Abstract

The optical response of coherent thin-film multilayers is often represented with Fresnel coefficients in a 2 × 2 matrix configuration. Here the usual transfer matrix was modified to a generic form, with the ability to use the absolute squares of the Fresnel coefficients, so as to include incoherent (thick layers) and partially coherent (rough surface or interfaces) reflection and transmission. The method is integrated by use of models for refractive-index depth profiling. The utility of the method is illustrated with various multilayer structures formed by ion implantation into Si, including buried insulating and conducting layers, and multilayers with a thick incoherent layer in an arbitrary position.

© 2002 Optical Society of America

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    [CrossRef]
  9. C. C. Katsidis, D. I. Siapkas, D. Panknin, N. Hatzopoulos, W. Skorupa, “Optical characterization of doped Simox structures using FTIR spectroscopy,” Microelectron. Eng. 28, 439–442 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  32. D. I. 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]
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2001

R. Z. Vitlina, G. I. Surdutovich, “A ‘blurred film’ model in polarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D. Appl. Phys. 34, 2593–2598 (2001).
[CrossRef]

C. C. Katsidis, D. I. Siapkas, A. K. Robinson, P. L. F. Hemment, “Formation of conducting and insulating layered structures in Si by ion implantation: process control using FTIR spectroscopy,” J. Electrochem. Soc. 148, G704–G716 (2001).
[CrossRef]

2000

N. Hatzopoulos, W. Skorupa, D. Siapkas, “Double Simox structures formed by sequential high energy oxygen implantation into silicon,” J. Electrochem. Soc. 147, 354–362 (2000).
[CrossRef]

1997

1996

D. I. Siapkas, N. Hatzopoulos, C. C. Katsidis, T. Zorba, C. L. Mitsas, P. L. F. Hemment, “Structural and compositional characterization of high energy separation by implantation of oxygen structures using infrared spectroscopy,” J. Electrochem. Soc. 143, 3019–3032 (1996).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, W. Skorupa, “Formation and characterization of novel Si/SiO2 multilayer structures by oxygen ion implantation into silicon,” J. Appl. Phys. 80, 4960–4970 (1996).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Optical investigation of structures formed by 2MeV oxygen implantation into silicon,” Thin Solid Films 289, 90–94 (1996).
[CrossRef]

1995

C. C. Katsidis, D. I. Siapkas, D. Panknin, N. Hatzopoulos, W. Skorupa, “Optical characterization of doped Simox structures using FTIR spectroscopy,” Microelectron. Eng. 28, 439–442 (1995).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Oxide growth, refractive index, and composition depth profiles of structures formed by 2 MeV oxygen implantation into silicon,” J. Appl. Phys. 77, 577–586 (1995).
[CrossRef]

C. L. Mitsas, D. I. Siapkas, “Generalized matrix method for analysis of coherent and incoherent reflectance and transmittance of multiplayer structures with rough surfaces, interfaces, and finite substrates,” Appl. Opt. 34, 1678–1683 (1995).
[CrossRef] [PubMed]

J. Stoemenos, A. Carcia, B. Aspar, J. Margail, “Silicon on insulator obtained by high dose oxygen implantation, microstructure, and formation mechanism,” J. Electrochem. Soc. 142, 1248–1259 (1995).
[CrossRef]

1993

Z. Wenhua, L. Chenglu, S. Zuoyu, Z. Shichang, P. L. F. Hemment, A. Nejim, “Electrical characterization of thin film Simox structures,” Nucl. Instrum. Meth. B 74, 218–221 (1993).
[CrossRef]

1991

D. I. 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]

1990

A. K. Robinson, K. J. Reeson, P. L. F. Hemment, “Redistribution and electrical activation of implanted arsenic in silicon on insulator substrates formed by oxygen ion implantation,” J. Appl. Phys. 68, 4340–4342 (1990).
[CrossRef]

1989

1988

1985

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

1983

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

1981

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

1977

J. Szczyrbowski, A. Czapla, “Optical absorption in d.c. sputtered InAs films,” Thin Solid Films 46, 127–137 (1977).
[CrossRef]

1976

W. Tennant, J. Cape, “Study of the dielectric function of PbSnTe epitaxial film by far-infrared reflectivity,” Phys. Rev. B 13, 2540–2547 (1976).
[CrossRef]

1972

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

1971

C. J. Gabriel, A. Nedoluha, “Transmittance and reflectance of systems of thin and thick layers,” Opt. Acta 18, 415–423 (1971).
[CrossRef]

1968

A. M. Dioffo, “Étude théorique des caractéristiques optiques d’un système de lames diélectriques,” Rev. Opt. 47, 49–68 (1968).

