Abstract

We examined the influence of complex diffraction effects on low-coherence fringes created for high-aspect depth-to-width ratio structures called trenches. The coherence function was analyzed for these micrometer-wide trenches and was registered with a white-light interference microscope. For some types of surface structure we observed that additional low-coherence fringes that do not correspond directly to the surface topology are formed near the sharp edges of the structures. These additional coherence fringes were studied by rigorous numerical evaluations of vector diffractions, and these simulated interference fields were then compared with experimental results that were obtained with a white-light interference microscope.

© 2005 Optical Society of America

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References

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    [CrossRef]
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  8. M. Totzeck, H. Jacobsen, H. J. Tiziani, “Edge localization of subwavelength structures by use of polarization interferometry and extreme-value criteria,” Appl. Opt. 39, 6295–6305 (2000).
    [CrossRef]
  9. M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik (Stuttgart) 112, 399–406 (2001).
    [CrossRef]
  10. K. Leonhardt, H. J. Tiziani, “Optical topometry of surfaces with locally changing materials, layers and contaminations. 1. Topographic methods, based on two-beam interferometry,” J. Mod. Opt. 46, 101–114 (1999).
    [CrossRef]
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    [CrossRef]
  12. J. Schmit, K. Creath, “Window function influence on phase error in phase-shifting algorithms,” Appl. Opt. 35, 5642–5649 (1996).
    [CrossRef] [PubMed]
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2002 (1)

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of sub micrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

2001 (2)

M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik (Stuttgart) 112, 399–406 (2001).
[CrossRef]

M. Fleischer, R. Windecker, H. J. Tiziani, “Theoretical limits of scanning white-light interferometry signal evaluation algorithms,” Appl. Opt. 40, 2815–2820 (2001).
[CrossRef]

2000 (1)

1999 (1)

K. Leonhardt, H. J. Tiziani, “Optical topometry of surfaces with locally changing materials, layers and contaminations. 1. Topographic methods, based on two-beam interferometry,” J. Mod. Opt. 46, 101–114 (1999).
[CrossRef]

1996 (1)

1995 (2)

1994 (1)

1993 (1)

1977 (1)

H. H. Hopkins, “Image formation with partially coherent light,” Photograph. Sci. Eng. 21, 114–123 (1977).

Caber, P. J.

Creath, K.

J. Schmit, K. Creath, “Window function influence on phase error in phase-shifting algorithms,” Appl. Opt. 35, 5642–5649 (1996).
[CrossRef] [PubMed]

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
[CrossRef]

de Groot, P.

Deck, L.

Ettl, P.

P. Ettl, “Über die Signalentstehung bei Weiβlichtinterferametrie,” Ph.D. thesis (University of Erlangen-Nürnberg, 2001), pp. 46–50.

Fleischer, M.

Gaylord, T. K.

Grann, E. B.

Hopkins, H. H.

H. H. Hopkins, “Image formation with partially coherent light,” Photograph. Sci. Eng. 21, 114–123 (1977).

Jacobsen, H.

Kerwien, N.

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of sub micrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

Leonhardt, K.

K. Leonhardt, H. J. Tiziani, “Optical topometry of surfaces with locally changing materials, layers and contaminations. 1. Topographic methods, based on two-beam interferometry,” J. Mod. Opt. 46, 101–114 (1999).
[CrossRef]

Moharan, M. G.

Pommet, D. A.

Schmit, J.

Tavrov, A.

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of sub micrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

Tiziani, H. J.

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of sub micrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

M. Fleischer, R. Windecker, H. J. Tiziani, “Theoretical limits of scanning white-light interferometry signal evaluation algorithms,” Appl. Opt. 40, 2815–2820 (2001).
[CrossRef]

M. Totzeck, H. Jacobsen, H. J. Tiziani, “Edge localization of subwavelength structures by use of polarization interferometry and extreme-value criteria,” Appl. Opt. 39, 6295–6305 (2000).
[CrossRef]

K. Leonhardt, H. J. Tiziani, “Optical topometry of surfaces with locally changing materials, layers and contaminations. 1. Topographic methods, based on two-beam interferometry,” J. Mod. Opt. 46, 101–114 (1999).
[CrossRef]

Totzeck, M.

