Abstract

We report on a novel imaging ellipsometer using a high-numerical-aperture (NA) objective lens capable of measuring a two-dimensional ellipsometric signal with high resolution. Two-dimensional ellipsometric imaging is made possible by spatial filtering at the pupil plane of the objective. A Richards-Wolf vectorial diffraction model and geometrical optics model are developed to simulate the system. The thickness profile of patterned polymethyl methacrylate is measured for calibration purposes. Our instrument has a sensitivity of 5 Å and provides spatial resolution of approximately 0.5 µm with 632.8-nm illumination. Its capability of measuring refractive-index variations with high spatial resolution is also demonstrated.

© 2002 Optical Society of America

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References

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  1. R. M. A. Azzam, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  2. H. G. Tompkins, A Users’ Guide to Ellipsometry (Academic, New York, 1993).
  3. A. Albersdörfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 µm and 5 Å normal resolution,” Appl. Phys. Lett. 72, 2930–2932 (1998).
    [Crossref]
  4. G. Jin, R. Jansson, H. Arwin, “Imaging ellipsometry revisited: development for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67, 2930–2935 (1996).
    [Crossref]
  5. N. Gold, D. L. Willenborg, J. Opsal, A. Rosencwaig, “High resolution ellipsometric apparatus,” U.S. patent5,042,951 (2August1991).
  6. C. W. See, M. G. Somekh, R. D. Holmes, “Scanning optical microellipsometer for pure surface profiling,” Appl. Opt. 35, 6663–6668 (1996).
    [Crossref] [PubMed]
  7. M. Mansuripur, The Physical Principles of Magneto-Optical Recording (Cambridge U. Press, Cambridge, UK, 1995).
    [Crossref]
  8. Y.-C. Hsieh, M. Mansuripur, “Image contrast in polarization microscopy of magneto-optical disk data-storage media through birefringent plastic substrates,” Appl. Opt. 36, 4839–4852 (1997).
    [Crossref] [PubMed]
  9. E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
    [Crossref]
  10. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
    [Crossref]
  11. J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, J. Opsal, “Characterization of titanium nitride (TiN) films on various substrates using spectrophotometry, beam profile reflectometry, beam profile ellipsometry and spectroscopic beam profile ellipsometry,” Thin Solid Films 313–314, 308–313 (1998).

1998 (2)

A. Albersdörfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 µm and 5 Å normal resolution,” Appl. Phys. Lett. 72, 2930–2932 (1998).
[Crossref]

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, J. Opsal, “Characterization of titanium nitride (TiN) films on various substrates using spectrophotometry, beam profile reflectometry, beam profile ellipsometry and spectroscopic beam profile ellipsometry,” Thin Solid Films 313–314, 308–313 (1998).

1997 (1)

1996 (2)

G. Jin, R. Jansson, H. Arwin, “Imaging ellipsometry revisited: development for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67, 2930–2935 (1996).
[Crossref]

C. W. See, M. G. Somekh, R. D. Holmes, “Scanning optical microellipsometer for pure surface profiling,” Appl. Opt. 35, 6663–6668 (1996).
[Crossref] [PubMed]

1959 (2)

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[Crossref]

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[Crossref]

Albersdörfer, A.

A. Albersdörfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 µm and 5 Å normal resolution,” Appl. Phys. Lett. 72, 2930–2932 (1998).
[Crossref]

Arwin, H.

G. Jin, R. Jansson, H. Arwin, “Imaging ellipsometry revisited: development for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67, 2930–2935 (1996).
[Crossref]

Azzam, R. M. A.

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

Chen, J.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, J. Opsal, “Characterization of titanium nitride (TiN) films on various substrates using spectrophotometry, beam profile reflectometry, beam profile ellipsometry and spectroscopic beam profile ellipsometry,” Thin Solid Films 313–314, 308–313 (1998).

Elender, G.

A. Albersdörfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 µm and 5 Å normal resolution,” Appl. Phys. Lett. 72, 2930–2932 (1998).
[Crossref]

Fanton, J.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, J. Opsal, “Characterization of titanium nitride (TiN) films on various substrates using spectrophotometry, beam profile reflectometry, beam profile ellipsometry and spectroscopic beam profile ellipsometry,” Thin Solid Films 313–314, 308–313 (1998).

Gold, N.

N. Gold, D. L. Willenborg, J. Opsal, A. Rosencwaig, “High resolution ellipsometric apparatus,” U.S. patent5,042,951 (2August1991).