1961

Aspar, B.

J. Stoemenos, A. Carcia, B. Aspar, J. Margail, “Silicon on insulator obtained by high dose oxygen implantation, microstructure, and formation mechanism,” J. Electrochem. Soc. 142, 1248–1259 (1995).
[CrossRef]

Bennett, H. E.

Bergquist, M.

Born, M.

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964), p. 254.

Burkey, B. C.

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

Cape, J.

W. Tennant, J. Cape, “Study of the dielectric function of PbSnTe epitaxial film by far-infrared reflectivity,” Phys. Rev. B 13, 2540–2547 (1976).
[CrossRef]

Carcia, A.

J. Stoemenos, A. Carcia, B. Aspar, J. Margail, “Silicon on insulator obtained by high dose oxygen implantation, microstructure, and formation mechanism,” J. Electrochem. Soc. 142, 1248–1259 (1995).
[CrossRef]

Chenglu, L.

Z. Wenhua, L. Chenglu, S. Zuoyu, Z. Shichang, P. L. F. Hemment, A. Nejim, “Electrical characterization of thin film Simox structures,” Nucl. Instrum. Meth. B 74, 218–221 (1993).
[CrossRef]

Czapla, A.

J. Szczyrbowski, A. Czapla, “Optical absorption in d.c. sputtered InAs films,” Thin Solid Films 46, 127–137 (1977).
[CrossRef]

Dioffo, A. M.

A. M. Dioffo, “Étude théorique des caractéristiques optiques d’un système de lames diélectriques,” Rev. Opt. 47, 49–68 (1968).

Dobrowolski, J.

Fillinski, I.

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

Fredrickson, J. E.

G. K. Hubler, P. R. Malmberg, C. N. Waddell, W. G. Spitzer, J. E. Fredrickson, in Ion Implantation for Materials Processing, F. A. Smidt, ed. (Noyes Data, Park Ridge, N.J., 1983), p. 195–218.

Gabriel, C. J.

C. J. Gabriel, A. Nedoluha, “Transmittance and reflectance of systems of thin and thick layers,” Opt. Acta 18, 415–423 (1971).
[CrossRef]

Hatzopoulos, N.

N. Hatzopoulos, W. Skorupa, D. Siapkas, “Double Simox structures formed by sequential high energy oxygen implantation into silicon,” J. Electrochem. Soc. 147, 354–362 (2000).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, W. Skorupa, “Formation and characterization of novel Si/SiO2 multilayer structures by oxygen ion implantation into silicon,” J. Appl. Phys. 80, 4960–4970 (1996).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Optical investigation of structures formed by 2MeV oxygen implantation into silicon,” Thin Solid Films 289, 90–94 (1996).
[CrossRef]

D. I. Siapkas, N. Hatzopoulos, C. C. Katsidis, T. Zorba, C. L. Mitsas, P. L. F. Hemment, “Structural and compositional characterization of high energy separation by implantation of oxygen structures using infrared spectroscopy,” J. Electrochem. Soc. 143, 3019–3032 (1996).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Oxide growth, refractive index, and composition depth profiles of structures formed by 2 MeV oxygen implantation into silicon,” J. Appl. Phys. 77, 577–586 (1995).
[CrossRef]

C. C. Katsidis, D. I. Siapkas, D. Panknin, N. Hatzopoulos, W. Skorupa, “Optical characterization of doped Simox structures using FTIR spectroscopy,” Microelectron. Eng. 28, 439–442 (1995).
[CrossRef]

C. C. Katsidis, D. I. Siapkas, W. Skorupa, N. Hatzopoulos, D. Panknin, Proceedings of the 10th International Conference on Ion Implantation Technology (Elsevier, Amsterdam, 1995), p. 959–962.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Films (Dover, New York, 1965), p. 69.

Hemment, P. L. F.

