Abstract

The refractive index and the thickness of a transparent pellicle are determined when the pellicle is placed between two vertical crossed polarizers and rotated in the horizontal plane. The transmission axes of the polarizers are neither parallel nor perpendicular to the plane of incidence. The light transmitted through the crossed polarizers reaches a minimum when the pellicle satisfies the absentee-layer condition. The refractive index and the film thickness are obtained from the pellicle orientation angles under such a condition.

© 1996 Optical Society of America

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References

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  1. W. A. Pliskin, E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43–51 (1964).
    [CrossRef]
  2. F. Reizmann, W. Van Gelder, “Optical thickness measurement of SiO2–Si3N4 films on silicon,” Solid-State Electron. 10, 625–632 (1967).
    [CrossRef]
  3. R. M. A. Azzam, “Polarization-independent reflectance matching (PIRM). A technique for the determination of the refractive index and thickness of the transparent films,” J. Opt. (Paris) 8, 201–205 (1977).
    [CrossRef]
  4. T. Kihara, K. Yokomori, “Simultaneous measurement of the refractive index and thickness of thin films by polarized reflectances,” Appl. Opt. 29, 5069–5073 (1990).
    [CrossRef] [PubMed]
  5. T. Kihara, K. Yokomori, “Simultaneous measurement of the refractive index and thickness of thin films by S-polarized reflectances,” Appl. Opt. 31, 4482–4487 (1992).
    [CrossRef] [PubMed]
  6. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  7. Ref. 6, Chap. 5, p. 386.
  8. Pellicle samples provided by National Photocolor Corp., Mamaroneck, New York 10543.

1992 (1)

1990 (1)

1977 (1)

R. M. A. Azzam, “Polarization-independent reflectance matching (PIRM). A technique for the determination of the refractive index and thickness of the transparent films,” J. Opt. (Paris) 8, 201–205 (1977).
[CrossRef]

1967 (1)

F. Reizmann, W. Van Gelder, “Optical thickness measurement of SiO2–Si3N4 films on silicon,” Solid-State Electron. 10, 625–632 (1967).
[CrossRef]

1964 (1)

W. A. Pliskin, E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43–51 (1964).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, “Polarization-independent reflectance matching (PIRM). A technique for the determination of the refractive index and thickness of the transparent films,” J. Opt. (Paris) 8, 201–205 (1977).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Conrad, E. E.

W. A. Pliskin, E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43–51 (1964).
[CrossRef]

Kihara, T.

Pliskin, W. A.

W. A. Pliskin, E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43–51 (1964).
[CrossRef]

Reizmann, F.

F. Reizmann, W. Van Gelder, “Optical thickness measurement of SiO2–Si3N4 films on silicon,” Solid-State Electron. 10, 625–632 (1967).
[CrossRef]

Van Gelder, W.

F. Reizmann, W. Van Gelder, “Optical thickness measurement of SiO2–Si3N4 films on silicon,” Solid-State Electron. 10, 625–632 (1967).
[CrossRef]

Yokomori, K.

Appl. Opt. (2)

IBM J. Res. Dev. (1)

W. A. Pliskin, E. E. Conrad, “Nondestructive determination of thickness and refractive index of transparent films,” IBM J. Res. Dev. 8, 43–51 (1964).
[CrossRef]

J. Opt. (Paris) (1)

R. M. A. Azzam, “Polarization-independent reflectance matching (PIRM). A technique for the determination of the refractive index and thickness of the transparent films,” J. Opt. (Paris) 8, 201–205 (1977).
[CrossRef]

Solid-State Electron. (1)

F. Reizmann, W. Van Gelder, “Optical thickness measurement of SiO2–Si3N4 films on silicon,” Solid-State Electron. 10, 625–632 (1967).
[CrossRef]

Other (3)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Ref. 6, Chap. 5, p. 386.

Pellicle samples provided by National Photocolor Corp., Mamaroneck, New York 10543.

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Figures (4)

Fig. 1
Fig. 1

Thin-film structure.

Fig. 2
Fig. 2

(a) Experimental setup of the PIRM, (b) relative orientation of the transmission axes t 1 and t 2 of the crossed polarizers.

Fig. 3
Fig. 3

Theoretically calculated result of the transmitted intensity after P2 in the setup in Fig. 2(a) versus the sample rotation angle φ. The inset is the enlargement of the first minimum transmission angle. A pellicle of thickness 4.56 μm and a refractive index of 1.5 at the 632.8-nm wavelength are assumed.

Fig. 4
Fig. 4

Theoretically calculated result of the angle of minimum transmission versus the thin-film thickness for different orders. The vertical dotted lines correspond to the two samples tested. A refractive index of 1.5 is assumed. The order number m is labeled on the top and right-hand side of the graph.

Tables (2)

Tables Icon

Table 1 Measured Angles of Minimum Transmission φ m and the Corresponding Calculated Order Numbers m, Refractive Index N 1, and the Thickness d of Pellicle Sample 1 at Two Wavelengths

Tables Icon

Table 2 Measured Angles of Minimum Transmission φ m and the Corresponding Calculated Order Numbers m, Refractive Index N 1, and the Thickness d of Pellicle Sample 2 at Two Wavelengths

Equations (4)

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R ν = r 01 ν + r 12 ν exp ( - j 2 π d / D φ ) 1 + r 01 ν r 12 ν exp ( - j 2 π d / D φ ) ,
N 1 2 = N 0 2 sin 2 φ m + m 2 ( λ 2 d ) 2 ,
N 1 = [ sin 2 φ m + m 2 ( sin 2 φ m - sin 2 φ m m 2 - m 2 ) ] 1 / 2 ( m = m or m ) , d = λ 2 ( m 2 - m 2 sin 2 φ m - sin 2 φ m ) 1 / 2 .
m = sin 2 φ m - 1 - sin 2 φ m + 1 4 sin 2 φ m - 2 ( sin 2 φ m - 1 + sin 2 φ m + 1 ) .

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