Abstract

We have developed an innovation of the polarized reflectances measurement technique for thickness and index (PRETTI) method, PRETTI-S, which is a simple and accurate technique to obtain the refractive index n and thickness d of a thin film by using S-polarized and P-polarized reflectances measured at oblique angles of incidence. In the PRETTI-S method, the n and d are determined by using only S-polarized reflectances. Therefore, the measurement and numerical procedure to extract the n and d are simpler than the conventional PRETTI method. As an example, measurement of a single-layer film (SiO2/Si) is carried out and excellent confirmation is obtained.

© 1992 Optical Society of America

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References

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  1. N. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k, and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
    [CrossRef]
  2. W. E. Case, “Algebraic method for extracting thin-film optical parameters from spectrophotometer measurements,” Appl. Opt. 22, 1832–1836 (1983).
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    [CrossRef]
  8. D. E. Aspnes, “Studies of surface, thin film and interface properties by automatic spectroscopic ellipsometry,” J. Vac. Sci. Technol. 18, 289–295 (1981).
    [CrossRef]
  9. G. H. Bu-Abbud, N. M. Bashara, “Parameter correlation and precision in multiple-angle ellipsometry,” Appl. Opt. 20, 3020–3026 (1981).
    [CrossRef] [PubMed]
  10. J. R. Zeidler, R. B. Kohles, N. M. Bashara, “Sensitivity of the ellipsometric parameters to angle-of-incidence variations,” Appl. Opt. 13, 1591–1594 (1974).
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  11. M. M. Ibrahim, N. M. Bashara, “Parameter correlation and computational considerations in multiple-angle ellipsometry,” J. Opt. Soc. Am. 61, 1622–1629 (1971).
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  12. I. Ohlidal, “Immersion spectroscopic reflectometry of multilayer systems. I. Theory,” J. Opt. Soc. Am. A 5, 459–464 (1988).
    [CrossRef]
  13. I. Ohlidal, K. Navratil, V. Holy, “Immersion spectroscopic reflectometry of multilayer systems. II. Experimental results,” J. Opt. Soc. Am. A 5, 465–470 (1988).
    [CrossRef]
  14. T. Kihara, K. Yokomori, “Simultaneous measurement of refractive index and thickness of thin film by polarized reflectances,” Appl. Opt. 29, 5069–5073 (1990).
    [CrossRef] [PubMed]
  15. T. Kihara, K. Yokomori, “Simultaneous measurement of refractive index and thickness of thin film by polarized reflectances,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1332, 783–791 (1990).
  16. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 13, p. 611. We replaced the equations in this reference by using Muller’s Nebraska conventions and definitions.17
  17. R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
    [CrossRef]

1990

1989

1988

1987

1986

1985

1984

H. Arwin, D. E. Aspnes, “Ambiguous determination of thickness and dielectric function of thin films by spectroscopic ellipsometry,” Thin Solid Films 113, 101–113 (1984).
[CrossRef]

1983

1981

G. H. Bu-Abbud, N. M. Bashara, “Parameter correlation and precision in multiple-angle ellipsometry,” Appl. Opt. 20, 3020–3026 (1981).
[CrossRef] [PubMed]

D. E. Aspnes, “Studies of surface, thin film and interface properties by automatic spectroscopic ellipsometry,” J. Vac. Sci. Technol. 18, 289–295 (1981).
[CrossRef]

1976

N. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k, and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

1974

1971

1969

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Arwin, H.

H. Arwin, D. E. Aspnes, “Ambiguous determination of thickness and dielectric function of thin films by spectroscopic ellipsometry,” Thin Solid Films 113, 101–113 (1984).
[CrossRef]

Aspnes, D. E.

H. Arwin, D. E. Aspnes, “Ambiguous determination of thickness and dielectric function of thin films by spectroscopic ellipsometry,” Thin Solid Films 113, 101–113 (1984).
[CrossRef]

D. E. Aspnes, “Studies of surface, thin film and interface properties by automatic spectroscopic ellipsometry,” J. Vac. Sci. Technol. 18, 289–295 (1981).
[CrossRef]

Bashara, N. M.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 13, p. 611. We replaced the equations in this reference by using Muller’s Nebraska conventions and definitions.17

Bu-Abbud, G. H.

