Abstract

This paper discusses an approach to the search for the starting approximations when inverse optical problems are to be solved to determine the refractive indices and thicknesses of dielectric films on substrates. It is proposed to use reflection spectra obtained at different angles of incidence of light on the sample, from which the refractive indices and thickness of the film are computed from the location of the intensity extrema. In monochromatic null ellipsometry, the measurement of the polarization parameters of light at different angles of incidence makes it possible to determine the refractive index and ellipsometric thickness for each angle. The starting approximation for the thickness for solving the inverse problem in ellipsometry, based on the data for all the angles of incidence used for light on the sample, is obtained from the optical thickness of the film, determined from the reflection spectra at small angles of incidence.

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  1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, Elsevier, New York, 1977, Mir, Moscow, 1981.
  2. B. M. Ayupov, "Choosing models for the study of dielectric-film–substrate systems by ellipsometric and spectroscopic methods," Poverkhnost’ Rentgen. Sinkh. Neĭtron. Issled. (4), 59 (2000).
  3. B. M. Ayupov, S. F. Devyatova, V. G. Erkov, and L. A. Semenova, "Refractive-index profiles of some thermal and CVD oxide films on silicon," Mikroélektronika 37, (3), 163 (2008).
  4. M. L. Kosinova, N. I. Fainer, Yu. M. Rumyantsev, E. A. Maximovski, F. A. Kuznetsov, M. Terauchi, K. Shibata, and F. Satoh, "Growth of homogeneous and gradient BCxNy films by PECVD using trimethylamino borane complex," The Electrochemical Society Proc. V. 2003-08, Chemical Vapor Deposition XVI (CVD-XVI) and EuroCVD 14, 2003, pp. 708‒715.
  5. V. A. Labusov, A. N. Put’makov, M. S. Saushkin, I. A. Zarubin, and D. O. Selyunin, "Multichannel spectrometer Kolibri-2 and its use for simultaneously determining the alkali and alkaline-earth metals by flame photometry," Zav. Lab. Diag. Mat. Spets. Vyp. 73, 35 (2007).
  6. B. M. Ayupov and I. G. Luk’yanova, "Spectrophotometric determination of the thicknesses of polycrystalline silicon films," Élektron. Tekhn. Ser. Mat. 12, (161), 59 (1981).
  7. B. M. Ayupov and N. A. Kozlova, "Detecting a disturbed layer on a silicon surface by means of monochromatic null ellipsometry," Opt. Zh. 73, (3), 72 (2006) [J. Opt. Technol. 73, 212 (2006)].
  8. F. Reisman, "Optical thickness measurement of thin transparent films on silicon," J. Appl. Phys. 36, 3804 (1965).
    [CrossRef]
  9. I. R. Shelpakova, I. G. Yudelevich, and B. M. Ayupov, Layer-by-Layer Analysis of the Materials of Electronic Engineering, Nauka, Novosibirsk, 1984.
  10. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, Pergamon Press, Oxford, 1970, Nauka, Moscow, 1973.
  11. D. A. Holmes, "On the calculation of thin-film refractive index and thickness by ellipsometry," Appl. Opt. 6, 168 (1967).
    [CrossRef]
  12. Y. Yoriume, "Method for numerical inversion of the ellipsometric equation for transparent films," J. Opt. Soc. Am. 73, 888 (1983).
    [CrossRef]
  13. A. V. Rzhanov, K. K. Svitashev, A. I. Semenenko, L. V. Semenenko, and V. K. Sokolov, Fundamentals of Ellipsometry, Nauka, Novosibirsk, 1979.
  14. B. Ayupov, K. Zherikova, N. Gelfond, and N. Morozova, "Optical properties of MOCVD HfO2 films," Phys. Status Solidi A 206, 281 (2009).
    [CrossRef]
  15. B. M. Ayupov, "Modification of the GS-5 goniometer," Prib. Tekh. Éksp. (5), 185 (1993).

