Abstract

A method to calculate the optical functions n(λ) and k(λ) by use of the transmission spectrum of a dielectric or semiconducting thin film measured at normal incidence is described. The spectrum should include the low-absorption region and the absorption edge to yield the relevant optical characteristics of the material. The formulas are derived from electromagnetic theory with no simplifying assumptions. Transparent films are considered as a particular case for which a simple method of calculation is proposed. In the general case of absorbing films the method takes advantage of some properties of the transmittance T(λ) to permit the parameters in the two regions mentioned above to be calculated separately. The interference fringes and the optical path at the extrema of T(λ) are exploited for determining with precision the refractive index and the film thickness. The absorption coefficient is computed at the absorption edge by an efficient iterative method. At the transition zone between the interference region and the absorption edge artifacts in the absorption curve are avoided. A small amount of absorption of the substrate is allowed for in the theory by means of a factor determined from an independent measurement, thus improving the quality of the results. Application of the method to a transmission spectrum of an a:SixN1-x:H film is illustrated in detail. Refractive index, dispersion parameters, film thickness, absorption coefficient, and optical gap are given with the help of tables and graphs.

© 1998 Optical Society of America

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  1. O. S. Heavens, Optical Properties of Thin Films (Butterworth, London, 1969).
  2. P. O. Nilsson, “Determination of optical constants from intensity measurements at normal incidence,” Appl. Opt. 7, 435–442 (1968).
    [CrossRef] [PubMed]
  3. F. Abelès, M. L. Thèye, “Méthode de calcul des constantes optiques des couches minces absorbantes à partir des mesures de réflexion et de transmission,” Surf. Sci. 5, 325–331 (1966).
    [CrossRef]
  4. J. M. Bennet, 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]
  5. J. H. Wohlgemuth, D. E. Brodie, “A method for calculating the index of refraction of thin films,” Can. J. Phys. 53, 1737–1742 (1975).
    [CrossRef]
  6. G. Galibert, K. Konan, R. El Grandi, J. Calas, J. L. Martin, “Accurate determination of the optical constants of absorbing thin films deposited on thick semitransparent substrates,” Mater. Sci. Eng. B 5, 37–42 (1989).
    [CrossRef]
  7. J. I. Cisneros, G. B. Rego, M. Tomiyama, S. Bilac, J. M. Gonçalves, A. E. Rodriguez, Z. P. Arguello, “A method for the determination of the complex refractive index of non metallic thin films using photometric measurements at normal incidence,” Thin Solid Films 100, 155–167 (1983).
    [CrossRef]
  8. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
    [CrossRef]
  9. S. F. Durrant, S. G. Castro, J. I. Cisneros, N. C. da Cruz, M. A. Bica de Moraes, “Amorphous oxygen-containing hydrogenated carbon films formed by plasma-enhanced chemical vapor deposition,” J. Vac. Sci. Technol. A 14, 1–7 (1996).
    [CrossRef]
  10. M. M. Guraya, H. Ascolani, G. Zampieri, J. I. Cisneros, J. H. Dias da Silva, M. P. Cantão, “Bond densities and electronic structure of amorphous SiNx:H,” Phys. Rev. B 42, 5677–5684 (1990).
    [CrossRef]
  11. M. M. Guraya, H. Ascolani, G. Zampieri, J. H. Dias da Silva, M. P. Cantão, J. I. Cisneros, “Electronic structure of amorphous Si–N compounds,” Phys. Rev. B 49, 13446–13451 (1994).
    [CrossRef]
  12. J. H. Dias da Silva, J. I. Cisneros, M. M. Guraya, G. Zampieri, “Effects of deviation from stoichiometry and thermal annealing on amorphous gallium antimonide films,” Phys. Rev. B. 51, 6272–6279 (1995).
    [CrossRef]
  13. H. Dias da Silva, J. I. Cisneros, L. P. Cardoso, “Crystallization process and chemical disorder in flash evaporated amorphous gallium antimonide films,” Mater. Res. Soc. Symp. Proc. 321, 645–650 (1994).
    [CrossRef]
  14. F. Alvarez, I. Chambouleyron, C. Constantino, J. I. Cisneros, “Doping effects in off-stoichiometric glow discharge amorphous silicon nitride,” Appl. Phys. Lett. 44, 116–118 (1984).
    [CrossRef]
  15. I. Chambouleyron, F. Marques, J. I. Cisneros, F. Alvarez, S. Moehlecke, W. Losch, I. Pereyra, “Optical properties of non-stoichiometric germanium nitride compounds (a-GeNx),” J. Non-Crystal. Solids 77 & 78, 1309–1312 (1985).
    [CrossRef]
  16. J. M. Berger, C. Ance, F. de Chelle, J. P. Ferraton, A. Donnadieu, J. I. Cisneros, J. H. Dias da Silva, “Temperature effects on the optical properties of amorphous hydrogenated silicon nitrogen alloys prepared by rf sputtering,” J. Non-Crystal. Solids 94, 353–364 (1987).
    [CrossRef]
  17. J. Torres, J. I. Cisneros, G. Gordillo, F. Alvarez, “A simple method to determine the optical constants and thicknesses of ZnxCd1-xS thin films,” Thin Solid Films 289, 238–241 (1996).
    [CrossRef]
  18. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).
  19. Z. Knittl, Optics of Thin Films (Wiley, New York, 1971), Chap. 11.
  20. S. H. Wemple, M. Didomenico, “Behavior of the electronic dielectric constant in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
    [CrossRef]
  21. J. I. Pankove, Optical Processes in Semiconductors (Dover, New York, 1971), Chap. 3.
  22. G. D. Cody, “The optical absorption edge of a-Si:H,” in Hydrogenated Amorphous Silicon, J. I. Pankove, ed., Vol. 21B of Semiconductors and Semimetals Series (Academic, Orlando, Fla., 1984), Chap. 2.
  23. J. Tauc, “Optical properties and electronic structure of amorphous semiconductors,” in Optical Properties of Solids, S. Nudelman, S. Mitra, eds. (Plenum, New York, 1969), Chap. 5.
    [CrossRef]

