Abstract

A new approach to automatic null ellipsometry is described in which the analyzer of a traditional polarizer compensator sample analyzer (PCSA) null ellipsometer is replaced with a heterodyne Michelson interferometer. One arm of this interferometer is modified such that it produces a fixed, linearly polarized reference beam, irrespective of the input polarization state. This beam is recombined interferometrically with the measurement beam and spatially separated into its p and s polarizations. The relative phase of the resulting temporal fringes is a linear function of the polarizer azimuthal angle P, and thus this component can be driven to its null position without iteration. Once at null, the azimuthal angle of the reflected, linearly polarized light is trivially determined from the relative amplitude of the fringes. Measurements made with this instrument on a native oxide film on a silicon wafer were in excellent agreement with those made with a traditional PCSA null ellipsometer.

© 2009 Optical Society of America

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References

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  1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).
  2. F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67A, 363-377(1963).
  3. H. P. Layer, “Circuit design for an electronic self-nulling ellipsometer,” Surf. Sci. 16, 177-192 (1969).
    [CrossRef]
  4. E. F. I. Roberts and A. Meadows, “A high precision automatic ellipsometer using grating goniometers,” J. Phys. E. 7, 379-386 (1974).
    [CrossRef]
  5. H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798-802 (1974).
    [CrossRef]
  6. H. Zhu, L. Liu, W. Wen, Z. Lu, and B. Zhang, “High-precision system for automatic null ellipsometric measurement,” Appl. Opt. 41, 4536-4540 (2002).
    [CrossRef] [PubMed]
  7. T. Yamaguchi, “A quick response recording ellipsometer,” Sci. Light 16, 64-71 (1967).
  8. H. Takasaki, “Automatic ellipsometer. Automatic polarimetry by means of an ADP polarization modulator III,” Appl. Opt. 5, 759-764 (1966).
    [CrossRef] [PubMed]
  9. K. Postava, A. Maziewski, T. Yamaguchi, R. Ossikovski, S. Visnovsky, and J. Pistora, “Null ellipsometer with phase modulation,” Opt. Express 12, 6040-6045 (2004).
    [CrossRef] [PubMed]
  10. H. Reisinger, “Minimization of errors in ellipsometric measurements,” Solid-State Electron. 35, 333-344 (1992).
    [CrossRef]
  11. 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]
  12. M. Fitzgibbon, A. W. Pilu, and R. B. Fisher, “Direct least-squares fitting of ellipses,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 476-480 (1999).
    [CrossRef]
  13. TFCompanion, SemiconSoft Inc., Southborough, Mass. 01772, USA.

2004 (1)

2002 (1)

1999 (1)

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

1994 (1)

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]

1992 (1)

H. Reisinger, “Minimization of errors in ellipsometric measurements,” Solid-State Electron. 35, 333-344 (1992).
[CrossRef]

1974 (2)

E. F. I. Roberts and A. Meadows, “A high precision automatic ellipsometer using grating goniometers,” J. Phys. E. 7, 379-386 (1974).
[CrossRef]

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798-802 (1974).
[CrossRef]

1969 (1)

H. P. Layer, “Circuit design for an electronic self-nulling ellipsometer,” Surf. Sci. 16, 177-192 (1969).
[CrossRef]

1967 (1)

T. Yamaguchi, “A quick response recording ellipsometer,” Sci. Light 16, 64-71 (1967).

1966 (1)

1963 (1)

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67A, 363-377(1963).

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).

Fisher, R. B.

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

Fitzgibbon, M.

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

Hemmes, K.

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]

Layer, H. P.

H. P. Layer, “Circuit design for an electronic self-nulling ellipsometer,” Surf. Sci. 16, 177-192 (1969).
[CrossRef]

Liu, L.

Lu, Z.

Mathieu, H. J.

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798-802 (1974).
[CrossRef]

Maziewski, A.

McClure, D. E.

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798-802 (1974).
[CrossRef]

McCrackin, F. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67A, 363-377(1963).

Meadows, A.

E. F. I. Roberts and A. Meadows, “A high precision automatic ellipsometer using grating goniometers,” J. Phys. E. 7, 379-386 (1974).
[CrossRef]

Muller, R. H.

