Abstract

In this paper, we have combined a Mach-Zehnder interferometer and an optical heterodyne using an AO modulator to set up an interferometric ellipsometer for measuring the optical properties of metal surfaces. Because there is no moving mechanism, e.g., compensators and quarterwave plates, we can eliminate the errors caused by these elements. By using a phase lock-in technique and computer processing, we can measure parameters Ψ and Δ in real time and with great accuracy (where Ψ is the amplitude ratio of the P- and S-waves, and Δ is the phase difference in the P- and S-waves).

© 1990 Optical Society of America

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References

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  1. R. N. Shagam, “Heterodyne Interferometric and Moire Test Methods for Surface Measurements,” Ph.D. Thesis, U. Arizona, Tucson (1980).
  2. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).
  3. D. Malacara, Optical Shop Testing (Wiley, New York, 1978).
  4. Stanford Research Inc., SR-530 Lock-In Amplifer (1985).
  5. M. Born, E. Wolf, Principle of Optics (MacMillan, New York, 1964).
  6. V. C. Vanderbilt, “Polarization Photometer to Measure Bidirectional Reflectance Factor R(55°,0°;55°,180°) of Leaves,” Opt. Eng. 25, 566 (1986).
  7. R. M. A. Azzam, “Two-Detector Ellipsometer,” Rev. Sci. Instru. 56, 1746 (1985).
    [CrossRef]
  8. R. Greef, M. M. Wind, “Polar Representation of Ellipsometric Data,” Appl. Opt. 25, 1627–1629 (1986).
    [CrossRef] [PubMed]
  9. E. Valkonen, C.-G. Ribbing, J.-E. Sundgren, “Optical Constants of Thin TiN Films: Thickness and Preparation Effects,” Appl. Opt. 25, 3624–3630 (1986).
    [CrossRef] [PubMed]
  10. M. J. Verkerk, J. M. M. Raaymakers, “Characterization of the Topography of Vacuum-Deposited Films. 1: Light Scattering,” Appl. Opt. 25, 3602–3609 (1986).
    [CrossRef] [PubMed]

1986 (4)

1985 (1)

R. M. A. Azzam, “Two-Detector Ellipsometer,” Rev. Sci. Instru. 56, 1746 (1985).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, “Two-Detector Ellipsometer,” Rev. Sci. Instru. 56, 1746 (1985).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).

Born, M.

M. Born, E. Wolf, Principle of Optics (MacMillan, New York, 1964).

Greef, R.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Raaymakers, J. M. M.

Ribbing, C.-G.

Shagam, R. N.

R. N. Shagam, “Heterodyne Interferometric and Moire Test Methods for Surface Measurements,” Ph.D. Thesis, U. Arizona, Tucson (1980).

Sundgren, J.-E.

Valkonen, E.

Vanderbilt, V. C.

V. C. Vanderbilt, “Polarization Photometer to Measure Bidirectional Reflectance Factor R(55°,0°;55°,180°) of Leaves,” Opt. Eng. 25, 566 (1986).

Verkerk, M. J.

Wind, M. M.

Wolf, E.

M. Born, E. Wolf, Principle of Optics (MacMillan, New York, 1964).

Appl. Opt. (3)

Opt. Eng. (1)

V. C. Vanderbilt, “Polarization Photometer to Measure Bidirectional Reflectance Factor R(55°,0°;55°,180°) of Leaves,” Opt. Eng. 25, 566 (1986).

Rev. Sci. Instru. (1)

R. M. A. Azzam, “Two-Detector Ellipsometer,” Rev. Sci. Instru. 56, 1746 (1985).
[CrossRef]

Other (5)

R. N. Shagam, “Heterodyne Interferometric and Moire Test Methods for Surface Measurements,” Ph.D. Thesis, U. Arizona, Tucson (1980).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Stanford Research Inc., SR-530 Lock-In Amplifer (1985).

M. Born, E. Wolf, Principle of Optics (MacMillan, New York, 1964).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Parameter Ψ vs incident angles.

Fig. 3
Fig. 3

Parameter Δ vs incident angles.

Tables (1)

Tables Icon

Table I The (Ψ,Δ) and Complex Index vs Incident Angles

Equations (19)

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I = I 1 + I 2 + 2 I 1 I 2 cos ( ϕ 1 - ϕ 2 ) ,
ϕ 1 = k 1 · r - ω 1 t + φ 1 ,
ϕ 2 = k 2 · r - ω 2 t + φ 2 ,
I cos [ ( k 1 - k 2 ) · r + ( ω 1 - ω 2 ) t + ( φ 1 - φ 2 ) ] .
X = ρ P cos ( ω t - δ p ) ,
Y = ρ s cos ( ω t - δ s ) ,
( X ρ p ) 2 + ( Y ρ s ) 2 - 2 ( X ρ p ) ( Y ρ s ) cos Δ = sin 2 Δ ,
tan Ψ = | ρ s ρ p | .
E p 1 = ρ p 2 A p T ˜ p 2 R ˜ p 2 x ˜ p ˜ exp { j [ ( ω 0 + ω t ) t + φ 1 + 2 δ p ] } , E p 2 = A p T ˜ p 2 R ˜ p 2 x ˜ p ˜ exp { j [ ( ω 0 + ω 2 ) t + φ 2 ] } , E s 1 = ρ s 2 A s T ˜ s 2 r ˜ s 2 x ˜ s ˜ exp { j [ ( ω 0 + ω 1 ) t + φ 1 + 2 δ s ] } , E p 2 = A s T ˜ s 2 R ˜ s 2 x ˜ s ˜ exp { j [ ( ω 0 + ω 2 ) t + φ 2 ] } .
I p = E p 1 + E p 2 2 = ( A p T ˜ p 2 R ˜ p 2 x ˜ p ˜ ) 2 [ ( ρ p 4 + 1 ) + 2 ρ p 2 cos ( ω t + φ + 2 δ p ) ] .
I s = E s 1 + E s 2 2 = ( A s T ˜ s 2 R ˜ s 2 x ˜ s ˜ ) 2 [ ( ρ s 4 + 1 ) + 2 ρ s 2 cos ( ω t + φ + 2 δ s ) ] .
V p = 2 ( A p T ˜ p 2 R ˜ p 2 x ˜ p ˜ ) 2 ρ p 2 cos ( 2 δ p + ω t + φ ) ,
V s = 2 ( A s T ˜ s 2 R ˜ s 2 x ˜ s ˜ ) 2 ρ s cos ( 2 δ s + ω t + φ ) .
Δ = ½ [ ( 2 δ s + φ ) - ( 2 δ p + φ ) ] = δ s - δ p .
Ψ = tan - 1 | ρ s ρ p | = tan - 1 ( | V s V p | / | ( A s T ˜ s 2 R ˜ s 2 x ˜ s ˜ ) 2 ( A p T ˜ p 2 R ˜ p 2 x ˜ p ˜ ) 2 | ) 1 / 2 .
V p = 2 ( A p T ˜ p 2 R ˜ p 2 x ˜ p ˜ ) 2 cos [ ( ω t ) + φ 1 ] , V s = 2 ( A s T ˜ s 2 R ˜ s 2 x ˜ s ˜ ) 2 cos [ ( ω t ) + φ 2 ] .
A s T ˜ s 2 R ˜ s 2 x ˜ s ˜ = A p T ˜ p 2 R ˜ p 2 x ˜ p ˜
| V s V p | = 1 ,
Ψ = tan - 1 | V s V p | 1 / 2 .

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