Abstract

An accurate optical coherent ellipsometer (OCE) is proposed and setup in which a two-frequency paired linear polarized laser beam is integrated with a common-path heterodyne interferometer. This OCE is able to precisely measure the optical properties of scattering specimen by measuring ellipsometric parameters (ψ, Δ). In the mean time the degree of polarization P, and degree of coherence χ of incident two-frequency linear polarized laser beam are measured too. In the experiment, both smooth and ground BK7 glass plates were tested in which the optical parameters (ψ, Δ, P, χ) were obtained precisely. Comparing with conventional ellipsometers, OCE can characterize scattering specimen precisely and excludes the scattering effect.

© 2008 Optical Society of America

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  1. R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1980).
  2. T. E. Jenkins, "Multiple-angle-of-incidence ellipsometry," J. Phys. D. Appl. Phys. 32, R45-R56 (1999).
    [CrossRef]
  3. D. E. Aspnes, "Expanding horizons: new developments in ellipsometry and polarimetry," Thin Solid Films 455-456, 3-13 (2004).
    [CrossRef]
  4. K. Riedling, Ellipsometry for Industrial Applications (Springer-Verlag, New York, 1988).
    [CrossRef]
  5. R. Greef, "An automatic ellipsometer for use in electrochemical investigations," Rev. Sci. Instrum. 41, 532-538 (1970).
    [CrossRef]
  6. C. V. Kent, "A photoelectric method for the determination of the parameters of elliptically polarized light," J. Opt. Soc. Am. 27, 117-119 (1937).
    [CrossRef]
  7. D. E. Aspnes, "Optimizing precision of rotating-analyzer ellipsometers," J. Opt. Soc. Am. 64, 639-646 (1974).
    [CrossRef]
  8. S. N. Jasperson and S. E. Schnatterly, "An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique," Rev. Sci. Instrum. 40, 761 (1969).
    [CrossRef]
  9. S. N. Jasperson, D. K. Burge, and R. C. O’Handley, "A modulated ellipsometer for studying thin film optical properties and surface dynamics," Surf. Sci. 37, 548-558 (1973).
    [CrossRef]
  10. C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, "Polarization modulation imaging ellipsometry for thin film thickness measurement," Opt. Commun. 273, 74-83 (2007).
    [CrossRef]
  11. M. W. Wang, F. H. Tsai, and Y. F. Chao, "In situ calibration technique for photoelastic modulator in ellipsometry," Thin Solid Films 455-456, 78-83 (2004).
    [CrossRef]
  12. S.-M. F. Nee and T. W. Nee, "Principal Mueller matrix of reflection and scattering measured for a one-dimensional rough surface," Opt. Eng. 41, 994-1001 (2002).
    [CrossRef]
  13. S. -M. F. Nee, "Error analysis of null ellipsometry with depolarization," Appl. Opt. 38, 5388-5398 (1999).
    [CrossRef]
  14. S. -M. F. Nee, "Depolarization and principal Mueller matrix measured by null ellipsometry," Appl. Opt. 40, 4933-4939 (2001).
    [CrossRef]
  15. C. H. Lin, C. Chou, K. S. Chang, "Real time interferometric ellipsometry with optical heterodyne and phase lock in technique," Appl. Opt. 29,5159-5162 (1990).
    [CrossRef] [PubMed]
  16. C. Chou, H. K. Teng, C. C. Tsai, and L. P. Yu, "Balanced detector interferometric ellipsometer," J. Opt. Soc. Am. A 23, 2871-2879 (2006).
    [CrossRef]
  17. H. F. Chang, C. Chou, H. K. Teng, H. T. Wu, and H. F. Yau, "The use of polarization and amplitude-sensitive optical heterodyne interferometry for linear birefringence parameters measurement," Opt. Commun. 260, 420-426 (2006).
    [CrossRef]
  18. D. C. Su, M. H. Chiu, and C. D. Chen, "Simple two-frequency laser," Prec. Eng. 18, 161-163 (1996).
    [CrossRef]

2007 (1)

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, "Polarization modulation imaging ellipsometry for thin film thickness measurement," Opt. Commun. 273, 74-83 (2007).
[CrossRef]

2006 (2)

C. Chou, H. K. Teng, C. C. Tsai, and L. P. Yu, "Balanced detector interferometric ellipsometer," J. Opt. Soc. Am. A 23, 2871-2879 (2006).
[CrossRef]

H. F. Chang, C. Chou, H. K. Teng, H. T. Wu, and H. F. Yau, "The use of polarization and amplitude-sensitive optical heterodyne interferometry for linear birefringence parameters measurement," Opt. Commun. 260, 420-426 (2006).
[CrossRef]

2004 (2)

