Abstract

The optical constants of plasma-enhanced chemical-vapor-deposited amorphous silicon (a-Si:H) thin film upon a transparent substrate are determined within the UV–visible region by measurement of the transmittance spectrum. Apart from thickness irregularities, the effects of vertical film inhomogeneities (refractive-index distribution) on the spectrum are discussed. In this respect, although consideration of any possible variation in thickness of the film within the area illuminated by the probe beam is sufficient for correcting the modulation of the extrema of interference fringes, including in the model the thin transitional regions at substrate–film and film–air interfaces might be an alternative method for understanding the overall optical behavior of the spectrum.

© 2000 Optical Society of America

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  1. S. Shokhovets, R. Goldhahn, V. Cimalla, T. S. Cheng, C. T. Foxon, “Reflectivity study of hexagonal GaN films grown on GaAs: surface roughness, interface layer, and refractive index,” J. Appl. Phys. 84, 1561–1566 (1998).
    [CrossRef]
  2. J. Rivory, “Characterization of inhomogeneous dielectric films by spectroscopic ellipsometry,” Thin Solid Films 313–314, 333–340 (1998).
    [CrossRef]
  3. A. V. Tikhonravov, M. K. Trubetskov, A. V. Krasilnikova, “Spectroscopic ellipsometry of slightly inhomogeneous nonabsorbing thin films with arbitrary refractive-index profiles: theoretical study,” Appl. Opt. 37, 5902–5911 (1998).
    [CrossRef]
  4. K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterization of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films 313–314, 379–383 (1998).
    [CrossRef]
  5. S. Callard, A. Gagnaire, J. Joseph, “Characterization of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry,” Thin Solid Films 313–314, 384–388 (1998).
    [CrossRef]
  6. K. Lamprecht, W. Papousek, G. Leising, “Problem of ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements,” Appl. Opt. 36, 6364–6371 (1997).
    [CrossRef]
  7. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. 9, 1002–1004 (1976).
  8. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), pp. 46–62.
  9. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. 16, 1214–1222 (1983).
  10. D. A. Minkov, “Method for determining the optical constants of a thin film on a transparent substrate,” J. Phys. D 22, 199–205 (1989).
    [CrossRef]
  11. J. I. Cisneros, “Optical characterization of dielectric and semiconductor thin films by use of transmission data,” Appl. Opt. 37, 5262–5270 (1998).
    [CrossRef]
  12. A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, J. A. Dobrowolski, “Influence of small inhomogeneities on the spectral characteristics of single thin films,” Appl. Opt. 36, 7188–7198 (1997).
    [CrossRef]
  13. R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
    [CrossRef]
  14. R. Jacobsson, “Light reflection from films of continuously varying refractive index,” Prog. Opt. 2, 247–286 (1966).
    [CrossRef]
  15. M. Born, E. Wolf, Principles of Optics, 4th. ed. (Pergamon, London, 1970), pp. 55–60.
  16. S. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontiers, Gif-sur-Yvette, France, 1992), pp. 1–26.
  17. M. Yamaguchi, K. Morigaki, “Effect of hydrogen dilution on the optical properties of hydrogenated amorphous silicon prepared by plasma deposition,” Philos. Mag. B 79, 387–405 (1999).
    [CrossRef]
  18. E. C. Freeman, W. Paul, “Optical constants of rf sputtered hydrogenated amorphous Si,” Phys. Rev. B 20, 716–728 (1979).
    [CrossRef]
  19. M. H. Brodsky, R. S. Title, K. Weiser, F. D. Pettit, “Structural, optical, and electrical properties of amorphous silicon films,” Phys. Rev. B 1, 2632–2640 (1970).
    [CrossRef]
  20. M. Harris, H. A. Macleod, S. Ogura, “The relationship between optical inhomogeneity and film structure,” Thin Solid Films 57, 173–178 (1979).
    [CrossRef]
  21. W. M. M. Kessels, R. J. Severans, M. C. M. Van de Sanden, D. C. Schram, “Temperature and growth-rate effects on the hydrogen incorporation in a-Si:H,” J. Non-Cryst. Solids 227–230, 133–137 (1998).
    [CrossRef]
  22. D. Das, S. M. Iftiquar, A. K. Barua, “Wide optical gap a-SiO:H films prepared by rf glow discharge,” J. Non-Cryst. Solids 210, 148–154 (1997).
    [CrossRef]
  23. A. Masuda, K. Itoh, K. Matsuda, Y. Yonezawa, M. Kumeda, T. Shimizu, “Nitrogen-doping effects on electrical, optical and structural properties in hydrogenated amorphous silicon,” J. Appl. Phys. 81, 6729–6737 (1997).
    [CrossRef]
  24. J. R. Elmiger, M. Kunst, “Investigation of the silicon–plasma silicon nitride interface with in situ transient photoconductivity measurements,” Appl. Surf. Sci. 103, 11–18 (1996).
    [CrossRef]
  25. R. Ruther, J. Livingstone, N. Dytlowski, D. Cohen, “Improved hydrogen depth profiles with in-chamber annealing of hydrogenated amorphous silicon thin films,” J. Appl. Phys. 79, 175–178 (1996).
    [CrossRef]