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798-802 (1974).
[CrossRef]

Ossikovski, R.

Passaglia, E.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67A, 363-377(1963).

Pilu, A. W.

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

Pistora, J.

Postava, K.

Reisinger, H.

H. Reisinger, “Minimization of errors in ellipsometric measurements,” Solid-State Electron. 35, 333-344 (1992).
[CrossRef]

Roberts, E. F. I.

E. F. I. Roberts and A. Meadows, “A high precision automatic ellipsometer using grating goniometers,” J. Phys. E. 7, 379-386 (1974).
[CrossRef]

Steinberg, H. L.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67A, 363-377(1963).

Stromberg, R. R.

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67A, 363-377(1963).

Takasaki, H.

Visnovsky, S.

Wen, W.

Wind, M. M.

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]

Yamaguchi, T.

Zhang, B.

Zhu, H.

Appl. Opt. (2)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

M. Fitzgibbon, A. W. 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. (1)

E. F. I. Roberts and A. Meadows, “A high precision automatic ellipsometer using grating goniometers,” J. Phys. E. 7, 379-386 (1974).
[CrossRef]

J. Res. Natl. Bur. Stand. (1)

F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, “Measurement of the thickness and refractive index of very thin films and the optical properties of surfaces by ellipsometry,” J. Res. Natl. Bur. Stand. 67A, 363-377(1963).

Meas. Sci. Technol. (1)

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]

Opt. Express (1)

Rev. Sci. Instrum. (1)

H. J. Mathieu, D. E. McClure, and R. H. Muller, “Fast self-compensating ellipsometer,” Rev. Sci. Instrum. 45, 798-802 (1974).
[CrossRef]

Sci. Light (1)

T. Yamaguchi, “A quick response recording ellipsometer,” Sci. Light 16, 64-71 (1967).

Solid-State Electron. (1)

H. Reisinger, “Minimization of errors in ellipsometric measurements,” Solid-State Electron. 35, 333-344 (1992).
[CrossRef]

Surf. Sci. (1)

H. P. Layer, “Circuit design for an electronic self-nulling ellipsometer,” Surf. Sci. 16, 177-192 (1969).
[CrossRef]

Other (2)

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

TFCompanion, SemiconSoft Inc., Southborough, Mass. 01772, USA.

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Figures (2)

Fig. 1
Fig. 1

Schematic of the modified PCSA null ellipsometer. L, laser; P, P 1 ; polarizers; C, compensator; S, sample, G, goniometer; BS, nonpolarizing beam splitter; PZT, piezoelectric transducer; M 1 , M 2 , mirrors; PD 1 , PD 2 , photodetectors; WP, Wollaston prism; A / D , analog-to-digital converter in a personal computer (PC).

Fig. 2
Fig. 2

ψ and Δ as a function of AOI for a Si O 2 film ( n = 1.457 , d = 2.35 nm ) on Si ( n = 3.88 , k = 0.019 ).

Equations (12)

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E m = B M 2 B [ cos A sin A ] exp ( i ω 1 t ) = 1 2 [ r p M 2 cos A r s M 2 sin A ] exp ( i ω 1 t ) ,
B = 1 2 [ 1 0 0 1 ] ,
M 2 = [ r p M 2 0 0 r s M 2 ]
E r B 1 2 [ 1 1 ] exp ( i ω 2 t ) = 1 2 [ 1 1 ] exp ( i ω 2 t ) ,
I p 1 + | r p M 2 | 2 cos 2 A + 2 cos A | r p M 2 | cos ( ω 0 t + δ p M 2 ) ,
I s 1 + | r s M 2 | 2 sin 2 A + 2 sin A | r s M 2 | cos ( ω 0 t + δ s M 2 ) ,
ϕ c = arg ( I p ) arg ( I s ) = δ p M 2 δ s M 2 ,
V r m = k s I s ac k p I p ac = k s | r s M 2 | sin A k p | r p M 2 | cos A ,
V r c = k s | r s M 2 | k p | r p M 2 | ,
A ˜ = tan 1 V r m V r c .
Δ 1 4 = 1 2 ( P 1 + P 3 P 2 P 4 ) .
ψ 1 4 = 1 4 ( i | A ˜ i | 360 ) .

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