Abstract

The role played by a glass substrate on the accurate determination of the optical constants and the thickness of a thin dielectric film deposited on it, when well-known envelope methods are used, is discussed. Analytical expressions for the two envelopes of the optical transmission spectra corresponding to films with both uniform and nonuniform thicknesses are derived, assuming the substrate to be a weakly absorbing layer. It is shown that accurate determination of the refractive index and the film thickness is notably improved when the absorption of the substrate is considered. The analytical expressions for the upper and lower envelopes are used to characterize optically and geometrically both uniform and nonuniform amorphous chalcogenide films. The results obtained are compared with those derived by use of expressions for the envelopes that neglect the substrate absorption. The comparison shows that overestimated refractive indexes and underestimated thicknesses are obtained when the conventional approach, in which the substrate absorption is neglected, is used.

© 2002 Optical Society of America

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References

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  1. J. A. Savage, Infrared Optical Materials and Their Antireflection Coatings (Hilger, Bristol, UK, 1985).
  2. H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Institute of Physics, Bristol, UK, 1986).
  3. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1991).
  4. K. Shwartz, The Physics of Optical Recording (Springer-Verlag, Berlin, 1994).
  5. R. G. Hunsperger, Integrated Optics: Theory and Technology, 4th ed. (Springer-Verlag, Berlin, 1995).
  6. 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. E. 9, 1002–1004 (1976).
    [CrossRef]
  7. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E. 16, 1214–1222 (1983).
    [CrossRef]
  8. R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
    [CrossRef]
  9. R. Swanepoel, “Transmission and reflection of an absorbing thin film on an absorbing substrate,” S. Afr. J. Phys. 12, 148–156 (1989).
  10. D. A. Minkov, “Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum,” J. Phys. D 22, 1157–1161 (1989).
    [CrossRef]
  11. E. Márquez, J. B. Ramírez-Malo, P. Villares, R. Jiménez-Garay, R. Swanepoel, “Optical characterization of wedge-shaped thin films of amorphous arsenic trisulphide based only on their shrunk transmission spectra,” Thin Solid Films 254, 83–91 (1995).
    [CrossRef]
  12. S. C. Chiao, B. G. Bovard, H. A. Macleod, “Optical-constant calculation over an extended spectral region: application to titanium dioxide film,” App. Opt. 34, 7355–7360 (1995).
    [CrossRef]
  13. J. J. Ruiz-Pérez, E. Márquez, Nuevos Métodos de Caracterización óptica de Semiconductores Basados en Medidas Espectroscópicas de Reflexión (Ministerio de Defensa, Secretaría General Técnica, Madrid, 1997), pp. 6–1.
  14. V. V. Filippov, “Method of the ratio of envelopes of the reflection spectrum for measuring optical constants and thickness of thin films,” Opt. Spectrosc. 88, 581–585 (2000).
    [CrossRef]
  15. J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D 34, 1–8 (2001).
    [CrossRef]
  16. Rusli, G. A. J. Amaratunga, “Determination of the optical constants and thickness of thin films on slightly absorbing substrate,” Appl. Opt. 34, 7914–7924 (1995).
  17. D. A. Minkov, “Flow-graph approach for optical analysis of planar structures,” Appl. Opt. 33, 7698–7703 (1994).
    [CrossRef] [PubMed]
  18. E. Márquez, J. M. González-Leal, R. Prieto-Alcón, R. Jiménez-Garay, M. Vlcek, “On the photo- and thermally-induced darkening phenomenon in As40S40Se20 amorphous chalcogenide thin films,” J. Phys. D 32, 3128–3134 (1999).
    [CrossRef]
  19. E. Márquez, J. M. González-Leal, R. Jiménez-Garay, M. Vlcek, “Thermally- and photo-induced changes in the structure and optical properties of amorphous As40S30Se30 films,” Thin Solid Films 396, 183–190 (2001).
    [CrossRef]
  20. E. Márquez, P. Nagels, J. M. González-Leal, A. M. Bernal-Oliva, E. Sleeckx, R. Callaerts, “On the optical constants of amorphous GexSe(1–x) thin films of non-uniform thickness prepared by plasma-enhanced chemical vapour deposition,” Vacuum 52, 55–60 (1998).
    [CrossRef]
  21. M. McClain, A. Feldman, D. Kahaner, X. Ying, “An algorithm and computer program for the calculation of envelope curves,” Comput. Phys. 5, 45–48 (1991).
    [CrossRef]
  22. D. A. Minkov, R. Swanepoel, “Computerization of the optical characterization of a thin dielectric film,” Opt. Eng. 32, 3333–3337 (1993).
    [CrossRef]
  23. S. R. Elliott, “Chalcogenide glasses,” in Materials Science and Technology, J. Zarzycki, ed. (VCH, Weinheim, 1991), Vol. 9, pp. 375–454.
  24. S. H. Wemple, M. DiDomenico, “Behavior of the electronic dielectric constants in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
    [CrossRef]

