Abstract

A generalized matrix method is presented for calculating the optical reflectance and transmittance of an arbitrary thin-solid-film multilayer structure on very thick substrates with rough surfaces and interfaces. We show that the effect of roughness and the influence of incoherently reflected light on the back side of a thick layer can be accounted for with a more general transfer matrix that enables the inclusion of modified complex Fresnel coefficients. Coherent, partially coherent, and incoherent multiply reflected light inside the multilayer structure is treated in the same way. We demonstrate the method by applying it to simulated and experimental reflectance spectra of thin epitaxial Si overlayers on very thick SiO2 substrates and on a separation by ion implantation of oxygen structure with a SiO2 buried layer exhibiting substantial roughness on both of its interfaces (Si/SiO2 and SiO2/Si).

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. M. Bennett, M. J. Booty, “Computational method for determining n and k for a thin film from the measured reflectance, transmittance, and film thickness,” Appl. Opt. 5, 41–43 (1966).
    [CrossRef] [PubMed]
  2. P. O. Nilsson, “Determination of optical constants from intensity measurements at normal incidence,” Appl. Opt. 7, 436–442 (1968).
    [CrossRef]
  3. G. Lubberts, B. C. Burkey, F. Moser, E. A. Trabka, “Optical properties of phosphorus-doped polycrystalline silicon layers,” J. Appl. Phys. 52, 6870–6878 (1981).
    [CrossRef]
  4. E. Elizalde, F. Rueda, “On the determination of the optical constants n(λ) and α(λ) of thin supported films,” Thin Solid Films 122, 45–57 (1984).
    [CrossRef]
  5. C. L. Mitsas, E. K. Polychroniadis, D. I. Siapkas, “The influence of the growth parameters on the structural and electronic properties of TlBiSe2 thin films,” Mater. Sci. Eng. B 14, 347–352 (1992).
    [CrossRef]
  6. C. L. Mitsas, D. I. Siapkas, “Phonon and electronic properties of TlBiSe2 thin films,” Solid State Commun. 83, 857–861 (1992).
    [CrossRef]
  7. L. Ward, The Optical Constants of Bulk Materials and Films (Hilger, Bristol, UK, 1988), pp. 165–170.
  8. J. E. Nestell, R. W. Christy, “Derivation of optical constants of metals from thin film measurements at oblique incidence,” Appl. Opt. 11, 643–651 (1972).
    [CrossRef] [PubMed]
  9. J. A. Dobrowolski, F. C. Ho, A. Waldorf, “Determination of optical constants of thin film coating materials based on inverse synthesis,” Appl. Opt. 22, 3191–3200 (1983).
    [CrossRef] [PubMed]
  10. H. W. Verleur, “Determination of optical constants from reflectance or transmittance measurements on bulk crystals or thin films,” J. Opt. Soc. Am. 58, 1356–1364 (1968).
    [CrossRef]
  11. J. C. Manifacier, J. Gasiot, J. P. Filliard, “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]
  12. D. B. Kushev, N. N. Zheleva, Y. Demakopoulou, D. Siapkas, “A new method for the determination of the thickness, the optical constants, and the relaxation time of weakly absorbing semiconducting thin films,” Infrared Phys. 26, 385–393 (1986).
    [CrossRef]
  13. A. Vasicek, Optics of Thin Films (North-HollandAmsterdam, 1960), pp. 254–261.
  14. M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), pp. 54–69.
  15. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), pp. 69–80.
  16. Z. Knittl, Optics of Thin Films (Wiley, London, 1976), pp. 41–46.
  17. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), pp. 102–114.
  18. E. D. Palik, ed., Handbook of Optical Constants of Solids I (Academic, New York, 1985), pp. 18–21.
  19. C. L. Mitsas, “The growth and characterization of III–V–VI2 ternary compound thin films,” Ph.D. dissertation (University of Thessaloníki, Thessaloníki, Greece, 1995).
  20. S. Schirar, L. Bayo, A. Melouah, J. Bougnot, C. Linares, A. Montaner, M. Galtier, “Nondestructive determination of free carrier density of epitaxial layers of GaSb by IR reflectivity measurement,” Thin Solid Films 155, 125–132 (1987).
    [CrossRef]
  21. J. Kavaliauskas, G. Krivaite, D. Senuliene, A. Sileika, “Characterization of the interface in CdxHg1–xTe/CdTe epilayers by IR reflectivity and electroreflectance,” Phys. Status Solidi A 126, K201–204 (1991).
    [CrossRef]
  22. P. M. Amirtharaj, S. Perkowitz, “Far infrared spatial probe of heteroepitaxial indium arsenide,” Thin Solid Films 62, 357–360 (1979).
    [CrossRef]
  23. Y. B. Li, R. A. Stradling, T. Knight, J. R. Birch, R. H. Thomas, C. C. Phillips, I. T. Ferguson, “Infrared reflection and transmission of undoped and Si-doped InAs grown on GaAs by molecular beam epitaxy,” Semicond. Sci. Technol. 9, 101–111 (1993).
    [CrossRef]
  24. S. Kotini, D. I. Siapkas, C. A. Dimitriadis, “Electronic and phonon properties of semiconductive FeSi2 films,” in Proceedings of the 20th International Conference on the Physics of Semiconductors, E. M. Anastassakis, J. D. Joannopoulos, eds. (World Scientific Publishing, Thessaloníki, Greece, 1990), Vol. 1, pp. 316–319.
  25. N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Oxide growth, refractive index and composition profiles of structures formed by 2-MeV oxygen implantation into Si,” J. Appl. Phys., in press.
  26. J. M. Pawlikowski, “Comments on the determination of the absorption coefficient of thin semiconductor films,” Thin Solid Films 127, 29–38 (1985).
    [CrossRef]
  27. I. Filinski, “The effects of sample imperfections on optical spectra,” Phys. Status Solidi B 49, 577–588 (1972).
    [CrossRef]
  28. J. Szczyrbowski, A. Czapla, “Optical absorption in d.c. sputtered InAs films,” Thin Solid Films 47, 127–137 (1977).
    [CrossRef]
  29. A. M. Goodman, “Optical interference method for the approximate determination of refractive index and thickness of a transparent layer,” Appl. Opt. 17, 2779–2787 (1978).
    [CrossRef] [PubMed]
  30. D. Siapkas, D. B. Kushev, N. N. Zheleva, J. Siapkas, I. Lelidis, “Optical constants of tin-telluride determined from infrared interference spectra,” Infrared Phys. 31, 425–433 (1991).
    [CrossRef]
  31. P. H. Berning, in Physics of Thin Films, Vol. 1, G. Hass, ed. (Academic, New York, 1963), pp. 69–71.

