Abstract

A novel high speed volumetric thickness profilometry based on a wavelength scanning full-field interferometer and its signal processing algorithm is described for a thin film deposited on pattern structures. A specially designed Michelson interferometer with a blocking plate in the reference path enables us to measure the volumetric thickness profile by decoupling two variables, thickness and profile, which affect the total phase function ϕ(k). We show experimentally that the proposed method provides a much faster solution in obtaining the volumetric thickness profile data while maintaining the similar level of accurate measurement capability as that of the least square fitting method.

© 2008 Optical Society of America

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References

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2007

Y. S. Ghim and S. W. Kim, "Fast, precise, tomograpic measurements of thin films," Appl. Phys. Lett. 91, 091903 (2007).
[CrossRef]

2006

2005

2004

2003

2002

2000

I. Yamaguchi, "Surface tomography by wavelength scanning interferometry," Opt. Eng. 39, 40-46 (2000).
[CrossRef]

1999

1997

1994

1993

1988

1984

1973

Akiyama, H.

Chen, J.

Cheng, Y.

Dakoff, A.

de Groot, P.

Deck, L.

Gass, J.

Ghim, Y. S.

Ishii, Y.

Javidi, B.

Kim, D.

Kim, G. H.

Kim, M. K.

Kim, S.

Kim, S. W.

Kinoshita, M.

Kitagawa, K.

K. Kitagawa, "Simultaneous measurement of film surface topography and thickness variation using white-light interferometry," Proc. SPIE 6375, 637507 (2006).
[CrossRef]

Kong, H.

Kurokawa, T.

Lee, Y.

Murata, K.

Pfortner, A.

Polhemus, C.

Sasaki, O.

Schwider, J.

Suzuki, T.

Takeda, M.

Watanabe, Y.

Wyant, J. C.

Yago, H.

Yamaguchi, I.

I. Yamaguchi, "Surface tomography by wavelength scanning interferometry," Opt. Eng. 39, 40-46 (2000).
[CrossRef]

I. Yamaguchi and T. Zhang, "Phase shifting digital holography," Opt. Lett. 22, 1268-1270 (1997).
[CrossRef] [PubMed]

You, J. W.

Zhang, T.

Zhou, L.

Appl. Opt.

Appl. Phys. Lett.

Y. S. Ghim and S. W. Kim, "Fast, precise, tomograpic measurements of thin films," Appl. Phys. Lett. 91, 091903 (2007).
[CrossRef]

Opt. Eng.

I. Yamaguchi, "Surface tomography by wavelength scanning interferometry," Opt. Eng. 39, 40-46 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

K. Kitagawa, "Simultaneous measurement of film surface topography and thickness variation using white-light interferometry," Proc. SPIE 6375, 637507 (2006).
[CrossRef]

Other

K. Creath, "Temperal phase measuring methods," in Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D. W. Robinson and G. T. Reid, eds., (Institute of Physics, Bristol, UK, 1993).

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Figures (9)

Fig. 1.
Fig. 1.

(a). Schematic of wavelength scanning full-field interferometer that is operated in two-step: blocking plate “ON” and “OFF” in the reference path. The focal length of objective and L2 lens is 45 mm and 200 mm, respectively. M is mirror. The inset describes film thickness d(x,y) and upper surface profile h(x,y). (b) 3-D data set obtained by wavelength scanning of AOTF

Fig. 2.
Fig. 2.

Error analysis of peak detection method

Fig. 3.
Fig. 3.

(a). diffraction angle of an AOTF (b) image shift calibration result

Fig. 4.
Fig. 4.

(a). Photograph of the rectangular pattern sample (b) cross sectional view of line A-B

Fig. 5.
Fig. 5.

Raw and smoothed spectral reflectance obtained at (a) A and (b) B in Fig. 4.

Fig. 6.
Fig. 6.

(a). Interference between the thin film sample and the reference mirror, (b) total phase ϕ (k) calculated using Eq. (9).

Fig. 7.
Fig. 7.

(a). ψ(k) due to thin film and (b) ψ(k)(dot), total phase ϕ(k)(dash) and its difference (solid).

Fig. 8.
Fig. 8.

Experimental results of thickness profile h(x,y) & d(x,y)

Fig. 9.
Fig. 9.

(a). Comparison of the thickness measured by the fitting method and the peak detection method, (b) thickness profile of thin film with step height of h1–h2.

Tables (1)

Tables Icon

Table 1. Comparison of the thickness measurement results

Equations (15)

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I ( x , y , k , h , d ) = E r ( x , y ) + E t ( x , y , h ) 2
= i 0 ( k , d ) [ 1 + γ ( k , d ) cos { 2 k h + ψ ( k , d ) } ]
ψ ( k , d ) = arctan ( B A )
R ( k , d ) = r 01 + r 12 exp [ j 2 d N ( k ) k cos θ ] 1 + r 01 r 12 exp [ j 2 d N ( k ) k cos θ ] = A + Bj
( k , d ) sample = G ( k , d ) sample G ( k , 0 ) reference ( k , 0 ) reference
d = ( n 1 ) π 2 { k 1 N ( k 1 ) k 2 N ( k 2 ) }
I ( x , y , k , h ) = i 0 ( x , y , k ) { 1 + γ ( x , y , k ) cos [ 2 ( k c + δ k ) ( h ' ( x , y ) + h 0 ) + ψ ( k , d ) ] }
i 0 ( x , y , k ) { 1 + γ ( x , y , k ) cos ( 2 k c h ( x , y ) + 2 h 0 δ k + ψ ( k , d ) ) } .
I 1 ( x , y ) = i 0 ( x , y ) { 1 + γ ( x , y ) cos [ 2 k c h ( x , y ) 2 h 0 ( 2 Δ k ) + ψ ( k c , d ) ] }
I 2 ( x , y ) = i 0 ( x , y ) { 1 + γ ( x , y ) cos [ 2 k c h ( x , y ) 2 h 0 2 Δ k + ψ ( k c , d ) ] }
I 3 ( x , y ) = i 0 ( x , y ) { 1 + γ ( x , y ) cos [ 2 k c h ( x , y ) + ψ ( k c , d ) ] }
I 4 ( x , y ) = i 0 ( x , y ) { 1 + γ ( x , y ) cos [ 2 k c h ( x , y ) + 2 h 0 Δ k + ψ ( k c , d ) ] }
I 5 ( x , y ) = i 0 ( x , y ) { 1 + γ ( x , y ) cos [ 2 k c h ( x , y ) + 2 h 0 ( 2 Δ k ) + ψ ( k c , d ) ] }
ϕ ( k c ) = tan 1 [ 1 cos ( 4 Δ k h 0 ) sin ( 2 Δ k h 0 ) ( I 2 I 4 2 I 3 I 5 I 1 ) ]
h = ( ϕ ( k 1 ) ϕ ( k 0 ) ) ( ψ ( k 1 ) ψ ( k 0 ) ) 2 ( k 1 k 0 )

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