2001 (2)

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D 34, 1–8 (2001).
[CrossRef]

E. Márquez, J. M. González-Leal, R. Jiménez-Garay, M. Vlcek, “Thermally- and photo-induced changes in the structure and optical properties of amorphous As40S30Se30 films,” Thin Solid Films 396, 183–190 (2001).
[CrossRef]

2000 (1)

V. V. Filippov, “Method of the ratio of envelopes of the reflection spectrum for measuring optical constants and thickness of thin films,” Opt. Spectrosc. 88, 581–585 (2000).
[CrossRef]

1999 (1)

E. Márquez, J. M. González-Leal, R. Prieto-Alcón, R. Jiménez-Garay, M. Vlcek, “On the photo- and thermally-induced darkening phenomenon in As40S40Se20 amorphous chalcogenide thin films,” J. Phys. D 32, 3128–3134 (1999).
[CrossRef]

1998 (1)

E. Márquez, P. Nagels, J. M. González-Leal, A. M. Bernal-Oliva, E. Sleeckx, R. Callaerts, “On the optical constants of amorphous GexSe(1–x) thin films of non-uniform thickness prepared by plasma-enhanced chemical vapour deposition,” Vacuum 52, 55–60 (1998).
[CrossRef]

1995 (3)

Rusli, G. A. J. Amaratunga, “Determination of the optical constants and thickness of thin films on slightly absorbing substrate,” Appl. Opt. 34, 7914–7924 (1995).

E. Márquez, J. B. Ramírez-Malo, P. Villares, R. Jiménez-Garay, R. Swanepoel, “Optical characterization of wedge-shaped thin films of amorphous arsenic trisulphide based only on their shrunk transmission spectra,” Thin Solid Films 254, 83–91 (1995).
[CrossRef]

S. C. Chiao, B. G. Bovard, H. A. Macleod, “Optical-constant calculation over an extended spectral region: application to titanium dioxide film,” App. Opt. 34, 7355–7360 (1995).
[CrossRef]

1994 (1)

1993 (1)

D. A. Minkov, R. Swanepoel, “Computerization of the optical characterization of a thin dielectric film,” Opt. Eng. 32, 3333–3337 (1993).
[CrossRef]

1991 (1)

M. McClain, A. Feldman, D. Kahaner, X. Ying, “An algorithm and computer program for the calculation of envelope curves,” Comput. Phys. 5, 45–48 (1991).
[CrossRef]

1989 (2)

R. Swanepoel, “Transmission and reflection of an absorbing thin film on an absorbing substrate,” S. Afr. J. Phys. 12, 148–156 (1989).

D. A. Minkov, “Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum,” J. Phys. D 22, 1157–1161 (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. E. 16, 1214–1222 (1983).
[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. E. 9, 1002–1004 (1976).
[CrossRef]

1971 (1)

S. H. Wemple, M. DiDomenico, “Behavior of the electronic dielectric constants in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
[CrossRef]

Amaratunga, G. A. J.

Bernal-Oliva, A. M.