2009

B. Ayupov, K. Zherikova, N. Gelfond, and N. Morozova, "Optical properties of MOCVD HfO2 films," Phys. Status Solidi A 206, 281 (2009).
[CrossRef]

2008

B. M. Ayupov, S. F. Devyatova, V. G. Erkov, and L. A. Semenova, "Refractive-index profiles of some thermal and CVD oxide films on silicon," Mikroélektronika 37, (3), 163 (2008).

2007

V. A. Labusov, A. N. Put’makov, M. S. Saushkin, I. A. Zarubin, and D. O. Selyunin, "Multichannel spectrometer Kolibri-2 and its use for simultaneously determining the alkali and alkaline-earth metals by flame photometry," Zav. Lab. Diag. Mat. Spets. Vyp. 73, 35 (2007).

2006

B. M. Ayupov and N. A. Kozlova, "Detecting a disturbed layer on a silicon surface by means of monochromatic null ellipsometry," Opt. Zh. 73, (3), 72 (2006) [J. Opt. Technol. 73, 212 (2006)].

2000

B. M. Ayupov, "Choosing models for the study of dielectric-film–substrate systems by ellipsometric and spectroscopic methods," Poverkhnost’ Rentgen. Sinkh. Neĭtron. Issled. (4), 59 (2000).

1993

B. M. Ayupov, "Modification of the GS-5 goniometer," Prib. Tekh. Éksp. (5), 185 (1993).

1983

1981

B. M. Ayupov and I. G. Luk’yanova, "Spectrophotometric determination of the thicknesses of polycrystalline silicon films," Élektron. Tekhn. Ser. Mat. 12, (161), 59 (1981).

1967

1965

F. Reisman, "Optical thickness measurement of thin transparent films on silicon," J. Appl. Phys. 36, 3804 (1965).
[CrossRef]

Ayupov, B.

B. Ayupov, K. Zherikova, N. Gelfond, and N. Morozova, "Optical properties of MOCVD HfO2 films," Phys. Status Solidi A 206, 281 (2009).
[CrossRef]

Ayupov, B. M.

B. M. Ayupov, S. F. Devyatova, V. G. Erkov, and L. A. Semenova, "Refractive-index profiles of some thermal and CVD oxide films on silicon," Mikroélektronika 37, (3), 163 (2008).

B. M. Ayupov and N. A. Kozlova, "Detecting a disturbed layer on a silicon surface by means of monochromatic null ellipsometry," Opt. Zh. 73, (3), 72 (2006) [J. Opt. Technol. 73, 212 (2006)].

B. M. Ayupov, "Choosing models for the study of dielectric-film–substrate systems by ellipsometric and spectroscopic methods," Poverkhnost’ Rentgen. Sinkh. Neĭtron. Issled. (4), 59 (2000).

B. M. Ayupov, "Modification of the GS-5 goniometer," Prib. Tekh. Éksp. (5), 185 (1993).

B. M. Ayupov and I. G. Luk’yanova, "Spectrophotometric determination of the thicknesses of polycrystalline silicon films," Élektron. Tekhn. Ser. Mat. 12, (161), 59 (1981).

I. R. Shelpakova, I. G. Yudelevich, and B. M. Ayupov, Layer-by-Layer Analysis of the Materials of Electronic Engineering, Nauka, Novosibirsk, 1984.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, Elsevier, New York, 1977, Mir, Moscow, 1981.

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, Elsevier, New York, 1977, Mir, Moscow, 1981.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, Pergamon Press, Oxford, 1970, Nauka, Moscow, 1973.

Devyatova, S. F.

B. M. Ayupov, S. F. Devyatova, V. G. Erkov, and L. A. Semenova, "Refractive-index profiles of some thermal and CVD oxide films on silicon," Mikroélektronika 37, (3), 163 (2008).

Erkov, V. G.

B. M. Ayupov, S. F. Devyatova, V. G. Erkov, and L. A. Semenova, "Refractive-index profiles of some thermal and CVD oxide films on silicon," Mikroélektronika 37, (3), 163 (2008).

Fainer, N. I.