1993 (1)

Y. B. Li, R. A. Stradling, T. Knight, J. R. Birch, R. H. Thomas, C. C. Phillips, I. T. Ferguson, “Infrared reflection and transmission of undoped and Si-doped InAs grown on GaAs by molecular beam epitaxy,” Semicond. Sci. Technol. 9, 101–111 (1993).
[CrossRef]

1992 (2)

C. L. Mitsas, E. K. Polychroniadis, D. I. Siapkas, “The influence of the growth parameters on the structural and electronic properties of TlBiSe2 thin films,” Mater. Sci. Eng. B 14, 347–352 (1992).
[CrossRef]

C. L. Mitsas, D. I. Siapkas, “Phonon and electronic properties of TlBiSe2 thin films,” Solid State Commun. 83, 857–861 (1992).
[CrossRef]

1991 (2)

J. Kavaliauskas, G. Krivaite, D. Senuliene, A. Sileika, “Characterization of the interface in CdxHg1–xTe/CdTe epilayers by IR reflectivity and electroreflectance,” Phys. Status Solidi A 126, K201–204 (1991).
[CrossRef]

D. Siapkas, D. B. Kushev, N. N. Zheleva, J. Siapkas, I. Lelidis, “Optical constants of tin-telluride determined from infrared interference spectra,” Infrared Phys. 31, 425–433 (1991).
[CrossRef]

1987 (1)

S. Schirar, L. Bayo, A. Melouah, J. Bougnot, C. Linares, A. Montaner, M. Galtier, “Nondestructive determination of free carrier density of epitaxial layers of GaSb by IR reflectivity measurement,” Thin Solid Films 155, 125–132 (1987).
[CrossRef]

1986 (1)

D. B. Kushev, N. N. Zheleva, Y. Demakopoulou, D. Siapkas, “A new method for the determination of the thickness, the optical constants, and the relaxation time of weakly absorbing semiconducting thin films,” Infrared Phys. 26, 385–393 (1986).
[CrossRef]

1985 (1)

J. M. Pawlikowski, “Comments on the determination of the absorption coefficient of thin semiconductor films,” Thin Solid Films 127, 29–38 (1985).
[CrossRef]

1984 (1)

E. Elizalde, F. Rueda, “On the determination of the optical constants n(λ) and α(λ) of thin supported films,” Thin Solid Films 122, 45–57 (1984).
[CrossRef]

