Abstract

We present a technique for ellipsometric analysis of materials with high lateral resolution. A Michelson-type phase-shifting interferometer measures the phase distribution in the back focal plane of a high numerical aperture objective. Local measurements of the ellipsometric parameter delta are performed over the entire spectrum of angles of incidence. We show that delta is to leading order linearly proportional to the phase change on reflection of normally incident light. We furthermore invert the Fresnel reflection equations and derive expressions for the real and imaginary parts of the refractive index as functions of the phase change on reflection and the reflectivity at normal incidence, both of which are measurable with the same apparatus. Hence we accomplish local measurements of the refractive indices of our samples. Determination of the phase change on reflection permits correction of interferometric topography measurements of heterogeneous specimens.

© 1998 Optical Society of America

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References

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  1. L. Deck, P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994).
    [CrossRef] [PubMed]
  2. Y. Li, F. E. Talke, “Limitations and corrections of optical profilometry in surface characterization of carbon coated magnetic recording disks,” ASME J. Tribol. 112, 670–677 (1990).
    [CrossRef]
  3. M. Smallen, J. J. K. Lee, “Pole tip recession measurements on thin film heads using optical profilometry with phase correction and atomic force microscopy,” ASME J. Tribol. 115, 382–386 (1993).
    [CrossRef]
  4. J. F. Biegen, “Determination of the phase change on reflection from two-beam interference,” Opt. Lett. 19, 1690–1692 (1995).
    [CrossRef]
  5. C. W. See, M. G. Somekh, R. D. Holmes, “Scanning optical microellipsometer for pure surface profiling,” Appl. Opt. 35, 6663–6668 (1996).
    [CrossRef] [PubMed]
  6. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1992), Chap. 3, pp. 153–157.
  7. A. Rosencwaig, J. Opsal, D. L. Willenborg, S. M. Kelso, J. T. Fanton, “Beam profile reflectometry: a new technique for dielectric film measurements,” Appl. Phys. Lett. 60, 1301–1303 (1992).
    [CrossRef]
  8. M. Pluta, Advanced Light Microscopy (Polish Scientific Publishers, Warsaw, 1993), Vol. 3, pp. 265–271.
  9. S. V. Shatalin, R. Juškaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
    [CrossRef]
  10. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 4, pp. 167–169.
  11. Ref. 8, Chap. 1, pp. 36–41.
  12. P. de Groot, “Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt. 34, 4723–4730 (1995).
    [CrossRef]
  13. T. Wilson, R. Juškaitis, “On the extinction coefficient in confocal polarization microscopy,” J. Microsc. 179, 238–240 (1995).
    [CrossRef]
  14. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).
  15. G. Schulz, K.-E. Elssner, “Errors in phase-measurement interferometry with high numerical apertures,” Appl. Opt. 30, 4500–4506 (1991).
    [CrossRef] [PubMed]
  16. C. P. Brophy, “Effect of intensity error correlation on the computed phase of phase-shifting interferometry,” J. Opt. Soc. Am. A 7, 537–541 (1990).
    [CrossRef]

1996 (1)

1995 (4)

S. V. Shatalin, R. Juškaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

T. Wilson, R. Juškaitis, “On the extinction coefficient in confocal polarization microscopy,” J. Microsc. 179, 238–240 (1995).
[CrossRef]

J. F. Biegen, “Determination of the phase change on reflection from two-beam interference,” Opt. Lett. 19, 1690–1692 (1995).
[CrossRef]

P. de Groot, “Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt. 34, 4723–4730 (1995).
[CrossRef]

1994 (1)

1993 (1)

M. Smallen, J. J. K. Lee, “Pole tip recession measurements on thin film heads using optical profilometry with phase correction and atomic force microscopy,” ASME J. Tribol. 115, 382–386 (1993).
[CrossRef]

1992 (1)

A. Rosencwaig, J. Opsal, D. L. Willenborg, S. M. Kelso, J. T. Fanton, “Beam profile reflectometry: a new technique for dielectric film measurements,” Appl. Phys. Lett. 60, 1301–1303 (1992).
[CrossRef]

1991 (1)

1990 (2)

C. P. Brophy, “Effect of intensity error correlation on the computed phase of phase-shifting interferometry,” J. Opt. Soc. Am. A 7, 537–541 (1990).
[CrossRef]

Y. Li, F. E. Talke, “Limitations and corrections of optical profilometry in surface characterization of carbon coated magnetic recording disks,” ASME J. Tribol. 112, 670–677 (1990).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1992), Chap. 3, pp. 153–157.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1992), Chap. 3, pp. 153–157.