M. L. Kosinova, N. I. Fainer, Yu. M. Rumyantsev, E. A. Maximovski, F. A. Kuznetsov, M. Terauchi, K. Shibata, and F. Satoh, "Growth of homogeneous and gradient BCxNy films by PECVD using trimethylamino borane complex," The Electrochemical Society Proc. V. 2003-08, Chemical Vapor Deposition XVI (CVD-XVI) and EuroCVD 14, 2003, pp. 708‒715.

Gelfond, N.

B. Ayupov, K. Zherikova, N. Gelfond, and N. Morozova, "Optical properties of MOCVD HfO2 films," Phys. Status Solidi A 206, 281 (2009).
[CrossRef]

Holmes, D. A.

Kosinova, M. L.

M. L. Kosinova, N. I. Fainer, Yu. M. Rumyantsev, E. A. Maximovski, F. A. Kuznetsov, M. Terauchi, K. Shibata, and F. Satoh, "Growth of homogeneous and gradient BCxNy films by PECVD using trimethylamino borane complex," The Electrochemical Society Proc. V. 2003-08, Chemical Vapor Deposition XVI (CVD-XVI) and EuroCVD 14, 2003, pp. 708‒715.

Kozlova, N. A.

B. M. Ayupov and N. A. Kozlova, "Detecting a disturbed layer on a silicon surface by means of monochromatic null ellipsometry," Opt. Zh. 73, (3), 72 (2006) [J. Opt. Technol. 73, 212 (2006)].

Kuznetsov, F. A.

M. L. Kosinova, N. I. Fainer, Yu. M. Rumyantsev, E. A. Maximovski, F. A. Kuznetsov, M. Terauchi, K. Shibata, and F. Satoh, "Growth of homogeneous and gradient BCxNy films by PECVD using trimethylamino borane complex," The Electrochemical Society Proc. V. 2003-08, Chemical Vapor Deposition XVI (CVD-XVI) and EuroCVD 14, 2003, pp. 708‒715.

Labusov, V. A.

V. A. Labusov, A. N. Put’makov, M. S. Saushkin, I. A. Zarubin, and D. O. Selyunin, "Multichannel spectrometer Kolibri-2 and its use for simultaneously determining the alkali and alkaline-earth metals by flame photometry," Zav. Lab. Diag. Mat. Spets. Vyp. 73, 35 (2007).

Luk’yanova, I. G.

B. M. Ayupov and I. G. Luk’yanova, "Spectrophotometric determination of the thicknesses of polycrystalline silicon films," Élektron. Tekhn. Ser. Mat. 12, (161), 59 (1981).

Maximovski, E. A.

M. L. Kosinova, N. I. Fainer, Yu. M. Rumyantsev, E. A. Maximovski, F. A. Kuznetsov, M. Terauchi, K. Shibata, and F. Satoh, "Growth of homogeneous and gradient BCxNy films by PECVD using trimethylamino borane complex," The Electrochemical Society Proc. V. 2003-08, Chemical Vapor Deposition XVI (CVD-XVI) and EuroCVD 14, 2003, pp. 708‒715.

Morozova, N.

B. Ayupov, K. Zherikova, N. Gelfond, and N. Morozova, "Optical properties of MOCVD HfO2 films," Phys. Status Solidi A 206, 281 (2009).
[CrossRef]

Put’makov, A. N.

V. A. Labusov, A. N. Put’makov, M. S. Saushkin, I. A. Zarubin, and D. O. Selyunin, "Multichannel spectrometer Kolibri-2 and its use for simultaneously determining the alkali and alkaline-earth metals by flame photometry," Zav. Lab. Diag. Mat. Spets. Vyp. 73, 35 (2007).

Reisman, F.

F. Reisman, "Optical thickness measurement of thin transparent films on silicon," J. Appl. Phys. 36, 3804 (1965).
[CrossRef]

Rumyantsev, Yu. M.

M. L. Kosinova, N. I. Fainer, Yu. M. Rumyantsev, E. A. Maximovski, F. A. Kuznetsov, M. Terauchi, K. Shibata, and F. Satoh, "Growth of homogeneous and gradient BCxNy films by PECVD using trimethylamino borane complex," The Electrochemical Society Proc. V. 2003-08, Chemical Vapor Deposition XVI (CVD-XVI) and EuroCVD 14, 2003, pp. 708‒715.