E. Márquez, P. Nagels, J. M. González-Leal, A. M. Bernal-Oliva, E. Sleeckx, R. Callaerts, “On the optical constants of amorphous GexSe(1–x) thin films of non-uniform thickness prepared by plasma-enhanced chemical vapour deposition,” Vacuum 52, 55–60 (1998).
[CrossRef]

Bovard, B. G.

S. C. Chiao, B. G. Bovard, H. A. Macleod, “Optical-constant calculation over an extended spectral region: application to titanium dioxide film,” App. Opt. 34, 7355–7360 (1995).
[CrossRef]

Callaerts, R.

E. Márquez, P. Nagels, J. M. González-Leal, A. M. Bernal-Oliva, E. Sleeckx, R. Callaerts, “On the optical constants of amorphous GexSe(1–x) thin films of non-uniform thickness prepared by plasma-enhanced chemical vapour deposition,” Vacuum 52, 55–60 (1998).
[CrossRef]

Chiao, S. C.

S. C. Chiao, B. G. Bovard, H. A. Macleod, “Optical-constant calculation over an extended spectral region: application to titanium dioxide film,” App. Opt. 34, 7355–7360 (1995).
[CrossRef]

DiDomenico, M.

S. H. Wemple, M. DiDomenico, “Behavior of the electronic dielectric constants in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
[CrossRef]

Elliott, S. R.

S. R. Elliott, “Chalcogenide glasses,” in Materials Science and Technology, J. Zarzycki, ed. (VCH, Weinheim, 1991), Vol. 9, pp. 375–454.

Feldman, A.

M. McClain, A. Feldman, D. Kahaner, X. Ying, “An algorithm and computer program for the calculation of envelope curves,” Comput. Phys. 5, 45–48 (1991).
[CrossRef]

Filippov, V. V.

V. V. Filippov, “Method of the ratio of envelopes of the reflection spectrum for measuring optical constants and thickness of thin films,” Opt. Spectrosc. 88, 581–585 (2000).
[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. E. 9, 1002–1004 (1976).
[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. E. 9, 1002–1004 (1976).
[CrossRef]

González-Leal, J. M.

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D 34, 1–8 (2001).
[CrossRef]

E. Márquez, J. M. González-Leal, R. Jiménez-Garay, M. Vlcek, “Thermally- and photo-induced changes in the structure and optical properties of amorphous As40S30Se30 films,” Thin Solid Films 396, 183–190 (2001).
[CrossRef]

E. Márquez, J. M. González-Leal, R. Prieto-Alcón, R. Jiménez-Garay, M. Vlcek, “On the photo- and thermally-induced darkening phenomenon in As40S40Se20 amorphous chalcogenide thin films,” J. Phys. D 32, 3128–3134 (1999).
[CrossRef]

E. Márquez, P. Nagels, J. M. González-Leal, A. M. Bernal-Oliva, E. Sleeckx, R. Callaerts, “On the optical constants of amorphous GexSe(1–x) thin films of non-uniform thickness prepared by plasma-enhanced chemical vapour deposition,” Vacuum 52, 55–60 (1998).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1991).

Hunsperger, R. G.

R. G. Hunsperger, Integrated Optics: Theory and Technology, 4th ed. (Springer-Verlag, Berlin, 1995).

Jiménez-Garay, R.

E. Márquez, J. M. González-Leal, R. Jiménez-Garay, M. Vlcek, “Thermally- and photo-induced changes in the structure and optical properties of amorphous As40S30Se30 films,” Thin Solid Films 396, 183–190 (2001).
[CrossRef]

E. Márquez, J. M. González-Leal, R. Prieto-Alcón, R. Jiménez-Garay, M. Vlcek, “On the photo- and thermally-induced darkening phenomenon in As40S40Se20 amorphous chalcogenide thin films,” J. Phys. D 32, 3128–3134 (1999).
[CrossRef]

E. Márquez, J. B. Ramírez-Malo, P. Villares, R. Jiménez-Garay, R. Swanepoel, “Optical characterization of wedge-shaped thin films of amorphous arsenic trisulphide based only on their shrunk transmission spectra,” Thin Solid Films 254, 83–91 (1995).
[CrossRef]

Kahaner, D.