1999 (1)

M. Yamaguchi, K. Morigaki, “Effect of hydrogen dilution on the optical properties of hydrogenated amorphous silicon prepared by plasma deposition,” Philos. Mag. B 79, 387–405 (1999).
[CrossRef]

1998 (7)

S. Shokhovets, R. Goldhahn, V. Cimalla, T. S. Cheng, C. T. Foxon, “Reflectivity study of hexagonal GaN films grown on GaAs: surface roughness, interface layer, and refractive index,” J. Appl. Phys. 84, 1561–1566 (1998).
[CrossRef]

J. Rivory, “Characterization of inhomogeneous dielectric films by spectroscopic ellipsometry,” Thin Solid Films 313–314, 333–340 (1998).
[CrossRef]

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterization of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films 313–314, 379–383 (1998).
[CrossRef]

S. Callard, A. Gagnaire, J. Joseph, “Characterization of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry,” Thin Solid Films 313–314, 384–388 (1998).
[CrossRef]

W. M. M. Kessels, R. J. Severans, M. C. M. Van de Sanden, D. C. Schram, “Temperature and growth-rate effects on the hydrogen incorporation in a-Si:H,” J. Non-Cryst. Solids 227–230, 133–137 (1998).
[CrossRef]

J. I. Cisneros, “Optical characterization of dielectric and semiconductor thin films by use of transmission data,” Appl. Opt. 37, 5262–5270 (1998).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, A. V. Krasilnikova, “Spectroscopic ellipsometry of slightly inhomogeneous nonabsorbing thin films with arbitrary refractive-index profiles: theoretical study,” Appl. Opt. 37, 5902–5911 (1998).
[CrossRef]

1997 (4)

D. Das, S. M. Iftiquar, A. K. Barua, “Wide optical gap a-SiO:H films prepared by rf glow discharge,” J. Non-Cryst. Solids 210, 148–154 (1997).
[CrossRef]

A. Masuda, K. Itoh, K. Matsuda, Y. Yonezawa, M. Kumeda, T. Shimizu, “Nitrogen-doping effects on electrical, optical and structural properties in hydrogenated amorphous silicon,” J. Appl. Phys. 81, 6729–6737 (1997).
[CrossRef]

K. Lamprecht, W. Papousek, G. Leising, “Problem of ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements,” Appl. Opt. 36, 6364–6371 (1997).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, J. A. Dobrowolski, “Influence of small inhomogeneities on the spectral characteristics of single thin films,” Appl. Opt. 36, 7188–7198 (1997).
[CrossRef]

1996 (2)

J. R. Elmiger, M. Kunst, “Investigation of the silicon–plasma silicon nitride interface with in situ transient photoconductivity measurements,” Appl. Surf. Sci. 103, 11–18 (1996).
[CrossRef]

R. Ruther, J. Livingstone, N. Dytlowski, D. Cohen, “Improved hydrogen depth profiles with in-chamber annealing of hydrogenated amorphous silicon thin films,” J. Appl. Phys. 79, 175–178 (1996).
[CrossRef]

1989 (1)

D. A. Minkov, “Method for determining the optical constants of a thin film on a transparent substrate,” J. Phys. D 22, 199–205 (1989).
[CrossRef]

1984 (1)

R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
[CrossRef]

1983 (1)

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. 16, 1214–1222 (1983).