Holmes, R. D.

Hsieh, Y.-C.

Jansson, R.

G. Jin, R. Jansson, H. Arwin, “Imaging ellipsometry revisited: development for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67, 2930–2935 (1996).
[Crossref]

Jin, G.

G. Jin, R. Jansson, H. Arwin, “Imaging ellipsometry revisited: development for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67, 2930–2935 (1996).
[Crossref]

Leng, J. M.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, J. Opsal, “Characterization of titanium nitride (TiN) films on various substrates using spectrophotometry, beam profile reflectometry, beam profile ellipsometry and spectroscopic beam profile ellipsometry,” Thin Solid Films 313–314, 308–313 (1998).

Mansuripur, M.

Mathe, G.

A. Albersdörfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 µm and 5 Å normal resolution,” Appl. Phys. Lett. 72, 2930–2932 (1998).
[Crossref]

Neumaier, K. R.

A. Albersdörfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 µm and 5 Å normal resolution,” Appl. Phys. Lett. 72, 2930–2932 (1998).
[Crossref]

Opsal, J.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, J. Opsal, “Characterization of titanium nitride (TiN) films on various substrates using spectrophotometry, beam profile reflectometry, beam profile ellipsometry and spectroscopic beam profile ellipsometry,” Thin Solid Films 313–314, 308–313 (1998).

N. Gold, D. L. Willenborg, J. Opsal, A. Rosencwaig, “High resolution ellipsometric apparatus,” U.S. patent5,042,951 (2August1991).

Paduschek, P.

A. Albersdörfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 µm and 5 Å normal resolution,” Appl. Phys. Lett. 72, 2930–2932 (1998).
[Crossref]

Richards, B.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[Crossref]

Ritz, K.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, J. Opsal, “Characterization of titanium nitride (TiN) films on various substrates using spectrophotometry, beam profile reflectometry, beam profile ellipsometry and spectroscopic beam profile ellipsometry,” Thin Solid Films 313–314, 308–313 (1998).

Rosencwaig, A.

N. Gold, D. L. Willenborg, J. Opsal, A. Rosencwaig, “High resolution ellipsometric apparatus,” U.S. patent5,042,951 (2August1991).

Sackmann, E.

A. Albersdörfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 µm and 5 Å normal resolution,” Appl. Phys. Lett. 72, 2930–2932 (1998).
[Crossref]

See, C. W.

Senko, M.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, J. Opsal, “Characterization of titanium nitride (TiN) films on various substrates using spectrophotometry, beam profile reflectometry, beam profile ellipsometry and spectroscopic beam profile ellipsometry,” Thin Solid Films 313–314, 308–313 (1998).

Somekh, M. G.

Tompkins, H. G.

H. G. Tompkins, A Users’ Guide to Ellipsometry (Academic, New York, 1993).

Willenborg, D. L.

N. Gold, D. L. Willenborg, J. Opsal, A. Rosencwaig, “High resolution ellipsometric apparatus,” U.S. patent5,042,951 (2August1991).

Wolf, E.

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[Crossref]

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. Albersdörfer, G. Elender, G. Mathe, K. R. Neumaier, P. Paduschek, E. Sackmann, “High resolution imaging microellipsometry of soft surfaces at 3 µm and 5 Å normal resolution,” Appl. Phys. Lett. 72, 2930–2932 (1998).
[Crossref]

Proc. R. Soc. London Ser. A (2)

E. Wolf, “Electromagnetic diffraction in optical systems. I. An integral representation of the image field,” Proc. R. Soc. London Ser. A 253, 349–357 (1959).
[Crossref]

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[Crossref]

Rev. Sci. Instrum. (1)

G. Jin, R. Jansson, H. Arwin, “Imaging ellipsometry revisited: development for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67, 2930–2935 (1996).
[Crossref]

Thin Solid Films (1)

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, J. Opsal, “Characterization of titanium nitride (TiN) films on various substrates using spectrophotometry, beam profile reflectometry, beam profile ellipsometry and spectroscopic beam profile ellipsometry,” Thin Solid Films 313–314, 308–313 (1998).

Other (4)

N. Gold, D. L. Willenborg, J. Opsal, A. Rosencwaig, “High resolution ellipsometric apparatus,” U.S. patent5,042,951 (2August1991).