C. C. Katsidis, D. I. Siapkas, A. K. Robinson, P. L. F. Hemment, “Formation of conducting and insulating layered structures in Si by ion implantation: process control using FTIR spectroscopy,” J. Electrochem. Soc. 148, G704–G716 (2001).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Optical investigation of structures formed by 2MeV oxygen implantation into silicon,” Thin Solid Films 289, 90–94 (1996).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, W. Skorupa, “Formation and characterization of novel Si/SiO2 multilayer structures by oxygen ion implantation into silicon,” J. Appl. Phys. 80, 4960–4970 (1996).
[CrossRef]

D. I. Siapkas, N. Hatzopoulos, C. C. Katsidis, T. Zorba, C. L. Mitsas, P. L. F. Hemment, “Structural and compositional characterization of high energy separation by implantation of oxygen structures using infrared spectroscopy,” J. Electrochem. Soc. 143, 3019–3032 (1996).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Oxide growth, refractive index, and composition depth profiles of structures formed by 2 MeV oxygen implantation into silicon,” J. Appl. Phys. 77, 577–586 (1995).
[CrossRef]

Z. Wenhua, L. Chenglu, S. Zuoyu, Z. Shichang, P. L. F. Hemment, A. Nejim, “Electrical characterization of thin film Simox structures,” Nucl. Instrum. Meth. B 74, 218–221 (1993).
[CrossRef]

A. K. Robinson, K. J. Reeson, P. L. F. Hemment, “Redistribution and electrical activation of implanted arsenic in silicon on insulator substrates formed by oxygen ion implantation,” J. Appl. Phys. 68, 4340–4342 (1990).
[CrossRef]

Hubler, G. K.

G. K. Hubler, P. R. Malmberg, C. N. Waddell, W. G. Spitzer, J. E. Fredrickson, in Ion Implantation for Materials Processing, F. A. Smidt, ed. (Noyes Data, Park Ridge, N.J., 1983), p. 195–218.

Katsidis, C. C.

C. C. Katsidis, D. I. Siapkas, A. K. Robinson, P. L. F. Hemment, “Formation of conducting and insulating layered structures in Si by ion implantation: process control using FTIR spectroscopy,” J. Electrochem. Soc. 148, G704–G716 (2001).
[CrossRef]

D. I. Siapkas, N. Hatzopoulos, C. C. Katsidis, T. Zorba, C. L. Mitsas, P. L. F. Hemment, “Structural and compositional characterization of high energy separation by implantation of oxygen structures using infrared spectroscopy,” J. Electrochem. Soc. 143, 3019–3032 (1996).
[CrossRef]

C. C. Katsidis, D. I. Siapkas, D. Panknin, N. Hatzopoulos, W. Skorupa, “Optical characterization of doped Simox structures using FTIR spectroscopy,” Microelectron. Eng. 28, 439–442 (1995).
[CrossRef]

C. C. Katsidis, D. I. Siapkas, W. Skorupa, N. Hatzopoulos, D. Panknin, Proceedings of the 10th International Conference on Ion Implantation Technology (Elsevier, Amsterdam, 1995), p. 959–962.

C. C. Katsidis, D. I. Siapkas, in Proceedings of NATO ASI on Application of Particle and Laser Beams in Materials Technology, P. Misaelides, ed. (Kluwer Academic, Dordrecht, 1995), p. 603–612.
[CrossRef]

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, London, 1976), p. 41.

Krishnan, K.

K. Krishnan, P. J. Stout, M. Watanabe, Practical Fourier Transform Infrared Spectroscopy (Academic, New York, 1990), p. 294.

Kushev, D. B.

D. I. 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]

Lelidis, I.

D. I. 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]

Lubberts, G.

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

Malmberg, P. R.

G. K. Hubler, P. R. Malmberg, C. N. Waddell, W. G. Spitzer, J. E. Fredrickson, in Ion Implantation for Materials Processing, F. A. Smidt, ed. (Noyes Data, Park Ridge, N.J., 1983), p. 195–218.

Margail, J.

J. Stoemenos, A. Carcia, B. Aspar, J. Margail, “Silicon on insulator obtained by high dose oxygen implantation, microstructure, and formation mechanism,” J. Electrochem. Soc. 142, 1248–1259 (1995).
[CrossRef]

Mitsas, C. L.

