Abstract

A sinusoidal wavelength-scanning interferometer for measuring thickness and surfaces profiles of a thin film has been proposed in which a superluminescent laser diode and an acousto-optic tunable filter are used. The interference signal contains an amplitude Zb of a time-varying phase and a constant phase α. Two values of an optical path difference (OPD) obtained from Zb and α, respectively, are combined to measure an OPD longer than a wavelength. The values of Zb and α are estimated by minimizing the difference between the detected signals and theoretical ones. From the estimated values, thickness and surface of a silicon dioxide film coated on an IC wafer with different thicknesses of 1 μm and 4 μm are measured with an error less than 5 nm.

© 2005 Optical Society of America

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References

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Appl. Opt. (5)

Opt. Express (1)

Opt. Lett. (1)

Opt. Rev. (1)

H. Akiyama, O. Sasaki and T. Suzuki, "Thickness and surface profile measurement by a sinusoidal wavelength-scanning interferometer," Opt. Rev. 12, 319-323 (2005).
[CrossRef]

Proc. SPIE (2)

O. Sasaki, K. Tsuji, S. Sato, T. Kuwahara and T. Suzuki, "Sinusoidal wavelength-scanning interferometers," in Laser Interferometry IX: techniques and Analysis, M. Kujawinska, G. M. Brown, and M. Takeda, eds., Proc. SPIE 3478, 37-44 (1998).
[CrossRef]

O. Sasaki, Y. Shimakura, and T. Suzuki, "Sinusoidal wavelength-scanning superluminescent diode interferometer for two-dimensional step-profile measurement," in Advanced Materials and Devices for Sensing and Imaging, J. Yao and Y. Ishii, eds., Proc. SPIE 4919, 220-226 (2002).

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Figures (9)

Fig. 1.
Fig. 1.

Interferometer for measuring thickness and surface profiles of thin film.

Fig. 2.
Fig. 2.

Multiple reflections by a thin film.

Fig. 3.
Fig. 3.

Two dimensional shapes of the object along Ix.

Fig. 4.
Fig. 4.

Measured OPD Lzi calculated from Zbi of the (a) front surface and (b) rear surface.

Fig. 5.
Fig. 5.

Measured OPD Lαi calculated from αi of the (a) front surface and (b) rear surface.

Fig. 6.
Fig. 6.

Distribution of the fringe order (a) m1 and (b) m2.

Fig. 7.
Fig. 7.

Position P2 of the object in the case of m1R=12 and m1R=13 along Ix at Iy=15 with m1L=20, m2L=24, m2R=27.

Fig. 8.
Fig. 8.

Measured positions P1 and P2 of the surfaces.

Fig. 9.
Fig. 9.

Measured thickness of the object.

Tables (1)

Tables Icon

Table 1. Measured values along one line of Ix at Iy=15.

Equations (21)

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λ ( t ) = λ 0 + b cos ( ω b t ) ,
S ( t ) = M ( t ) i a i cos [ Z c cos ( ω c t + θ ) + Z bi cos ( ω b t ) + α i ] , ( i = 1,2,3 )
Z c = 4 πa λ 0 ,
Z bi = 2 πb L i λ 0 2 , ( i = 1,2 )
Z b 3 = Z b 1 + 2 ( Z b 2 Z b 1 ) ,
α i = 2 π L i λ 0 , ( i = 1,2 )
α 3 = α 1 + 2 ( α 2 α 1 ) + π .
S ( t ) = M ( t ) A cos [ Z c cos ( ω c t + θ ) + Φ ( t ) ] ,
A exp [ ( t ) ] = i a i exp ( j Φ i ) ( i = 1,2,3 )
[ A sin Φ ( t ) ] = 0 ,
[ A cos Φ ( t ) ] = 0 , ω > ω c 2
F 1 ( ω ω c ) = J 1 ( Z c ) exp ( ) [ A sin Φ ( t ) ] ,
F 2 ( ω 2 ω c ) = J 2 ( Z c ) exp ( j 2 θ ) [ A cos Φ ( t ) ] ,
A s ( t ) = A sin Φ ( t ) = a i sin [ Z bi cos ( ω b t ) + α i ] ,
A c ( t ) = A cos Φ ( t ) = a i cos [ Z bi cos ( ω b t ) + α i ] . ( i = 1,2,3 )
H = m { [ A ̂ s ( t m ) A s ( t m ) ] 2 + [ A ̂ c ( t m ) A c ( t m ) ] 2 } ,
m ci = ( L zi L αi ) λ 0 .
L i = m i λ 0 + L αi .
P 1 = ( m 1 λ 0 + L αi ) 2 , P 2 = P 1 + [ m λ 0 + ( L α 2 L α 1 ) ] 2 n 2 ,
A s ( t ) = C 1 + K 2 a 1 sin [ Z b 2 cos ( ω b t ) + α 2 ] + K 3 a 1 sin [ Z b 3 cos ( ω b t ) + α 3 ] ,
A c ( t ) = C 2 + K 2 a 1 cos [ Z b 2 cos ( ω b t ) + α 2 ] + K 3 a 1 cos [ Z b 3 cos ( ω b t ) + α 3 ] ,

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