M. W. Wang, F. H. Tsai, and Y. F. Chao, "In situ calibration technique for photoelastic modulator in ellipsometry," Thin Solid Films 455-456, 78-83 (2004).
[CrossRef]

D. E. Aspnes, "Expanding horizons: new developments in ellipsometry and polarimetry," Thin Solid Films 455-456, 3-13 (2004).
[CrossRef]

2002 (1)

S.-M. F. Nee and T. W. Nee, "Principal Mueller matrix of reflection and scattering measured for a one-dimensional rough surface," Opt. Eng. 41, 994-1001 (2002).
[CrossRef]

2001 (1)

1999 (2)

T. E. Jenkins, "Multiple-angle-of-incidence ellipsometry," J. Phys. D. Appl. Phys. 32, R45-R56 (1999).
[CrossRef]

S. -M. F. Nee, "Error analysis of null ellipsometry with depolarization," Appl. Opt. 38, 5388-5398 (1999).
[CrossRef]

1996 (1)

D. C. Su, M. H. Chiu, and C. D. Chen, "Simple two-frequency laser," Prec. Eng. 18, 161-163 (1996).
[CrossRef]

1990 (1)

1974 (1)

1973 (1)

S. N. Jasperson, D. K. Burge, and R. C. O’Handley, "A modulated ellipsometer for studying thin film optical properties and surface dynamics," Surf. Sci. 37, 548-558 (1973).
[CrossRef]

1970 (1)

R. Greef, "An automatic ellipsometer for use in electrochemical investigations," Rev. Sci. Instrum. 41, 532-538 (1970).
[CrossRef]

1969 (1)

S. N. Jasperson and S. E. Schnatterly, "An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique," Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

1937 (1)

Aspnes, D. E.

D. E. Aspnes, "Expanding horizons: new developments in ellipsometry and polarimetry," Thin Solid Films 455-456, 3-13 (2004).
[CrossRef]

D. E. Aspnes, "Optimizing precision of rotating-analyzer ellipsometers," J. Opt. Soc. Am. 64, 639-646 (1974).
[CrossRef]

Burge, D. K.

S. N. Jasperson, D. K. Burge, and R. C. O’Handley, "A modulated ellipsometer for studying thin film optical properties and surface dynamics," Surf. Sci. 37, 548-558 (1973).
[CrossRef]

Chang, H. F.

H. F. Chang, C. Chou, H. K. Teng, H. T. Wu, and H. F. Yau, "The use of polarization and amplitude-sensitive optical heterodyne interferometry for linear birefringence parameters measurement," Opt. Commun. 260, 420-426 (2006).
[CrossRef]

Chang, K. S.

Chao, Y. F.

M. W. Wang, F. H. Tsai, and Y. F. Chao, "In situ calibration technique for photoelastic modulator in ellipsometry," Thin Solid Films 455-456, 78-83 (2004).
[CrossRef]

Chen, C. D.

D. C. Su, M. H. Chiu, and C. D. Chen, "Simple two-frequency laser," Prec. Eng. 18, 161-163 (1996).
[CrossRef]

Chiu, M. H.

D. C. Su, M. H. Chiu, and C. D. Chen, "Simple two-frequency laser," Prec. Eng. 18, 161-163 (1996).
[CrossRef]

Chou, C.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, "Polarization modulation imaging ellipsometry for thin film thickness measurement," Opt. Commun. 273, 74-83 (2007).
[CrossRef]

H. F. Chang, C. Chou, H. K. Teng, H. T. Wu, and H. F. Yau, "The use of polarization and amplitude-sensitive optical heterodyne interferometry for linear birefringence parameters measurement," Opt. Commun. 260, 420-426 (2006).
[CrossRef]

C. Chou, H. K. Teng, C. C. Tsai, and L. P. Yu, "Balanced detector interferometric ellipsometer," J. Opt. Soc. Am. A 23, 2871-2879 (2006).
[CrossRef]

C. H. Lin, C. Chou, K. S. Chang, "Real time interferometric ellipsometry with optical heterodyne and phase lock in technique," Appl. Opt. 29,5159-5162 (1990).
[CrossRef] [PubMed]

Greef, R.

R. Greef, "An automatic ellipsometer for use in electrochemical investigations," Rev. Sci. Instrum. 41, 532-538 (1970).
[CrossRef]

Huang, H. S.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, "Polarization modulation imaging ellipsometry for thin film thickness measurement," Opt. Commun. 273, 74-83 (2007).
[CrossRef]

Jasperson, S. N.

S. N. Jasperson, D. K. Burge, and R. C. O’Handley, "A modulated ellipsometer for studying thin film optical properties and surface dynamics," Surf. Sci. 37, 548-558 (1973).
[CrossRef]

S. N. Jasperson and S. E. Schnatterly, "An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique," Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

Jenkins, T. E.

