Abstract

An interferometric ellipsometer, with no moving parts and an inexpensive laser diode source, is demonstrated. Temporal fringes are produced by a small modulation of the laser diode bias current and unbalanced arms in the interferometer. Fringe analysis algorithms are developed, and accurate measurements of the optical properties of a number of samples are made. Temperature tuning the laser diode center wavelength allows the frequency dependence of the optical properties to be determined over a wavelength range of approximately 1 nm.

© 2004 Optical Society of America

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References

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  1. H. F. Hazebroek, W. M. Visser, “Automated laser interferometric ellipsometry and precision reflectometry,” J. Phys. E. 16, 654–661 (1983).
    [CrossRef]
  2. H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E. 6, 822–826 (1973).
    [CrossRef]
  3. M. M. Wind, K. Hemmes, “New ultra-fast interferometric ellipsometry 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, H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond and faster,” Thin Solid Films 313–314, 40–46 (1998).
    [CrossRef]
  5. K. Tatsuno, Y. Tsunoda, “Diode laser direct modulation heterodyne interferometer,” Appl. Opt. 26, 37–40 (1987).
    [CrossRef] [PubMed]
  6. K. G. Libbrecht, J. L. Hall, “A low-noise high-speed diode laser current controller,” Rev. Sci. Instrum. 64, 2133–2135 (1993).
    [CrossRef]
  7. J. R. Zeidler, R. B. Kohles, N. M. Bashara, “High precision alignment procedure for an ellipsometer,” Appl. Opt. 13, 1115–1120 (1974).
    [CrossRef] [PubMed]
  8. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarised Light (North-Holland, Amsterdam, 1996).
  9. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran (Cambridge U. Press, Cambridge, UK, 1992).

1998 (1)

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

1994 (1)

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

1993 (1)

K. G. Libbrecht, J. L. Hall, “A low-noise high-speed diode laser current controller,” Rev. Sci. Instrum. 64, 2133–2135 (1993).
[CrossRef]

1987 (1)

1983 (1)

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

1974 (1)

1973 (1)

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

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarised Light (North-Holland, Amsterdam, 1996).

Bashara, N. M.

Bender, H.

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

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran (Cambridge U. Press, Cambridge, UK, 1992).

Hall, J. L.

K. G. Libbrecht, J. L. Hall, “A low-noise high-speed diode laser current controller,” Rev. Sci. Instrum. 64, 2133–2135 (1993).
[CrossRef]

Hamstra, M. A.

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

Hazebroek, H. F.

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

H. F. Hazebroek, A. 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, H. Bender, “Evaluation of interferometric ellipsometer systems with a time resolution of one microsecond and faster,” Thin Solid Films 313–314, 40–46 (1998).
[CrossRef]

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

Holscher, A. A.

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

Kohles, R. B.

Koops, K. R.

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

Laet, J. de.

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

Libbrecht, K. G.

K. G. Libbrecht, J. L. Hall, “A low-noise high-speed diode laser current controller,” Rev. Sci. Instrum. 64, 2133–2135 (1993).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran (Cambridge U. Press, Cambridge, UK, 1992).

Schram, T.

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

Tatsuno, K.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran (Cambridge U. Press, Cambridge, UK, 1992).

Tsunoda, Y.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran (Cambridge U. Press, Cambridge, UK, 1992).

Visser, W. M.

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

Wind, M. M.

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

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

Zeidler, J. R.

Appl. Opt. (2)

J. Phys. E. (2)

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

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

Meas. Sci. Technol. (1)

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

Rev. Sci. Instrum. (1)

K. G. Libbrecht, J. L. Hall, “A low-noise high-speed diode laser current controller,” Rev. Sci. Instrum. 64, 2133–2135 (1993).
[CrossRef]

Thin Solid Films (1)

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

Other (2)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarised Light (North-Holland, Amsterdam, 1996).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran (Cambridge U. Press, Cambridge, UK, 1992).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup. LD, laser diode; CL, collimating lens; OI, optical isolators; A, aperture; HWP, half-wave plate; P, polarizer; BS, beam splitter; WP, Wollaston prism; Dp and Ds, photodetectors; M1, M2, M3, mirrors; G, goniometer; S, sample; ADC, analog-to-digital converter.

Fig. 2
Fig. 2

Sampled fringes for p and s polarizations.

Fig. 3
Fig. 3

Lissajou figure of corrected fringe data and fitted ellipse.

Fig. 4
Fig. 4

Retardation as a function of wavelength for a multiorder λ/4 plate with a best-fit line.

Tables (3)

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Table 1 Ellipsometric Angles for BK7 Glass Sample at 75.00°

Tables Icon

Table 2 Retardation of a Multiorder λ/4 Plate

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Table 3 Ellipsometric Angles for Thin Teflon Film

Equations (13)

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

ω0=4πνL2-L1λ-νt24πνL2-L1λ2
Vpt=kp1+|rp|4+2|rp|2×cosω0t+2δrp+δ,
Vst=ks1+|rs|4+2|rs|2×cosω0t+2δsp+γ,
Vsam=kp|rp|2ks|rs|2=kpkstan2 ψ,
Φsam=2δrp-2δsp+δ-γ=2Δ+δ-γ,
Vref=kpks, Φref=δ-γ.
tan ψ=Vsam/Vref1/2,
Δ=Φsam-Φref/2.
Vin=min+1Vidc+Vipk cos2πnτ/T+ϕi,
ϕp-ϕspp1-ps1pp1-νp1π.
v1n=VpnVppk=cos2πnτ/T+θ,
v2n=VsnVspk=cos2πnτ/T.
cos2θ-2v1v2 cosθ+v12+v22-1=0,

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