1979 (2)

M. Harris, H. A. Macleod, S. Ogura, “The relationship between optical inhomogeneity and film structure,” Thin Solid Films 57, 173–178 (1979).
[CrossRef]

E. C. Freeman, W. Paul, “Optical constants of rf sputtered hydrogenated amorphous Si,” Phys. Rev. B 20, 716–728 (1979).
[CrossRef]

1976 (1)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. 9, 1002–1004 (1976).

1970 (1)

M. H. Brodsky, R. S. Title, K. Weiser, F. D. Pettit, “Structural, optical, and electrical properties of amorphous silicon films,” Phys. Rev. B 1, 2632–2640 (1970).
[CrossRef]

1966 (1)

R. Jacobsson, “Light reflection from films of continuously varying refractive index,” Prog. Opt. 2, 247–286 (1966).
[CrossRef]

Barua, A. K.

D. Das, S. M. Iftiquar, A. K. Barua, “Wide optical gap a-SiO:H films prepared by rf glow discharge,” J. Non-Cryst. Solids 210, 148–154 (1997).
[CrossRef]

Bertran, E.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterization of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films 313–314, 379–383 (1998).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th. ed. (Pergamon, London, 1970), pp. 55–60.

Bosch, S.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterization of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films 313–314, 379–383 (1998).
[CrossRef]

Brodsky, M. H.

M. H. Brodsky, R. S. Title, K. Weiser, F. D. Pettit, “Structural, optical, and electrical properties of amorphous silicon films,” Phys. Rev. B 1, 2632–2640 (1970).
[CrossRef]

Callard, S.

S. Callard, A. Gagnaire, J. Joseph, “Characterization of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry,” Thin Solid Films 313–314, 384–388 (1998).
[CrossRef]

Campmany, J.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterization of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films 313–314, 379–383 (1998).
[CrossRef]

Canillas, A.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterization of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films 313–314, 379–383 (1998).
[CrossRef]

Cheng, T. S.

S. Shokhovets, R. Goldhahn, V. Cimalla, T. S. Cheng, C. T. Foxon, “Reflectivity study of hexagonal GaN films grown on GaAs: surface roughness, interface layer, and refractive index,” J. Appl. Phys. 84, 1561–1566 (1998).
[CrossRef]

Cimalla, V.

S. Shokhovets, R. Goldhahn, V. Cimalla, T. S. Cheng, C. T. Foxon, “Reflectivity study of hexagonal GaN films grown on GaAs: surface roughness, interface layer, and refractive index,” J. Appl. Phys. 84, 1561–1566 (1998).
[CrossRef]

Cisneros, J. I.

Cohen, D.

R. Ruther, J. Livingstone, N. Dytlowski, D. Cohen, “Improved hydrogen depth profiles with in-chamber annealing of hydrogenated amorphous silicon thin films,” J. Appl. Phys. 79, 175–178 (1996).
[CrossRef]

Das, D.

D. Das, S. M. Iftiquar, A. K. Barua, “Wide optical gap a-SiO:H films prepared by rf glow discharge,” J. Non-Cryst. Solids 210, 148–154 (1997).
[CrossRef]

Dobrowolski, J. A.

Dytlowski, N.

R. Ruther, J. Livingstone, N. Dytlowski, D. Cohen, “Improved hydrogen depth profiles with in-chamber annealing of hydrogenated amorphous silicon thin films,” J. Appl. Phys. 79, 175–178 (1996).
[CrossRef]

Elmiger, J. R.

J. R. Elmiger, M. Kunst, “Investigation of the silicon–plasma silicon nitride interface with in situ transient photoconductivity measurements,” Appl. Surf. Sci. 103, 11–18 (1996).
[CrossRef]

Fillard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. 9, 1002–1004 (1976).

Foxon, C. T.

S. Shokhovets, R. Goldhahn, V. Cimalla, T. S. Cheng, C. T. Foxon, “Reflectivity study of hexagonal GaN films grown on GaAs: surface roughness, interface layer, and refractive index,” J. Appl. Phys. 84, 1561–1566 (1998).
[CrossRef]

Freeman, E. C.