D. I. Siapkas, N. Hatzopoulos, C. C. Katsidis, T. Zorba, C. L. Mitsas, P. L. F. Hemment, “Structural and compositional characterization of high energy separation by implantation of oxygen structures using infrared spectroscopy,” J. Electrochem. Soc. 143, 3019–3032 (1996).
[CrossRef]

C. L. Mitsas, D. I. Siapkas, “Generalized matrix method for analysis of coherent and incoherent reflectance and transmittance of multiplayer structures with rough surfaces, interfaces, and finite substrates,” Appl. Opt. 34, 1678–1683 (1995).
[CrossRef] [PubMed]

Moser, F.

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

Nedoluha, A.

C. J. Gabriel, A. Nedoluha, “Transmittance and reflectance of systems of thin and thick layers,” Opt. Acta 18, 415–423 (1971).
[CrossRef]

Nejim, A.

Z. Wenhua, L. Chenglu, S. Zuoyu, Z. Shichang, P. L. F. Hemment, A. Nejim, “Electrical characterization of thin film Simox structures,” Nucl. Instrum. Meth. B 74, 218–221 (1993).
[CrossRef]

Panknin, D.

C. C. Katsidis, D. I. Siapkas, D. Panknin, N. Hatzopoulos, W. Skorupa, “Optical characterization of doped Simox structures using FTIR spectroscopy,” Microelectron. Eng. 28, 439–442 (1995).
[CrossRef]

C. C. Katsidis, D. I. Siapkas, W. Skorupa, N. Hatzopoulos, D. Panknin, Proceedings of the 10th International Conference on Ion Implantation Technology (Elsevier, Amsterdam, 1995), p. 959–962.

Pawlikovski, J.

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

Porteus, J. O.

Reeson, K. J.

A. K. Robinson, K. J. Reeson, P. L. F. Hemment, “Redistribution and electrical activation of implanted arsenic in silicon on insulator substrates formed by oxygen ion implantation,” J. Appl. Phys. 68, 4340–4342 (1990).
[CrossRef]

Ribbing, C.

Robinson, A. K.

C. C. Katsidis, D. I. Siapkas, A. K. Robinson, P. L. F. Hemment, “Formation of conducting and insulating layered structures in Si by ion implantation: process control using FTIR spectroscopy,” J. Electrochem. Soc. 148, G704–G716 (2001).
[CrossRef]

A. K. Robinson, K. J. Reeson, P. L. F. Hemment, “Redistribution and electrical activation of implanted arsenic in silicon on insulator substrates formed by oxygen ion implantation,” J. Appl. Phys. 68, 4340–4342 (1990).
[CrossRef]

Roos, A.

Shichang, Z.

Z. Wenhua, L. Chenglu, S. Zuoyu, Z. Shichang, P. L. F. Hemment, A. Nejim, “Electrical characterization of thin film Simox structures,” Nucl. Instrum. Meth. B 74, 218–221 (1993).
[CrossRef]

Siapkas, D.

N. Hatzopoulos, W. Skorupa, D. Siapkas, “Double Simox structures formed by sequential high energy oxygen implantation into silicon,” J. Electrochem. Soc. 147, 354–362 (2000).
[CrossRef]

Siapkas, D. I.

C. C. Katsidis, D. I. Siapkas, A. K. Robinson, P. L. F. Hemment, “Formation of conducting and insulating layered structures in Si by ion implantation: process control using FTIR spectroscopy,” J. Electrochem. Soc. 148, G704–G716 (2001).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, W. Skorupa, “Formation and characterization of novel Si/SiO2 multilayer structures by oxygen ion implantation into silicon,” J. Appl. Phys. 80, 4960–4970 (1996).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Optical investigation of structures formed by 2MeV oxygen implantation into silicon,” Thin Solid Films 289, 90–94 (1996).
[CrossRef]

D. I. Siapkas, N. Hatzopoulos, C. C. Katsidis, T. Zorba, C. L. Mitsas, P. L. F. Hemment, “Structural and compositional characterization of high energy separation by implantation of oxygen structures using infrared spectroscopy,” J. Electrochem. Soc. 143, 3019–3032 (1996).
[CrossRef]

C. L. Mitsas, D. I. Siapkas, “Generalized matrix method for analysis of coherent and incoherent reflectance and transmittance of multiplayer structures with rough surfaces, interfaces, and finite substrates,” Appl. Opt. 34, 1678–1683 (1995).
[CrossRef] [PubMed]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Oxide growth, refractive index, and composition depth profiles of structures formed by 2 MeV oxygen implantation into silicon,” J. Appl. Phys. 77, 577–586 (1995).
[CrossRef]

