Phys. D 27, 1333-1336 (1994).
[CrossRef]

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L. Wang and A. Zunger, "Dielectric constants of silicon quantum dots," Phys. Rev. Lett. 73, 1039-1042 (1994).
[CrossRef] [PubMed]

Yamamoto, Y.

N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
[CrossRef]

Yerokhov, V. Y.

V. Y. Yerokhov and I. I. Melnyk, "Porous silicon in solar cell structures: a review of achievements and modern directions of further use," Renewable Sustainable Energy Rev. 3, 291-322 (1999).
[CrossRef]

Zunger, A.

L. Wang and A. Zunger, "Dielectric constants of silicon quantum dots," Phys. Rev. Lett. 73, 1039-1042 (1994).
[CrossRef] [PubMed]

Ann. Phys.

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N. Koshida, H. Koyama, Y. Suda, Y. Yamamoto, M. Araki, T. Saito, K. Sato, N. Sato, and S. Shin, "Optical characterization of porous silicon by synchrotron radiation reflectance spectra analyses," Appl. Phys. Lett. 63, 2774-2776 (1993).
[CrossRef]

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[CrossRef]

S. F. Chuang, S. D. Collins, and R. L. Smith, "Porous silicon microstructure as studied by transmission electron microscopy," Appl. Phys. Lett. 55, 1540-1542 (1989).
[CrossRef]

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[CrossRef]

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R. J. Martin-Palma, P. Herrero, R. Guerrero-Lemus, J. D. Moreno, and J. M. Martinez-Duart, "Cross-section TEM and optical characterization of porous silicon multilayer stacks," J. Mater. Sci. Lett. 17, 845-847 (1998).
[CrossRef]

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C. Pickering, M. J. Beale, D. J. Robbins, P. J. Pearson, and R. Greef, "Optical studies of the structure of porous silicon films formed in p-type degenerate and non-degenerate silicon," J. Phys. C 17, 6535-6552 (1984).
[CrossRef]

J. Phys. D

M. G. Berger, C. Dieker, M. Thonissen, L. Vescan, H. Luth, and H. Munder, "Porosity superlattices: a new class of Si heterostructures," J. Phys. D 27, 1333-1336 (1994).
[CrossRef]

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V. Lucarini, Y. Ino, K. E. Peiponen, and M. Kuwata-Gonokami, "Detection and correction of the misplacement error in terahertz spectroscopy by application of singly subtractive Kramers-Kronig relations," Phys. Rev. B 72, 125107 (2005).
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[CrossRef] [PubMed]

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[CrossRef]

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V. Y. Yerokhov and I. I. Melnyk, "Porous silicon in solar cell structures: a review of achievements and modern directions of further use," Renewable Sustainable Energy Rev. 3, 291-322 (1999).
[CrossRef]

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V. Lucarini, F. Bassani, K. E. Peiponen, and J. J. Saarinen, "Dispersion theory and sum rules in linear and nonlinear optics," Riv. Nuovo Cimento 26, 1-120 (2003).

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[CrossRef]

Other

S. M. Vernon, N. M. Kalkhoran, H. P. Maruska, and W. D. Halverson, "High performance porous silicon solar cell development," in Proceedings of the First World Conference on Photovoltaic Energy Conversion (IEEE, 1994), pp. 1583-1586.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1997).

V. Lucarini, J. J. Saarinen, K. E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

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Figures (6)

Fig. 1
Fig. 1

Surface views of scanning electron micrographs of the (a) n-type Si wafer and PS samples fabricated in etching solution with anodization times of (b) 10 min and (c) 20 min .

Fig. 2
Fig. 2

n and k versus photon energy of Si data from Ref. [9] (dashed curve) and our samples' values obtained by Kramers–Kronig analysis (solid curve).

Fig. 3
Fig. 3

(a) n versus energy, (b) k versus energy, (c) ε 1 versus energy, (d) ε 2 versus energy for the Si and PS sample of 10 min anodization.

Fig. 4
Fig. 4

Reflectance curves versus wavelength for the n type Si sample, PS sample ( 10 min ) , and PS sample ( 20 min ) .

Fig. 5
Fig. 5

n and k versus energy in the visible region for the Si sample, PS sample for 10 min anodization, and PS sample for 20 min anodization. Top three curves are n and bottom three curves are k.

Fig. 6
Fig. 6

Variation of ε 1 , ε 2 curves versus photon energy for n-type Si, PS ( 10 min ) , and PS ( 20 min ) .

Equations (98)

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

3000 nm
θ ( E ) = ( E / π ) P 0 [ { ln [ R ( E ) ] ln [ R ( E ) ] } / ( E 2 E 2 ) ] d E ,
E
E 1 E E 2
R ( E ) = R ( E 2 ) ( E 2 / E ) m ,
θ ( E ) = ( E / π ) 0 E 2 [ { ln [ R ( E ) ] ln [ R ( E ) ] } / ( E 2 E 2 ) ] × d E + ( 1 / 2 π ) ln [ R ( E ) / R ( E 2 ) ] × ln [ ( E 2 + E ) / ( E 2 E ) ] + ( 1 / π ) q = 0 [ m ( E / E 2 ) 2 q + 1 ] × ( 2 q + 1 ) 2 .
r ( E ) = R 1 / 2 ( E ) exp [ i θ ( E ) ] ,
θ ( E )
θ ( E )
k ( E ) = { [ 2 r sin θ ( E ) ] / [ 1 + r 2 2 r cos θ ( E ) ] } ,
n ( E ) = { ( 1 r 2 ) / [ 1 + r 2 2 r cos θ ( E ) ] } ,
ε ( E ) = ε 1 + i ε 2 ,
ε 1
ε 2
ε 1 = n 2 k 2
ε 2 = 2 n k
ε 1
ε 2
1.5 Ω cm
( HF:C 2 H 5 OH = 1 : 1 )
25 mA / cm 2
1 nm
200 3000 nm
θ ( E )
θ ( E )
20 min
20 min
10 min
20 min
20 30 μ m
200 3000 nm
7.5 ± 0.3
θ ( E )
θ ( E )
E 2 = 6 eV
10 min
2 < E < 6 eV
1.2 < E < 3 eV
n PS < n Si
k PS > k Si
0 < E < 1.2
eV
4 + 0 i
E = 1.2   to   0 eV ,
0.5 < E < 1.3 eV
ε 1
ε 2
( ε 2 )
( < 10 nm )
1100 nm
10 min
20 min
( 400 800 nm )
( 10 min )
( 20 min )
( 20 min )
( 20 min )
( 10 min )
( 20 min )
10 min
20 min
( 10 min )
( 10 min )
( 20 min )
( 10 min )
( 10 min )
( 20 min )
( 10 min )
( 20 min )
( 10 min )
( 20 min )
( 10 min )
( 20 min )
ε 1
ε 1
( 10 min )
( 20 min )
( 10 min )
( 20 min )
( ε 2 )
( 20 min )
ε 2
( 10 min )
ε 2
( 10 min )
10 min
20 min
ε 1
ε 2
10 min
( 10 min )
( 20 min )
10 min
20 min
ε 1
ε 2
( 10 min )
( 20 min )

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