Abstract

Exact theoretical expressions including absorption, multiple reflections, and interference effects are derived for the intensity of Raman scattering from thin films. A concept of interference enhanced Raman scattering is presented based on a two-layer configuration that has been verified experimentally by Raman scattering measurements on thin amorphous hydrogenated carbon films deposited on crystalline Si substrates. It is shown how the model can be generalized to describe the Raman scattering intensity for a sample layer inside a multilayer structure.

© 1989 Optical Society of America

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  1. W. Richter, “Resonant Raman Scattering in Semiconductors,” Solid State Physics, G. Höhler, E. A. Niekisch, Eds. (Springer-Verlag, Berlin1976), pp. 121–272.
  2. G. A. N. Connell, R. J. Nemanich, C. C. Tsai, “Interference-Enhanced Raman Scattering from Very Thin Absorbing Films,” Appl. Phys. Lett. 36, 31–33 (1980).
    [CrossRef]
  3. R. J. Nemanich, C. C. Tsai, G. A. N. Connell, “Interference-Enhanced Raman Scattering of Very Thin Titanium and Titanium Oxide Films,” Phys. Rev. Lett. 44, 273–276 (1980).
    [CrossRef]
  4. R. J. Nemanich, C. C. Tsai, M. J. Thompson, T. W. Sigmon, “Interference Enhanced Raman Scattering Study of the Interfacial Reaction of Pd on a-Si:H,” J. Vac. Sci. Technol. 19, 685–688 (1981).
    [CrossRef]
  5. A. Hugot-Le Groff, “Structure of Very Thin TiO2 Films Studied by Raman Spectroscopy with Interference Enhancement,” Thin Solid Films 142, 193–197 (1986).
    [CrossRef]
  6. L. S. Hsu, C. Y. She, G. J. Exarhos, “Reduction of Substrate Interference in Raman Spectroscopy of Submicron Titania Coatings,” Appl. Opt. 23, 3049–3051 (1984).
    [CrossRef] [PubMed]
  7. R. A. Craig, G. J. Exarhos, W. T. Pawlewicz, R. E. Williford, “Interference-Enhanced Raman Scattering from TiO2/SiO2 Multilayers: Measurement and Theory,”Appl. Opt. 26, 4193– 4197 (1987).
    [CrossRef] [PubMed]
  8. A. Bubenzer, P. Koidl, “Exact Expressions for Calculating Thin-Film Absorption Coefficients from Laser Calorimetric Data,” Appl. Opt. 23, 2886–2891 (1984).
    [CrossRef] [PubMed]
  9. See, e.g., H. A. Macleod, in Thin-film optical filters (Adam Hilger Ltd., Bristol, 1986). However we have chosen another possible definition of the phase, nrkdr, instead of −nrkdr.
  10. M. Cardona, “Resonance Phenomena,” in Light Scattering in Solids II, M. Cardona, G. Güntherodt, Eds. (Springer-Verlag, Berlin, 1982), pp. 19–178.
  11. J. C. Angus, P. Koidl, S. Domitz, “Carbon Thin Films,” Chapt. 4 in Plasma Deposited Thin Films, J. Mort, F. Jansen, Eds. (CRC, Boca Raton, 1986).
  12. A. Bubenzer, B. Dischler, G. Brandt, P. Koidl, “RF-Plasma Deposited Amorphous Hydrogenated Hard Carbon Thin Films: Preparation, Properties, and Applications,” J. Appl. Phys. 54, 4590–4595 (1983).
    [CrossRef]
  13. C. Wild, J. Wagner, P. Koidl, “Process Monitoring of a–C:H Plasma Deposition,” J. Vac. Sci. Technol. A5, 2227–2230 (1987).
  14. K. Enke, H. Dimigen, H. Hüibsch, “Frictional Properties of Diamondlike Carbon Layers,” Appl. Phys. Lett. 36, 291–294 (1980).
    [CrossRef]
  15. J. Fink et al., “Investigation of Hydrocarbon-Plasma-Generated Carbon Films by Electron-Energy-Loss Spectroscopy,” Phys. Rev. B30, 4713–4718 (1984).
  16. J. Wagner, P. Lautenschlager, “Hard Amorphous Carbon Studied by Ellipsometry and Photoluminescence,” J. Appl. Phys. 59, 2044–2047 (1986) and references therein.
    [CrossRef]
  17. See, e.g., J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Characterization of a–C:H films by Raman and Luminescence Spectroscopy,” in Proc. of the European Materials Research Society Vol. XVII; Amorphous Hydrogenated Carbon Films, P. Koidl, P. Oelhafen, Eds. (Les Editons de Physique, Paris, 1987) and references therein.
  18. M. Ramsteiner, J. Wagner, C. Wild, P. Koidl, “Raman Scattering of Amorphous Carbon/Semiconductor Interface Layers,” Solid State Commun. 67, 15–18 (1988).
    [CrossRef]
  19. D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B27, 985–1009 (1983).
  20. M. Ramsteiner, J. Wagner, “Resonance Raman Scattering of Hydrogenated Amorphous Carbon: Evidence for π-Bonded Carbon Clusters,” Appl. Phys. Lett. 51, 1355–1357 (1987).
    [CrossRef]
  21. J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Resonant Raman Scattering of Amorphous Carbon and Polycrystalline Diamond Films,” to appear in Phys. Rev. B, July15,1989.
    [CrossRef]