T. E. Jenkins, "Multiple-angle-of-incidence ellipsometry," J. Phys. D. Appl. Phys. 32, R45-R56 (1999).
[CrossRef]

Kent, C. V.

Lin, C. H.

Nee, S. -M. F.

Nee, S.-M. F.

S.-M. F. Nee and T. W. Nee, "Principal Mueller matrix of reflection and scattering measured for a one-dimensional rough surface," Opt. Eng. 41, 994-1001 (2002).
[CrossRef]

Nee, T. W.

S.-M. F. Nee and T. W. Nee, "Principal Mueller matrix of reflection and scattering measured for a one-dimensional rough surface," Opt. Eng. 41, 994-1001 (2002).
[CrossRef]

O’Handley, R. C.

S. N. Jasperson, D. K. Burge, and R. C. O’Handley, "A modulated ellipsometer for studying thin film optical properties and surface dynamics," Surf. Sci. 37, 548-558 (1973).
[CrossRef]

Schnatterly, S. E.

S. N. Jasperson and S. E. Schnatterly, "An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique," Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

Su, D. C.

D. C. Su, M. H. Chiu, and C. D. Chen, "Simple two-frequency laser," Prec. Eng. 18, 161-163 (1996).
[CrossRef]

Teng, H. K.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, "Polarization modulation imaging ellipsometry for thin film thickness measurement," Opt. Commun. 273, 74-83 (2007).
[CrossRef]

H. F. Chang, C. Chou, H. K. Teng, H. T. Wu, and H. F. Yau, "The use of polarization and amplitude-sensitive optical heterodyne interferometry for linear birefringence parameters measurement," Opt. Commun. 260, 420-426 (2006).
[CrossRef]

C. Chou, H. K. Teng, C. C. Tsai, and L. P. Yu, "Balanced detector interferometric ellipsometer," J. Opt. Soc. Am. A 23, 2871-2879 (2006).
[CrossRef]

Tsai, C. C.

Tsai, F. H.

M. W. Wang, F. H. Tsai, and Y. F. Chao, "In situ calibration technique for photoelastic modulator in ellipsometry," Thin Solid Films 455-456, 78-83 (2004).
[CrossRef]

Wang, M. W.

M. W. Wang, F. H. Tsai, and Y. F. Chao, "In situ calibration technique for photoelastic modulator in ellipsometry," Thin Solid Films 455-456, 78-83 (2004).
[CrossRef]

Wu, H. T.

H. F. Chang, C. Chou, H. K. Teng, H. T. Wu, and H. F. Yau, "The use of polarization and amplitude-sensitive optical heterodyne interferometry for linear birefringence parameters measurement," Opt. Commun. 260, 420-426 (2006).
[CrossRef]

Yau, H. F.

H. F. Chang, C. Chou, H. K. Teng, H. T. Wu, and H. F. Yau, "The use of polarization and amplitude-sensitive optical heterodyne interferometry for linear birefringence parameters measurement," Opt. Commun. 260, 420-426 (2006).
[CrossRef]

Yu, C. J.

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, "Polarization modulation imaging ellipsometry for thin film thickness measurement," Opt. Commun. 273, 74-83 (2007).
[CrossRef]

Yu, L. P.

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Phys. D. Appl. Phys. (1)

T. E. Jenkins, "Multiple-angle-of-incidence ellipsometry," J. Phys. D. Appl. Phys. 32, R45-R56 (1999).
[CrossRef]

Opt. Commun. (2)

H. F. Chang, C. Chou, H. K. Teng, H. T. Wu, and H. F. Yau, "The use of polarization and amplitude-sensitive optical heterodyne interferometry for linear birefringence parameters measurement," Opt. Commun. 260, 420-426 (2006).
[CrossRef]

C. Chou, H. K. Teng, C. J. Yu, and H. S. Huang, "Polarization modulation imaging ellipsometry for thin film thickness measurement," Opt. Commun. 273, 74-83 (2007).
[CrossRef]

Opt. Eng. (1)

S.-M. F. Nee and T. W. Nee, "Principal Mueller matrix of reflection and scattering measured for a one-dimensional rough surface," Opt. Eng. 41, 994-1001 (2002).
[CrossRef]

Prec. Eng. (1)

D. C. Su, M. H. Chiu, and C. D. Chen, "Simple two-frequency laser," Prec. Eng. 18, 161-163 (1996).
[CrossRef]

Rev. Sci. Instrum. (2)

R. Greef, "An automatic ellipsometer for use in electrochemical investigations," Rev. Sci. Instrum. 41, 532-538 (1970).
[CrossRef]