M. McClain, A. Feldman, D. Kahaner, X. Ying, “An algorithm and computer program for the calculation of envelope curves,” Comput. Phys. 5, 45–48 (1991).
[CrossRef]

Macleod, H. A.

S. C. Chiao, B. G. Bovard, H. A. Macleod, “Optical-constant calculation over an extended spectral region: application to titanium dioxide film,” App. Opt. 34, 7355–7360 (1995).
[CrossRef]

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Institute of Physics, Bristol, UK, 1986).

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. E. 9, 1002–1004 (1976).
[CrossRef]

Márquez, E.

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D 34, 1–8 (2001).
[CrossRef]

E. Márquez, J. M. González-Leal, R. Jiménez-Garay, M. Vlcek, “Thermally- and photo-induced changes in the structure and optical properties of amorphous As40S30Se30 films,” Thin Solid Films 396, 183–190 (2001).
[CrossRef]

E. Márquez, J. M. González-Leal, R. Prieto-Alcón, R. Jiménez-Garay, M. Vlcek, “On the photo- and thermally-induced darkening phenomenon in As40S40Se20 amorphous chalcogenide thin films,” J. Phys. D 32, 3128–3134 (1999).
[CrossRef]

E. Márquez, P. Nagels, J. M. González-Leal, A. M. Bernal-Oliva, E. Sleeckx, R. Callaerts, “On the optical constants of amorphous GexSe(1–x) thin films of non-uniform thickness prepared by plasma-enhanced chemical vapour deposition,” Vacuum 52, 55–60 (1998).
[CrossRef]

E. Márquez, J. B. Ramírez-Malo, P. Villares, R. Jiménez-Garay, R. Swanepoel, “Optical characterization of wedge-shaped thin films of amorphous arsenic trisulphide based only on their shrunk transmission spectra,” Thin Solid Films 254, 83–91 (1995).
[CrossRef]

J. J. Ruiz-Pérez, E. Márquez, Nuevos Métodos de Caracterización óptica de Semiconductores Basados en Medidas Espectroscópicas de Reflexión (Ministerio de Defensa, Secretaría General Técnica, Madrid, 1997), pp. 6–1.

McClain, M.

M. McClain, A. Feldman, D. Kahaner, X. Ying, “An algorithm and computer program for the calculation of envelope curves,” Comput. Phys. 5, 45–48 (1991).
[CrossRef]

Minkov, D. A.

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D 34, 1–8 (2001).
[CrossRef]

D. A. Minkov, “Flow-graph approach for optical analysis of planar structures,” Appl. Opt. 33, 7698–7703 (1994).
[CrossRef] [PubMed]

D. A. Minkov, R. Swanepoel, “Computerization of the optical characterization of a thin dielectric film,” Opt. Eng. 32, 3333–3337 (1993).
[CrossRef]

D. A. Minkov, “Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum,” J. Phys. D 22, 1157–1161 (1989).
[CrossRef]

Nagels, P.

E. Márquez, P. Nagels, J. M. González-Leal, A. M. Bernal-Oliva, E. Sleeckx, R. Callaerts, “On the optical constants of amorphous GexSe(1–x) thin films of non-uniform thickness prepared by plasma-enhanced chemical vapour deposition,” Vacuum 52, 55–60 (1998).
[CrossRef]

Prieto-Alcón, R.

E. Márquez, J. M. González-Leal, R. Prieto-Alcón, R. Jiménez-Garay, M. Vlcek, “On the photo- and thermally-induced darkening phenomenon in As40S40Se20 amorphous chalcogenide thin films,” J. Phys. D 32, 3128–3134 (1999).
[CrossRef]

Ramírez-Malo, J. B.