1989

J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Resonant Raman Scattering of Amorphous Carbon and Polycrystalline Diamond Films,” to appear in Phys. Rev. B, July15,1989.
[CrossRef]

1988

M. Ramsteiner, J. Wagner, C. Wild, P. Koidl, “Raman Scattering of Amorphous Carbon/Semiconductor Interface Layers,” Solid State Commun. 67, 15–18 (1988).
[CrossRef]

1987

M. Ramsteiner, J. Wagner, “Resonance Raman Scattering of Hydrogenated Amorphous Carbon: Evidence for π-Bonded Carbon Clusters,” Appl. Phys. Lett. 51, 1355–1357 (1987).
[CrossRef]

C. Wild, J. Wagner, P. Koidl, “Process Monitoring of a–C:H Plasma Deposition,” J. Vac. Sci. Technol. A5, 2227–2230 (1987).

R. A. Craig, G. J. Exarhos, W. T. Pawlewicz, R. E. Williford, “Interference-Enhanced Raman Scattering from TiO2/SiO2 Multilayers: Measurement and Theory,”Appl. Opt. 26, 4193– 4197 (1987).
[CrossRef] [PubMed]

1986

A. Hugot-Le Groff, “Structure of Very Thin TiO2 Films Studied by Raman Spectroscopy with Interference Enhancement,” Thin Solid Films 142, 193–197 (1986).
[CrossRef]

J. Wagner, P. Lautenschlager, “Hard Amorphous Carbon Studied by Ellipsometry and Photoluminescence,” J. Appl. Phys. 59, 2044–2047 (1986) and references therein.
[CrossRef]

1984

1983

A. Bubenzer, B. Dischler, G. Brandt, P. Koidl, “RF-Plasma Deposited Amorphous Hydrogenated Hard Carbon Thin Films: Preparation, Properties, and Applications,” J. Appl. Phys. 54, 4590–4595 (1983).
[CrossRef]

D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B27, 985–1009 (1983).

1981

R. J. Nemanich, C. C. Tsai, M. J. Thompson, T. W. Sigmon, “Interference Enhanced Raman Scattering Study of the Interfacial Reaction of Pd on a-Si:H,” J. Vac. Sci. Technol. 19, 685–688 (1981).
[CrossRef]

1980

G. A. N. Connell, R. J. Nemanich, C. C. Tsai, “Interference-Enhanced Raman Scattering from Very Thin Absorbing Films,” Appl. Phys. Lett. 36, 31–33 (1980).
[CrossRef]

R. J. Nemanich, C. C. Tsai, G. A. N. Connell, “Interference-Enhanced Raman Scattering of Very Thin Titanium and Titanium Oxide Films,” Phys. Rev. Lett. 44, 273–276 (1980).
[CrossRef]

K. Enke, H. Dimigen, H. Hüibsch, “Frictional Properties of Diamondlike Carbon Layers,” Appl. Phys. Lett. 36, 291–294 (1980).
[CrossRef]

Angus, J. C.

