Abstract

In this investigation, refractive indices of a silicon (Si) wafer were measured by low-coherence scanning interferometry adopting the sub-sampling technique to reduce measurement time. Based on Fourier domain analysis method, the sub-sampled correlogram was analyzed and the refractive indices were calculated by the simple refractive index model and curve fitting of the phase extracted from the sub-sampled correlogram. In the experiment to verify the proposed technique, near-infrared light emitted by a super-luminescent diode with 1050 nm center wavelength was used as an optical source because it is partially transparent to an undoped Si wafer. As the result of measuring an undoped double-side polished Si wafer, group and phase refractive indices were successfully obtained with the sub-sampled correlogram, and the deviations from the reference value were within 0.001.

© 2013 Optical Society of America

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References

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[CrossRef]

2007

2003

2002

2000

M. Ohmi, Y. Ohnishi, K. Yoden, and M. Haruna, “In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry,” IEEE Trans. Biomed. Eng. 47, 1266–1270 (2000).
[CrossRef]

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[CrossRef]

1996

1994

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de Groot, P.

Deck, L.

Devillers, R.

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

Fukano, T.

Galli, M.

Green, M. A.

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300  K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92, 1305–1310 (2008).
[CrossRef]

Guizzetti, G.

Haruna, M.

Hashimoto, M.

Hirai, A.

Inoue, S.

Joo, K.-N.

Kim, K. H.

Kim, S. H.

Kim, S.-W.

Kim, Y. G.

Lee, S. H.

Lim, J. I.

Marabelli, F.

Maruyama, H.

Matsumoto, H.

Mitsuyama, T.

Ohmi, M.

Ohnishi, Y.

M. Ohmi, Y. Ohnishi, K. Yoden, and M. Haruna, “In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry,” IEEE Trans. Biomed. Eng. 47, 1266–1270 (2000).
[CrossRef]

Olszak, A.

Plata, A.

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

Sandoz, P.

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

Schmit, J.

Seo, Y. B.

Tajiri, H.

Tatian, B.

Yamaguchi, I.

Yoden, K.

M. Ohmi, Y. Ohnishi, K. Yoden, and M. Haruna, “In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry,” IEEE Trans. Biomed. Eng. 47, 1266–1270 (2000).
[CrossRef]

Appl. Opt.

IEEE Trans. Biomed. Eng.

M. Ohmi, Y. Ohnishi, K. Yoden, and M. Haruna, “In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry,” IEEE Trans. Biomed. Eng. 47, 1266–1270 (2000).
[CrossRef]

J. Mod. Opt.

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

Opt. Express

Opt. Lett.

Sol. Energy Mater. Sol. Cells

M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300  K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92, 1305–1310 (2008).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Sub-sampled correlogram with 1.9 μm scanning step size compared to the correlogram sampled with 50 nm step size.

Fig. 2.
Fig. 2.

Example of surface profile measurement (8.3mm×6.25mm FOV) of an undoped double-side polished Si wafer using the sub-sampling technique with 650 nm step size: (a) the front surface and (b) the rear surface.

Fig. 3.
Fig. 3.

(a) Broadened correlogram by the dispersion of a Si wafer compared to the original correlogram and (b) second-order polynomial curve fitting of the phase extracted from the broadened correlogram by the dispersion.

Fig. 4.
Fig. 4.

Simulation results of phase refractive indices of the Si wafer determined by LCSI with 50 nm step size and 1.9 μm step size for sub-sampling compared to the reference values.

Fig. 5.
Fig. 5.

Correlograms obtained from (a) the front surface and (b) the rear surface with 50 nm step size and 1.9 μm step size for sub-sampling.

Fig. 6.
Fig. 6.

Measurement results of phase refractive indices in cases of 50 nm and 1.9 μm step sizes compared to the reference values.

Tables (1)

Tables Icon

Table 1. Measurement Examples of Phase Refractive Indices of the Si Wafer With Several Scanning Step Sizes For Sub-Sampling

Equations (6)

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I(z)=A(hz)cos[2kc(hz)]=A(hz)cos[2π(2λc)(hz)],
ϕ=2kn(λ)t=2πσn(σ)t,
ϕσ|σ=σ0=2πtn(σ0)2πtσ0nσ|σ=σ0=2πtN(σ0),
N(σ0)t=12πϕσ|σ=σ0,
n(σ)=n0+n1(σσ0),
ϕ=2πσn(σ)t=2πt[(n0n1σ0)σ+n1σ2].

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