Case, W. E.

Chang, M.

Elizalde, E.

Fillard, J. P.

N. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k, and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Frigerio, J. M.

Gasiot, J.

N. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k, and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Gibson, U. J.

Gustin, K. M.

Holtslag, A. H. M.

Holy, V.

Ibrahim, M. M.

Kihara, T.

T. Kihara, K. Yokomori, “Simultaneous measurement of refractive index and thickness of thin film by polarized reflectances,” Appl. Opt. 29, 5069–5073 (1990).
[CrossRef] [PubMed]

T. Kihara, K. Yokomori, “Simultaneous measurement of refractive index and thickness of thin film by polarized reflectances,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1332, 783–791 (1990).

Kohles, R. B.

Manifacier, N. J. C.

N. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k, and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Muller, R. H.

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Navratil, K.

Ohlidal, I.

Rivory, J.

Scholte, P. M. L. O.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 13, p. 611. We replaced the equations in this reference by using Muller’s Nebraska conventions and definitions.17

Yokomori, K.

T. Kihara, K. Yokomori, “Simultaneous measurement of refractive index and thickness of thin film by polarized reflectances,” Appl. Opt. 29, 5069–5073 (1990).
[CrossRef] [PubMed]

T. Kihara, K. Yokomori, “Simultaneous measurement of refractive index and thickness of thin film by polarized reflectances,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1332, 783–791 (1990).

Zeidler, J. R.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. E

N. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k, and the thickness of a weakly absorbing thin film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

J. Vac. Sci. Technol.

D. E. Aspnes, “Studies of surface, thin film and interface properties by automatic spectroscopic ellipsometry,” J. Vac. Sci. Technol. 18, 289–295 (1981).
[CrossRef]

Surf. Sci.

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Thin Solid Films

H. Arwin, D. E. Aspnes, “Ambiguous determination of thickness and dielectric function of thin films by spectroscopic ellipsometry,” Thin Solid Films 113, 101–113 (1984).
[CrossRef]

Other

T. Kihara, K. Yokomori, “Simultaneous measurement of refractive index and thickness of thin film by polarized reflectances,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. P. Grover, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1332, 783–791 (1990).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980), Chap. 13, p. 611. We replaced the equations in this reference by using Muller’s Nebraska conventions and definitions.17

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of reflections from a transparent film on a substrate.

Fig. 2
Fig. 2

Thickness curves of SiO2 film (n1 = 1.460, d1 = 500.0 nm) on a Si substrate (n2 = 3.858–0.018i), varying the film index from 1.3 to 1.8.

Fig. 3
Fig. 3

Dependence of the reflectances on angle of incidence for SiO2 film (n1 = 1.460, d1 = 700.0 nm) on a Si substrate (n2 = 3.858 − 0.018i).

Fig. 4
Fig. 4

Errors of the film index values obtained as a function of film thickness: dashed curve, for 65° and 55°; solid curve, for 40° and 30°.

Fig. 5
Fig. 5

Lower errors of the film index values obtained as a function of film thickness.

Fig. 6
Fig. 6

Errors of the film index values obtained as a function of film thickness for a glass film(n1 = 1.530) on a glass substrate (n2 = 1.460).

Fig. 7
Fig. 7

Schematic of the measurement apparatus.

Fig. 8
Fig. 8

Measured reflectance curve and the theoretically calculated curve of |r02s|2 of a SiO2/Si film, varying the angle of incidence from 10° to 80°.

Tables (2)

Tables Icon

Table 1 Values of n1 and d1 at the Cross Points, the Theoretical Reflectances and Differences between the Measured and Theoretical Reflectances at Angle θ03

Tables Icon

Table 2 Values of n1 and d1 at the Cross Points and the Differences between the Measured and Theoretical Reflectances at 40° for SiO2/Si Film

Equations (20)