1996 (2)

S. F. Durrant, S. G. Castro, J. I. Cisneros, N. C. da Cruz, M. A. Bica de Moraes, “Amorphous oxygen-containing hydrogenated carbon films formed by plasma-enhanced chemical vapor deposition,” J. Vac. Sci. Technol. A 14, 1–7 (1996).
[CrossRef]

J. Torres, J. I. Cisneros, G. Gordillo, F. Alvarez, “A simple method to determine the optical constants and thicknesses of ZnxCd1-xS thin films,” Thin Solid Films 289, 238–241 (1996).
[CrossRef]

1995 (1)

J. H. Dias da Silva, J. I. Cisneros, M. M. Guraya, G. Zampieri, “Effects of deviation from stoichiometry and thermal annealing on amorphous gallium antimonide films,” Phys. Rev. B. 51, 6272–6279 (1995).
[CrossRef]

1994 (2)

H. Dias da Silva, J. I. Cisneros, L. P. Cardoso, “Crystallization process and chemical disorder in flash evaporated amorphous gallium antimonide films,” Mater. Res. Soc. Symp. Proc. 321, 645–650 (1994).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. H. Dias da Silva, M. P. Cantão, J. I. Cisneros, “Electronic structure of amorphous Si–N compounds,” Phys. Rev. B 49, 13446–13451 (1994).
[CrossRef]

1990 (1)

M. M. Guraya, H. Ascolani, G. Zampieri, J. I. Cisneros, J. H. Dias da Silva, M. P. Cantão, “Bond densities and electronic structure of amorphous SiNx:H,” Phys. Rev. B 42, 5677–5684 (1990).
[CrossRef]

1989 (1)

G. Galibert, K. Konan, R. El Grandi, J. Calas, J. L. Martin, “Accurate determination of the optical constants of absorbing thin films deposited on thick semitransparent substrates,” Mater. Sci. Eng. B 5, 37–42 (1989).
[CrossRef]

1987 (1)

J. M. Berger, C. Ance, F. de Chelle, J. P. Ferraton, A. Donnadieu, J. I. Cisneros, J. H. Dias da Silva, “Temperature effects on the optical properties of amorphous hydrogenated silicon nitrogen alloys prepared by rf sputtering,” J. Non-Crystal. Solids 94, 353–364 (1987).
[CrossRef]

1985 (1)

I. Chambouleyron, F. Marques, J. I. Cisneros, F. Alvarez, S. Moehlecke, W. Losch, I. Pereyra, “Optical properties of non-stoichiometric germanium nitride compounds (a-GeNx),” J. Non-Crystal. Solids 77 & 78, 1309–1312 (1985).
[CrossRef]

1984 (1)

F. Alvarez, I. Chambouleyron, C. Constantino, J. I. Cisneros, “Doping effects in off-stoichiometric glow discharge amorphous silicon nitride,” Appl. Phys. Lett. 44, 116–118 (1984).
[CrossRef]

1983 (2)

J. I. Cisneros, G. B. Rego, M. Tomiyama, S. Bilac, J. M. Gonçalves, A. E. Rodriguez, Z. P. Arguello, “A method for the determination of the complex refractive index of non metallic thin films using photometric measurements at normal incidence,” Thin Solid Films 100, 155–167 (1983).
[CrossRef]

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

1975 (1)

J. H. Wohlgemuth, D. E. Brodie, “A method for calculating the index of refraction of thin films,” Can. J. Phys. 53, 1737–1742 (1975).
[CrossRef]

1971 (1)

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

1968 (1)

1966 (2)

F. Abelès, M. L. Thèye, “Méthode de calcul des constantes optiques des couches minces absorbantes à partir des mesures de réflexion et de transmission,” Surf. Sci. 5, 325–331 (1966).
[CrossRef]

J. M. Bennet, 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]

Abelès, F.

