Abstract

We describe an interferometric ellipsometer that, in contrast to previous designs, requires a single reflection from a sample surface so that tanψ and Δ are measured directly. A reference beam is created in one arm of a modified Mach–Zehnder interferometer such that the p and s polarizations have a common phase and fixed relative amplitude, irrespective of the sample. This beam is combined interferometrically with the measurement beam. The output beam is spatially separated into its polarization components and temporal fringes created at the photodetectors via mechanical scanning of one of the mirrors. Measurements made on a reference SiO2 film are in excellent agreement with the calibration certificate while those made on a glass surface demonstrate measurement capabilities for low reflectivity samples. Estimates of the noise performance indicate a precision, in air, of 41pm.

© 2008 Optical Society of America

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References

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  1. H. Hazebroek and W. Visser, “Automated laser interferometric ellipsometry and precision reflectometry,” J. Phys. E 16, 654-661 (1983).
    [CrossRef]
  2. H. Hazebroek and A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822-826 (1973).
    [CrossRef]
  3. M. Wind and K. Hemmes, “New ultra-fast interferometric systems based on a Zeeman two-frequency laser,” Meas. Sci. Technol. 5, 37-46 (1994).
    [CrossRef]
  4. K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. de Laet, and H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond or faster,” Thin Solid Films 313-314, 40-46 (1998).
    [CrossRef]
  5. L. Watkins and M. Hoogerland, “Interferometric ellipsometer with wavelength-modulated source,” Appl. Opt. 43, 4362-4366 (2004).
    [CrossRef] [PubMed]
  6. C.-H. Lin, C. Chou, and K.-S. Chang, “Real time interferometric ellipsometry with optical heterodyne and phase lock-in techniques,” Appl. Opt. 29, 5159-5162 (1990).
    [CrossRef] [PubMed]
  7. J. Shamir and P. Graff, “Optical parameters of partially transmitting thin films. 1: Basic theory of a novel method for their determinations,” Appl. Opt. 14, 3053-3056 (1975).
    [PubMed]
  8. J. Shamir, “Optical parameters of partially transmitting thin films. 2: Experiment and further analysis of a novel method for their determination,” Appl. Opt. 15, 120-126 (1976).
    [CrossRef] [PubMed]
  9. J. Shamir, “Double-beam interferometers for analysis of thin films,” Opt. Eng. 19, 801-805 (1980).
  10. H. Rosen and J. Shamir, “Interferometric determination of ellipsometric parameters,” J. Phys. E 11, 905-908 (1978).
    [CrossRef]
  11. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).
  12. A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least-squares fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 476-480 (1999).
    [CrossRef]
  13. A. Fitzgibbon, “Direct least-squares fitting of ellipses,” http://research.microsoft.com/awf/ellipse/.

2004

1999

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least-squares fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 476-480 (1999).
[CrossRef]

1998

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. de Laet, and H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond or faster,” Thin Solid Films 313-314, 40-46 (1998).
[CrossRef]

1994

M. Wind and K. Hemmes, “New ultra-fast interferometric systems based on a Zeeman two-frequency laser,” Meas. Sci. Technol. 5, 37-46 (1994).
[CrossRef]

1990

1983

H. Hazebroek and W. Visser, “Automated laser interferometric ellipsometry and precision reflectometry,” J. Phys. E 16, 654-661 (1983).
[CrossRef]

1980

J. Shamir, “Double-beam interferometers for analysis of thin films,” Opt. Eng. 19, 801-805 (1980).

1978

H. Rosen and J. Shamir, “Interferometric determination of ellipsometric parameters,” J. Phys. E 11, 905-908 (1978).
[CrossRef]

1976

1975

1973

H. Hazebroek and A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822-826 (1973).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

Bender, H.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. de Laet, and H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond or faster,” Thin Solid Films 313-314, 40-46 (1998).
[CrossRef]

Chang, K.-S.

Chou, C.

de Laet, J.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. de Laet, and H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond or faster,” Thin Solid Films 313-314, 40-46 (1998).
[CrossRef]

Fisher, R. B.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least-squares fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 476-480 (1999).
[CrossRef]

Fitzgibbon, A.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least-squares fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 476-480 (1999).
[CrossRef]

A. Fitzgibbon, “Direct least-squares fitting of ellipses,” http://research.microsoft.com/awf/ellipse/.

Graff, P.

Hamstra, M. A.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. de Laet, and H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond or faster,” Thin Solid Films 313-314, 40-46 (1998).
[CrossRef]

Hazebroek, H.

H. Hazebroek and W. Visser, “Automated laser interferometric ellipsometry and precision reflectometry,” J. Phys. E 16, 654-661 (1983).
[CrossRef]

H. Hazebroek and A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822-826 (1973).
[CrossRef]

Hemmes, K.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. de Laet, and H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond or faster,” Thin Solid Films 313-314, 40-46 (1998).
[CrossRef]

M. Wind and K. Hemmes, “New ultra-fast interferometric systems based on a Zeeman two-frequency laser,” Meas. Sci. Technol. 5, 37-46 (1994).
[CrossRef]

Holscher, A.

H. Hazebroek and A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822-826 (1973).
[CrossRef]

Hoogerland, M.

Koops, K. R.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. de Laet, and H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond or faster,” Thin Solid Films 313-314, 40-46 (1998).
[CrossRef]

Lin, C.-H.

Pilu, M.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least-squares fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 476-480 (1999).
[CrossRef]

Rosen, H.

