Total physical thickness measurement of a multi-layered wafer using a spectral-domain interferometer with an optical comb

Jaeseok Bae; Jungjae Park; Heulbi Ahn; Jonghan Jin

doi:10.1364/OE.25.012689

Total physical thickness measurement of a multi-layered wafer using a spectral-domain interferometer with an optical comb

Jaeseok Bae, Jungjae Park, Heulbi Ahn, and Jonghan Jin

Optics Express
Vol. 25,
Issue 11,
pp. 12689-12697
(2017)
•https://doi.org/10.1364/OE.25.012689

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Jaeseok Bae, Jungjae Park, Heulbi Ahn, and Jonghan Jin, "Total physical thickness measurement of a multi-layered wafer using a spectral-domain interferometer with an optical comb," Opt. Express 25, 12689-12697 (2017)

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Related Topics
Table of Contents Category
- Instrumentation, Measurement, and Metrology
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Interferometry (120.3180)
- Spectrometers and spectroscopic instrumentation (120.6200)
- Semiconductor materials (160.6000)

About this Article
History
- Original Manuscript: April 4, 2017
- Revised Manuscript: May 5, 2017
- Manuscript Accepted: May 15, 2017
- Published: May 22, 2017

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Open Access

Abstract

An interferometric method using an optical comb is proposed and realized to measure the total physical thickness of a multi-layered wafer even if the refractive index of each layer is not given. For a feasibility test, two-layered and three-layered silicon-on-glass wafers were chosen as samples and were measured. An uncertainty evaluation was conducted to estimate the performance capabilities of the proposed method. To verify the measured values, the wafers were also measured by a contact-type standard instrument. For the three-layered wafer, the total physical thickness distribution was determined in a selected area.

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References

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Year
|
Author
|
Publication

G. K. Celler and S. Cristoloveanu, “Frontiers of silicon-on-insulator,” J. Appl. Phys. 93(9), 4955–4978 (2003).
[Crossref]
F. Boeuf, S. Cremer, E. Temporiti, M. Fere, M. Shaw, C. Baudot, N. Vulliet, T. Pinguet, A. Mekis, G. Masini, H. Petiton, P. Le Maitre, M. Traldi, and L. Maggi, “Silicon photonics R&D and manufacturing on 300-mm wafer platform,” J. Lightwave Technol. 34(2), 286–295 (2016).
[Crossref]
W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18(23), 23598–23607 (2010).
[Crossref] [PubMed]
M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1), 38–39 (1999).
[Crossref]
J. Jin, “Dimensional metrology using the optical comb of a mode-locked laser,” Meas. Sci. Technol. 27(2), 1–17 (2016).
[Crossref]
J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express 18(17), 18339–18346 (2010).
[Crossref] [PubMed]
J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and S. Lee, “Precision depth measurement of through silicon vias (TSVs) on 3D semiconductor packaging process,” Opt. Express 20(5), 5011–5016 (2012).
[Crossref] [PubMed]
S. Maeng, J. Park, B. O, and J. Jin, “Uncertainty improvement of geometrical thickness and refractive index measurement of a silicon wafer using a femtosecond pulse laser,” Opt. Express 20(11), 12184–12190 (2012).
[Crossref] [PubMed]
J. Park, J. Jin, J. Wan Kim, and J.-A. Kim, “Measurement of thickness profile and refractive index variation of a silicon wafer using the optical comb of a femtosecond pulse laser,” Opt. Commun. 305(15), 170–174 (2013).
[Crossref]
J. Jin, S. Maeng, J. Park, J.-A. Kim, and J. W. Kim, “Fizeau-type interferometric probe to measure geometrical thickness of silicon wafers,” Opt. Express 22(19), 23427–23432 (2014).
[Crossref] [PubMed]
J. Park, J. Bae, J. Jin, J.-A. Kim, and J. W. Kim, “Vibration-insensitive measurements of the thickness profile of large glass panels,” Opt. Express 23(26), 32941–32949 (2015).
[Crossref] [PubMed]
J. Park, J. Jin, J.-A. Kim, and J. W. Kim, “Absolute distance measurement method without a non-measurable range and directional ambiguity based on the spectral-domain interferometer using the optical comb of the femtosecond pulse laser,” Appl. Phys. Lett. 109(24), 244103 (2016).
[Crossref]
H. Ahn, J. Park, J.-A. Kim, and J. Jin, “Optical fiber-based confocal and interferometric system for measuring the depth and diameter of through silicon vias,” J. Lightwave Technol. 34(23), 5462–5466 (2016).
[Crossref]
P. Balling, P. Mašika, P. Křen, and M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[Crossref]
J. Na, H. Y. Choi, E. S. Choi, C. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 48(13), 2461–2467 (2009).
[Crossref] [PubMed]
K. Zhang, L. Tao, W. Cheng, J. Liu, and Z. Chen, “Air etalon facilitated simultaneous measurement of group refractive index and thickness using spectral interferometry,” Appl. Opt. 53(31), 7483–7486 (2014).
[Crossref] [PubMed]
H. Lee and K.-N. Joo, “Optical interferometric approach for measuring the geometrical dimension and refractive index profiles of a double-sided polished undoped Si wafer,” Meas. Sci. Technol. 25(7), 075202 (2014).
[Crossref]
S. C. Zilio, “Simultaneous thickness and group index measurement with a single arm low-coherence interferometer,” Opt. Express 22(22), 27392–27397 (2014).
[Crossref] [PubMed]
C. Moreno-Hernández, D. Monzón-Hernández, I. Hernández-Romano, and J. Villatoro, “Single tapered fiber tip for simultaneous measurements of thickness, refractive index and distance to a sample,” Opt. Express 23(17), 22141–22148 (2015).
[Crossref] [PubMed]
BIPM, “Guide to the expression of uncertainty in measurement,” (JCGM 100:2008), http://www.bipm.org/en/publications/guides/gum.html .

