Abstract

White-light scanning interferometry is increasingly used for precision profile metrology of engineering surfaces, but its current applications are limited primarily to opaque surfaces with relatively simple optical reflection behavior. A new attempt is made to extend the interferometric method to the thickness-profile measurement of transparent thin-film layers. An extensive frequency-domain analysis of multiple reflection is performed to allow both the top and the bottom interfaces of a thin-film layer to be measured independently at the same time by the nonlinear least-squares technique. This rigorous approach provides not only point-by-point thickness probing but also complete volumetric film profiles digitized in three dimensions.

© 1999 Optical Society of America

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1998 (3)

E. W. Rogala, H. H. Barrett, “Phase-shifting interferometer/ellipsometer capable of measuring the complex index of refraction and the surface profile of a test surface,” J. Opt. Soc. Am 15, 538–548 (1998).
[CrossRef]

K. Leonhardt, U. Droste, H. J. Tiziani, “Topometry for locally changing materials,” Opt. Lett. 23, 1772–1174 (1998).
[CrossRef]

G. D. Feke, D. P. Snow, R. D. Grober, P. de Groot, L. Deck, “Interferometric back focal plane microellipsometry,” Appl. Opt. 37, 1796–1802 (1998).
[CrossRef]

1997 (3)

1996 (2)

S. Diddams, J. C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. 13, 1120–1129 (1996).
[CrossRef]

K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. A 13, 832–843 (1996).
[CrossRef]

1995 (1)

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

1994 (2)

1993 (2)

1992 (1)

1990 (2)

1968 (1)

L. J. Fried, H. A. Froot, “Thickness measurements of silicon dioxide films over small geometries,” J. Appl. Phys. 39, 5732–5735 (1968).
[CrossRef]

Azzam, R.

R. Azzam, N. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), p. 283.

Barrett, H. H.

E. W. Rogala, H. H. Barrett, “Phase-shifting interferometer/ellipsometer capable of measuring the complex index of refraction and the surface profile of a test surface,” J. Opt. Soc. Am 15, 538–548 (1998).
[CrossRef]

Bashara, N.

R. Azzam, N. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), p. 283.

Biegen, J. F.

Brophy, C.

D. Cohen, P. J. Caber, C. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (28July1992).

Caber, P. J.

P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993).
[CrossRef] [PubMed]

D. Cohen, P. J. Caber, C. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (28July1992).

Chim, S. S. C.

Cohen, D.

D. Cohen, P. J. Caber, C. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (28July1992).

Creath, K.

K. Creath, “Sampling requirements for white light interferometry,” presented at the Third International Workshop on Automatic Processing of Fringe Patterns, Bremen Institute of Applied Beam Technology, Bremen, Germany, 15–17 September 1997.

de Groot, P.

Deck, L.

Devillers, R.

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Diddams, S.

S. Diddams, J. C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. 13, 1120–1129 (1996).
[CrossRef]

Diels, J. C.

S. Diddams, J. C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. 13, 1120–1129 (1996).
[CrossRef]

Doi, T.

Droste, U.

Feke, G. D.

Fried, L. J.

L. J. Fried, H. A. Froot, “Thickness measurements of silicon dioxide films over small geometries,” J. Appl. Phys. 39, 5732–5735 (1968).
[CrossRef]

Froot, H. A.

L. J. Fried, H. A. Froot, “Thickness measurements of silicon dioxide films over small geometries,” J. Appl. Phys. 39, 5732–5735 (1968).
[CrossRef]

Grober, R. D.

Jenkins, F. F.

F. F. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976), p. 479.

Kino, G. S.

Larkin, K. G.

Leonhardt, K.

Merklein, T. M.

Plata, A.

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Rogala, E. W.

E. W. Rogala, H. H. Barrett, “Phase-shifting interferometer/ellipsometer capable of measuring the complex index of refraction and the surface profile of a test surface,” J. Opt. Soc. Am 15, 538–548 (1998).
[CrossRef]

Sandoz, P.

P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett. 22, 1065–1067 (1997).
[CrossRef] [PubMed]

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Snow, D. P.

Tanimura, Y.

Tiziani, H. J.

Toyoda, K.

White, H. E.

F. F. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976), p. 479.

Appl. Opt. (7)

J. Appl. Phys. (1)

L. J. Fried, H. A. Froot, “Thickness measurements of silicon dioxide films over small geometries,” J. Appl. Phys. 39, 5732–5735 (1968).
[CrossRef]

J. Mod. Opt. (2)

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

J. Opt. Soc. Am (1)

E. W. Rogala, H. H. Barrett, “Phase-shifting interferometer/ellipsometer capable of measuring the complex index of refraction and the surface profile of a test surface,” J. Opt. Soc. Am 15, 538–548 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

S. Diddams, J. C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. 13, 1120–1129 (1996).
[CrossRef]

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

Opt. Lett. (4)

Other (5)

The Levenberg-Marquardt function is available as leastsq in the matlab software. For details, refer to Optimization Toolbox for Use with matlab (MathWorks, Natick, Mass., 1992).

R. Azzam, N. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), p. 283.

F. F. Jenkins, H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976), p. 479.

K. Creath, “Sampling requirements for white light interferometry,” presented at the Third International Workshop on Automatic Processing of Fringe Patterns, Bremen Institute of Applied Beam Technology, Bremen, Germany, 15–17 September 1997.

D. Cohen, P. J. Caber, C. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (28July1992).

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Figures (7)

Fig. 1
Fig. 1

Measurement of the thickness profile for reconstruction of a complete three-dimensional map of transparent thin film layers: (a) sectional view of a patterned wafer, (b) measured thickness profile of the film layer.

Fig. 2
Fig. 2

Multiple reflection of light within a transparent thin-film layer.

Fig. 3
Fig. 3

Schematic of white-light scanning interferometry.

Fig. 4
Fig. 4

Actual phase distributions measured from two representative surfaces: (a) an uncoated mirror and (b) a SiO2-coated Si substrate.

Fig. 5
Fig. 5

Simulation results for comparison of true and measured thickness values.

Fig. 6
Fig. 6

Exemplary measurement result: (a) microscopic top view of the test sample, (b) measured three-dimensional thickness profile.

Fig. 7
Fig. 7

Experimental results, showing movement of the phase spectrum with various objective magnifications.

Tables (2)

Tables Icon

Table 1 Comparison of Sample Step Heights Measured by Two Methods

Tables Icon

Table 2 Comparison of Sample Thicknesses Measured with Three Objectives

Equations (9)

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

R=r01+r12 exp-j2β1+r01r12 exp-j2β,
β=kdN1 cos θ1,
N1=A+Bλ2+Cλ4,
Ψ=R=tan-1b/a,  R=a+jb.
Iwz=γ kc-Δk/2kc+Δk/2 Fk0θ0cos2kh-zcos θ+ψk, d, θsin θ cos θdθdk,
Iwz=12 γθ02kc-Δk/2kc+Δk/2 Fkcos2kh-z+ψk, ddk.
rij=Ni-NjNi+Nj,  rij=r01, r12,
Φck; h, d=2hk+ψk, d.
χh, d=kc-Δk/2kc+Δk/2Φmk-Φck; h, d2dk.

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