E. Márquez, J. B. Ramírez-Malo, P. Villares, R. Jiménez-Garay, R. Swanepoel, “Optical characterization of wedge-shaped thin films of amorphous arsenic trisulphide based only on their shrunk transmission spectra,” Thin Solid Films 254, 83–91 (1995).
[CrossRef]

Ruiz-Pérez, J. J.

J. J. Ruiz-Pérez, E. Márquez, Nuevos Métodos de Caracterización óptica de Semiconductores Basados en Medidas Espectroscópicas de Reflexión (Ministerio de Defensa, Secretaría General Técnica, Madrid, 1997), pp. 6–1.

Ruíz-Pérez, J. J.

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D 34, 1–8 (2001).
[CrossRef]

Rusli,

Savage, J. A.

J. A. Savage, Infrared Optical Materials and Their Antireflection Coatings (Hilger, Bristol, UK, 1985).

Shwartz, K.

K. Shwartz, The Physics of Optical Recording (Springer-Verlag, Berlin, 1994).

Sleeckx, E.

E. Márquez, P. Nagels, J. M. González-Leal, A. M. Bernal-Oliva, E. Sleeckx, R. Callaerts, “On the optical constants of amorphous GexSe(1–x) thin films of non-uniform thickness prepared by plasma-enhanced chemical vapour deposition,” Vacuum 52, 55–60 (1998).
[CrossRef]

Swanepoel, R.

E. Márquez, J. B. Ramírez-Malo, P. Villares, R. Jiménez-Garay, R. Swanepoel, “Optical characterization of wedge-shaped thin films of amorphous arsenic trisulphide based only on their shrunk transmission spectra,” Thin Solid Films 254, 83–91 (1995).
[CrossRef]

D. A. Minkov, R. Swanepoel, “Computerization of the optical characterization of a thin dielectric film,” Opt. Eng. 32, 3333–3337 (1993).
[CrossRef]

R. Swanepoel, “Transmission and reflection of an absorbing thin film on an absorbing substrate,” S. Afr. J. Phys. 12, 148–156 (1989).

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. E. 16, 1214–1222 (1983).
[CrossRef]

Villares, P.

E. Márquez, J. B. Ramírez-Malo, P. Villares, R. Jiménez-Garay, R. Swanepoel, “Optical characterization of wedge-shaped thin films of amorphous arsenic trisulphide based only on their shrunk transmission spectra,” Thin Solid Films 254, 83–91 (1995).
[CrossRef]

Vlcek, M.

E. Márquez, J. M. González-Leal, R. Jiménez-Garay, M. Vlcek, “Thermally- and photo-induced changes in the structure and optical properties of amorphous As40S30Se30 films,” Thin Solid Films 396, 183–190 (2001).
[CrossRef]

E. Márquez, J. M. González-Leal, R. Prieto-Alcón, R. Jiménez-Garay, M. Vlcek, “On the photo- and thermally-induced darkening phenomenon in As40S40Se20 amorphous chalcogenide thin films,” J. Phys. D 32, 3128–3134 (1999).
[CrossRef]

Wemple, S. H.

S. H. Wemple, M. DiDomenico, “Behavior of the electronic dielectric constants in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
[CrossRef]

Ying, X.

M. McClain, A. Feldman, D. Kahaner, X. Ying, “An algorithm and computer program for the calculation of envelope curves,” Comput. Phys. 5, 45–48 (1991).
[CrossRef]

App. Opt. (1)

S. C. Chiao, B. G. Bovard, H. A. Macleod, “Optical-constant calculation over an extended spectral region: application to titanium dioxide film,” App. Opt. 34, 7355–7360 (1995).
[CrossRef]

Appl. Opt. (2)

Comput. Phys. (1)

M. McClain, A. Feldman, D. Kahaner, X. Ying, “An algorithm and computer program for the calculation of envelope curves,” Comput. Phys. 5, 45–48 (1991).
[CrossRef]

J. Phys. D (3)

J. J. Ruíz-Pérez, J. M. González-Leal, D. A. Minkov, E. Márquez, “Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra,” J. Phys. D 34, 1–8 (2001).
[CrossRef]