1983 (1)

1981 (1)

G. Lubberts, B. C. Burkey, F. Moser, E. A. Trabka, “Optical properties of phosphorus-doped polycrystalline silicon layers,” J. Appl. Phys. 52, 6870–6878 (1981).
[CrossRef]

1979 (1)

P. M. Amirtharaj, S. Perkowitz, “Far infrared spatial probe of heteroepitaxial indium arsenide,” Thin Solid Films 62, 357–360 (1979).
[CrossRef]

1978 (1)

1977 (1)

J. Szczyrbowski, A. Czapla, “Optical absorption in d.c. sputtered InAs films,” Thin Solid Films 47, 127–137 (1977).
[CrossRef]

1976 (1)

J. C. Manifacier, J. Gasiot, J. P. Filliard, “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]

1972 (2)

1968 (2)

H. W. Verleur, “Determination of optical constants from reflectance or transmittance measurements on bulk crystals or thin films,” J. Opt. Soc. Am. 58, 1356–1364 (1968).
[CrossRef]

P. O. Nilsson, “Determination of optical constants from intensity measurements at normal incidence,” Appl. Opt. 7, 436–442 (1968).
[CrossRef]

1966 (1)

Amirtharaj, P. M.

P. M. Amirtharaj, S. Perkowitz, “Far infrared spatial probe of heteroepitaxial indium arsenide,” Thin Solid Films 62, 357–360 (1979).
[CrossRef]

Bayo, L.

S. Schirar, L. Bayo, A. Melouah, J. Bougnot, C. Linares, A. Montaner, M. Galtier, “Nondestructive determination of free carrier density of epitaxial layers of GaSb by IR reflectivity measurement,” Thin Solid Films 155, 125–132 (1987).
[CrossRef]

Bennett, J. M.

Berning, P. H.

P. H. Berning, in Physics of Thin Films, Vol. 1, G. Hass, ed. (Academic, New York, 1963), pp. 69–71.

Birch, J. R.

Y. B. Li, R. A. Stradling, T. Knight, J. R. Birch, R. H. Thomas, C. C. Phillips, I. T. Ferguson, “Infrared reflection and transmission of undoped and Si-doped InAs grown on GaAs by molecular beam epitaxy,” Semicond. Sci. Technol. 9, 101–111 (1993).
[CrossRef]

Booty, M. J.

Born, M.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), pp. 54–69.

Bougnot, J.

S. Schirar, L. Bayo, A. Melouah, J. Bougnot, C. Linares, A. Montaner, M. Galtier, “Nondestructive determination of free carrier density of epitaxial layers of GaSb by IR reflectivity measurement,” Thin Solid Films 155, 125–132 (1987).
[CrossRef]

Burkey, B. C.

G. Lubberts, B. C. Burkey, F. Moser, E. A. Trabka, “Optical properties of phosphorus-doped polycrystalline silicon layers,” J. Appl. Phys. 52, 6870–6878 (1981).
[CrossRef]

Christy, R. W.

Czapla, A.

J. Szczyrbowski, A. Czapla, “Optical absorption in d.c. sputtered InAs films,” Thin Solid Films 47, 127–137 (1977).
[CrossRef]

Demakopoulou, Y.

D. B. Kushev, N. N. Zheleva, Y. Demakopoulou, D. Siapkas, “A new method for the determination of the thickness, the optical constants, and the relaxation time of weakly absorbing semiconducting thin films,” Infrared Phys. 26, 385–393 (1986).
[CrossRef]

Dimitriadis, C. A.

S. Kotini, D. I. Siapkas, C. A. Dimitriadis, “Electronic and phonon properties of semiconductive FeSi2 films,” in Proceedings of the 20th International Conference on the Physics of Semiconductors, E. M. Anastassakis, J. D. Joannopoulos, eds. (World Scientific Publishing, Thessaloníki, Greece, 1990), Vol. 1, pp. 316–319.

Dobrowolski, J. A.

Elizalde, E.

E. Elizalde, F. Rueda, “On the determination of the optical constants n(λ) and α(λ) of thin supported films,” Thin Solid Films 122, 45–57 (1984).
[CrossRef]

Ferguson, I. T.

Y. B. Li, R. A. Stradling, T. Knight, J. R. Birch, R. H. Thomas, C. C. Phillips, I. T. Ferguson, “Infrared reflection and transmission of undoped and Si-doped InAs grown on GaAs by molecular beam epitaxy,” Semicond. Sci. Technol. 9, 101–111 (1993).
[CrossRef]

Filinski, I.