F. Abelès, M. L. Thèye, “Méthode de calcul des constantes optiques des couches minces absorbantes à partir des mesures de réflexion et de transmission,” Surf. Sci. 5, 325–331 (1966).
[CrossRef]

Alvarez, F.

J. Torres, J. I. Cisneros, G. Gordillo, F. Alvarez, “A simple method to determine the optical constants and thicknesses of ZnxCd1-xS thin films,” Thin Solid Films 289, 238–241 (1996).
[CrossRef]

I. Chambouleyron, F. Marques, J. I. Cisneros, F. Alvarez, S. Moehlecke, W. Losch, I. Pereyra, “Optical properties of non-stoichiometric germanium nitride compounds (a-GeNx),” J. Non-Crystal. Solids 77 & 78, 1309–1312 (1985).
[CrossRef]

F. Alvarez, I. Chambouleyron, C. Constantino, J. I. Cisneros, “Doping effects in off-stoichiometric glow discharge amorphous silicon nitride,” Appl. Phys. Lett. 44, 116–118 (1984).
[CrossRef]

Ance, C.

J. M. Berger, C. Ance, F. de Chelle, J. P. Ferraton, A. Donnadieu, J. I. Cisneros, J. H. Dias da Silva, “Temperature effects on the optical properties of amorphous hydrogenated silicon nitrogen alloys prepared by rf sputtering,” J. Non-Crystal. Solids 94, 353–364 (1987).
[CrossRef]

Arguello, Z. P.

J. I. Cisneros, G. B. Rego, M. Tomiyama, S. Bilac, J. M. Gonçalves, A. E. Rodriguez, Z. P. Arguello, “A method for the determination of the complex refractive index of non metallic thin films using photometric measurements at normal incidence,” Thin Solid Films 100, 155–167 (1983).
[CrossRef]

Ascolani, H.

M. M. Guraya, H. Ascolani, G. Zampieri, J. H. Dias da Silva, M. P. Cantão, J. I. Cisneros, “Electronic structure of amorphous Si–N compounds,” Phys. Rev. B 49, 13446–13451 (1994).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. I. Cisneros, J. H. Dias da Silva, M. P. Cantão, “Bond densities and electronic structure of amorphous SiNx:H,” Phys. Rev. B 42, 5677–5684 (1990).
[CrossRef]

Bennet, J. M.

Berger, J. M.

J. M. Berger, C. Ance, F. de Chelle, J. P. Ferraton, A. Donnadieu, J. I. Cisneros, J. H. Dias da Silva, “Temperature effects on the optical properties of amorphous hydrogenated silicon nitrogen alloys prepared by rf sputtering,” J. Non-Crystal. Solids 94, 353–364 (1987).
[CrossRef]

Bica de Moraes, M. A.

S. F. Durrant, S. G. Castro, J. I. Cisneros, N. C. da Cruz, M. A. Bica de Moraes, “Amorphous oxygen-containing hydrogenated carbon films formed by plasma-enhanced chemical vapor deposition,” J. Vac. Sci. Technol. A 14, 1–7 (1996).
[CrossRef]

Bilac, S.

J. I. Cisneros, G. B. Rego, M. Tomiyama, S. Bilac, J. M. Gonçalves, A. E. Rodriguez, Z. P. Arguello, “A method for the determination of the complex refractive index of non metallic thin films using photometric measurements at normal incidence,” Thin Solid Films 100, 155–167 (1983).
[CrossRef]

Booty, M. J.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

Brodie, D. E.

J. H. Wohlgemuth, D. E. Brodie, “A method for calculating the index of refraction of thin films,” Can. J. Phys. 53, 1737–1742 (1975).
[CrossRef]

Calas, J.

G. Galibert, K. Konan, R. El Grandi, J. Calas, J. L. Martin, “Accurate determination of the optical constants of absorbing thin films deposited on thick semitransparent substrates,” Mater. Sci. Eng. B 5, 37–42 (1989).
[CrossRef]

Cantão, M. P.

M. M. Guraya, H. Ascolani, G. Zampieri, J. H. Dias da Silva, M. P. Cantão, J. I. Cisneros, “Electronic structure of amorphous Si–N compounds,” Phys. Rev. B 49, 13446–13451 (1994).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. I. Cisneros, J. H. Dias da Silva, M. P. Cantão, “Bond densities and electronic structure of amorphous SiNx:H,” Phys. Rev. B 42, 5677–5684 (1990).
[CrossRef]

Cardoso, L. P.

H. Dias da Silva, J. I. Cisneros, L. P. Cardoso, “Crystallization process and chemical disorder in flash evaporated amorphous gallium antimonide films,” Mater. Res. Soc. Symp. Proc. 321, 645–650 (1994).
[CrossRef]

Castro, S. G.

