Abstract

The variations of the intensity of the reflected light near null as a function of the angle of incidence are compared for three ellipsometric techniques. For films of either SiO2 or Si3N4 on silicon, the highest accuracy of the film thickness measurement is always obtained when the angle of incidence is either equal or nearly equal to the principal angle for all thicknesses of the film layer. Based on these results, it is shown that a variable angle of incidence spectroscopic ellipsometer operated at the principal angle of incidence and using a rotating analyzer combines the advantage of versatility with near maximum accuracy and sensitivity.

© 1982 Optical Society of America

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References

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  1. D. E. Aspnes, in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), p. 799.
  2. D. E. Aspnes, J. Vac. Sci. Technol. 18, 289 (1981).
    [Crossref]
  3. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977), Chap. 4.
  4. D. E. Aspnes, A. A. Studna, Appl. Opt. 14, 220 (1975).
    [Crossref] [PubMed]
  5. C. V. Kent, J. Lawson, J. Opt. Soc. Am. 27, 117 (1937).
    [Crossref]
  6. D. E. Aspnes, J. Opt. Soc. Am. 64, 639 (1974).
    [Crossref]
  7. H. M. O’Bryan, J. Opt. Soc. Am. 26, 122 (1936).
    [Crossref]
  8. K. Kinosta, M. Yamamoto, Surf. Sci. 56, 64 (1976).
    [Crossref]
  9. M. Yamamoto, Opt. Commun. 10, 200 (1974).
    [Crossref]
  10. R. M. A. Azzam, A. R. M. Zaghloul, J. Opt. Soc. Am. 67, 1058 (1977).
    [Crossref]
  11. M. Yamamoto, O. S. Heavens, Surf. Sci. 96, 202 (1980).
    [Crossref]
  12. D. E. Aspnes, Appl. Opt. 14, 1131 (1975).
    [Crossref] [PubMed]
  13. U. Merkt, Appl. Opt. 20, 307 (1981).
    [Crossref] [PubMed]
  14. G. H. Bu-Abbud, N. M. Bashara, Appl. Opt. 20, 3020 (1981).
    [Crossref] [PubMed]
  15. M. M. Ibrahim, N. M. Bashara, J. Opt. Soc. Am. 61, 1622 (1971).
    [Crossref]

1981 (3)

1980 (1)

M. Yamamoto, O. S. Heavens, Surf. Sci. 96, 202 (1980).
[Crossref]

1977 (1)

1976 (1)

K. Kinosta, M. Yamamoto, Surf. Sci. 56, 64 (1976).
[Crossref]

1975 (2)

1974 (2)

1971 (1)

1937 (1)

1936 (1)

Aspnes, D. E.

D. E. Aspnes, J. Vac. Sci. Technol. 18, 289 (1981).
[Crossref]

D. E. Aspnes, A. A. Studna, Appl. Opt. 14, 220 (1975).
[Crossref] [PubMed]

D. E. Aspnes, Appl. Opt. 14, 1131 (1975).
[Crossref] [PubMed]

D. E. Aspnes, J. Opt. Soc. Am. 64, 639 (1974).
[Crossref]

D. E. Aspnes, in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), p. 799.

Azzam, R. M. A.

R. M. A. Azzam, A. R. M. Zaghloul, J. Opt. Soc. Am. 67, 1058 (1977).
[Crossref]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977), Chap. 4.

Bashara, N. M.

G. H. Bu-Abbud, N. M. Bashara, Appl. Opt. 20, 3020 (1981).
[Crossref] [PubMed]

M. M. Ibrahim, N. M. Bashara, J. Opt. Soc. Am. 61, 1622 (1971).
[Crossref]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977), Chap. 4.

Bu-Abbud, G. H.

Heavens, O. S.

M. Yamamoto, O. S. Heavens, Surf. Sci. 96, 202 (1980).
[Crossref]

Ibrahim, M. M.

Kent, C. V.

Kinosta, K.

K. Kinosta, M. Yamamoto, Surf. Sci. 56, 64 (1976).
[Crossref]

Lawson, J.

Merkt, U.

O’Bryan, H. M.

Studna, A. A.

Yamamoto, M.

M. Yamamoto, O. S. Heavens, Surf. Sci. 96, 202 (1980).
[Crossref]

K. Kinosta, M. Yamamoto, Surf. Sci. 56, 64 (1976).
[Crossref]

M. Yamamoto, Opt. Commun. 10, 200 (1974).
[Crossref]

Zaghloul, A. R. M.

Appl. Opt. (4)

J. Opt. Soc. Am. (5)

J. Vac. Sci. Technol. (1)

D. E. Aspnes, J. Vac. Sci. Technol. 18, 289 (1981).
[Crossref]

Opt. Commun. (1)

M. Yamamoto, Opt. Commun. 10, 200 (1974).
[Crossref]

Surf. Sci. (2)

K. Kinosta, M. Yamamoto, Surf. Sci. 56, 64 (1976).
[Crossref]

M. Yamamoto, O. S. Heavens, Surf. Sci. 96, 202 (1980).
[Crossref]

Other (2)

D. E. Aspnes, in Optical Properties of Solids: New Developments, B. O. Seraphin, Ed. (North-Holland, Amsterdam, 1976), p. 799.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, New York, 1977), Chap. 4.