E. C. Freeman, W. Paul, “Optical constants of rf sputtered hydrogenated amorphous Si,” Phys. Rev. B 20, 716–728 (1979).
[CrossRef]

Furman, S. A.

S. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontiers, Gif-sur-Yvette, France, 1992), pp. 1–26.

Gagnaire, A.

S. Callard, A. Gagnaire, J. Joseph, “Characterization of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry,” Thin Solid Films 313–314, 384–388 (1998).
[CrossRef]

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. 9, 1002–1004 (1976).

Goldhahn, R.

S. Shokhovets, R. Goldhahn, V. Cimalla, T. S. Cheng, C. T. Foxon, “Reflectivity study of hexagonal GaN films grown on GaAs: surface roughness, interface layer, and refractive index,” J. Appl. Phys. 84, 1561–1566 (1998).
[CrossRef]

Harris, M.

M. Harris, H. A. Macleod, S. Ogura, “The relationship between optical inhomogeneity and film structure,” Thin Solid Films 57, 173–178 (1979).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), pp. 46–62.

Iftiquar, S. M.

D. Das, S. M. Iftiquar, A. K. Barua, “Wide optical gap a-SiO:H films prepared by rf glow discharge,” J. Non-Cryst. Solids 210, 148–154 (1997).
[CrossRef]

Itoh, K.

A. Masuda, K. Itoh, K. Matsuda, Y. Yonezawa, M. Kumeda, T. Shimizu, “Nitrogen-doping effects on electrical, optical and structural properties in hydrogenated amorphous silicon,” J. Appl. Phys. 81, 6729–6737 (1997).
[CrossRef]

Jacobsson, R.

R. Jacobsson, “Light reflection from films of continuously varying refractive index,” Prog. Opt. 2, 247–286 (1966).
[CrossRef]

Joseph, J.

S. Callard, A. Gagnaire, J. Joseph, “Characterization of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry,” Thin Solid Films 313–314, 384–388 (1998).
[CrossRef]

Kessels, W. M. M.

W. M. M. Kessels, R. J. Severans, M. C. M. Van de Sanden, D. C. Schram, “Temperature and growth-rate effects on the hydrogen incorporation in a-Si:H,” J. Non-Cryst. Solids 227–230, 133–137 (1998).
[CrossRef]

Krasilnikova, A. V.

Kumeda, M.

A. Masuda, K. Itoh, K. Matsuda, Y. Yonezawa, M. Kumeda, T. Shimizu, “Nitrogen-doping effects on electrical, optical and structural properties in hydrogenated amorphous silicon,” J. Appl. Phys. 81, 6729–6737 (1997).
[CrossRef]

Kunst, M.

J. R. Elmiger, M. Kunst, “Investigation of the silicon–plasma silicon nitride interface with in situ transient photoconductivity measurements,” Appl. Surf. Sci. 103, 11–18 (1996).
[CrossRef]

Lamprecht, K.

Leising, G.

Livingstone, J.

R. Ruther, J. Livingstone, N. Dytlowski, D. Cohen, “Improved hydrogen depth profiles with in-chamber annealing of hydrogenated amorphous silicon thin films,” J. Appl. Phys. 79, 175–178 (1996).
[CrossRef]

Macleod, H. A.

M. Harris, H. A. Macleod, S. Ogura, “The relationship between optical inhomogeneity and film structure,” Thin Solid Films 57, 173–178 (1979).
[CrossRef]

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. 9, 1002–1004 (1976).

Masuda, A.

A. Masuda, K. Itoh, K. Matsuda, Y. Yonezawa, M. Kumeda, T. Shimizu, “Nitrogen-doping effects on electrical, optical and structural properties in hydrogenated amorphous silicon,” J. Appl. Phys. 81, 6729–6737 (1997).
[CrossRef]

Matsuda, K.

A. Masuda, K. Itoh, K. Matsuda, Y. Yonezawa, M. Kumeda, T. Shimizu, “Nitrogen-doping effects on electrical, optical and structural properties in hydrogenated amorphous silicon,” J. Appl. Phys. 81, 6729–6737 (1997).
[CrossRef]

Minkov, D. A.