S. F. Durrant, S. G. Castro, J. I. Cisneros, N. C. da Cruz, M. A. Bica de Moraes, “Amorphous oxygen-containing hydrogenated carbon films formed by plasma-enhanced chemical vapor deposition,” J. Vac. Sci. Technol. A 14, 1–7 (1996).
[CrossRef]

Chambouleyron, I.

I. Chambouleyron, F. Marques, J. I. Cisneros, F. Alvarez, S. Moehlecke, W. Losch, I. Pereyra, “Optical properties of non-stoichiometric germanium nitride compounds (a-GeNx),” J. Non-Crystal. Solids 77 & 78, 1309–1312 (1985).
[CrossRef]

F. Alvarez, I. Chambouleyron, C. Constantino, J. I. Cisneros, “Doping effects in off-stoichiometric glow discharge amorphous silicon nitride,” Appl. Phys. Lett. 44, 116–118 (1984).
[CrossRef]

Cisneros, J. I.

J. Torres, J. I. Cisneros, G. Gordillo, F. Alvarez, “A simple method to determine the optical constants and thicknesses of ZnxCd1-xS thin films,” Thin Solid Films 289, 238–241 (1996).
[CrossRef]

S. F. Durrant, S. G. Castro, J. I. Cisneros, N. C. da Cruz, M. A. Bica de Moraes, “Amorphous oxygen-containing hydrogenated carbon films formed by plasma-enhanced chemical vapor deposition,” J. Vac. Sci. Technol. A 14, 1–7 (1996).
[CrossRef]

J. H. Dias da Silva, J. I. Cisneros, M. M. Guraya, G. Zampieri, “Effects of deviation from stoichiometry and thermal annealing on amorphous gallium antimonide films,” Phys. Rev. B. 51, 6272–6279 (1995).
[CrossRef]

H. Dias da Silva, J. I. Cisneros, L. P. Cardoso, “Crystallization process and chemical disorder in flash evaporated amorphous gallium antimonide films,” Mater. Res. Soc. Symp. Proc. 321, 645–650 (1994).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. H. Dias da Silva, M. P. Cantão, J. I. Cisneros, “Electronic structure of amorphous Si–N compounds,” Phys. Rev. B 49, 13446–13451 (1994).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. I. Cisneros, J. H. Dias da Silva, M. P. Cantão, “Bond densities and electronic structure of amorphous SiNx:H,” Phys. Rev. B 42, 5677–5684 (1990).
[CrossRef]

J. M. Berger, C. Ance, F. de Chelle, J. P. Ferraton, A. Donnadieu, J. I. Cisneros, J. H. Dias da Silva, “Temperature effects on the optical properties of amorphous hydrogenated silicon nitrogen alloys prepared by rf sputtering,” J. Non-Crystal. Solids 94, 353–364 (1987).
[CrossRef]

I. Chambouleyron, F. Marques, J. I. Cisneros, F. Alvarez, S. Moehlecke, W. Losch, I. Pereyra, “Optical properties of non-stoichiometric germanium nitride compounds (a-GeNx),” J. Non-Crystal. Solids 77 & 78, 1309–1312 (1985).
[CrossRef]

F. Alvarez, I. Chambouleyron, C. Constantino, J. I. Cisneros, “Doping effects in off-stoichiometric glow discharge amorphous silicon nitride,” Appl. Phys. Lett. 44, 116–118 (1984).
[CrossRef]

J. I. Cisneros, G. B. Rego, M. Tomiyama, S. Bilac, J. M. Gonçalves, A. E. Rodriguez, Z. P. Arguello, “A method for the determination of the complex refractive index of non metallic thin films using photometric measurements at normal incidence,” Thin Solid Films 100, 155–167 (1983).
[CrossRef]

Cody, G. D.

G. D. Cody, “The optical absorption edge of a-Si:H,” in Hydrogenated Amorphous Silicon, J. I. Pankove, ed., Vol. 21B of Semiconductors and Semimetals Series (Academic, Orlando, Fla., 1984), Chap. 2.

Constantino, C.

F. Alvarez, I. Chambouleyron, C. Constantino, J. I. Cisneros, “Doping effects in off-stoichiometric glow discharge amorphous silicon nitride,” Appl. Phys. Lett. 44, 116–118 (1984).
[CrossRef]

da Cruz, N. C.

S. F. Durrant, S. G. Castro, J. I. Cisneros, N. C. da Cruz, M. A. Bica de Moraes, “Amorphous oxygen-containing hydrogenated carbon films formed by plasma-enhanced chemical vapor deposition,” J. Vac. Sci. Technol. A 14, 1–7 (1996).
[CrossRef]

de Chelle, F.

J. M. Berger, C. Ance, F. de Chelle, J. P. Ferraton, A. Donnadieu, J. I. Cisneros, J. H. Dias da Silva, “Temperature effects on the optical properties of amorphous hydrogenated silicon nitrogen alloys prepared by rf sputtering,” J. Non-Crystal. Solids 94, 353–364 (1987).
[CrossRef]

Dias da Silva, H.

