Abstract

A new technique to obtain the refractive index and thickness of a thin film simultaneously is presented. The of p-polarized light and s-polarized light are measured at various angles of incidence, and by a reflectances numerical procedure the film index and thickness are extracted from the measured reflectances. The and numerical procedure are simple, and the values obtained are accurate. As an example, we measurements made measurements on a single layer film (SiO2/Si) and a double layer film (SiON/SiO2/Si) and confirmed that the values obtained were consistent.

© 1990 Optical Society of America

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References

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  1. F. Reizmann, W. Van Gelder, “Optical Thickness Measurement of SiO2–Si3N4 Films on Silicon,” Solid-State Electron. 10, 625–632 (1967).
    [CrossRef]
  2. W. A. Pliskin, Progress in Analytic Chemistry, Vol. 2, E. M. Murt, W. G. Guedner, Ed. (Plenum, New York, 1969), pp. 1–34.
  3. 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]
  4. R. M. A. Azzam, A. R. M. Zaghloul, “Polarization-Independent Reflectance Matching (PIRM) a Technique for the Determining of the Refractive Index and Thickness of Transparent Films,” J. Opt. Paris 8, 201–205 (1977).
    [CrossRef]
  5. R. J. Archer, “Determination of Properties of Films on Silicon by the Method of Ellipsometry,” J. Opt. Soc. Am. 52, 970–977 (1962).
    [CrossRef]
  6. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  7. J. Shewchun, E. C. Rowe, “Ellipsometric Technique for Obtaining Substrate Optical Constants,” J. Appl. Phys. 41, 4128–4138 (1970).
    [CrossRef]
  8. M. M. Ibrahim, N. M. Bashara, “Parameter-Correlation and Computational Consideration in Multiple-Angle Ellipsometry,” J. Opt. Soc. Am. 61, 1622 (1971).
    [CrossRef]
  9. 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).
    [CrossRef] [PubMed]
  10. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Sec. 13.4. We replaced the equations in this reference by using Muller’s Nebraska conventions and definitions.11
  11. R. H. Muller, “Definitions and Conventions in Ellipsometry,” Surf. Sci. 16, 14–33 (1969).
    [CrossRef]

1977

R. M. A. Azzam, A. R. M. Zaghloul, “Polarization-Independent Reflectance Matching (PIRM) a Technique for the Determining of the Refractive Index and Thickness of Transparent Films,” J. Opt. Paris 8, 201–205 (1977).
[CrossRef]

1974

1971

1970

J. Shewchun, E. C. Rowe, “Ellipsometric Technique for Obtaining Substrate Optical Constants,” J. Appl. Phys. 41, 4128–4138 (1970).
[CrossRef]

1969

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

1967

F. Reizmann, W. Van Gelder, “Optical Thickness Measurement of SiO2–Si3N4 Films on Silicon,” Solid-State Electron. 10, 625–632 (1967).
[CrossRef]

1964

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]

1962

Archer, R. J.

Azzam, R. M. A.

R. M. A. Azzam, A. R. M. Zaghloul, “Polarization-Independent Reflectance Matching (PIRM) a Technique for the Determining of the Refractive Index and Thickness of 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.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Sec. 13.4. We replaced the equations in this reference by using Muller’s Nebraska conventions and definitions.11

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]

Ibrahim, M. M.

Kohles, R. B.

Muller, R. H.

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

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]

W. A. Pliskin, Progress in Analytic Chemistry, Vol. 2, E. M. Murt, W. G. Guedner, Ed. (Plenum, New York, 1969), pp. 1–34.

Reizmann, F.

F. Reizmann, W. Van Gelder, “Optical Thickness Measurement of SiO2–Si3N4 Films on Silicon,” Solid-State Electron. 10, 625–632 (1967).
[CrossRef]

Rowe, E. C.

J. Shewchun, E. C. Rowe, “Ellipsometric Technique for Obtaining Substrate Optical Constants,” J. Appl. Phys. 41, 4128–4138 (1970).
[CrossRef]

Shewchun, J.

J. Shewchun, E. C. Rowe, “Ellipsometric Technique for Obtaining Substrate Optical Constants,” J. Appl. Phys. 41, 4128–4138 (1970).
[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]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Sec. 13.4. We replaced the equations in this reference by using Muller’s Nebraska conventions and definitions.11

Zaghloul, A. R. M.

R. M. A. Azzam, A. R. M. Zaghloul, “Polarization-Independent Reflectance Matching (PIRM) a Technique for the Determining of the Refractive Index and Thickness of Transparent Films,” J. Opt. Paris 8, 201–205 (1977).
[CrossRef]

Zeidler, J. R.

Appl. Opt.

IBM J. Res. Dev.

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. Appl. Phys.