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

H. G. Tompkins, A Users’ Guide to Ellipsometry (Academic, New York, 1993).

M. Mansuripur, The Physical Principles of Magneto-Optical Recording (Cambridge U. Press, Cambridge, UK, 1995).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Diagram of the setup used in the optical model. The transmission axis of the polarizer is aligned with the x direction, and the transmission axis of the analyzer is aligned with the y direction.

Fig. 2
Fig. 2

Vetorial diffraction simulation results of the amplitude and phase of the x and y components of the reflected field at the pupil: (a) amplitude of the x component, (b) amplitude of the y component, (c) phase of the x component, (d) phase of the y component. A plane-wave illumination with unit amplitude was used in the simulation. The maximum magnitude of the x component in (a) is approximately 20 times that of the y component in (b).

Fig. 3
Fig. 3

Simulation results for the two intensities, where h is the thickness of the sample, λ is the wavelength inside of the sample, I 1 is the intensity on the detector with quarter-wave plate π/4 with respect to the x axis, and I 2 is the intensity on the detector with quarter-wave plate -π/4 with respect to the x axis.

Fig. 4
Fig. 4

Diagram of the coordinate system used in the geometrical optics model, where ∠xop = P, ∠xoa = A, and ∠xoc = C with op and oa as the transmission axis of the polarizer and analyzer and oc as the fast axis of the quarter-wave plate.

Fig. 5
Fig. 5

Illustration of the coordinates transform. This effect is a pure geometry effect that is due to the definition of the s and p direction before and after reflection.

Fig. 6
Fig. 6

Diagram of the calculation of the optimal spatial filter.

Fig. 7
Fig. 7

Diagram of the imaging ellipsometer experimental setup.

Fig. 8
Fig. 8

Illustration of the patterned PMMA sample.

Fig. 9
Fig. 9

Experimental results of the thickness measurement. (a) Two-dimensional ellipsometric image and (b) line scan of image in (a) after we converted the ellipsometric signal into thickness.

Fig. 10
Fig. 10

Cross section of the sample for index of refraction measurement.

Fig. 11
Fig. 11

Experimental results for the index of refraction measurement. (a) Two-dimensional ellipsometric image and (b) line scan of the image in (a).

Equations (21)

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TP=R-P1000RP,
RP=cos Psin P-sin Pcos P
Lθ, φ=1cos θ1001
TSθ, φ=rpθ00rsθ
L-1θ, φ=cos θ1001
M=0110
TC=R-C100-jRC,
TA=R-A1000RA,
Eθ, φ=EoxEoy=TtotalEixEiy,
Ei=EixEiy
Ttotal=TATCR-π2+φ×ML-1θ, φTSθ, φLθ, φRφTP.
Ttotal=T11T1200,
T11=-cosA-CcosC-φrp-j sinA-C×sinC-φrpcosP-φcos P+cosA-C×sinC-φrs-j sinA-CcosC-φrs×sinP-φcos P,
T12=-cosA-CcosC-φrp-j sinA-C×sinC-φrpcosP-φsin P+cosA-C×sinC-φrs-j sinA-CcosC-φrs×sinP-φsin P.
Ei=10,
Pθ, φ=|Eθ, φ|2dS =12 |rp|2 cos2 φ+12 |rs|2 sin2 φ-12 |rprs|sin 2φ sin δp,sdS
Pθ, φ=|Eθ, φ|2dS=12 |rp|2 cos2 φ+12 |rs|2 sin2 φ+12 |rprs|sin 2φ sin δp,sdS
I1=K20θmax f2 sin θdθ Φdφ12 |rp|2 cos2 φ+12 |rs|2 sin2 φ-12 |rprs|sin 2φ sin δp,s =K220θmax f2 sin θdθ Φdφ|rp|2 cos2 φ+|rs|2 sin2 φ-K220θmax f2 sin θdθ×Φdφ|rprs|sin 2φ sin δp,s=I0-Iint.
I2=K20θmax f2 sin θdθ Φdφ12 |rp|2 cos2 φ+12 |rs|2 sin2 φ+12 |rprs|sin 2φ sin δp, s =K220θmax f2 sin θdθ Φdφ|rp|2 cos2 φ+|rs|2 sin2 φ+K220θmax f2 sin θdθ×Φdφ|rprs|sin 2φ sin δp,s =I0+Iint,
Iint=K220θmax f2 sin θ|rprs|sin δp,sdθ Φsin 2φdφ=RθmaxΦsin 2φdφ,
0φmaxsin 2φdφ=1-cos 2φmax2,

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