Rzhanov, A. V.

A. V. Rzhanov, K. K. Svitashev, A. I. Semenenko, L. V. Semenenko, and V. K. Sokolov, Fundamentals of Ellipsometry, Nauka, Novosibirsk, 1979.

Satoh, F.

M. L. Kosinova, N. I. Fainer, Yu. M. Rumyantsev, E. A. Maximovski, F. A. Kuznetsov, M. Terauchi, K. Shibata, and F. Satoh, "Growth of homogeneous and gradient BCxNy films by PECVD using trimethylamino borane complex," The Electrochemical Society Proc. V. 2003-08, Chemical Vapor Deposition XVI (CVD-XVI) and EuroCVD 14, 2003, pp. 708‒715.

Saushkin, M. S.

V. A. Labusov, A. N. Put’makov, M. S. Saushkin, I. A. Zarubin, and D. O. Selyunin, "Multichannel spectrometer Kolibri-2 and its use for simultaneously determining the alkali and alkaline-earth metals by flame photometry," Zav. Lab. Diag. Mat. Spets. Vyp. 73, 35 (2007).

Selyunin, D. O.

V. A. Labusov, A. N. Put’makov, M. S. Saushkin, I. A. Zarubin, and D. O. Selyunin, "Multichannel spectrometer Kolibri-2 and its use for simultaneously determining the alkali and alkaline-earth metals by flame photometry," Zav. Lab. Diag. Mat. Spets. Vyp. 73, 35 (2007).

Semenenko, A. I.

A. V. Rzhanov, K. K. Svitashev, A. I. Semenenko, L. V. Semenenko, and V. K. Sokolov, Fundamentals of Ellipsometry, Nauka, Novosibirsk, 1979.

Semenenko, L. V.

A. V. Rzhanov, K. K. Svitashev, A. I. Semenenko, L. V. Semenenko, and V. K. Sokolov, Fundamentals of Ellipsometry, Nauka, Novosibirsk, 1979.

Semenova, L. A.

B. M. Ayupov, S. F. Devyatova, V. G. Erkov, and L. A. Semenova, "Refractive-index profiles of some thermal and CVD oxide films on silicon," Mikroélektronika 37, (3), 163 (2008).

Shelpakova, I. R.

I. R. Shelpakova, I. G. Yudelevich, and B. M. Ayupov, Layer-by-Layer Analysis of the Materials of Electronic Engineering, Nauka, Novosibirsk, 1984.

Shibata, K.

M. L. Kosinova, N. I. Fainer, Yu. M. Rumyantsev, E. A. Maximovski, F. A. Kuznetsov, M. Terauchi, K. Shibata, and F. Satoh, "Growth of homogeneous and gradient BCxNy films by PECVD using trimethylamino borane complex," The Electrochemical Society Proc. V. 2003-08, Chemical Vapor Deposition XVI (CVD-XVI) and EuroCVD 14, 2003, pp. 708‒715.

Sokolov, V. K.

A. V. Rzhanov, K. K. Svitashev, A. I. Semenenko, L. V. Semenenko, and V. K. Sokolov, Fundamentals of Ellipsometry, Nauka, Novosibirsk, 1979.

Svitashev, K. K.

A. V. Rzhanov, K. K. Svitashev, A. I. Semenenko, L. V. Semenenko, and V. K. Sokolov, Fundamentals of Ellipsometry, Nauka, Novosibirsk, 1979.

Terauchi, M.

M. L. Kosinova, N. I. Fainer, Yu. M. Rumyantsev, E. A. Maximovski, F. A. Kuznetsov, M. Terauchi, K. Shibata, and F. Satoh, "Growth of homogeneous and gradient BCxNy films by PECVD using trimethylamino borane complex," The Electrochemical Society Proc. V. 2003-08, Chemical Vapor Deposition XVI (CVD-XVI) and EuroCVD 14, 2003, pp. 708‒715.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, Pergamon Press, Oxford, 1970, Nauka, Moscow, 1973.