J. C. Angus, P. Koidl, S. Domitz, “Carbon Thin Films,” Chapt. 4 in Plasma Deposited Thin Films, J. Mort, F. Jansen, Eds. (CRC, Boca Raton, 1986).

Aspnes, D. E.

D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B27, 985–1009 (1983).

Brandt, G.

A. Bubenzer, B. Dischler, G. Brandt, P. Koidl, “RF-Plasma Deposited Amorphous Hydrogenated Hard Carbon Thin Films: Preparation, Properties, and Applications,” J. Appl. Phys. 54, 4590–4595 (1983).
[CrossRef]

Bubenzer, A.

A. Bubenzer, P. Koidl, “Exact Expressions for Calculating Thin-Film Absorption Coefficients from Laser Calorimetric Data,” Appl. Opt. 23, 2886–2891 (1984).
[CrossRef] [PubMed]

A. Bubenzer, B. Dischler, G. Brandt, P. Koidl, “RF-Plasma Deposited Amorphous Hydrogenated Hard Carbon Thin Films: Preparation, Properties, and Applications,” J. Appl. Phys. 54, 4590–4595 (1983).
[CrossRef]

Cardona, M.

M. Cardona, “Resonance Phenomena,” in Light Scattering in Solids II, M. Cardona, G. Güntherodt, Eds. (Springer-Verlag, Berlin, 1982), pp. 19–178.

Connell, G. A. N.

G. A. N. Connell, R. J. Nemanich, C. C. Tsai, “Interference-Enhanced Raman Scattering from Very Thin Absorbing Films,” Appl. Phys. Lett. 36, 31–33 (1980).
[CrossRef]

R. J. Nemanich, C. C. Tsai, G. A. N. Connell, “Interference-Enhanced Raman Scattering of Very Thin Titanium and Titanium Oxide Films,” Phys. Rev. Lett. 44, 273–276 (1980).
[CrossRef]

Craig, R. A.

Dimigen, H.

K. Enke, H. Dimigen, H. Hüibsch, “Frictional Properties of Diamondlike Carbon Layers,” Appl. Phys. Lett. 36, 291–294 (1980).
[CrossRef]

Dischler, B.

A. Bubenzer, B. Dischler, G. Brandt, P. Koidl, “RF-Plasma Deposited Amorphous Hydrogenated Hard Carbon Thin Films: Preparation, Properties, and Applications,” J. Appl. Phys. 54, 4590–4595 (1983).
[CrossRef]

Domitz, S.

J. C. Angus, P. Koidl, S. Domitz, “Carbon Thin Films,” Chapt. 4 in Plasma Deposited Thin Films, J. Mort, F. Jansen, Eds. (CRC, Boca Raton, 1986).

Enke, K.

K. Enke, H. Dimigen, H. Hüibsch, “Frictional Properties of Diamondlike Carbon Layers,” Appl. Phys. Lett. 36, 291–294 (1980).
[CrossRef]

Exarhos, G. J.

Fink, J.

J. Fink et al., “Investigation of Hydrocarbon-Plasma-Generated Carbon Films by Electron-Energy-Loss Spectroscopy,” Phys. Rev. B30, 4713–4718 (1984).

Hsu, L. S.

Hugot-Le Groff, A.

A. Hugot-Le Groff, “Structure of Very Thin TiO2 Films Studied by Raman Spectroscopy with Interference Enhancement,” Thin Solid Films 142, 193–197 (1986).
[CrossRef]

Hüibsch, H.

K. Enke, H. Dimigen, H. Hüibsch, “Frictional Properties of Diamondlike Carbon Layers,” Appl. Phys. Lett. 36, 291–294 (1980).
[CrossRef]

Koidl, P.

