Abstract

Single-pass polarizer-surface-analyzer null ellipsometry (PSA-NE) can be used to characterize film-substrate systems, provided that the film thickness lies within one of a set of permissible-thickness bands (PTB). For a transparent film on a transparent or absorbing substrate, the PTB structure consists of a small number of finite-bandwidth bands followed by a continuum band that extends from a film thickness of about half the wavelength of light to infinity. We show that this band structure is a direct consequence of the periodicity of the ellipsometric function ρ (the ratio <i>R<sub>p</sub></i>/<i>R<sub>s</sub></i>, of the complex amplitude-reflection coefficients for the <i>p</i> and <i>s</i> polarizations) with film thickness. The PTB for the SiO<sub>2</sub>-Si film-substrate system at He-Ne laser and mercury spectral lines are calculated. The angles of incidence for PSA-NE ona film-substrate system with known film thickness are easily predicted with the help of a graphical construction in the angle of incidence-vs-thickness φ<i>d</i> plane. PSA-NE is generally applicable to the determination of both film thickness and optical properties of a film-substrate system. The procedure for its application to the special, but important, case of film-thickness measurement alone, when the optical properties are known, is given and is checked experimentally by the determination of the oxide-film thickness on Si wafers. In an automated form, PSA-NE can be a serious competitor for interferometric reflectance methods.

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  1. R. J. Archer, J. Opt. Soc. Am. 52, 970 (1962); D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 57, 466 (1967); W. G. Oldham, J. Opt. Soc. Am. 47, 617 (1967); P. H. Smith, Surf. Sci. 16, 34 (1969); F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970); J. A. Johnson and N. M. Bashara, J. Opt. Soc. Am. 60, 221 (1970); R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 222 (1972).
  2. H. M. O'Bryan, J. Opt. Soc. Am. 26, 122 (1936). In this paper, O'Bryan mentions the similarity of his idea to that of Brewster, who over a century earlier [Philos. Trans. 69, 133 (1830)] observed that light multiply reflected between a pair of parallel mirrors can be extinguished between two Nicol prisms. In this case, the phase shift per reflection is π/M, so that for M reflections, the cummulative shift is (π/M) × M=π.
  3. M. Yamamoto, Opt. Commun. 10, 200 (1974).
  4. R. M. A. Azzam, A. -R. M. Zaghloul, and N. M. Bashara, J. Opt. Soc. Am. 65, 252 (1975).
  5. The existence of PTB has also been encountered in the design of film-substrate reflection retarders; A. -R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, J. Opt. Soc. Am. 65, 1043 (1975).
  6. See Eq. (13) and Fig. 3 of Ref. 4.
  7. s or p suppression refers to the total extinction of the s or p components of the incident light upon reflection and identifies the condition when the film-substrate system acts as a reflection polarizer.
  8. The vertical translation of a base band by a multiple of the thickness period preserves the range of ψ (high or low).
  9. Note the difference of notation between dl1m and dmldl1m indicates the lower edge of a translated band, whereas dml is the lower edge of a higher band. A translated band may or may not constitute a higher band, dependent on the overlapping of all translated bands.
  10. Ellipsometric Tables of the Si-SiO2 System for Mercury and He-Ne Laser Spectral Lines, edited by G. Gergely (Akademiai Kiado, Budapest, 1971).
  11. W. A. Pliskin, in Progress in Analytic Chemistry; Vol. 2, edited by E. M. Murt and W. G. Guldner (Plenum, New York, 1969), pp. 1–34.
  12. B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969).
  13. D. E. Aspnes, Opt. Commun. 8, 222 (1973); D. E. Aspnes and A. A. Studna, Appl. Opt. 14, 220 (1975).
  14. P. S. Hauge and F. H. Dill, IBM J. Res. Devel. 17, 472 (1973).
  15. Y. J. van der Meulen and N. C. Hien, J. Opt. Soc. Am. 64, 804 (1974).
  16. R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 64, 1459 (1974).
  17. An important parameter for the precise determination of the null by the PSA ellipsometer is the value of the derivative ∂Δ/∂φ at the nulling angle φ. This derivative determines how rapidly the reflected light becomes elliptically polarized as the angle of incidence is offset from its null position. An initial investigation shows a tendency for high values of ∂Δ/∂φ at null, in most cases, leading to very precise null definition.

Archer, R. J.

R. J. Archer, J. Opt. Soc. Am. 52, 970 (1962); D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 57, 466 (1967); W. G. Oldham, J. Opt. Soc. Am. 47, 617 (1967); P. H. Smith, Surf. Sci. 16, 34 (1969); F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970); J. A. Johnson and N. M. Bashara, J. Opt. Soc. Am. 60, 221 (1970); R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 222 (1972).

Aspnes, D. E.

D. E. Aspnes, Opt. Commun. 8, 222 (1973); D. E. Aspnes and A. A. Studna, Appl. Opt. 14, 220 (1975).

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 64, 1459 (1974).

The existence of PTB has also been encountered in the design of film-substrate reflection retarders; A. -R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, J. Opt. Soc. Am. 65, 1043 (1975).

R. M. A. Azzam, A. -R. M. Zaghloul, and N. M. Bashara, J. Opt. Soc. Am. 65, 252 (1975).

Bashara, N. M.