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r s = r 01 s + r 12 s exp ( - 2 i β 1 ) 1 + r 01 s r 12 s exp ( - 2 i β 1 ) ,
r 01 s = n 0 cos θ 0 - n 1 cos θ 1 n 0 cos θ 0 + n 1 cos θ 1 ,
r 12 s = n 1 cos θ 1 - n 2 cos θ 2 n 1 cos θ 1 + n 2 cos θ 2 ,
2 β 1 = 4 π d 1 ( n 1 2 - n 0 2 sin 2 θ 0 ) 1 / 2 / λ .
r 12 s ρ 12 s exp ( i Φ 12 s ) .
ρ 12 s 2 = ( n 1 cos θ 1 - u 2 ) 2 + v 2 2 ( n 1 cos θ 1 + u 2 ) 2 + v 2 2 ,
tan Φ 12 s = 2 v 2 n 1 cos θ 1 u 2 2 + v 2 2 - n 1 2 cos 2 θ 1 .
2 u 2 2 = ( n 2 2 - k 2 2 ) - n 0 2 sin 2 θ 0 + [ ( n 2 2 - k 2 2 - n 0 2 sin 2 θ 0 ) 2 + 4 n 2 2 k 2 2 ] 1 / 2 ,
2 v 2 2 = - ( n 2 2 - k 2 2 ) + n 0 2 sin 2 θ 0 + [ ( n 2 2 - k 2 2 - n 0 2 sin 2 θ 0 ) 2 + 4 n 2 2 k 2 2 ] 1 / 2 .
Φ 12 s = f s ( n 0 , n 1 , n 2 , θ 0 ) .
R s = r 01 s 2 + ρ 12 s 2 + 2 r 01 s ρ 12 s cos ( Φ 12 s - 2 β 1 ) 1 + r 01 s 2 ρ 12 s 2 + 2 r 01 s ρ 12 s cos ( Φ 12 s - 2 β 1 ) .
cos ( Φ 12 s - 2 β 1 ) = r 01 s 2 + ρ 12 s 2 - R s ( 1 + r 01 s 2 ρ 12 s 2 ) 2 r 01 s ρ 12 s ( R s - 1 ) .
cos ( Φ 12 s - 2 β 1 ) = g s ( n 0 , n 1 , n 2 , θ 0 , λ , R s ) .
d 1 = λ [ f s ( n 0 , n 1 , n 2 , θ 0 , λ ) ± cos - 1 g s ( n 0 , n 1 , n 2 , θ 0 , λ , R s ) + 2 m π ] 4 π ( n 1 2 - n 0 2 sin 2 θ 0 ) 1 / 2 ,             ( - π cos - 1 g s π )
d 1 = λ [ f s ( n 0 , n 1 , n 2 , θ 02 , λ ) ± cos - 1 g s ( n 0 , n 1 , n 2 , θ 01 , λ , R s 1 ) + 2 m 1 π ] 4 π ( n 1 2 - n 0 2 sin 2 θ 01 ) 1 / 2 ,
d 1 = λ [ f s ( n 0 , n 1 , n 2 , θ 02 , λ ) ± cos - 1 g s ( n 0 , n 1 , n 2 , θ 02 , λ , R s 2 ) + 2 m 2 π ] 4 π ( n 1 2 - n 0 2 sin 2 θ 02 ) 1 / 2
λ [ f s ( n 0 , n 1 , n 2 , θ 01 , λ ) ± cos - 1 g s ( n 0 , n 1 , n 2 , θ 01 , λ , R s 1 ) + 2 m 1 π ] 4 π ( n 1 2 - n 0 2 sin 2 θ 01 ) 1 / 2 = λ [ f s ( n 0 , n 1 , n 2 , θ 02 , λ ) ± cos - 1 g s ( n 0 , n 1 , n 2 , θ 02 , λ , R s 2 ) + 2 m 2 π ] 4 π ( n 1 2 - n 0 2 sin 2 θ 02 ) 1 / 2 .
2 β 1 = 4 π d 1 ( n 1 2 - n 0 2 sin 2 θ 0 a ) 1 / 2 / λ = 2 m π ,
r s = r 01 s + r 12 s 1 + r 01 s r 12 s = n 0 cos θ 0 - n 2 cos θ 2 n 0 cos θ 0 + n 2 cos θ 2 .
d 1 a ( θ 0 a , m ) = λ 2 ( n 1 2 - n 0 2 sin 2 θ 0 a ) 1 / 2 m ,

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