Biegen, J. F.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 4, pp. 167–169.

Brophy, C. P.

de Groot, P.

Deck, L.

Elssner, K.-E.

Fanton, J. T.

A. Rosencwaig, J. Opsal, D. L. Willenborg, S. M. Kelso, J. T. Fanton, “Beam profile reflectometry: a new technique for dielectric film measurements,” Appl. Phys. Lett. 60, 1301–1303 (1992).
[CrossRef]

Holmes, R. D.

Juškaitis, R.

S. V. Shatalin, R. Juškaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

T. Wilson, R. Juškaitis, “On the extinction coefficient in confocal polarization microscopy,” J. Microsc. 179, 238–240 (1995).
[CrossRef]

Kelso, S. M.

A. Rosencwaig, J. Opsal, D. L. Willenborg, S. M. Kelso, J. T. Fanton, “Beam profile reflectometry: a new technique for dielectric film measurements,” Appl. Phys. Lett. 60, 1301–1303 (1992).
[CrossRef]

Lee, J. J. K.

M. Smallen, J. J. K. Lee, “Pole tip recession measurements on thin film heads using optical profilometry with phase correction and atomic force microscopy,” ASME J. Tribol. 115, 382–386 (1993).
[CrossRef]

Li, Y.

Y. Li, F. E. Talke, “Limitations and corrections of optical profilometry in surface characterization of carbon coated magnetic recording disks,” ASME J. Tribol. 112, 670–677 (1990).
[CrossRef]

Opsal, J.

A. Rosencwaig, J. Opsal, D. L. Willenborg, S. M. Kelso, J. T. Fanton, “Beam profile reflectometry: a new technique for dielectric film measurements,” Appl. Phys. Lett. 60, 1301–1303 (1992).
[CrossRef]

Pluta, M.

M. Pluta, Advanced Light Microscopy (Polish Scientific Publishers, Warsaw, 1993), Vol. 3, pp. 265–271.

Rosencwaig, A.

A. Rosencwaig, J. Opsal, D. L. Willenborg, S. M. Kelso, J. T. Fanton, “Beam profile reflectometry: a new technique for dielectric film measurements,” Appl. Phys. Lett. 60, 1301–1303 (1992).
[CrossRef]

Schulz, G.

See, C. W.

Shatalin, S. V.

S. V. Shatalin, R. Juškaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

Smallen, M.

M. Smallen, J. J. K. Lee, “Pole tip recession measurements on thin film heads using optical profilometry with phase correction and atomic force microscopy,” ASME J. Tribol. 115, 382–386 (1993).
[CrossRef]

Somekh, M. G.

Talke, F. E.

Y. Li, F. E. Talke, “Limitations and corrections of optical profilometry in surface characterization of carbon coated magnetic recording disks,” ASME J. Tribol. 112, 670–677 (1990).
[CrossRef]

Tan, J. B.

S. V. Shatalin, R. Juškaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

Willenborg, D. L.

A. Rosencwaig, J. Opsal, D. L. Willenborg, S. M. Kelso, J. T. Fanton, “Beam profile reflectometry: a new technique for dielectric film measurements,” Appl. Phys. Lett. 60, 1301–1303 (1992).
[CrossRef]

Wilson, T.

S. V. Shatalin, R. Juškaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

T. Wilson, R. Juškaitis, “On the extinction coefficient in confocal polarization microscopy,” J. Microsc. 179, 238–240 (1995).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 4, pp. 167–169.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

A. Rosencwaig, J. Opsal, D. L. Willenborg, S. M. Kelso, J. T. Fanton, “Beam profile reflectometry: a new technique for dielectric film measurements,” Appl. Phys. Lett. 60, 1301–1303 (1992).
[CrossRef]

ASME J. Tribol. (2)

Y. Li, F. E. Talke, “Limitations and corrections of optical profilometry in surface characterization of carbon coated magnetic recording disks,” ASME J. Tribol. 112, 670–677 (1990).
[CrossRef]

M. Smallen, J. J. K. Lee, “Pole tip recession measurements on thin film heads using optical profilometry with phase correction and atomic force microscopy,” ASME J. Tribol. 115, 382–386 (1993).
[CrossRef]

J. Microsc. (2)

S. V. Shatalin, R. Juškaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin film structures,” J. Microsc. 179, 241–252 (1995).
[CrossRef]

T. Wilson, R. Juškaitis, “On the extinction coefficient in confocal polarization microscopy,” J. Microsc. 179, 238–240 (1995).
[CrossRef]

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

Opt. Lett. (1)

Other (5)

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 4, pp. 167–169.