C. C. Katsidis, D. I. Siapkas, D. Panknin, N. Hatzopoulos, W. Skorupa, “Optical characterization of doped Simox structures using FTIR spectroscopy,” Microelectron. Eng. 28, 439–442 (1995).
[CrossRef]

D. I. 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]

C. C. Katsidis, D. I. Siapkas, in Proceedings of NATO ASI on Application of Particle and Laser Beams in Materials Technology, P. Misaelides, ed. (Kluwer Academic, Dordrecht, 1995), p. 603–612.
[CrossRef]

C. C. Katsidis, D. I. Siapkas, W. Skorupa, N. Hatzopoulos, D. Panknin, Proceedings of the 10th International Conference on Ion Implantation Technology (Elsevier, Amsterdam, 1995), p. 959–962.

Siapkas, J.

D. I. 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]

Skorupa, W.

N. Hatzopoulos, W. Skorupa, D. Siapkas, “Double Simox structures formed by sequential high energy oxygen implantation into silicon,” J. Electrochem. Soc. 147, 354–362 (2000).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, W. Skorupa, “Formation and characterization of novel Si/SiO2 multilayer structures by oxygen ion implantation into silicon,” J. Appl. Phys. 80, 4960–4970 (1996).
[CrossRef]

C. C. Katsidis, D. I. Siapkas, D. Panknin, N. Hatzopoulos, W. Skorupa, “Optical characterization of doped Simox structures using FTIR spectroscopy,” Microelectron. Eng. 28, 439–442 (1995).
[CrossRef]

C. C. Katsidis, D. I. Siapkas, W. Skorupa, N. Hatzopoulos, D. Panknin, Proceedings of the 10th International Conference on Ion Implantation Technology (Elsevier, Amsterdam, 1995), p. 959–962.

Spitzer, W. G.

G. K. Hubler, P. R. Malmberg, C. N. Waddell, W. G. Spitzer, J. E. Fredrickson, in Ion Implantation for Materials Processing, F. A. Smidt, ed. (Noyes Data, Park Ridge, N.J., 1983), p. 195–218.

Stoemenos, J.

J. Stoemenos, A. Carcia, B. Aspar, J. Margail, “Silicon on insulator obtained by high dose oxygen implantation, microstructure, and formation mechanism,” J. Electrochem. Soc. 142, 1248–1259 (1995).
[CrossRef]

Stout, P. J.

K. Krishnan, P. J. Stout, M. Watanabe, Practical Fourier Transform Infrared Spectroscopy (Academic, New York, 1990), p. 294.

Sullivan, B.

Surdutovich, G. I.

R. Z. Vitlina, G. I. Surdutovich, “A ‘blurred film’ model in polarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D. Appl. Phys. 34, 2593–2598 (2001).
[CrossRef]

Swanepoel, R.

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

Szczyrbowski, J.

J. Szczyrbowski, A. Czapla, “Optical absorption in d.c. sputtered InAs films,” Thin Solid Films 46, 127–137 (1977).
[CrossRef]

Tennant, W.

W. Tennant, J. Cape, “Study of the dielectric function of PbSnTe epitaxial film by far-infrared reflectivity,” Phys. Rev. B 13, 2540–2547 (1976).
[CrossRef]

Tikhonravov, A.

Trabka, E. A.

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

Trubetskov, M.

Vitlina, R. Z.

R. Z. Vitlina, G. I. Surdutovich, “A ‘blurred film’ model in polarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D. Appl. Phys. 34, 2593–2598 (2001).
[CrossRef]

Waddell, C. N.

G. K. Hubler, P. R. Malmberg, C. N. Waddell, W. G. Spitzer, J. E. Fredrickson, in Ion Implantation for Materials Processing, F. A. Smidt, ed. (Noyes Data, Park Ridge, N.J., 1983), p. 195–218.

Watanabe, M.

K. Krishnan, P. J. Stout, M. Watanabe, Practical Fourier Transform Infrared Spectroscopy (Academic, New York, 1990), p. 294.

Wenhua, Z.

Z. Wenhua, L. Chenglu, S. Zuoyu, Z. Shichang, P. L. F. Hemment, A. Nejim, “Electrical characterization of thin film Simox structures,” Nucl. Instrum. Meth. B 74, 218–221 (1993).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964), p. 254.