I. Filinski, “The effects of sample imperfections on optical spectra,” Phys. Status Solidi B 49, 577–588 (1972).
[CrossRef]

Filliard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Filliard, “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]

Galtier, M.

S. Schirar, L. Bayo, A. Melouah, J. Bougnot, C. Linares, A. Montaner, M. Galtier, “Nondestructive determination of free carrier density of epitaxial layers of GaSb by IR reflectivity measurement,” Thin Solid Films 155, 125–132 (1987).
[CrossRef]

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Filliard, “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]

Goodman, A. M.

Hatzopoulos, N.

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Oxide growth, refractive index and composition profiles of structures formed by 2-MeV oxygen implantation into Si,” J. Appl. Phys., in press.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), pp. 69–80.

Hemment, P. L. F.

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Oxide growth, refractive index and composition profiles of structures formed by 2-MeV oxygen implantation into Si,” J. Appl. Phys., in press.

Ho, F. C.

Kavaliauskas, J.

J. Kavaliauskas, G. Krivaite, D. Senuliene, A. Sileika, “Characterization of the interface in CdxHg1–xTe/CdTe epilayers by IR reflectivity and electroreflectance,” Phys. Status Solidi A 126, K201–204 (1991).
[CrossRef]

Knight, T.

Y. B. Li, R. A. Stradling, T. Knight, J. R. Birch, R. H. Thomas, C. C. Phillips, I. T. Ferguson, “Infrared reflection and transmission of undoped and Si-doped InAs grown on GaAs by molecular beam epitaxy,” Semicond. Sci. Technol. 9, 101–111 (1993).
[CrossRef]

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, London, 1976), pp. 41–46.

Kotini, S.

S. Kotini, D. I. Siapkas, C. A. Dimitriadis, “Electronic and phonon properties of semiconductive FeSi2 films,” in Proceedings of the 20th International Conference on the Physics of Semiconductors, E. M. Anastassakis, J. D. Joannopoulos, eds. (World Scientific Publishing, Thessaloníki, Greece, 1990), Vol. 1, pp. 316–319.

Krivaite, G.

J. Kavaliauskas, G. Krivaite, D. Senuliene, A. Sileika, “Characterization of the interface in CdxHg1–xTe/CdTe epilayers by IR reflectivity and electroreflectance,” Phys. Status Solidi A 126, K201–204 (1991).
[CrossRef]

Kushev, D. B.

D. Siapkas, D. B. Kushev, N. N. Zheleva, J. Siapkas, I. Lelidis, “Optical constants of tin-telluride determined from infrared interference spectra,” Infrared Phys. 31, 425–433 (1991).
[CrossRef]

D. B. Kushev, N. N. Zheleva, Y. Demakopoulou, D. Siapkas, “A new method for the determination of the thickness, the optical constants, and the relaxation time of weakly absorbing semiconducting thin films,” Infrared Phys. 26, 385–393 (1986).
[CrossRef]

Lelidis, I.

D. Siapkas, D. B. Kushev, N. N. Zheleva, J. Siapkas, I. Lelidis, “Optical constants of tin-telluride determined from infrared interference spectra,” Infrared Phys. 31, 425–433 (1991).
[CrossRef]

Li, Y. B.

Y. B. Li, R. A. Stradling, T. Knight, J. R. Birch, R. H. Thomas, C. C. Phillips, I. T. Ferguson, “Infrared reflection and transmission of undoped and Si-doped InAs grown on GaAs by molecular beam epitaxy,” Semicond. Sci. Technol. 9, 101–111 (1993).
[CrossRef]

Linares, C.

S. Schirar, L. Bayo, A. Melouah, J. Bougnot, C. Linares, A. Montaner, M. Galtier, “Nondestructive determination of free carrier density of epitaxial layers of GaSb by IR reflectivity measurement,” Thin Solid Films 155, 125–132 (1987).
[CrossRef]

Lubberts, G.

G. Lubberts, B. C. Burkey, F. Moser, E. A. Trabka, “Optical properties of phosphorus-doped polycrystalline silicon layers,” J. Appl. Phys. 52, 6870–6878 (1981).
[CrossRef]

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Filliard, “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]

Melouah, A.

S. Schirar, L. Bayo, A. Melouah, J. Bougnot, C. Linares, A. Montaner, M. Galtier, “Nondestructive determination of free carrier density of epitaxial layers of GaSb by IR reflectivity measurement,” Thin Solid Films 155, 125–132 (1987).
[CrossRef]

Mitsas, C. L.