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of sub micrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik (Stuttgart) 112, 399–406 (2001).
[CrossRef]

M. Totzeck, H. Jacobsen, H. J. Tiziani, “Edge localization of subwavelength structures by use of polarization interferometry and extreme-value criteria,” Appl. Opt. 39, 6295–6305 (2000).
[CrossRef]

Windecker, R.

Appl. Opt. (5)

J. Mod. Opt. (1)

K. Leonhardt, H. J. Tiziani, “Optical topometry of surfaces with locally changing materials, layers and contaminations. 1. Topographic methods, based on two-beam interferometry,” J. Mod. Opt. 46, 101–114 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

A. Tavrov, M. Totzeck, N. Kerwien, H. J. Tiziani, “Rigorous coupled-wave analysis calculus of sub micrometer interference pattern and resolving edge position versus signal-to-noise ratio,” Opt. Eng. 41, 1886–1892 (2002).
[CrossRef]

Optik (Stuttgart) (1)

M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik (Stuttgart) 112, 399–406 (2001).
[CrossRef]

Photograph. Sci. Eng. (1)

H. H. Hopkins, “Image formation with partially coherent light,” Photograph. Sci. Eng. 21, 114–123 (1977).

Other (2)

P. Ettl, “Über die Signalentstehung bei Weiβlichtinterferametrie,” Ph.D. thesis (University of Erlangen-Nürnberg, 2001), pp. 46–50.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Schematic of the white-light interferometry setup.

Fig. 2
Fig. 2

Linnik interferometer microscope: 1, light source; 2, field stop; 3, condenser lens; 4, microscope objective in the measurement arm; 5, beam splitter; 6, microscope objective in the reference arm; 7, reference mirror; 8, measured object; 9, CCD lens; 10, CCD; 11, linear polarizer; 12, analyzer.

Fig. 3
Fig. 3

Trench topology 5 μm wide and 23 μm deep and its evaluated correlogram intensity distribution.

Fig. 4
Fig. 4

Left, the fringe contrast distributions for trench topology 5 μm wide and 23 μm deep. Right, the reconstructed corresponding trench profiles. (a), (b) TM; (c), (d) TE; (e), (f) circular polarization.

Fig. 5
Fig. 5

Cross sections of fringe contrast (a) along the top level marked (a) and along the bottom level marked (b) in Fig. 4(c).

Fig. 6
Fig. 6

Fringe contrast images and cross sections along the lines marked (b) and (c) in (a) and marked (e) and (f) in (d), evaluated for trench topologies 5 μm wide and 50 μm deep in (a)–(c) and 5 μm wide and 80 μm deep in (d)–(f).

Fig. 7
Fig. 7

Contrast versus NA for the induced coherence level contrast maximum (darker curve) and for fringes at the bottom actual interface (lighter curve), evaluated for the trench topology with 5/23-μm geometry.

Fig. 8
Fig. 8

WLI measurements of the topology for 9-μm-period and 5-μm-wide trench gratings: (a) correlogram; (b) fringe contrast; (c) reconstructed profile; (d), (e) cross sections of the contrast image along the lines marked in (b).

Fig. 9
Fig. 9

WLI measurements of the topology for 14-μm-period and 10-μm-wide trench gratings: (a) correlogram; (b) fringe contrast; (c) reconstructed profile; (d), (e) cross sections of contrast image along the lines marked in (b).

Fig. 10
Fig. 10

Correlogram maps for trenches 5 μm wide and 15 μm deep in (a) white-light illumination (150-nm semiwidth of a quasi-Gaussian spectrum) and (b) filtered white light (20-nm semiwidth of a quasi-Gaussian spectrum).

Equations (9)

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

γ = F ( λ ) F ( λ Δ z ) d λ ,
κ = NA il NA obj .
J x , y , z = μ L ( k μ ) × { ν H ( k ν , μ ) exp ( i k ν , μ r ) cos 1 / 2 ( ν ) [ E x ( k ν , μ ) E y ( k ν , μ ) ] } 2 ,
A = J 1 T J 2 *
= I 0 γ exp ( i φ ) 2 ,
I = ( J 1 + J 2 ) T ( J 1 + J 2 ) *
= I 0 [ 1 + γ cos ( φ ) ] .
J 2 = [ cos ( Θ ) , sin ( Θ ) ] .
J 2 = 1 2 [ 1 , i ] .

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