H. Rosen and J. Shamir, “Interferometric determination of ellipsometric parameters,” J. Phys. E 11, 905-908 (1978).
[CrossRef]

Schram, T.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. de Laet, and H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond or faster,” Thin Solid Films 313-314, 40-46 (1998).
[CrossRef]

Shamir, J.

Visser, W.

H. Hazebroek and W. Visser, “Automated laser interferometric ellipsometry and precision reflectometry,” J. Phys. E 16, 654-661 (1983).
[CrossRef]

Watkins, L.

Wind, M.

M. Wind and K. Hemmes, “New ultra-fast interferometric systems based on a Zeeman two-frequency laser,” Meas. Sci. Technol. 5, 37-46 (1994).
[CrossRef]

Wind, M. M.

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. de Laet, and H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond or faster,” Thin Solid Films 313-314, 40-46 (1998).
[CrossRef]

Appl. Opt.

IEEE Trans. Pattern Anal. Mach. Intell.

A. Fitzgibbon, M. Pilu, and R. B. Fisher, “Direct least-squares fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 476-480 (1999).
[CrossRef]

J. Phys. E

H. Rosen and J. Shamir, “Interferometric determination of ellipsometric parameters,” J. Phys. E 11, 905-908 (1978).
[CrossRef]

H. Hazebroek and W. Visser, “Automated laser interferometric ellipsometry and precision reflectometry,” J. Phys. E 16, 654-661 (1983).
[CrossRef]

H. Hazebroek and A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822-826 (1973).
[CrossRef]

Meas. Sci. Technol.

M. Wind and K. Hemmes, “New ultra-fast interferometric systems based on a Zeeman two-frequency laser,” Meas. Sci. Technol. 5, 37-46 (1994).
[CrossRef]

Opt. Eng.

J. Shamir, “Double-beam interferometers for analysis of thin films,” Opt. Eng. 19, 801-805 (1980).

Thin Solid Films

K. Hemmes, M. A. Hamstra, K. R. Koops, M. M. Wind, T. Schram, J. de Laet, and H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond or faster,” Thin Solid Films 313-314, 40-46 (1998).
[CrossRef]

Other

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

A. Fitzgibbon, “Direct least-squares fitting of ellipses,” http://research.microsoft.com/awf/ellipse/.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the interferometric ellipsometer: L, laser; S, sample; G, goniometer; BS 1 and BS 2 , nonpolarizing beam splitters; P 1 and P 2 , polarizers; WP, optional wave plate; PZT, piezoelectric transducer; PD 1 and PD 2 , photodetectors; W, Wollaston prism; A / D , analog-to-digital converter in personal computer (PC).

Fig. 2
Fig. 2

tan ψ and Δ as a function of AOI for Si O 2 ( n = 1.457 and d = 102.73 nm ) on Si ( n = 3.88 , and k = 0.019 ). Solid curves, expected values; open symbols, experimental values.

Fig. 3
Fig. 3

tan ψ and Δ as a function of AOI for water film ( n = 1.33 and d = 2.2 nm ) on BK7 glass ( n = 1.515 ). Solid curves, best fit values; open symbols, experimental values.

Fig. 4
Fig. 4

Observed noise for Si O 2 film on Si at 75 ° AOI.

Fig. 5
Fig. 5

Observed noise for straight-through measurement.

Equations (13)

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E in = [ cos A cos ε i sin A sin ε sin A cos ε + i cos A sin ε ] = [ u exp ( ι ξ ) v exp ( ι η ) ] ,
E m = B 2 B 1 E in exp ( i ω 1 t ) = 1 2 [ u exp ( ι ξ ) v exp ( ι η ) ] exp ( i ω 1 t ) ,
E r = B 2 R ( P ) P 2 R ( P ) M 2 M 1 R ( π 2 ) P 1 R ( π 2 ) × B 1 E in exp ( i ω 2 t ) = 1 2 r s M 1 r s M 2 υ sin P exp ( i η ) [ cos P sin P ] exp ( i ω 2 t ) = 1 2 ω exp ( i φ ) [ cos P sin P ] exp ( i ω 2 t ) ,
I p c 1 4 u 2 + 1 4 ω 2 cos 2 P + 1 2 u ω cos P cos ( ω 0 t + ξ φ ) ,
I s c 1 4 υ 2 + 1 4 ω 2 sin 2 P + 1 2 υ ω sin P cos ( ω 0 t + η φ ) ,
V r c = ( k p I p k s I s ) ac = k p k s u cos P υ sin P ,
Δ ϕ c = arg ( I p ) a c arg ( I s ) a c = ξ η .
E in [ | r p | u exp ( i [ ξ + δ p ] ) | r s | υ exp ( i [ η + δ s ] ) ] ,
I p m 1 4 u 2 | r p | 2 + 1 4 ω 2 | r s | 2 cos 2 P + 1 2 u ω | r p | | r s | cos P × cos ( ω 0 t + ξ φ + δ p δ s ) ,
I s m 1 4 υ 2 | r s | 2 + 1 4 ω 2 | r s | 2 sin 2 P + 1 2 υ ω | r s | 2 sin P × cos ( ω 0 t + η φ ) .
V r m = k p k s u cos P υ sin P | r p | | r s | = V r c tan ψ ,
Δ ϕ m = ξ η + δ p δ s = Δ ϕ c + Δ .
ε = AOI [ ( ρ m ρ c ) 2 + ( Δ m Δ c ) 2 ] ,

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