S. N. Jasperson and S. E. Schnatterly, "An Improved Method for High Reflectivity Ellipsometry Based on a New Polarization Modulation Technique," Rev. Sci. Instrum. 40, 761 (1969).
[CrossRef]

Surf. Sci. (1)

S. N. Jasperson, D. K. Burge, and R. C. O’Handley, "A modulated ellipsometer for studying thin film optical properties and surface dynamics," Surf. Sci. 37, 548-558 (1973).
[CrossRef]

Thin Solid Films (2)

D. E. Aspnes, "Expanding horizons: new developments in ellipsometry and polarimetry," Thin Solid Films 455-456, 3-13 (2004).
[CrossRef]

M. W. Wang, F. H. Tsai, and Y. F. Chao, "In situ calibration technique for photoelastic modulator in ellipsometry," Thin Solid Films 455-456, 78-83 (2004).
[CrossRef]

Other (2)

K. Riedling, Ellipsometry for Industrial Applications (Springer-Verlag, New York, 1988).
[CrossRef]

R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1980).

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Figures (6)

Fig. 1.
Fig. 1.

The optical setup of OCE, S: specimen, A: analyzer, D: photo detector, DVM: digital voltmeter, PC: Personal computer.

Fig. 2.
Fig. 2.

DOC χ as a function of ψ for different P. Notice that χ<P<1 always.

Fig. 3.
Fig. 3.

The phase retardation of SBC measurement, A1, A2: analyzers, LIA: lock-in amplifier, D1, D2: photo detectors, BS: beam splitter, PC: personal computer.

Fig. 4.
Fig. 4.

The optical setup of DOP measurement for a scattering glass plate (G), A; analyzer, D: photo detector, DVM: digital voltmeter, PC: personal computer.

Fig. 5.
Fig. 5.

The measured ψ of a glass plate at (a) 10.63°, (b) 16.38°, (c) 25.68° and (d) 36° are obtained by theoretical curve (solid line) fitting with the experimental data (dots).

Fig. 6.
Fig. 6.

The phase retardation of SBC versus calibrated data (Special optics 8-400-UNCTD).

Tables (2)

Tables Icon

Table 1. Phase retardation of SBC.

Tables Icon

Table 2. Depolarization by ground glass plate.

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

r p = r p exp ( i φ p ) ,
r s = r s exp ( i φ s ) .
ρ = r p r s = tan ψ exp ( i Δ ) ,
ψ = tan 1 ( r p r s ) ,
Δ = φ p φ s .
M = T ( 1 P cos 2 ψ 0 0 P cos 2 ψ 1 2 D v 0 0 0 0 P sin 2 ψ cos Δ P sin 2 ψ sin Δ 0 0 P sin 2 ψ sin Δ P sin 2 ψ cos Δ ) .
D 1 P = D u + D v .
S in = ( 1 0 0 0 0 1 0 0 0 0 cos δ ω t sin δ ω t 0 0 sin δ ω t cos δ ω t ) ( 1 0 1 0 ) I 0 = ( 1 0 cos δ ω t sin δ ω t ) I 0
I sig = D · A · M · S in
= ( 1 0 0 0 ) t T a ( 1 cos 2 A sin 2 A 0 cos 2 A cos 2 2 A sin 2 A cos 2 A 0 sin 2 A sin 2 A cos 2 A sin 2 2 A 0 0 0 0 0 )
· T ( 1 P cos 2 ψ 0 0 P cos 2 ψ 1 2 D v 0 0 0 0 P sin 2 ψ cos Δ P sin 2 ψ sin Δ 0 0 P sin 2 ψ sin Δ P sin 2 ψ cos Δ ) I 0 ( 1 0 cos δ ω t sin δ ω t )
    = I dc + I ac cos ( δ ω t + Δ ) ,
I dc = T a TI 0 ( 1 P cos 2 ψ cos 2 A ) ,
I ac = T a TI 0 ( P sin 2 ψ sin 2 A ) .
γ = I ac I dc = P sin 2 ψ sin 2 A 1 P cos 2 ψ cos 2 A ,
γ = P sin 2 ψ sin 2 A + γ P cos 2 ψ cos 2 A .
cos 2 A = P cos 2 ψ
χ = max ( γ ) = P sin 2 ψ ( 1 P 2 cos 2 2 ψ ) 1 2 ,
M c = T c ( 1 0 0 0 0 1 0 0 0 0 cos Γ sin Γ 0 0 sin Γ cos Γ )
I sig = T a T BS T c I 0 [ 1 + cos ( δ ω t + Γ ) ]
I ref = T a R BS I 0 ( 1 + cos δ ω t )
S sca = M sca · S in = T sca ( 1 0 P sca cos δ ω t P sca sin δ ω t )
P T = P 2 · P 1
γ ( A = 45 ° ) = I ac I dc = P

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