E. Márquez, J. M. González-Leal, R. Prieto-Alcón, R. Jiménez-Garay, M. Vlcek, “On the photo- and thermally-induced darkening phenomenon in As40S40Se20 amorphous chalcogenide thin films,” J. Phys. D 32, 3128–3134 (1999).
[CrossRef]

D. A. Minkov, “Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum,” J. Phys. D 22, 1157–1161 (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]

J. Phys. E. (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. E. 9, 1002–1004 (1976).
[CrossRef]

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

Opt. Eng. (1)

D. A. Minkov, R. Swanepoel, “Computerization of the optical characterization of a thin dielectric film,” Opt. Eng. 32, 3333–3337 (1993).
[CrossRef]

Opt. Spectrosc. (1)

V. V. Filippov, “Method of the ratio of envelopes of the reflection spectrum for measuring optical constants and thickness of thin films,” Opt. Spectrosc. 88, 581–585 (2000).
[CrossRef]

Phys. Rev. B (1)

S. H. Wemple, M. DiDomenico, “Behavior of the electronic dielectric constants in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
[CrossRef]

S. Afr. J. Phys. (1)

R. Swanepoel, “Transmission and reflection of an absorbing thin film on an absorbing substrate,” S. Afr. J. Phys. 12, 148–156 (1989).

Thin Solid Films (2)

E. Márquez, J. B. Ramírez-Malo, P. Villares, R. Jiménez-Garay, R. Swanepoel, “Optical characterization of wedge-shaped thin films of amorphous arsenic trisulphide based only on their shrunk transmission spectra,” Thin Solid Films 254, 83–91 (1995).
[CrossRef]

E. Márquez, J. M. González-Leal, R. Jiménez-Garay, M. Vlcek, “Thermally- and photo-induced changes in the structure and optical properties of amorphous As40S30Se30 films,” Thin Solid Films 396, 183–190 (2001).
[CrossRef]

Vacuum (1)

E. Márquez, P. Nagels, J. M. González-Leal, A. M. Bernal-Oliva, E. Sleeckx, R. Callaerts, “On the optical constants of amorphous GexSe(1–x) thin films of non-uniform thickness prepared by plasma-enhanced chemical vapour deposition,” Vacuum 52, 55–60 (1998).
[CrossRef]

Other (7)

J. J. Ruiz-Pérez, E. Márquez, Nuevos Métodos de Caracterización óptica de Semiconductores Basados en Medidas Espectroscópicas de Reflexión (Ministerio de Defensa, Secretaría General Técnica, Madrid, 1997), pp. 6–1.

J. A. Savage, Infrared Optical Materials and Their Antireflection Coatings (Hilger, Bristol, UK, 1985).

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Institute of Physics, Bristol, UK, 1986).

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1991).

K. Shwartz, The Physics of Optical Recording (Springer-Verlag, Berlin, 1994).

R. G. Hunsperger, Integrated Optics: Theory and Technology, 4th ed. (Springer-Verlag, Berlin, 1995).

S. R. Elliott, “Chalcogenide glasses,” in Materials Science and Technology, J. Zarzycki, ed. (VCH, Weinheim, 1991), Vol. 9, pp. 375–454.

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Figures (5)

Fig. 1
Fig. 1

Optical transmission spectra taken at normal incidence for some of the most popular borosilicate glass substrates used for thin-film optical studies. The transmission spectrum corresponding to a CaF2 substrate is shown for comparison.

Fig. 2
Fig. 2

Optical transmission and reflection spectra taken at normal incidence, T s (λ) and R s (λ), respectively, for a representative BDH glass substrate. The T s (λ) + R s (λ) curve clearly shows significant losses in the spectral range of interest, i.e., T s (λ) + R s (λ) < 1.