H. Dias da Silva, J. I. Cisneros, L. P. Cardoso, “Crystallization process and chemical disorder in flash evaporated amorphous gallium antimonide films,” Mater. Res. Soc. Symp. Proc. 321, 645–650 (1994).
[CrossRef]

Dias da Silva, J. H.

J. H. Dias da Silva, J. I. Cisneros, M. M. Guraya, G. Zampieri, “Effects of deviation from stoichiometry and thermal annealing on amorphous gallium antimonide films,” Phys. Rev. B. 51, 6272–6279 (1995).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. H. Dias da Silva, M. P. Cantão, J. I. Cisneros, “Electronic structure of amorphous Si–N compounds,” Phys. Rev. B 49, 13446–13451 (1994).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. I. Cisneros, J. H. Dias da Silva, M. P. Cantão, “Bond densities and electronic structure of amorphous SiNx:H,” Phys. Rev. B 42, 5677–5684 (1990).
[CrossRef]

J. M. Berger, C. Ance, F. de Chelle, J. P. Ferraton, A. Donnadieu, J. I. Cisneros, J. H. Dias da Silva, “Temperature effects on the optical properties of amorphous hydrogenated silicon nitrogen alloys prepared by rf sputtering,” J. Non-Crystal. Solids 94, 353–364 (1987).
[CrossRef]

Didomenico, M.

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

Donnadieu, A.

J. M. Berger, C. Ance, F. de Chelle, J. P. Ferraton, A. Donnadieu, J. I. Cisneros, J. H. Dias da Silva, “Temperature effects on the optical properties of amorphous hydrogenated silicon nitrogen alloys prepared by rf sputtering,” J. Non-Crystal. Solids 94, 353–364 (1987).
[CrossRef]

Durrant, S. F.

S. F. Durrant, S. G. Castro, J. I. Cisneros, N. C. da Cruz, M. A. Bica de Moraes, “Amorphous oxygen-containing hydrogenated carbon films formed by plasma-enhanced chemical vapor deposition,” J. Vac. Sci. Technol. A 14, 1–7 (1996).
[CrossRef]

El Grandi, R.

G. Galibert, K. Konan, R. El Grandi, J. Calas, J. L. Martin, “Accurate determination of the optical constants of absorbing thin films deposited on thick semitransparent substrates,” Mater. Sci. Eng. B 5, 37–42 (1989).
[CrossRef]

Ferraton, J. P.

J. M. Berger, C. Ance, F. de Chelle, J. P. Ferraton, A. Donnadieu, J. I. Cisneros, J. H. Dias da Silva, “Temperature effects on the optical properties of amorphous hydrogenated silicon nitrogen alloys prepared by rf sputtering,” J. Non-Crystal. Solids 94, 353–364 (1987).
[CrossRef]

Galibert, G.

G. Galibert, K. Konan, R. El Grandi, J. Calas, J. L. Martin, “Accurate determination of the optical constants of absorbing thin films deposited on thick semitransparent substrates,” Mater. Sci. Eng. B 5, 37–42 (1989).
[CrossRef]

Gonçalves, J. M.

J. I. Cisneros, G. B. Rego, M. Tomiyama, S. Bilac, J. M. Gonçalves, A. E. Rodriguez, Z. P. Arguello, “A method for the determination of the complex refractive index of non metallic thin films using photometric measurements at normal incidence,” Thin Solid Films 100, 155–167 (1983).
[CrossRef]

Gordillo, G.

J. Torres, J. I. Cisneros, G. Gordillo, F. Alvarez, “A simple method to determine the optical constants and thicknesses of ZnxCd1-xS thin films,” Thin Solid Films 289, 238–241 (1996).
[CrossRef]

Guraya, M. M.

J. H. Dias da Silva, J. I. Cisneros, M. M. Guraya, G. Zampieri, “Effects of deviation from stoichiometry and thermal annealing on amorphous gallium antimonide films,” Phys. Rev. B. 51, 6272–6279 (1995).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. H. Dias da Silva, M. P. Cantão, J. I. Cisneros, “Electronic structure of amorphous Si–N compounds,” Phys. Rev. B 49, 13446–13451 (1994).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. I. Cisneros, J. H. Dias da Silva, M. P. Cantão, “Bond densities and electronic structure of amorphous SiNx:H,” Phys. Rev. B 42, 5677–5684 (1990).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Films (Butterworth, London, 1969).

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, New York, 1971), Chap. 11.

Konan, K.

G. Galibert, K. Konan, R. El Grandi, J. Calas, J. L. Martin, “Accurate determination of the optical constants of absorbing thin films deposited on thick semitransparent substrates,” Mater. Sci. Eng. B 5, 37–42 (1989).
[CrossRef]

Losch, W.