C. L. Mitsas, D. I. Siapkas, “Phonon and electronic properties of TlBiSe2 thin films,” Solid State Commun. 83, 857–861 (1992).
[CrossRef]

C. L. Mitsas, E. K. Polychroniadis, D. I. Siapkas, “The influence of the growth parameters on the structural and electronic properties of TlBiSe2 thin films,” Mater. Sci. Eng. B 14, 347–352 (1992).
[CrossRef]

C. L. Mitsas, “The growth and characterization of III–V–VI2 ternary compound thin films,” Ph.D. dissertation (University of Thessaloníki, Thessaloníki, Greece, 1995).

Montaner, A.

S. Schirar, L. Bayo, A. Melouah, J. Bougnot, C. Linares, A. Montaner, M. Galtier, “Nondestructive determination of free carrier density of epitaxial layers of GaSb by IR reflectivity measurement,” Thin Solid Films 155, 125–132 (1987).
[CrossRef]

Moser, F.

G. Lubberts, B. C. Burkey, F. Moser, E. A. Trabka, “Optical properties of phosphorus-doped polycrystalline silicon layers,” J. Appl. Phys. 52, 6870–6878 (1981).
[CrossRef]

Nestell, J. E.

Nilsson, P. O.

P. O. Nilsson, “Determination of optical constants from intensity measurements at normal incidence,” Appl. Opt. 7, 436–442 (1968).
[CrossRef]

Pawlikowski, J. M.

J. M. Pawlikowski, “Comments on the determination of the absorption coefficient of thin semiconductor films,” Thin Solid Films 127, 29–38 (1985).
[CrossRef]

Perkowitz, S.

P. M. Amirtharaj, S. Perkowitz, “Far infrared spatial probe of heteroepitaxial indium arsenide,” Thin Solid Films 62, 357–360 (1979).
[CrossRef]

Phillips, C. C.

Y. B. Li, R. A. Stradling, T. Knight, J. R. Birch, R. H. Thomas, C. C. Phillips, I. T. Ferguson, “Infrared reflection and transmission of undoped and Si-doped InAs grown on GaAs by molecular beam epitaxy,” Semicond. Sci. Technol. 9, 101–111 (1993).
[CrossRef]

Polychroniadis, E. K.

C. L. Mitsas, E. K. Polychroniadis, D. I. Siapkas, “The influence of the growth parameters on the structural and electronic properties of TlBiSe2 thin films,” Mater. Sci. Eng. B 14, 347–352 (1992).
[CrossRef]

Rueda, F.

E. Elizalde, F. Rueda, “On the determination of the optical constants n(λ) and α(λ) of thin supported films,” Thin Solid Films 122, 45–57 (1984).
[CrossRef]

Schirar, S.

S. Schirar, L. Bayo, A. Melouah, J. Bougnot, C. Linares, A. Montaner, M. Galtier, “Nondestructive determination of free carrier density of epitaxial layers of GaSb by IR reflectivity measurement,” Thin Solid Films 155, 125–132 (1987).
[CrossRef]

Senuliene, D.

J. Kavaliauskas, G. Krivaite, D. Senuliene, A. Sileika, “Characterization of the interface in CdxHg1–xTe/CdTe epilayers by IR reflectivity and electroreflectance,” Phys. Status Solidi A 126, K201–204 (1991).
[CrossRef]

Siapkas, D.

D. Siapkas, D. B. Kushev, N. N. Zheleva, J. Siapkas, I. Lelidis, “Optical constants of tin-telluride determined from infrared interference spectra,” Infrared Phys. 31, 425–433 (1991).
[CrossRef]

D. B. Kushev, N. N. Zheleva, Y. Demakopoulou, D. Siapkas, “A new method for the determination of the thickness, the optical constants, and the relaxation time of weakly absorbing semiconducting thin films,” Infrared Phys. 26, 385–393 (1986).
[CrossRef]

Siapkas, D. I.

C. L. Mitsas, E. K. Polychroniadis, D. I. Siapkas, “The influence of the growth parameters on the structural and electronic properties of TlBiSe2 thin films,” Mater. Sci. Eng. B 14, 347–352 (1992).
[CrossRef]

C. L. Mitsas, D. I. Siapkas, “Phonon and electronic properties of TlBiSe2 thin films,” Solid State Commun. 83, 857–861 (1992).
[CrossRef]

S. Kotini, D. I. Siapkas, C. A. Dimitriadis, “Electronic and phonon properties of semiconductive FeSi2 films,” in Proceedings of the 20th International Conference on the Physics of Semiconductors, E. M. Anastassakis, J. D. Joannopoulos, eds. (World Scientific Publishing, Thessaloníki, Greece, 1990), Vol. 1, pp. 316–319.