J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Resonant Raman Scattering of Amorphous Carbon and Polycrystalline Diamond Films,” to appear in Phys. Rev. B, July15,1989.
[CrossRef]

M. Ramsteiner, J. Wagner, C. Wild, P. Koidl, “Raman Scattering of Amorphous Carbon/Semiconductor Interface Layers,” Solid State Commun. 67, 15–18 (1988).
[CrossRef]

C. Wild, J. Wagner, P. Koidl, “Process Monitoring of a–C:H Plasma Deposition,” J. Vac. Sci. Technol. A5, 2227–2230 (1987).

A. Bubenzer, P. Koidl, “Exact Expressions for Calculating Thin-Film Absorption Coefficients from Laser Calorimetric Data,” Appl. Opt. 23, 2886–2891 (1984).
[CrossRef] [PubMed]

A. Bubenzer, B. Dischler, G. Brandt, P. Koidl, “RF-Plasma Deposited Amorphous Hydrogenated Hard Carbon Thin Films: Preparation, Properties, and Applications,” J. Appl. Phys. 54, 4590–4595 (1983).
[CrossRef]

See, e.g., J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Characterization of a–C:H films by Raman and Luminescence Spectroscopy,” in Proc. of the European Materials Research Society Vol. XVII; Amorphous Hydrogenated Carbon Films, P. Koidl, P. Oelhafen, Eds. (Les Editons de Physique, Paris, 1987) and references therein.

J. C. Angus, P. Koidl, S. Domitz, “Carbon Thin Films,” Chapt. 4 in Plasma Deposited Thin Films, J. Mort, F. Jansen, Eds. (CRC, Boca Raton, 1986).

Lautenschlager, P.

J. Wagner, P. Lautenschlager, “Hard Amorphous Carbon Studied by Ellipsometry and Photoluminescence,” J. Appl. Phys. 59, 2044–2047 (1986) and references therein.
[CrossRef]

Macleod, H. A.

See, e.g., H. A. Macleod, in Thin-film optical filters (Adam Hilger Ltd., Bristol, 1986). However we have chosen another possible definition of the phase, nrkdr, instead of −nrkdr.

Nemanich, R. J.

R. J. Nemanich, C. C. Tsai, M. J. Thompson, T. W. Sigmon, “Interference Enhanced Raman Scattering Study of the Interfacial Reaction of Pd on a-Si:H,” J. Vac. Sci. Technol. 19, 685–688 (1981).
[CrossRef]

G. A. N. Connell, R. J. Nemanich, C. C. Tsai, “Interference-Enhanced Raman Scattering from Very Thin Absorbing Films,” Appl. Phys. Lett. 36, 31–33 (1980).
[CrossRef]

R. J. Nemanich, C. C. Tsai, G. A. N. Connell, “Interference-Enhanced Raman Scattering of Very Thin Titanium and Titanium Oxide Films,” Phys. Rev. Lett. 44, 273–276 (1980).
[CrossRef]

Pawlewicz, W. T.

Ramsteiner, M.

J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Resonant Raman Scattering of Amorphous Carbon and Polycrystalline Diamond Films,” to appear in Phys. Rev. B, July15,1989.
[CrossRef]

M. Ramsteiner, J. Wagner, C. Wild, P. Koidl, “Raman Scattering of Amorphous Carbon/Semiconductor Interface Layers,” Solid State Commun. 67, 15–18 (1988).
[CrossRef]

M. Ramsteiner, J. Wagner, “Resonance Raman Scattering of Hydrogenated Amorphous Carbon: Evidence for π-Bonded Carbon Clusters,” Appl. Phys. Lett. 51, 1355–1357 (1987).
[CrossRef]

See, e.g., J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Characterization of a–C:H films by Raman and Luminescence Spectroscopy,” in Proc. of the European Materials Research Society Vol. XVII; Amorphous Hydrogenated Carbon Films, P. Koidl, P. Oelhafen, Eds. (Les Editons de Physique, Paris, 1987) and references therein.

Richter, W.

W. Richter, “Resonant Raman Scattering in Semiconductors,” Solid State Physics, G. Höhler, E. A. Niekisch, Eds. (Springer-Verlag, Berlin1976), pp. 121–272.