D. A. Minkov, “Method for determining the optical constants of a thin film on a transparent substrate,” J. Phys. D 22, 199–205 (1989).
[CrossRef]

Morigaki, K.

M. Yamaguchi, K. Morigaki, “Effect of hydrogen dilution on the optical properties of hydrogenated amorphous silicon prepared by plasma deposition,” Philos. Mag. B 79, 387–405 (1999).
[CrossRef]

Ogura, S.

M. Harris, H. A. Macleod, S. Ogura, “The relationship between optical inhomogeneity and film structure,” Thin Solid Films 57, 173–178 (1979).
[CrossRef]

Papousek, W.

Paul, W.

E. C. Freeman, W. Paul, “Optical constants of rf sputtered hydrogenated amorphous Si,” Phys. Rev. B 20, 716–728 (1979).
[CrossRef]

Pettit, F. D.

M. H. Brodsky, R. S. Title, K. Weiser, F. D. Pettit, “Structural, optical, and electrical properties of amorphous silicon films,” Phys. Rev. B 1, 2632–2640 (1970).
[CrossRef]

Popov, K. V.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterization of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films 313–314, 379–383 (1998).
[CrossRef]

Rivory, J.

J. Rivory, “Characterization of inhomogeneous dielectric films by spectroscopic ellipsometry,” Thin Solid Films 313–314, 333–340 (1998).
[CrossRef]

Ruther, R.

R. Ruther, J. Livingstone, N. Dytlowski, D. Cohen, “Improved hydrogen depth profiles with in-chamber annealing of hydrogenated amorphous silicon thin films,” J. Appl. Phys. 79, 175–178 (1996).
[CrossRef]

Schram, D. C.

W. M. M. Kessels, R. J. Severans, M. C. M. Van de Sanden, D. C. Schram, “Temperature and growth-rate effects on the hydrogen incorporation in a-Si:H,” J. Non-Cryst. Solids 227–230, 133–137 (1998).
[CrossRef]

Severans, R. J.

W. M. M. Kessels, R. J. Severans, M. C. M. Van de Sanden, D. C. Schram, “Temperature and growth-rate effects on the hydrogen incorporation in a-Si:H,” J. Non-Cryst. Solids 227–230, 133–137 (1998).
[CrossRef]

Shimizu, T.

A. Masuda, K. Itoh, K. Matsuda, Y. Yonezawa, M. Kumeda, T. Shimizu, “Nitrogen-doping effects on electrical, optical and structural properties in hydrogenated amorphous silicon,” J. Appl. Phys. 81, 6729–6737 (1997).
[CrossRef]

Shokhovets, S.

S. Shokhovets, R. Goldhahn, V. Cimalla, T. S. Cheng, C. T. Foxon, “Reflectivity study of hexagonal GaN films grown on GaAs: surface roughness, interface layer, and refractive index,” J. Appl. Phys. 84, 1561–1566 (1998).
[CrossRef]

Sullivan, B. T.

Swanepoel, R.

R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
[CrossRef]

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. 16, 1214–1222 (1983).

Tikhonravov, A. V.

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterization of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films 313–314, 379–383 (1998).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, A. V. Krasilnikova, “Spectroscopic ellipsometry of slightly inhomogeneous nonabsorbing thin films with arbitrary refractive-index profiles: theoretical study,” Appl. Opt. 37, 5902–5911 (1998).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, J. A. Dobrowolski, “Influence of small inhomogeneities on the spectral characteristics of single thin films,” Appl. Opt. 36, 7188–7198 (1997).
[CrossRef]

S. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontiers, Gif-sur-Yvette, France, 1992), pp. 1–26.

Title, R. S.

M. H. Brodsky, R. S. Title, K. Weiser, F. D. Pettit, “Structural, optical, and electrical properties of amorphous silicon films,” Phys. Rev. B 1, 2632–2640 (1970).
[CrossRef]

Trubetskov, M. K.

Van de Sanden, M. C. M.