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Oxide growth, refractive index and composition profiles of structures formed by 2-MeV oxygen implantation into Si,” J. Appl. Phys., in press.

Siapkas, J.

D. Siapkas, D. B. Kushev, N. N. Zheleva, J. Siapkas, I. Lelidis, “Optical constants of tin-telluride determined from infrared interference spectra,” Infrared Phys. 31, 425–433 (1991).
[CrossRef]

Sileika, A.

J. Kavaliauskas, G. Krivaite, D. Senuliene, A. Sileika, “Characterization of the interface in CdxHg1–xTe/CdTe epilayers by IR reflectivity and electroreflectance,” Phys. Status Solidi A 126, K201–204 (1991).
[CrossRef]

Stradling, R. A.

Y. B. Li, R. A. Stradling, T. Knight, J. R. Birch, R. H. Thomas, C. C. Phillips, I. T. Ferguson, “Infrared reflection and transmission of undoped and Si-doped InAs grown on GaAs by molecular beam epitaxy,” Semicond. Sci. Technol. 9, 101–111 (1993).
[CrossRef]

Szczyrbowski, J.

J. Szczyrbowski, A. Czapla, “Optical absorption in d.c. sputtered InAs films,” Thin Solid Films 47, 127–137 (1977).
[CrossRef]

Thomas, R. H.

Y. B. Li, R. A. Stradling, T. Knight, J. R. Birch, R. H. Thomas, C. C. Phillips, I. T. Ferguson, “Infrared reflection and transmission of undoped and Si-doped InAs grown on GaAs by molecular beam epitaxy,” Semicond. Sci. Technol. 9, 101–111 (1993).
[CrossRef]

Trabka, E. A.

G. Lubberts, B. C. Burkey, F. Moser, E. A. Trabka, “Optical properties of phosphorus-doped polycrystalline silicon layers,” J. Appl. Phys. 52, 6870–6878 (1981).
[CrossRef]

Vasicek, A.

A. Vasicek, Optics of Thin Films (North-HollandAmsterdam, 1960), pp. 254–261.

Verleur, H. W.

Waldorf, A.

Ward, L.

L. Ward, The Optical Constants of Bulk Materials and Films (Hilger, Bristol, UK, 1988), pp. 165–170.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), pp. 54–69.

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), pp. 102–114.

Zheleva, N. N.

D. Siapkas, D. B. Kushev, N. N. Zheleva, J. Siapkas, I. Lelidis, “Optical constants of tin-telluride determined from infrared interference spectra,” Infrared Phys. 31, 425–433 (1991).
[CrossRef]

D. B. Kushev, N. N. Zheleva, Y. Demakopoulou, D. Siapkas, “A new method for the determination of the thickness, the optical constants, and the relaxation time of weakly absorbing semiconducting thin films,” Infrared Phys. 26, 385–393 (1986).
[CrossRef]

Appl. Opt. (5)

Infrared Phys. (2)

D. Siapkas, D. B. Kushev, N. N. Zheleva, J. Siapkas, I. Lelidis, “Optical constants of tin-telluride determined from infrared interference spectra,” Infrared Phys. 31, 425–433 (1991).
[CrossRef]

D. B. Kushev, N. N. Zheleva, Y. Demakopoulou, D. Siapkas, “A new method for the determination of the thickness, the optical constants, and the relaxation time of weakly absorbing semiconducting thin films,” Infrared Phys. 26, 385–393 (1986).
[CrossRef]

J. Appl. Phys. (1)

G. Lubberts, B. C. Burkey, F. Moser, E. A. Trabka, “Optical properties of phosphorus-doped polycrystalline silicon layers,” J. Appl. Phys. 52, 6870–6878 (1981).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. E (1)

J. C. Manifacier, J. Gasiot, J. P. Filliard, “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]

Mater. Sci. Eng. B (1)

C. L. Mitsas, E. K. Polychroniadis, D. I. Siapkas, “The influence of the growth parameters on the structural and electronic properties of TlBiSe2 thin films,” Mater. Sci. Eng. B 14, 347–352 (1992).
[CrossRef]

Phys. Status Solidi A (1)

J. Kavaliauskas, G. Krivaite, D. Senuliene, A. Sileika, “Characterization of the interface in CdxHg1–xTe/CdTe epilayers by IR reflectivity and electroreflectance,” Phys. Status Solidi A 126, K201–204 (1991).
[CrossRef]