Yeh, P.

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

Zheleva, N. N.

D. I. 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]

Zorba, T.

D. I. Siapkas, N. Hatzopoulos, C. C. Katsidis, T. Zorba, C. L. Mitsas, P. L. F. Hemment, “Structural and compositional characterization of high energy separation by implantation of oxygen structures using infrared spectroscopy,” J. Electrochem. Soc. 143, 3019–3032 (1996).
[CrossRef]

Zuoyu, S.

Z. Wenhua, L. Chenglu, S. Zuoyu, Z. Shichang, P. L. F. Hemment, A. Nejim, “Electrical characterization of thin film Simox structures,” Nucl. Instrum. Meth. B 74, 218–221 (1993).
[CrossRef]

Appl. Opt.

Infrared Phys.

D. I. 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]

J. Appl. Phys.

A. K. Robinson, K. J. Reeson, P. L. F. Hemment, “Redistribution and electrical activation of implanted arsenic in silicon on insulator substrates formed by oxygen ion implantation,” J. Appl. Phys. 68, 4340–4342 (1990).
[CrossRef]

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

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Oxide growth, refractive index, and composition depth profiles of structures formed by 2 MeV oxygen implantation into silicon,” J. Appl. Phys. 77, 577–586 (1995).
[CrossRef]

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, W. Skorupa, “Formation and characterization of novel Si/SiO2 multilayer structures by oxygen ion implantation into silicon,” J. Appl. Phys. 80, 4960–4970 (1996).
[CrossRef]

J. Electrochem. Soc.

C. C. Katsidis, D. I. Siapkas, A. K. Robinson, P. L. F. Hemment, “Formation of conducting and insulating layered structures in Si by ion implantation: process control using FTIR spectroscopy,” J. Electrochem. Soc. 148, G704–G716 (2001).
[CrossRef]

D. I. Siapkas, N. Hatzopoulos, C. C. Katsidis, T. Zorba, C. L. Mitsas, P. L. F. Hemment, “Structural and compositional characterization of high energy separation by implantation of oxygen structures using infrared spectroscopy,” J. Electrochem. Soc. 143, 3019–3032 (1996).
[CrossRef]

J. Stoemenos, A. Carcia, B. Aspar, J. Margail, “Silicon on insulator obtained by high dose oxygen implantation, microstructure, and formation mechanism,” J. Electrochem. Soc. 142, 1248–1259 (1995).
[CrossRef]

N. Hatzopoulos, W. Skorupa, D. Siapkas, “Double Simox structures formed by sequential high energy oxygen implantation into silicon,” J. Electrochem. Soc. 147, 354–362 (2000).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. D. Appl. Phys.

R. Z. Vitlina, G. I. Surdutovich, “A ‘blurred film’ model in polarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D. Appl. Phys. 34, 2593–2598 (2001).
[CrossRef]

J. Phys. E

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

Microelectron. Eng.

C. C. Katsidis, D. I. Siapkas, D. Panknin, N. Hatzopoulos, W. Skorupa, “Optical characterization of doped Simox structures using FTIR spectroscopy,” Microelectron. Eng. 28, 439–442 (1995).
[CrossRef]

Nucl. Instrum. Meth. B

Z. Wenhua, L. Chenglu, S. Zuoyu, Z. Shichang, P. L. F. Hemment, A. Nejim, “Electrical characterization of thin film Simox structures,” Nucl. Instrum. Meth. B 74, 218–221 (1993).
[CrossRef]

Opt. Acta

C. J. Gabriel, A. Nedoluha, “Transmittance and reflectance of systems of thin and thick layers,” Opt. Acta 18, 415–423 (1971).
[CrossRef]

Phys. Rev. B

W. Tennant, J. Cape, “Study of the dielectric function of PbSnTe epitaxial film by far-infrared reflectivity,” Phys. Rev. B 13, 2540–2547 (1976).
[CrossRef]

Phys. Status Solidi

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

Rev. Opt.

A. M. Dioffo, “Étude théorique des caractéristiques optiques d’un système de lames diélectriques,” Rev. Opt. 47, 49–68 (1968).