I. Chambouleyron, F. Marques, J. I. Cisneros, F. Alvarez, S. Moehlecke, W. Losch, I. Pereyra, “Optical properties of non-stoichiometric germanium nitride compounds (a-GeNx),” J. Non-Crystal. Solids 77 & 78, 1309–1312 (1985).
[CrossRef]

Marques, F.

I. Chambouleyron, F. Marques, J. I. Cisneros, F. Alvarez, S. Moehlecke, W. Losch, I. Pereyra, “Optical properties of non-stoichiometric germanium nitride compounds (a-GeNx),” J. Non-Crystal. Solids 77 & 78, 1309–1312 (1985).
[CrossRef]

Martin, J. L.

G. Galibert, K. Konan, R. El Grandi, J. Calas, J. L. Martin, “Accurate determination of the optical constants of absorbing thin films deposited on thick semitransparent substrates,” Mater. Sci. Eng. B 5, 37–42 (1989).
[CrossRef]

Moehlecke, S.

I. Chambouleyron, F. Marques, J. I. Cisneros, F. Alvarez, S. Moehlecke, W. Losch, I. Pereyra, “Optical properties of non-stoichiometric germanium nitride compounds (a-GeNx),” J. Non-Crystal. Solids 77 & 78, 1309–1312 (1985).
[CrossRef]

Nilsson, P. O.

Pankove, J. I.

J. I. Pankove, Optical Processes in Semiconductors (Dover, New York, 1971), Chap. 3.

Pereyra, I.

I. Chambouleyron, F. Marques, J. I. Cisneros, F. Alvarez, S. Moehlecke, W. Losch, I. Pereyra, “Optical properties of non-stoichiometric germanium nitride compounds (a-GeNx),” J. Non-Crystal. Solids 77 & 78, 1309–1312 (1985).
[CrossRef]

Rego, G. B.

J. I. Cisneros, G. B. Rego, M. Tomiyama, S. Bilac, J. M. Gonçalves, A. E. Rodriguez, Z. P. Arguello, “A method for the determination of the complex refractive index of non metallic thin films using photometric measurements at normal incidence,” Thin Solid Films 100, 155–167 (1983).
[CrossRef]

Rodriguez, A. E.

J. I. Cisneros, G. B. Rego, M. Tomiyama, S. Bilac, J. M. Gonçalves, A. E. Rodriguez, Z. P. Arguello, “A method for the determination of the complex refractive index of non metallic thin films using photometric measurements at normal incidence,” Thin Solid Films 100, 155–167 (1983).
[CrossRef]

Swanepoel, R.

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

Tauc, J.

J. Tauc, “Optical properties and electronic structure of amorphous semiconductors,” in Optical Properties of Solids, S. Nudelman, S. Mitra, eds. (Plenum, New York, 1969), Chap. 5.
[CrossRef]

Thèye, M. L.

F. Abelès, M. L. Thèye, “Méthode de calcul des constantes optiques des couches minces absorbantes à partir des mesures de réflexion et de transmission,” Surf. Sci. 5, 325–331 (1966).
[CrossRef]

Tomiyama, M.

J. I. Cisneros, G. B. Rego, M. Tomiyama, S. Bilac, J. M. Gonçalves, A. E. Rodriguez, Z. P. Arguello, “A method for the determination of the complex refractive index of non metallic thin films using photometric measurements at normal incidence,” Thin Solid Films 100, 155–167 (1983).
[CrossRef]

Torres, J.

J. Torres, J. I. Cisneros, G. Gordillo, F. Alvarez, “A simple method to determine the optical constants and thicknesses of ZnxCd1-xS thin films,” Thin Solid Films 289, 238–241 (1996).
[CrossRef]

Wemple, S. H.

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

Wohlgemuth, J. H.

J. H. Wohlgemuth, D. E. Brodie, “A method for calculating the index of refraction of thin films,” Can. J. Phys. 53, 1737–1742 (1975).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

Zampieri, G.

J. H. Dias da Silva, J. I. Cisneros, M. M. Guraya, G. Zampieri, “Effects of deviation from stoichiometry and thermal annealing on amorphous gallium antimonide films,” Phys. Rev. B. 51, 6272–6279 (1995).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. H. Dias da Silva, M. P. Cantão, J. I. Cisneros, “Electronic structure of amorphous Si–N compounds,” Phys. Rev. B 49, 13446–13451 (1994).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. I. Cisneros, J. H. Dias da Silva, M. P. Cantão, “Bond densities and electronic structure of amorphous SiNx:H,” Phys. Rev. B 42, 5677–5684 (1990).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

F. Alvarez, I. Chambouleyron, C. Constantino, J. I. Cisneros, “Doping effects in off-stoichiometric glow discharge amorphous silicon nitride,” Appl. Phys. Lett. 44, 116–118 (1984).
[CrossRef]

Can. J. Phys. (1)

J. H. Wohlgemuth, D. E. Brodie, “A method for calculating the index of refraction of thin films,” Can. J. Phys. 53, 1737–1742 (1975).
[CrossRef]