R. M. A. Azzam, A. -R. M. Zaghloul, and N. M. Bashara, J. Opt. Soc. Am. 65, 252 (1975).

The existence of PTB has also been encountered in the design of film-substrate reflection retarders; A. -R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, J. Opt. Soc. Am. 65, 1043 (1975).

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 64, 1459 (1974).

Cahan, B. D.

B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969).

Dill, F. H.

P. S. Hauge and F. H. Dill, IBM J. Res. Devel. 17, 472 (1973).

Hauge, P. S.

P. S. Hauge and F. H. Dill, IBM J. Res. Devel. 17, 472 (1973).

Hien, N. C.

Y. J. van der Meulen and N. C. Hien, J. Opt. Soc. Am. 64, 804 (1974).

O’Bryan, H. M.

H. M. O'Bryan, J. Opt. Soc. Am. 26, 122 (1936). In this paper, O'Bryan mentions the similarity of his idea to that of Brewster, who over a century earlier [Philos. Trans. 69, 133 (1830)] observed that light multiply reflected between a pair of parallel mirrors can be extinguished between two Nicol prisms. In this case, the phase shift per reflection is π/M, so that for M reflections, the cummulative shift is (π/M) × M=π.

Pliskin, W. A.

W. A. Pliskin, in Progress in Analytic Chemistry; Vol. 2, edited by E. M. Murt and W. G. Guldner (Plenum, New York, 1969), pp. 1–34.

Spanier, R. F.

B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969).

van der Meulen, Y. J.

Y. J. van der Meulen and N. C. Hien, J. Opt. Soc. Am. 64, 804 (1974).

Yamamoto, M.

M. Yamamoto, Opt. Commun. 10, 200 (1974).

Zaghloul, A. -R. M.

The existence of PTB has also been encountered in the design of film-substrate reflection retarders; A. -R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, J. Opt. Soc. Am. 65, 1043 (1975).

R. M. A. Azzam, A. -R. M. Zaghloul, and N. M. Bashara, J. Opt. Soc. Am. 65, 252 (1975).

Other

R. J. Archer, J. Opt. Soc. Am. 52, 970 (1962); D. A. Holmes and D. L. Feucht, J. Opt. Soc. Am. 57, 466 (1967); W. G. Oldham, J. Opt. Soc. Am. 47, 617 (1967); P. H. Smith, Surf. Sci. 16, 34 (1969); F. L. McCrackin, J. Opt. Soc. Am. 60, 57 (1970); J. A. Johnson and N. M. Bashara, J. Opt. Soc. Am. 60, 221 (1970); R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 62, 222 (1972).

H. M. O'Bryan, J. Opt. Soc. Am. 26, 122 (1936). In this paper, O'Bryan mentions the similarity of his idea to that of Brewster, who over a century earlier [Philos. Trans. 69, 133 (1830)] observed that light multiply reflected between a pair of parallel mirrors can be extinguished between two Nicol prisms. In this case, the phase shift per reflection is π/M, so that for M reflections, the cummulative shift is (π/M) × M=π.

M. Yamamoto, Opt. Commun. 10, 200 (1974).

R. M. A. Azzam, A. -R. M. Zaghloul, and N. M. Bashara, J. Opt. Soc. Am. 65, 252 (1975).

The existence of PTB has also been encountered in the design of film-substrate reflection retarders; A. -R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, J. Opt. Soc. Am. 65, 1043 (1975).

See Eq. (13) and Fig. 3 of Ref. 4.

s or p suppression refers to the total extinction of the s or p components of the incident light upon reflection and identifies the condition when the film-substrate system acts as a reflection polarizer.

The vertical translation of a base band by a multiple of the thickness period preserves the range of ψ (high or low).

Note the difference of notation between dl1m and dmldl1m indicates the lower edge of a translated band, whereas dml is the lower edge of a higher band. A translated band may or may not constitute a higher band, dependent on the overlapping of all translated bands.

Ellipsometric Tables of the Si-SiO2 System for Mercury and He-Ne Laser Spectral Lines, edited by G. Gergely (Akademiai Kiado, Budapest, 1971).

W. A. Pliskin, in Progress in Analytic Chemistry; Vol. 2, edited by E. M. Murt and W. G. Guldner (Plenum, New York, 1969), pp. 1–34.

B. D. Cahan and R. F. Spanier, Surf. Sci. 16, 166 (1969).

D. E. Aspnes, Opt. Commun. 8, 222 (1973); D. E. Aspnes and A. A. Studna, Appl. Opt. 14, 220 (1975).

P. S. Hauge and F. H. Dill, IBM J. Res. Devel. 17, 472 (1973).

Y. J. van der Meulen and N. C. Hien, J. Opt. Soc. Am. 64, 804 (1974).

R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. 64, 1459 (1974).

An important parameter for the precise determination of the null by the PSA ellipsometer is the value of the derivative ∂Δ/∂φ at the nulling angle φ. This derivative determines how rapidly the reflected light becomes elliptically polarized as the angle of incidence is offset from its null position. An initial investigation shows a tendency for high values of ∂Δ/∂φ at null, in most cases, leading to very precise null definition.

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