She, C. Y.

Sigmon, T. W.

R. J. Nemanich, C. C. Tsai, M. J. Thompson, T. W. Sigmon, “Interference Enhanced Raman Scattering Study of the Interfacial Reaction of Pd on a-Si:H,” J. Vac. Sci. Technol. 19, 685–688 (1981).
[CrossRef]

Studna, A. A.

D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B27, 985–1009 (1983).

Thompson, M. J.

R. J. Nemanich, C. C. Tsai, M. J. Thompson, T. W. Sigmon, “Interference Enhanced Raman Scattering Study of the Interfacial Reaction of Pd on a-Si:H,” J. Vac. Sci. Technol. 19, 685–688 (1981).
[CrossRef]

Tsai, C. C.

R. J. Nemanich, C. C. Tsai, M. J. Thompson, T. W. Sigmon, “Interference Enhanced Raman Scattering Study of the Interfacial Reaction of Pd on a-Si:H,” J. Vac. Sci. Technol. 19, 685–688 (1981).
[CrossRef]

R. J. Nemanich, C. C. Tsai, G. A. N. Connell, “Interference-Enhanced Raman Scattering of Very Thin Titanium and Titanium Oxide Films,” Phys. Rev. Lett. 44, 273–276 (1980).
[CrossRef]

G. A. N. Connell, R. J. Nemanich, C. C. Tsai, “Interference-Enhanced Raman Scattering from Very Thin Absorbing Films,” Appl. Phys. Lett. 36, 31–33 (1980).
[CrossRef]

Wagner, J.

J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Resonant Raman Scattering of Amorphous Carbon and Polycrystalline Diamond Films,” to appear in Phys. Rev. B, July15,1989.
[CrossRef]

M. Ramsteiner, J. Wagner, C. Wild, P. Koidl, “Raman Scattering of Amorphous Carbon/Semiconductor Interface Layers,” Solid State Commun. 67, 15–18 (1988).
[CrossRef]

M. Ramsteiner, J. Wagner, “Resonance Raman Scattering of Hydrogenated Amorphous Carbon: Evidence for π-Bonded Carbon Clusters,” Appl. Phys. Lett. 51, 1355–1357 (1987).
[CrossRef]

C. Wild, J. Wagner, P. Koidl, “Process Monitoring of a–C:H Plasma Deposition,” J. Vac. Sci. Technol. A5, 2227–2230 (1987).

J. Wagner, P. Lautenschlager, “Hard Amorphous Carbon Studied by Ellipsometry and Photoluminescence,” J. Appl. Phys. 59, 2044–2047 (1986) and references therein.
[CrossRef]

See, e.g., J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Characterization of a–C:H films by Raman and Luminescence Spectroscopy,” in Proc. of the European Materials Research Society Vol. XVII; Amorphous Hydrogenated Carbon Films, P. Koidl, P. Oelhafen, Eds. (Les Editons de Physique, Paris, 1987) and references therein.

Wild, C.

J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Resonant Raman Scattering of Amorphous Carbon and Polycrystalline Diamond Films,” to appear in Phys. Rev. B, July15,1989.
[CrossRef]

M. Ramsteiner, J. Wagner, C. Wild, P. Koidl, “Raman Scattering of Amorphous Carbon/Semiconductor Interface Layers,” Solid State Commun. 67, 15–18 (1988).
[CrossRef]

C. Wild, J. Wagner, P. Koidl, “Process Monitoring of a–C:H Plasma Deposition,” J. Vac. Sci. Technol. A5, 2227–2230 (1987).

See, e.g., J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Characterization of a–C:H films by Raman and Luminescence Spectroscopy,” in Proc. of the European Materials Research Society Vol. XVII; Amorphous Hydrogenated Carbon Films, P. Koidl, P. Oelhafen, Eds. (Les Editons de Physique, Paris, 1987) and references therein.

Williford, R. E.

Appl. Opt.

Appl. Phys. Lett.