Yoriume, Y.

Yudelevich, I. G.

I. R. Shelpakova, I. G. Yudelevich, and B. M. Ayupov, Layer-by-Layer Analysis of the Materials of Electronic Engineering, Nauka, Novosibirsk, 1984.

Zarubin, I. A.

V. A. Labusov, A. N. Put’makov, M. S. Saushkin, I. A. Zarubin, and D. O. Selyunin, "Multichannel spectrometer Kolibri-2 and its use for simultaneously determining the alkali and alkaline-earth metals by flame photometry," Zav. Lab. Diag. Mat. Spets. Vyp. 73, 35 (2007).

Zherikova, K.

B. Ayupov, K. Zherikova, N. Gelfond, and N. Morozova, "Optical properties of MOCVD HfO2 films," Phys. Status Solidi A 206, 281 (2009).
[CrossRef]

Appl. Opt.

Élektron. Tekhn. Ser. Mat.

B. M. Ayupov and I. G. Luk’yanova, "Spectrophotometric determination of the thicknesses of polycrystalline silicon films," Élektron. Tekhn. Ser. Mat. 12, (161), 59 (1981).

J. Appl. Phys.

F. Reisman, "Optical thickness measurement of thin transparent films on silicon," J. Appl. Phys. 36, 3804 (1965).
[CrossRef]

J. Opt. Soc. Am.

Mikroélektronika

B. M. Ayupov, S. F. Devyatova, V. G. Erkov, and L. A. Semenova, "Refractive-index profiles of some thermal and CVD oxide films on silicon," Mikroélektronika 37, (3), 163 (2008).

Opt. Zh.

B. M. Ayupov and N. A. Kozlova, "Detecting a disturbed layer on a silicon surface by means of monochromatic null ellipsometry," Opt. Zh. 73, (3), 72 (2006) [J. Opt. Technol. 73, 212 (2006)].

Phys. Status Solidi A

B. Ayupov, K. Zherikova, N. Gelfond, and N. Morozova, "Optical properties of MOCVD HfO2 films," Phys. Status Solidi A 206, 281 (2009).
[CrossRef]

Poverkhnost’ Rentgen. Sinkh. Neitron. Issled.

B. M. Ayupov, "Choosing models for the study of dielectric-film–substrate systems by ellipsometric and spectroscopic methods," Poverkhnost’ Rentgen. Sinkh. Neĭtron. Issled. (4), 59 (2000).

Prib. Tekh. Éksp.

B. M. Ayupov, "Modification of the GS-5 goniometer," Prib. Tekh. Éksp. (5), 185 (1993).

Zav. Lab. Diag. Mat. Spets. Vyp.

V. A. Labusov, A. N. Put’makov, M. S. Saushkin, I. A. Zarubin, and D. O. Selyunin, "Multichannel spectrometer Kolibri-2 and its use for simultaneously determining the alkali and alkaline-earth metals by flame photometry," Zav. Lab. Diag. Mat. Spets. Vyp. 73, 35 (2007).

Other

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, Elsevier, New York, 1977, Mir, Moscow, 1981.

M. L. Kosinova, N. I. Fainer, Yu. M. Rumyantsev, E. A. Maximovski, F. A. Kuznetsov, M. Terauchi, K. Shibata, and F. Satoh, "Growth of homogeneous and gradient BCxNy films by PECVD using trimethylamino borane complex," The Electrochemical Society Proc. V. 2003-08, Chemical Vapor Deposition XVI (CVD-XVI) and EuroCVD 14, 2003, pp. 708‒715.

I. R. Shelpakova, I. G. Yudelevich, and B. M. Ayupov, Layer-by-Layer Analysis of the Materials of Electronic Engineering, Nauka, Novosibirsk, 1984.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, Pergamon Press, Oxford, 1970, Nauka, Moscow, 1973.

A. V. Rzhanov, K. K. Svitashev, A. I. Semenenko, L. V. Semenenko, and V. K. Sokolov, Fundamentals of Ellipsometry, Nauka, Novosibirsk, 1979.

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