W. M. M. Kessels, R. J. Severans, M. C. M. Van de Sanden, D. C. Schram, “Temperature and growth-rate effects on the hydrogen incorporation in a-Si:H,” J. Non-Cryst. Solids 227–230, 133–137 (1998).
[CrossRef]

Weiser, K.

M. H. Brodsky, R. S. Title, K. Weiser, F. D. Pettit, “Structural, optical, and electrical properties of amorphous silicon films,” Phys. Rev. B 1, 2632–2640 (1970).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th. ed. (Pergamon, London, 1970), pp. 55–60.

Yamaguchi, M.

M. Yamaguchi, K. Morigaki, “Effect of hydrogen dilution on the optical properties of hydrogenated amorphous silicon prepared by plasma deposition,” Philos. Mag. B 79, 387–405 (1999).
[CrossRef]

Yonezawa, Y.

A. Masuda, K. Itoh, K. Matsuda, Y. Yonezawa, M. Kumeda, T. Shimizu, “Nitrogen-doping effects on electrical, optical and structural properties in hydrogenated amorphous silicon,” J. Appl. Phys. 81, 6729–6737 (1997).
[CrossRef]

Appl. Opt. (4)

Appl. Surf. Sci. (1)

J. R. Elmiger, M. Kunst, “Investigation of the silicon–plasma silicon nitride interface with in situ transient photoconductivity measurements,” Appl. Surf. Sci. 103, 11–18 (1996).
[CrossRef]

J. Appl. Phys. (3)

R. Ruther, J. Livingstone, N. Dytlowski, D. Cohen, “Improved hydrogen depth profiles with in-chamber annealing of hydrogenated amorphous silicon thin films,” J. Appl. Phys. 79, 175–178 (1996).
[CrossRef]

A. Masuda, K. Itoh, K. Matsuda, Y. Yonezawa, M. Kumeda, T. Shimizu, “Nitrogen-doping effects on electrical, optical and structural properties in hydrogenated amorphous silicon,” J. Appl. Phys. 81, 6729–6737 (1997).
[CrossRef]

S. Shokhovets, R. Goldhahn, V. Cimalla, T. S. Cheng, C. T. Foxon, “Reflectivity study of hexagonal GaN films grown on GaAs: surface roughness, interface layer, and refractive index,” J. Appl. Phys. 84, 1561–1566 (1998).
[CrossRef]

J. Non-Cryst. Solids (2)

W. M. M. Kessels, R. J. Severans, M. C. M. Van de Sanden, D. C. Schram, “Temperature and growth-rate effects on the hydrogen incorporation in a-Si:H,” J. Non-Cryst. Solids 227–230, 133–137 (1998).
[CrossRef]

D. Das, S. M. Iftiquar, A. K. Barua, “Wide optical gap a-SiO:H films prepared by rf glow discharge,” J. Non-Cryst. Solids 210, 148–154 (1997).
[CrossRef]

J. Phys. (2)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. 9, 1002–1004 (1976).

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. 16, 1214–1222 (1983).

J. Phys. D (1)

D. A. Minkov, “Method for determining the optical constants of a thin film on a transparent substrate,” J. Phys. D 22, 199–205 (1989).
[CrossRef]

J. Phys. E (1)

R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
[CrossRef]

Philos. Mag. B (1)

M. Yamaguchi, K. Morigaki, “Effect of hydrogen dilution on the optical properties of hydrogenated amorphous silicon prepared by plasma deposition,” Philos. Mag. B 79, 387–405 (1999).
[CrossRef]

Phys. Rev. B (2)

E. C. Freeman, W. Paul, “Optical constants of rf sputtered hydrogenated amorphous Si,” Phys. Rev. B 20, 716–728 (1979).
[CrossRef]

M. H. Brodsky, R. S. Title, K. Weiser, F. D. Pettit, “Structural, optical, and electrical properties of amorphous silicon films,” Phys. Rev. B 1, 2632–2640 (1970).
[CrossRef]

Prog. Opt. (1)

R. Jacobsson, “Light reflection from films of continuously varying refractive index,” Prog. Opt. 2, 247–286 (1966).
[CrossRef]

Thin Solid Films (4)

J. Rivory, “Characterization of inhomogeneous dielectric films by spectroscopic ellipsometry,” Thin Solid Films 313–314, 333–340 (1998).
[CrossRef]