J. Shewchun, E. C. Rowe, “Ellipsometric Technique for Obtaining Substrate Optical Constants,” J. Appl. Phys. 41, 4128–4138 (1970).
[CrossRef]

J. Opt. Paris

R. M. A. Azzam, A. R. M. Zaghloul, “Polarization-Independent Reflectance Matching (PIRM) a Technique for the Determining of the Refractive Index and Thickness of Transparent Films,” J. Opt. Paris 8, 201–205 (1977).
[CrossRef]

J. Opt. Soc. Am.

Solid-State Electron.

F. Reizmann, W. Van Gelder, “Optical Thickness Measurement of SiO2–Si3N4 Films on Silicon,” Solid-State Electron. 10, 625–632 (1967).
[CrossRef]

Surf. Sci.

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

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Sec. 13.4. We replaced the equations in this reference by using Muller’s Nebraska conventions and definitions.11

W. A. Pliskin, Progress in Analytic Chemistry, Vol. 2, E. M. Murt, W. G. Guedner, Ed. (Plenum, New York, 1969), pp. 1–34.

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

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Figures (5)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

Determination of the reflection coefficients of a multilayer film.

Fig. 3
Fig. 3

Schematic diagram of the measurement apparatus.

Fig. 4
Fig. 4

Measured and calculated reflectance curves of a SiO2/Si film as varying the angle of incidence from 10.00 to 70.00°.

Fig. 5
Fig. 5

Measured and calculated reflectance curves of a SiON/SiO2/Si film as varying the angle of incidence from 10.00 to 70.00°.

Equations (28)

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r p = r 01 p + r 12 p exp ( - 2 i β 1 ) 1 + r 01 p r 12 p exp ( - 2 i β 1 ) ,
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 ) ,
2 β 1 = 4 π d 1 ( n 1 2 - n 0 2 sin 2 θ 0 ) 1 / 2 / λ .
r 01 p = n 1 cos θ 0 - n 0 cos θ 1 n 1 cos θ 0 + n 0 cos θ 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 p = n 2 cos θ 1 - n 1 cos θ 2 n 2 cos θ 1 + n 1 cos θ 2 ,
r 12 s = n 1 cos θ 1 - n 2 cos θ 2 n 1 cos θ 1 + n 2 cos θ 2 ,
r 12 p = ρ 12 p exp ( i Φ 12 p ) ,
r 12 s = ρ 12 s exp ( i Φ 12 s ) .
ρ 12 p 2 = [ ( n 2 2 - k 2 2 ) cos θ 1 - n 1 u 2 ] 2 + ( 2 n 2 k 2 cos θ 1 + n 1 v 2 ) 2 [ ( n 2 2 - k 2 2 ) cos θ 1 + n 1 u 2 ] 2 + ( - 2 n 2 k 2 cos θ 1 + n 1 v 2 ) 2 ,
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 p = - 2 n 1 cos θ 1 [ 2 n 2 k 2 u 2 + ( n 2 2 - k 2 2 ) v 2 ] ( n 2 2 + k 2 2 ) 2 cos 2 θ 1 - n 1 2 ( 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 p = f p ( n 0 , n 1 , n 2 , θ 0 , λ ) ,
Φ 12 s = f s ( n 0 , n 1 , n 2 , θ 0 , λ ) ,
R p = r 01 p 2 + ρ 12 p 2 + 2 r 01 p ρ 12 p cos ( Φ 12 p - 2 β 1 ) 1 + r 01 p 2 ρ 12 p 2 + 2 r 01 p ρ 12 p cos ( Φ 12 p - 2 β 1 ) ,
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 p - 2 β 1 ) = r 01 p 2 + ρ 12 p 2 - R p ( 1 + r 01 p 2 ρ 12 p 2 ) 2 r 01 p ρ 12 p ( R p - 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 p - 2 β 1 ) = g p ( n 0 , n 1 , n 2 , θ 0 , λ , R p ) ,
cos ( Φ 12 s - 2 β 1 ) = g s ( n 0 , n 1 , n 2 , θ 0 , λ , R s ) ,
cos - 1 g p ( n 0 , n 1 , n 2 , θ 0 , λ , R p ) - cos - 1 g s ( n 0 , n 1 , n 2 , θ 0 , λ , R s ) = f p ( n 0 , n 1 , n 2 , θ 0 , λ ) - f s ( n 0 , n 1 , n 2 , θ 0 , λ ) .
d 1 ( M ) = λ ( ± cos - 1 G s + F s ) 4 π ( n 1 2 - n 0 2 sin 2 θ 0 ) 1 / 2 - λ 2 ( n 1 2 - n 0 2 sin 2 θ 0 ) 1 / 2 M ,
r p = r 01 p + r 12 p exp ( - 2 i β 1 ) 1 + r 01 p r 12 p exp ( - 2 i β 1 ) ,
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 ) ,
H ( n 1 , d 1 ) = 1 N { i = 1 N [ R c p ( n 1 , d 1 , θ i ) - R p ( θ i ) ] 2 } + 1 4 { i = 1 N [ R c s ( n 1 , d 1 , θ i ) - R s ( θ i ) ] 2 } .

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