Phys. Status Solidi B (1)

I. Filinski, “The effects of sample imperfections on optical spectra,” Phys. Status Solidi B 49, 577–588 (1972).
[CrossRef]

Semicond. Sci. Technol. (1)

Y. B. Li, R. A. Stradling, T. Knight, J. R. Birch, R. H. Thomas, C. C. Phillips, I. T. Ferguson, “Infrared reflection and transmission of undoped and Si-doped InAs grown on GaAs by molecular beam epitaxy,” Semicond. Sci. Technol. 9, 101–111 (1993).
[CrossRef]

Solid State Commun. (1)

C. L. Mitsas, D. I. Siapkas, “Phonon and electronic properties of TlBiSe2 thin films,” Solid State Commun. 83, 857–861 (1992).
[CrossRef]

Thin Solid Films (5)

P. M. Amirtharaj, S. Perkowitz, “Far infrared spatial probe of heteroepitaxial indium arsenide,” Thin Solid Films 62, 357–360 (1979).
[CrossRef]

S. Schirar, L. Bayo, A. Melouah, J. Bougnot, C. Linares, A. Montaner, M. Galtier, “Nondestructive determination of free carrier density of epitaxial layers of GaSb by IR reflectivity measurement,” Thin Solid Films 155, 125–132 (1987).
[CrossRef]

J. M. Pawlikowski, “Comments on the determination of the absorption coefficient of thin semiconductor films,” Thin Solid Films 127, 29–38 (1985).
[CrossRef]

J. Szczyrbowski, A. Czapla, “Optical absorption in d.c. sputtered InAs films,” Thin Solid Films 47, 127–137 (1977).
[CrossRef]

E. Elizalde, F. Rueda, “On the determination of the optical constants n(λ) and α(λ) of thin supported films,” Thin Solid Films 122, 45–57 (1984).
[CrossRef]

Other (11)

A. Vasicek, Optics of Thin Films (North-HollandAmsterdam, 1960), pp. 254–261.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), pp. 54–69.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), pp. 69–80.

Z. Knittl, Optics of Thin Films (Wiley, London, 1976), pp. 41–46.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), pp. 102–114.

E. D. Palik, ed., Handbook of Optical Constants of Solids I (Academic, New York, 1985), pp. 18–21.

C. L. Mitsas, “The growth and characterization of III–V–VI2 ternary compound thin films,” Ph.D. dissertation (University of Thessaloníki, Thessaloníki, Greece, 1995).

P. H. Berning, in Physics of Thin Films, Vol. 1, G. Hass, ed. (Academic, New York, 1963), pp. 69–71.

S. Kotini, D. I. Siapkas, C. A. Dimitriadis, “Electronic and phonon properties of semiconductive FeSi2 films,” in Proceedings of the 20th International Conference on the Physics of Semiconductors, E. M. Anastassakis, J. D. Joannopoulos, eds. (World Scientific Publishing, Thessaloníki, Greece, 1990), Vol. 1, pp. 316–319.

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Oxide growth, refractive index and composition profiles of structures formed by 2-MeV oxygen implantation into Si,” J. Appl. Phys., in press.

L. Ward, The Optical Constants of Bulk Materials and Films (Hilger, Bristol, UK, 1988), pp. 165–170.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Figure 1
Figure 1

Multilayer structure composed of k layers and k + 1 interfaces. Also shown are the field amplitudes of the right and left moving waves on both sides of the structure.

Fig. 2
Fig. 2

Reflectance spectra calculated by the generalized transfer matrix method of a Si epilayer on SiO2, showing the influence of surface or/and interface roughness of magnitude Z = 1000 Å for both cases. A semi-infinite SiO2 substrate is assumed.

Fig. 3
Fig. 3

Multilayer structure composed of m − 1 thin layers and a thick mth layer (substrate).

Fig. 4
Fig. 4

Calculated reflectance spectrum of a Si/SiO2 epitaxial system of thicknesses d Si = 0.6 μm and d SiO 2 = 200 μ m by use of the coherent formulation of the matrix method [Eq. (3)].

Fig. 5
Fig. 5

Calculated reflectance spectrum of the system of Fig. 4, with the finite substrate correction included as obtained by the generalized transfer matrix method [Eq. (1)] and by use of the semi-infinite substrate approximation.

Fig. 6
Fig. 6

Experimental (circles) and calculated reflectance spectra of a simple SIMOX structure exhibiting substantial roughness on both SiO2 buried layer interfaces.