J. Non-Crystal. Solids (2)

I. Chambouleyron, F. Marques, J. I. Cisneros, F. Alvarez, S. Moehlecke, W. Losch, I. Pereyra, “Optical properties of non-stoichiometric germanium nitride compounds (a-GeNx),” J. Non-Crystal. Solids 77 & 78, 1309–1312 (1985).
[CrossRef]

J. M. Berger, C. Ance, F. de Chelle, J. P. Ferraton, A. Donnadieu, J. I. Cisneros, J. H. Dias da Silva, “Temperature effects on the optical properties of amorphous hydrogenated silicon nitrogen alloys prepared by rf sputtering,” J. Non-Crystal. Solids 94, 353–364 (1987).
[CrossRef]

J. Phys. E (1)

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

J. Vac. Sci. Technol. A (1)

S. F. Durrant, S. G. Castro, J. I. Cisneros, N. C. da Cruz, M. A. Bica de Moraes, “Amorphous oxygen-containing hydrogenated carbon films formed by plasma-enhanced chemical vapor deposition,” J. Vac. Sci. Technol. A 14, 1–7 (1996).
[CrossRef]

Mater. Res. Soc. Symp. Proc. (1)

H. Dias da Silva, J. I. Cisneros, L. P. Cardoso, “Crystallization process and chemical disorder in flash evaporated amorphous gallium antimonide films,” Mater. Res. Soc. Symp. Proc. 321, 645–650 (1994).
[CrossRef]

Mater. Sci. Eng. B (1)

G. Galibert, K. Konan, R. El Grandi, J. Calas, J. L. Martin, “Accurate determination of the optical constants of absorbing thin films deposited on thick semitransparent substrates,” Mater. Sci. Eng. B 5, 37–42 (1989).
[CrossRef]

Phys. Rev. B (3)

M. M. Guraya, H. Ascolani, G. Zampieri, J. I. Cisneros, J. H. Dias da Silva, M. P. Cantão, “Bond densities and electronic structure of amorphous SiNx:H,” Phys. Rev. B 42, 5677–5684 (1990).
[CrossRef]

M. M. Guraya, H. Ascolani, G. Zampieri, J. H. Dias da Silva, M. P. Cantão, J. I. Cisneros, “Electronic structure of amorphous Si–N compounds,” Phys. Rev. B 49, 13446–13451 (1994).
[CrossRef]

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

Phys. Rev. B. (1)

J. H. Dias da Silva, J. I. Cisneros, M. M. Guraya, G. Zampieri, “Effects of deviation from stoichiometry and thermal annealing on amorphous gallium antimonide films,” Phys. Rev. B. 51, 6272–6279 (1995).
[CrossRef]

Surf. Sci. (1)

F. Abelès, M. L. Thèye, “Méthode de calcul des constantes optiques des couches minces absorbantes à partir des mesures de réflexion et de transmission,” Surf. Sci. 5, 325–331 (1966).
[CrossRef]

Thin Solid Films (2)

J. Torres, J. I. Cisneros, G. Gordillo, F. Alvarez, “A simple method to determine the optical constants and thicknesses of ZnxCd1-xS thin films,” Thin Solid Films 289, 238–241 (1996).
[CrossRef]

J. I. Cisneros, G. B. Rego, M. Tomiyama, S. Bilac, J. M. Gonçalves, A. E. Rodriguez, Z. P. Arguello, “A method for the determination of the complex refractive index of non metallic thin films using photometric measurements at normal incidence,” Thin Solid Films 100, 155–167 (1983).
[CrossRef]

Other (6)

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).

Z. Knittl, Optics of Thin Films (Wiley, New York, 1971), Chap. 11.

O. S. Heavens, Optical Properties of Thin Films (Butterworth, London, 1969).

J. I. Pankove, Optical Processes in Semiconductors (Dover, New York, 1971), Chap. 3.

G. D. Cody, “The optical absorption edge of a-Si:H,” in Hydrogenated Amorphous Silicon, J. I. Pankove, ed., Vol. 21B of Semiconductors and Semimetals Series (Academic, Orlando, Fla., 1984), Chap. 2.

J. Tauc, “Optical properties and electronic structure of amorphous semiconductors,” in Optical Properties of Solids, S. Nudelman, S. Mitra, eds. (Plenum, New York, 1969), Chap. 5.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Optical parameters and directions of the transmittance and reflectance adopted for the film–substrate assembly: (a) semi-infinite substrate, (b) finite substrate.

Fig. 2
Fig. 2

Calculated transmittance of a thin transparent film when n 2 < n 3 (upper curve) and n 2 > n 3 (lower curve), showing the points where the transmittance of the film is tangential to the transmittance of the substrate (even orders of interference). The interference order m is indicated at each extremum. The refractive indices are n 1 = 1, n 2 = 2, n 2 = 3.8, and n 3 = 3.