Ref. 8, Chap. 1, pp. 36–41.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1992), Chap. 3, pp. 153–157.

M. Pluta, Advanced Light Microscopy (Polish Scientific Publishers, Warsaw, 1993), Vol. 3, pp. 265–271.

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Figures (7)

Fig. 1
Fig. 1

Principle of back focal plane microellipsometry.

Fig. 2
Fig. 2

Theoretical reflected phase curves for aluminum (n′ = 1.8 + 7.7i). ϕ0 and the average of ϕπ and ϕσ are roughly equal out to θ i = 50° (NA = 0.77).

Fig. 3
Fig. 3

Schematic of the interferometric back focal plane microellipsometer: NA, numerical aperture; PZT, piezoelectric transducer; BFP, back focal plane; PC, personal computer.

Fig. 4
Fig. 4

Subtraction of phase maps to obtain the difference map. By convention, the first phase map has input polarization along the x axis, and the second has input polarization along the y axis.

Fig. 5
Fig. 5

Difference maps for gold, aluminum, and silicon.

Fig. 6
Fig. 6

Line-cut averages from Fig. 5. The data (■) are fit (- - - -) according to Eq. (9), and the results are compared with the theoretical curves (—) from the literature values of the refractive indices.

Fig. 7
Fig. 7

Measured ϕ0 as a function of defocus.

Tables (2)

Tables Icon

Table 1 Comparison of Values for ϕ0

Tables Icon

Table 2 Comparison of Values for Reflectivity and Refractive Index

Equations (25)

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

sin   θ i = ρ / ρ max sin θ max ,
r π = tan θ i - θ t tan θ i + θ t ,     r σ = - sin θ i - θ t sin θ i + θ t .
sin   θ i = n   sin   θ t ,
r 0 = n - 1 n + 1 .
δ ϕ π - ϕ σ = arg r π - arg r σ + π .
ϕ 0 = arg r 0 .
tan   ψ | r π | / | r σ | .
ϕ 0 1.41 δ ,
δ ϕ 0 θ i 2 + θ i 4 / 6 ,
R 0 = | r 0 | 2 .
κ R 0 ,   ϕ 0 = 4 R 0 cos   ϕ 0 + 2 R 0 1 + R 0 1 + R 0 2 sin 2   ϕ 0 + 1 - R 0 2 cos 2   ϕ 0 sin   ϕ 0 ,
η ϕ 0 ,   κ = 2 κ   cot   ϕ 0 - κ 2 + 1 1 / 2 .
η R 0 ,   κ = 1 + R 0 + 4 R 0 - κ 2 1 - R 0 2 1 / 2 1 - R 0 ,
tan   ϕ = 7 I - 1 - I 1 - I - 3 - I 3 - 4 I - 2 - I 2 + 8 I 0 ,
E x - pol = E x E y x - pol = E 0 2 R + + R - cos   2 Ω R - sin   2 Ω , E y - pol = E x E y y - pol = E 0 2 R - sin   2 Ω R + - R - cos   2 Ω ,
ϕ x - pol = arg E x x - pol ,     ϕ y - pol = arg E y y - pol .
ϕ diff = ϕ x - pol - ϕ y - pol .
ϕ diff Ω = 0 = ϕ diff Ω = π = δ ,
ϕ diff Ω = π / 2 = ϕ diff Ω = 3 π / 2 = - δ .
ϕ diff Ω = m π / 4 = 0 ,     m = 1 ,   3 ,   5 ,   7 .
ϕ defocus = 4 π H / λ cos   θ i .
ϕ total ,   x - pol = ϕ x - pol + ϕ defocus , ϕ total ,   y - pol = ϕ y - pol + ϕ defocus .
I n = I max 1 + V 1 + V   cos ϕ + n   π 2 ,
Δ ϕ 2 = Δ I 2 n ϕ I max , n 2 ,
Δ ϕ 2 ϕ = Δ I I max 2 196 + 49 V 2 512 V 2 .

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