K. Enke, H. Dimigen, H. Hüibsch, “Frictional Properties of Diamondlike Carbon Layers,” Appl. Phys. Lett. 36, 291–294 (1980).
[CrossRef]

M. Ramsteiner, J. Wagner, “Resonance Raman Scattering of Hydrogenated Amorphous Carbon: Evidence for π-Bonded Carbon Clusters,” Appl. Phys. Lett. 51, 1355–1357 (1987).
[CrossRef]

G. A. N. Connell, R. J. Nemanich, C. C. Tsai, “Interference-Enhanced Raman Scattering from Very Thin Absorbing Films,” Appl. Phys. Lett. 36, 31–33 (1980).
[CrossRef]

J. Appl. Phys.

J. Wagner, P. Lautenschlager, “Hard Amorphous Carbon Studied by Ellipsometry and Photoluminescence,” J. Appl. Phys. 59, 2044–2047 (1986) and references therein.
[CrossRef]

A. Bubenzer, B. Dischler, G. Brandt, P. Koidl, “RF-Plasma Deposited Amorphous Hydrogenated Hard Carbon Thin Films: Preparation, Properties, and Applications,” J. Appl. Phys. 54, 4590–4595 (1983).
[CrossRef]

J. Vac. Sci. Technol.

C. Wild, J. Wagner, P. Koidl, “Process Monitoring of a–C:H Plasma Deposition,” J. Vac. Sci. Technol. A5, 2227–2230 (1987).

R. J. Nemanich, C. C. Tsai, M. J. Thompson, T. W. Sigmon, “Interference Enhanced Raman Scattering Study of the Interfacial Reaction of Pd on a-Si:H,” J. Vac. Sci. Technol. 19, 685–688 (1981).
[CrossRef]

Phys. Rev.

D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B27, 985–1009 (1983).

J. Fink et al., “Investigation of Hydrocarbon-Plasma-Generated Carbon Films by Electron-Energy-Loss Spectroscopy,” Phys. Rev. B30, 4713–4718 (1984).

Phys. Rev. B

J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Resonant Raman Scattering of Amorphous Carbon and Polycrystalline Diamond Films,” to appear in Phys. Rev. B, July15,1989.
[CrossRef]

Phys. Rev. Lett.

R. J. Nemanich, C. C. Tsai, G. A. N. Connell, “Interference-Enhanced Raman Scattering of Very Thin Titanium and Titanium Oxide Films,” Phys. Rev. Lett. 44, 273–276 (1980).
[CrossRef]

Solid State Commun.

M. Ramsteiner, J. Wagner, C. Wild, P. Koidl, “Raman Scattering of Amorphous Carbon/Semiconductor Interface Layers,” Solid State Commun. 67, 15–18 (1988).
[CrossRef]

Thin Solid Films

A. Hugot-Le Groff, “Structure of Very Thin TiO2 Films Studied by Raman Spectroscopy with Interference Enhancement,” Thin Solid Films 142, 193–197 (1986).
[CrossRef]

Other

W. Richter, “Resonant Raman Scattering in Semiconductors,” Solid State Physics, G. Höhler, E. A. Niekisch, Eds. (Springer-Verlag, Berlin1976), pp. 121–272.

See, e.g., J. Wagner, M. Ramsteiner, C. Wild, P. Koidl, “Characterization of a–C:H films by Raman and Luminescence Spectroscopy,” in Proc. of the European Materials Research Society Vol. XVII; Amorphous Hydrogenated Carbon Films, P. Koidl, P. Oelhafen, Eds. (Les Editons de Physique, Paris, 1987) and references therein.

See, e.g., H. A. Macleod, in Thin-film optical filters (Adam Hilger Ltd., Bristol, 1986). However we have chosen another possible definition of the phase, nrkdr, instead of −nrkdr.

M. Cardona, “Resonance Phenomena,” in Light Scattering in Solids II, M. Cardona, G. Güntherodt, Eds. (Springer-Verlag, Berlin, 1982), pp. 19–178.

J. C. Angus, P. Koidl, S. Domitz, “Carbon Thin Films,” Chapt. 4 in Plasma Deposited Thin Films, J. Mort, F. Jansen, Eds. (CRC, Boca Raton, 1986).

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