Fig. 3
Fig. 3

Experimental transmission spectrum of an a-Si x N1-x :H film, showing the interference (low-absorption) region and the absorption edge. The transmission is plotted as a function of the wave number to show the details of the absorption edge.

Fig. 4
Fig. 4

Refractive index of the film of Fig. 3, including the experimental points and the W-D fitting. Inset, W-D plot used in determining the parameters E m and E d of the model.

Fig. 5
Fig. 5

Absorption coefficient of the film of Fig. 3. The results cover the low-absorption region and the absorption edge. The Tauc plot for the determination of the optical gap is shown in the inset.

Tables (4)

Tables Icon

Table 1 Determination of Refractive Index n2 and Film Thickness d of an a-Si x N1-x Film by the Method of Section 3 (Transparent Film)

Tables Icon

Table 2 Calculation of the Absorption Coefficient of the a-Si x N1-x Film for Even Orders (Subsection 4.A, Low Absorption Region)a

Tables Icon

Table 3 Calculation of Refractive Index n2 and Thickness d for the Odd Orders (Subsection 4.A)a

Tables Icon

Table 4 Calculation of the Absorption Coefficient at the Absorption Edge (Subsection 4.B)

Equations (47)

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r ij = N i - N j N i + N j ,     t ij = 2 N i N i + N j .
t 123 = t 12 t 23 exp i Ψ / 2 1 + r 12 r 23 exp i Ψ ,
t 321 = t 32 t 21 exp i Ψ / 2 1 + r 32 r 21 exp i Ψ ,
r 123 = r 12 + r 23 exp i Ψ 1 + r 12 r 23 exp i Ψ ,
r 321 = r 32 + r 21 exp i Ψ 1 + r 32 r 21 exp i Ψ ,
ψ = 4 π N 2 d / λ
Re Ψ = 4 π n 2 d / λ = φ ,
Im Ψ = 4 π k 2 d / λ = α d .
R 123 = r 123 r 123 * ,
R 321 = r 321 r 321 * ,
T 123 = n 3 / n 1 t 123 t 123 * .
R = R 123 + T 123 2 - R 123 R 321 ρ U 2 1 - ρ R 321 U 2 ,
R = 1 - 2 ρ R 321 U 2 + ρ 1 - ρ R 321 U 2 ,
T = 1 - ρ T 123 U 1 - ρ R 321 U 2 .
ρ = n 1 - n 3 2 + k 3 2 / n 1 + n 3 2 + k 3 2
T = A   exp α d B   exp 2 α d + C   exp α d + D ,
4 π n 2 d / λ m = m π ,
φ = m π .
T even = 2 n 1 n 3 n 1 2 + n 3 2 ,
T odd = 4 n 1 n 2 2 n 3 n 1 2 + n 2 2 n 2 2 + n 3 2 .
m - 1 λ m - 1 m λ m m + 1 λ m + 1 .
m λ m - 1 + λ m + 1 λ m - 1 - λ m + 1 , m λ m - 1 λ m - 1 - λ m , m λ m + 1 λ m - λ m + 1 .
s λ m = dn 2 λ m = m λ m / 4 ,
n 2 = β ± β 2 - n 1 2 n 3 2 1 / 2 1 / 2 ,
β = 2 n 1 n 3 T odd - n 1 2 + n 3 2 2 .
n 2 E = 1 + E m E d E m 2 - E 2 ,
T n 2 ,   k 2 ,   λ ,   d ,   n 1 ,   n 3 - T exp = 0 ,
exp α d = 1 2 B A T exp - C + A T exp - C 2 - 4 BD 1 / 2 ,
α = α 0 exp E / E 0 .
E ε 2 = γ E - E g ,
α nE = β E - E g ,
A = 16 n 3 1 - ρ n 2 2 + k 2 2 U ,
B = st - Usv ρ ,
C = 2 4 n 3 k 2 2 - ZY cos   φ + 4 k 2 n 3 Y + Z sin   φ - ρ U 2 4 k 2 Z - n 3 Y sin   φ - 2 ZY + 4 n 3 k 2 2 cos   φ ,
D = uv - U 2 tu ρ ,
u = n 1 - n 2 2 + k 2 2 ,
v = n 2 - n 3 2 + k 2 2 ,
s = n 1 + n 2 2 + k 2 2 ,
t = n 2 + n 3 2 + k 2 2 ,
Y = n 2 2 - n 1 2 + k 2 2 ,
Z = n 2 2 - n 3 2 + k 2 2 .
T S = 1 - ρ 1 + ρ ,
R S = 2 ρ 1 + ρ ,
n 3 = n 1 1 T s + 1 T s 2 - 1 1 / 2 .
T S = 1 - ρ 2 exp - α s d s 1 - ρ 2 exp - 2 α s d s
R S = ρ 1 + 1 - ρ 2 exp - 2 α s d s 1 - ρ 2 exp - 2 α s d s ,
U - 1 = 1 - ρ 2 2 T s + 1 - ρ 4 4 T s 2 + ρ 2 1 / 2 .

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