K. V. Popov, A. V. Tikhonravov, J. Campmany, E. Bertran, S. Bosch, A. Canillas, “Spectroscopic ellipsometric characterization of transparent thin film amorphous electronic materials: integrated analysis,” Thin Solid Films 313–314, 379–383 (1998).
[CrossRef]

S. Callard, A. Gagnaire, J. Joseph, “Characterization of graded refractive index silicon oxynitride thin films by spectroscopic ellipsometry,” Thin Solid Films 313–314, 384–388 (1998).
[CrossRef]

M. Harris, H. A. Macleod, S. Ogura, “The relationship between optical inhomogeneity and film structure,” Thin Solid Films 57, 173–178 (1979).
[CrossRef]

Other (3)

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), pp. 46–62.

M. Born, E. Wolf, Principles of Optics, 4th. ed. (Pergamon, London, 1970), pp. 55–60.

S. A. Furman, A. V. Tikhonravov, Basics of Optics of Multilayer Systems (Editions Frontiers, Gif-sur-Yvette, France, 1992), pp. 1–26.

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Figures (5)

Fig. 1
Fig. 1

Reflection and refraction of light by air–substrate–film systems (a) for which phase changes of the beam traversing the substrate are neglected, (b) for which the reflections from the back interface of the substrate are neglected, and (c) for which, although all multiply reflected and transmitted elements of the beam are taken into account, phase changes in the substrate are neglected.

Fig. 2
Fig. 2

Transmittance of a-Si with its envelopes, and transmittance T s of the substrate (Corning glass) alone.

Fig. 3
Fig. 3

(a) Thickness variation Δd computed by solution of Eqs. (4) and (5) numerically at each extremum point. (b) Thin film with a rough surface upon a transparent substrate.

Fig. 4
Fig. 4

(a) Refractive index of the substrate calculated from the transmittance spectrum of the substrate alone as shown in Fig. 2. (b) Graph of l/2 versus θ. (c) Extrema of the transmittance spectrum with corrected extrema values for which the film has no thickness variation (Δd = 0 nm). (d) Thicknesses d 1 and d 2 calculated with Eqs. (9) and (3), respectively. (e) Fringe order numbers calculated from Eq. (3) and from exact integer and half-integer values that are found from the calculated ones. (f) Refractive indices n 1 and n 2 calculated from Eq. (10) and from Eq. (3) with exact fringe numbers and average thickness 2 = 1264.9 nm, respectively. The continuous curve denotes fitted dispersion relation [Eq. (11)].

Fig. 5
Fig. 5

(a) Transmittance B is the spectrum of the film that is obtained by correction of curve A (original measured data) from the thickness modulation. (b) Transmittance C of a film that has refractive-index inhomogeneities at its interfaces, as shown in (c), fitted to curve A. (c) Refractive-index profile of the film that gives transmittance spectrum C.

Equations (18)

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2nd  Δl  2nsds,
T=AxB-Cx cos4πnd/λ+Dx2,
2nd=mλ,  m=0, 0.5, 1, 1.5,
2nd=l2+m1λ,  l2=0, 1, 2, 3,,
TM*=λ2πnΔda1-b21/2×arctan1+b1-b21/2tan2πnΔdλ,
Tm*=λ2πnΔda1-b21/2×arctan1-b1-b21/2tan2πnΔdλ,
TM*=TMTmθarctanTMTm tan θ,
Tm*=TMTmθarctanTmTM tan θ,
l2=d¯πΔdθ-m1.
d=λ1λ22λ1n2-λ2n1.
n=L+L2-ns21/21/2,
n=3.336+434119λ2.
Mj=cos2πnjzj-zj-1/λi/njsin2πnjzj-zj-1/λinj sin2πnjzj-zj-1/λcos2πnjzj-zj-1/λ
M=m11m12m21m22=j=13 Mj,
t=2nanam11+nsm22+nansm12+m21.
m11m12m21m22=j=31 Mj,
r=nsm11-nam22+nansm12-m21nsm11+nam22+nansm12+m21.
T=TiT31-R3Ri=4ns2|t|2ns+12-ns-12|r|2.

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