Fig. 3
Fig. 3

Sketches of the two studied optical systems: (a) a uniform thin film with constant thickness, t, on a thick substrate and (b) a nonuniform wedge-shaped thin film that is geometrically characterized by its average thickness, , and thickness variation, Δt, over the illuminated area (white rectangle) on a thick substrate.

Fig. 4
Fig. 4

(a) Experimental optical transmission spectrum, T(λ), taken at normal incidence, corresponding to a representative thermally-evaporated amorphous As40S60 uniform film. T +(λ) and T -(λ) are, respectively, the upper and lower envelopes, and T s (λ) is the transmission of the uncoated substrate. The order numbers, m’s, for some tangent points are marked for convenience. (b) Experimental optical transmission spectrum, T(λ), taken at normal incidence, corresponding to a representative amorphous As40S60 nonuniform film, prepared by plasma-enhanced chemical vapor deposition. T Δ+(λ) and T Δ-(λ) are, respectively, the upper and lower envelopes, and T s (λ) is the transmission of the uncoated substrate. The order numbers, m’s, for some tangent points are marked for convenience. Values for the thickness variation, Δt, derived by solution of the system of transcendental Eqs. (14), assuming x = 1, are plotted in the inset as a function of photon energy for the case of a quasi-constant spacing between the points. The system of Eqs. (14) is very sensitive to errors in the envelope drawing, and overestimated Δt values are usually obtained for smaller energies. The values of Δt drastically decrease for higher energies because the assumption x = 1 is not valid in this spectral region.

Fig. 5
Fig. 5

Final values of n (circles) and k (solid curve) as a function of the wavelength, derived from (a) the optical transmission spectrum shown in Fig. 4(a) (uniform film) and (b) the optical transmission spectrum shown in Fig. 4(b) (nonuniform film). The values of n (squares) and k (dotted curve) obtained by use of the traditional approach are also plotted for comparison. The difference between both sets of k values is insignificant. Dashed curves have been drawn by use of the refractive-index dispersion relationship given in Eq. (15). The values of the fitting parameters E o and E d , are shown in the figure.

Tables (2)

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Table 1 Calculation of the Thickness and the Refractive Index of a Representative Uniform Filma

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Table 2 Calculation of the Thickness and the Refractive Index of a Representative Nonuniform Filma

Equations (18)

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Tsm=1-R12xs1+R12xs2-2R1xs cosϕ,
Ts=12π02π Tsmdϕ=1-R12xs1-R12xs2.
Rs=R11+1-2R1xs21-R12xs2.
Tsλ-Tsλ; s, xs=0, Rsλ-Rsλ; s, xs=0,
Ts=2s1+s2,
Rs=1-s21+s2.
Tλ; n, x, t, s, xs=A/B,
A=1-R11-R21-R3xxs,B=1+R1R2x2-R1R3x2xs2-R2R3xs2+2r1r21-R3xs2x cosφ,R1=r12, R2=r22, R3=r32,r1=1-n1+n, r2=n-sn+s, r3=s-1s+1,α=4πk/λ, x=exp-αt,αs=4πks/λ, xs=exp-αsts,φ=4πnt/λ.
T±λ; n, x, s, xs=A/B±,
B±=1+R1R2x2-R1R3x2xs2-R2R3xs2±2r1r21-R3xs2x.
TΔt1φ2-φ1φ1φ2 Tdφ,
TΔλ; n, x, t¯, Δt, s, xs=12θAC2-D21/2×tan-1C+DC2-D21/2tanφ22-tan-1C+DC2-D21/2tanφ12,
C=1+R1R2x2-R1R3x2xs2+R1R2R3xs2, D=-2r1r21-R3xs2x, θ=2πnΔt/λ.
2nt¯=mλtan,
TΔ±λ; n, x, Δt, s, xs=1θAC2-D21/2×tan-1C±DC2-D21/2tan θ.
T+λ-T+λ; n, x=0, T-λ-T-λ; n, x=0
TΔ+λ-TΔ+λ; n, x, Δt=0, TΔ-λ-TΔ-λ; n, x, Δt=0
n2ω=1+EoEdEo2-ω2,

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