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Figures (11)

Fig. 1
Fig. 1

Relative intensity vs small changes near null in either the analyzer or polarizer angles for the CNE [see Eq. (6)]. The numbers beside each curve are the film thicknesses in nanometers.

Fig. 2
Fig. 2

Relative intensity vs small changes near null in the polarizer angle for the PA-RAE (δΔ = 0) [see Eq. (12)]. The numbers beside each curve are the film thicknesses in nanometers.

Fig. 3
Fig. 3

Relative intensity vs small changes near null in the angle of incidence for the PA-RAE (δP = 0) [see Eq. (12)]. The numbers beside each curve are the film thicknesses in nanometers.

Fig. 4
Fig. 4

Detected light intensity vs rotating analyzer angle A at the principal angle in polar coordinates for α = 0.5 (dumbbell) and α = ○ (circle) [see Eq. (20)].

Fig. 5
Fig. 5

Variation of ψ with angle of incidence and film thickness in the first order for the SiO2–Si structure. The heavy vertical curve at the right represents the locus of the principal angle of incidence. The numbers on each curve are the film thicknesses in nanometers and have been chosen in pairs to have the same PA.

Fig. 6
Fig. 6

Variation of Δ with angle of incidence for the SiO2–Si structure. Horizontal dashed lines are at Δ = ±π/2, which defines the principal angle of incidence.

Fig. 7
Fig. 7

Root-mean-square deviation in the film thickness determination vs angle of incidence for the Si–SiO2 structure for a range of thickness assuming measurement uncertainty or error in Δ and in ψ of 0.005 deg. The arrows on each curve indicate the principal angle which is the angle where the PA-RAE is nulled.

Fig. 8
Fig. 8

Root-mean-square deviation in the film refractive-index determination vs angle of incidence for the Si–SiO2 structure for a range of thickness assuming an error in Δ and ψ of 0.005 deg. The arrows on each curve indicate the principal angle which is the angle where the PA-RAE is nulled.

Fig. 9
Fig. 9

Variation of ψ with angle of incidence and film thickness in first order for the Si3N4–Si structure.

Fig. 10
Fig. 10

Variations of Δ with angle of incidence and film thickness in first order for the Si3N4–Si structure.

Fig. 11
Fig. 11

Root-mean-square deviation in the film thickness determination vs angle of incidence for the Si3N4–Si structure for a range of thickness assuming an error in Δ and ψ in of 0.005 deg. The arrows on each curve indicate the principal angle which is the angle where the PA-RAE is nulled.

Equations (25)

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R p = E r p E i p = R p exp ( i Δ p ) ,
R s = E r s E i s = R s exp ( i Δ s ) ,
R p / R s = tan ψ exp ( i Δ ) ,
Δ = Δ p - Δ s ,
tan ψ = R p R s .
I ( CNE ) = I 0 ( R p 2 + R s 2 ) [ 1 - cos 2 ψ cos 2 A + sin 2 ψ sin ( Δ - 2 P ) sin 2 A ] 4 ,
P = Δ 2 + π 4 ,
A = ± ψ .
P = Δ 2 ± π 4 + δ P ,
A = ± ψ + δ A .
I ( CNE ) = I 0 ( R s 2 + R p 2 ) [ ( δ A ) 2 + ( δ P ) 2 sin 2 2 ψ ] 2
I ( RAE ) = I 0 ( R s 2 sin 2 P + R p 2 cos 2 P ) [ 1 + α cos 2 A + β sin 2 A ) 2 ,
α = tan 2 ψ cot 2 P - 1 tan 2 ψ cot 2 P + 1 ,
β = 4 tan ψ cot P cos Δ tan 2 ψ cot 2 P + 1 .
Δ = ( ± π ) / 2 ,
ψ = ± P .
P = ± ψ + δ P ,
Δ = ( ± π ) / 2 + δ Δ ;
I ( PA - RAE ) = I 0 ( R s 2 sin 2 ) P + R p 2 cos 2 P ) × [ 1 - 2 δ P sin ( ± 2 P ) cos 2 A ± 4 δ Δ sin 2 A ]
I ( RAE ) 1 + α cos 2 A .
Δ = Δ ( T , N F ) ,
ψ = ψ ( T , N F ) .
δ T = [ ( ψ / N F ) 2 ( δ Δ ) 2 + ( Δ / N F ) 2 ( δ ψ ) 2 ] 1 / 2 S ,
δ N F = [ ( ψ / T ) 2 ( δ Δ ) 2 + ( Δ / T ) 2 ( δ ψ ) 2 ] 1 / 2 S ,
S = ( ψ / N F ) ( Δ / T ) - ( ψ / T ) ( Δ / N F ) .

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