Thin Solid Films

N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Optical investigation of structures formed by 2MeV oxygen implantation into silicon,” Thin Solid Films 289, 90–94 (1996).
[CrossRef]

J. Szczyrbowski, A. Czapla, “Optical absorption in d.c. sputtered InAs films,” Thin Solid Films 46, 127–137 (1977).
[CrossRef]

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

Other

K. Krishnan, P. J. Stout, M. Watanabe, Practical Fourier Transform Infrared Spectroscopy (Academic, New York, 1990), p. 294.

C. C. Katsidis, D. I. Siapkas, W. Skorupa, N. Hatzopoulos, D. Panknin, Proceedings of the 10th International Conference on Ion Implantation Technology (Elsevier, Amsterdam, 1995), p. 959–962.

C. C. Katsidis, D. I. Siapkas, in Proceedings of NATO ASI on Application of Particle and Laser Beams in Materials Technology, P. Misaelides, ed. (Kluwer Academic, Dordrecht, 1995), p. 603–612.
[CrossRef]

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964), p. 254.

O. S. Heavens, Optical Properties of Thin Films (Dover, New York, 1965), p. 69.

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

Z. Knittl, Optics of Thin Films (Wiley, London, 1976), p. 41.

G. K. Hubler, P. R. Malmberg, C. N. Waddell, W. G. Spitzer, J. E. Fredrickson, in Ion Implantation for Materials Processing, F. A. Smidt, ed. (Noyes Data, Park Ridge, N.J., 1983), p. 195–218.

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Figures (8)

Fig. 1
Fig. 1

Notation of electric field amplitudes within an arbitrary multilayer. The subscripts indicate the medium, the + and the - signs distinguish between left- and right-going waves, respectively, whereas a prime is used for waves at the right-hand side of an interface.

Fig. 2
Fig. 2

Influence of a rough surface or interface (Z = 1000 Å). Two sets of calculated reflectivity spectra for a 2-µm-thick SiC layer on a thick 300-µm Si substrate, introducing partial coherency in the generic matrix. The set of spectra with the high average reflectivity level were calculated assuming the Si substrate to be finite incoherent, whereas for the low-level set the semi-infinite substrate approximation was applied.

Fig. 3
Fig. 3

Comparison of the spectrum of bulk SiC with the spectrum of Fig. 2 corresponding to a 2-µm SiC layer on a semi-infinite Si substrate exhibiting a 1000Å rough interface (thick and thin solid curves, respectively). The influence of a rough surface (Z = 1000Å) is also shown in comparison (dashed and dotted–dashed curves).

Fig. 4
Fig. 4

Calculated reflectance spectra of a doped Si–SiO2–thick-Si structure with the generic matrix formulation (d Si = 0.08 µm, d SiO2 = 1.6 µm, d Si = 850 µm). The calculations were performed considering either a coherent substrate of finite thickness (spectrum with narrow oscillations) or an incoherent one (smooth spectrum).

Fig. 5
Fig. 5

Experimental and calculated reflectance of a doped-Si–Si structure (70 keV, 6 × 1015 As+cm-2, 0.5 h annealed at 950 °C) with application of either the incoherent finite-substrate correction or the semi-infinite substrate approximation. The 0.286-µm-thick inhomogeneous doped Si region was partitioned into 80 sampling layers simulating two half-joined Gaussians (R P = 3800Å, ΔR 1 = 95Å, ΔR 2 = 620Å).

Fig. 6
Fig. 6

Depth profiles of the real and the imaginary parts of the refractive index, n and k, corresponding to the free-carrier asymmetric-Gaussian profile in the doped Si–Si structure of Fig. 5 calculated at σ = 2000, 3000, and 4000 cm-1. As σ increases, the contribution of the free-carrier plasma dispersion diminishes and the magnitudes of the dip in n and the peak in k decrease. The inset exhibits two half-joined Gaussians modeling the carrier concentration depth profile.

Fig. 7
Fig. 7

Experimental and calculated reflectance spectra of a 370-µm-thick SiO2 layer between two thin poly-Si layers with thickness 0.34 and 0.35 µm, respectively. The best-fit reflectivity (thick solid curve) was calculated with the incoherent finite-substrate formalism for a thick intermediate layer. Roughness at both the front and the rear Si surfaces was detected: 800Å and 900Å, respectively. The thin solid curve designating a dense fringe pattern was calculated assuming the oxide substrate to be coherent, for comparison.