Equations (27)

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

r i R = E i L E i R , t i R = E i R E i R , r i L = E i R E i L , t i L = E i L E i L ,
Y i = H i R E i R = H i L E i L ,
E i R + E i L = E i R + E i L , Y i 1 E i R Y i 1 E i L = Y i E i R Y i E i L
W i 1 / i = 1 t i R ( 1 r i L r i R r i R t i L r i R r i L ) ,
r i R = Y i 1 Y i Y i 1 + Y i , t i R = 2 Y i 1 Y i 1 + Y i ,
r i L = Y i Y i 1 Y i 1 + Y i , t i L = 2 Y i Y i 1 + Y i .
W i 1 / i = 1 t i R ( 1 r i R r i R 1 ) ,
( E i 1 , R E i 1 , L ) = [ exp ( i φ i ) 0 0 exp ( i φ i ) ] ( E i R E i L ) ,
( E o R E o L ) = S ( E k + 1 , R E k + 1 , L )
S = W 01 U 1 W 12 U 2 , , W k / k + 1 = ( s 11 s 12 s 21 s 22 ) .
r R = s 21 s 11 , t R = 1 s 11 ,
r L = s 12 s 11 , t L = Det S s 11 ,
r o R = r o R ( o ) exp [ 2 ( s n o / λ ) 2 ] = a r o R ( o ) ,
r o L = r o L ( o ) exp [ 2 ( s n 1 / λ ) 2 ] = b r o L ( o ) ,
t o R = t o R ( o ) exp [ 1 / 2 ( s / λ ) 2 ( n 1 n 0 ) 2 ] = c t o R ( o ) ,
t o L = t o L ( o ) exp [ 1 / 2 ( s / λ ) 2 ( n 0 n 1 ) 2 ] = c t o L ( o ) ,
r i R = r i R ( o ) exp [ 2 ( s n i 1 / λ ) 2 ] = α r i R ( o )
r i L = r i L ( o ) exp [ 2 ( s n i / λ ) 2 ] = β r i L ( o ) ,
t i R = t i R ( o ) exp [ 1 / 2 ( s / λ ) 2 ( n i n i 1 ) 2 ] = γ t i R ( o ) ,
t i L = t i L ( o ) exp [ 1 / 2 ( s / λ ) 2 ( n i 1 n i ) 2 ] = γ t i L ( o ) ,
S = 1 c t o 1 R [ exp ( i φ 1 ) b r 1 R r o L exp ( i φ 1 ) r 1 R exp ( i φ 1 ) b r o L exp ( i φ 1 ) a r o R exp ( i φ 1 ) + A r 1 R exp ( i φ 1 ) a r o R r 1 R exp ( i φ 1 ) + A exp ( i φ 1 ) ] ,
r o 1 = a r o R + r 1 R A exp ( 2 i φ 1 ) 1 b r 1 R r o L exp ( 2 i φ 1 ) , t o 1 = c t o R t 1 R exp ( i φ 1 ) 1 b r 1 R r o L exp ( 2 i φ 1 ) .
S = 1 γ t o 1 R [ exp ( i φ 1 ) α r 1 R r o R exp ( i φ 1 ) β r 1 L exp ( i φ 1 ) + A r o R exp ( i φ 1 ) r o R exp ( i φ 1 ) + α r 1 R exp ( i φ 1 ) β r o R r 1 L exp ( i φ 1 ) + A exp ( i φ 1 ) ]
r o 1 = r o R + β r 1 R exp ( 2 i φ 1 ) 1 + β r 1 R r o R exp ( 2 i φ 1 ) , t o 1 = γ t o R t 1 R exp ( i φ 1 ) 1 + β r 1 R r o R exp ( 2 i φ 1 ) .
S = S 1 m U m W m / m + 1 .
S = 1 t o 1 R t 2 R [ exp ( i φ S ) r 2 R r o 1 R exp ( i φ S ) r o 1 L exp ( i φ S ) + r 2 R exp ( i φ S ) r o 1 R exp ( i φ S ) + r 2 R ( t o 1 R t o 1 L r o 1 R r o 1 L ) exp ( i φ S ) r 2 R r o 1 R exp ( i φ S ) + ( t o 1 R t o 1 L r o 1 R r o 1 L ) exp ( i φ S ) ] ,
r 1 s R = r o 1 R + r 2 R t o 1 R t o 1 L exp ( 2 i φ S ) 1 r o 1 R r 2 R exp ( 2 i φ S ) , t 1 s R = t o 1 R t 2 R exp ( i φ S ) 1 r 2 R r o 1 R exp ( 2 i φ S ) ,

Metrics