Fig. 8
Fig. 8

Combined action of incoherence and partial coherence within a multilayer. Symbols represent calculated reflectance spectra with refractive index and thickness parameters of the poly-Si–thick-SiO2–poly-Si structure of Fig. 7. Only one interface is considered to be rough (Z = 900 Å) at a time. Circles, no roughness; diamonds, surface rough; squares, front Si–SiO2 interface rough; crosses, rear Si–SiO2 interface rough; triangles, backsurface rough. The solid curve is the best-fit curve of Fig. 7: both poly-Si surfaces rough, Z 1 = 800 Å and Z 4 = 900 Å.

Equations (30)

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Em-1+Em-1-= Dm-1-1DmEm+Em= 1tm-1,m1rm-1,mrm-1,m1Em+Em.
Em-1+Em-1=Pm-1Em-1+Em-1-= expiδm-100exp-iδm-1Em-1+Em-1-,
E0+E0-= D0-1m=1NDmPmDm-1DN+1EN+1+EN+1-= T11T12T21T22EN+1+EN+1-.
r=r0,N+1= E0-E0+EN+1-=0= T21T11,
t=t0,N+1= EN+1+E0+EN+1-=0= 1T11,
r=rN+1,0= EN+1-EN+1+E0+=0=- T12T11,
t=tN+1,0= E0-EN+1+E0+=0= Det TT11Det T=T11T22-T12T21,
T0/ N+1= T11T12T21T22= 1t0,N+11-rN+1,0r0,N+1t0,N+1tN+1,0-r0,N+1rN+1,0.
Em-1+Em-1-= 1tm-1,m× 1-rm,m-1rm-1,mtm-1,mtm,m-1-rm-1,mrm,m-1× Em+Em-.
rm-1,m=rm-1,m0 exp-2snm-1σ2=αrm-1,m0,
rm,m-1=rm,m-10 exp-2snmσ2=βrm,m-10,
tm-1,m=tm-1,m0 exp-1/2 sσ2nm-nm-12=γtm-1,m0,
tm,m-1=tm,m-10 exp-1/2sσ2nm-1-nm2=γtm,m-10,
T0/mint= 1|t0,m|21-|rm,0|2|r0,m|2|t0,mtm,0|2-|r0,mrm,0|2,
Tm/N+1int= 1|tm,N+1|2× 1-|rN+1,m|2|rm,N+1|2|tm,N+1tN+1,m|2-|rm,N+1rN+1,m|2,
T0/mintPmintTm/N+1int=1t0,m21-rm,02r0,m2t0,mtm,02-r0,mrm,02× expiδm200exp-iδm2Pmint× 1tm,N+121-rN+1,m2rm,N+12tm,N+1tN+1,m2-rm,N+1rN+1,m2,
T0/N+1incoh=T11incohT12incohT21incohT22incoh= T0/mintPmintTm/N+1int,
Rincoh=T21incohT11incoh= r0,m2+ t0,mtm,0rm,N+12 exp-4σ/ckmdm)1-rm,0rm,N+12 exp-4σ/ckmdm,
Tincoh=1T11incoh= t0,m2tm,N+12 exp-2σ/ckmdm1-rm,0rm,N+12 exp-4σ/ckmdm,
T0/N+1= T11T12T21T22= T0/mPmTm/ N+1,
r0,N+1=T21T11=r0,m+ t0,mtm,0rm,N+1 exp-2σ/ckmdm1-rm,0rm,N+1 exp-2σ/ckmdm,
t0,N+1=1T11=t0,mtm,N+1 exp-σ/ckmdm1-rm,0rm,N+1 exp-2σ/ckmdm.
T0/N+1incoh=T0/mintPmintTm/jintPjintTj/N+1int.
1tm-1,mΔ11 expiδm-1-Δ12rm,m-1 expiδm-1Δ21rm-1,m exp-iδm-1Δ22tm-1,mtm,m-1-Δ22rm-1,mrm,m-1exp-iδm-1.
˜= jΔjωTOj2ωTOj2-ω2-iγjω- ωp2ω2+iγjω+.
Ncj=Nc,max exp-1/2-κΔR+jδx/ΔR2,
ωpj2= 4πNcje2m*,
cj=nj2-kj2=-ωpj2ω2+γp2,
cj=2njkj=γpωpj2ωω2+γp2.
nj=½j+ j2+j21/21/2, kj= ½-j+j2+j21/21/2.

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