2016 (4)

F. Boeuf, S. Cremer, E. Temporiti, M. Fere, M. Shaw, C. Baudot, N. Vulliet, T. Pinguet, A. Mekis, G. Masini, H. Petiton, P. Le Maitre, M. Traldi, and L. Maggi, “Silicon photonics R&D and manufacturing on 300-mm wafer platform,” J. Lightwave Technol. 34(2), 286–295 (2016).
[Crossref]

J. Jin, “Dimensional metrology using the optical comb of a mode-locked laser,” Meas. Sci. Technol. 27(2), 1–17 (2016).
[Crossref]

J. Park, J. Jin, J.-A. Kim, and J. W. Kim, “Absolute distance measurement method without a non-measurable range and directional ambiguity based on the spectral-domain interferometer using the optical comb of the femtosecond pulse laser,” Appl. Phys. Lett. 109(24), 244103 (2016).
[Crossref]

H. Ahn, J. Park, J.-A. Kim, and J. Jin, “Optical fiber-based confocal and interferometric system for measuring the depth and diameter of through silicon vias,” J. Lightwave Technol. 34(23), 5462–5466 (2016).
[Crossref]

2015 (2)

J. Park, J. Bae, J. Jin, J.-A. Kim, and J. W. Kim, “Vibration-insensitive measurements of the thickness profile of large glass panels,” Opt. Express 23(26), 32941–32949 (2015).
[Crossref] [PubMed]

C. Moreno-Hernández, D. Monzón-Hernández, I. Hernández-Romano, and J. Villatoro, “Single tapered fiber tip for simultaneous measurements of thickness, refractive index and distance to a sample,” Opt. Express 23(17), 22141–22148 (2015).
[Crossref] [PubMed]

2014 (4)

J. Jin, S. Maeng, J. Park, J.-A. Kim, and J. W. Kim, “Fizeau-type interferometric probe to measure geometrical thickness of silicon wafers,” Opt. Express 22(19), 23427–23432 (2014).
[Crossref] [PubMed]

K. Zhang, L. Tao, W. Cheng, J. Liu, and Z. Chen, “Air etalon facilitated simultaneous measurement of group refractive index and thickness using spectral interferometry,” Appl. Opt. 53(31), 7483–7486 (2014).
[Crossref] [PubMed]

H. Lee and K.-N. Joo, “Optical interferometric approach for measuring the geometrical dimension and refractive index profiles of a double-sided polished undoped Si wafer,” Meas. Sci. Technol. 25(7), 075202 (2014).
[Crossref]

S. C. Zilio, “Simultaneous thickness and group index measurement with a single arm low-coherence interferometer,” Opt. Express 22(22), 27392–27397 (2014).
[Crossref] [PubMed]

2013 (1)

J. Park, J. Jin, J. Wan Kim, and J.-A. Kim, “Measurement of thickness profile and refractive index variation of a silicon wafer using the optical comb of a femtosecond pulse laser,” Opt. Commun. 305(15), 170–174 (2013).
[Crossref]

2012 (3)

J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and S. Lee, “Precision depth measurement of through silicon vias (TSVs) on 3D semiconductor packaging process,” Opt. Express 20(5), 5011–5016 (2012).
[Crossref] [PubMed]

S. Maeng, J. Park, B. O, and J. Jin, “Uncertainty improvement of geometrical thickness and refractive index measurement of a silicon wafer using a femtosecond pulse laser,” Opt. Express 20(11), 12184–12190 (2012).
[Crossref] [PubMed]

P. Balling, P. Mašika, P. Křen, and M. Doležal, “Length and refractive index measurement by Fourier transform interferometry and frequency comb spectroscopy,” Meas. Sci. Technol. 23(9), 094001 (2012).
[Crossref]

2010 (2)

J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express 18(17), 18339–18346 (2010).
[Crossref] [PubMed]

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18(23), 23598–23607 (2010).
[Crossref] [PubMed]

2009 (1)

J. Na, H. Y. Choi, E. S. Choi, C. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 48(13), 2461–2467 (2009).
[Crossref] [PubMed]

2003 (1)

G. K. Celler and S. Cristoloveanu, “Frontiers of silicon-on-insulator,” J. Appl. Phys. 93(9), 4955–4978 (2003).
[Crossref]

1999 (1)

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1), 38–39 (1999).
[Crossref]

Ahn, H.

Bae, J.

Balling, P.

Baudot, C.

Boeuf, F.

Celler, G. K.

G. K. Celler and S. Cristoloveanu, “Frontiers of silicon-on-insulator,” J. Appl. Phys. 93(9), 4955–4978 (2003).
[Crossref]

Chen, Z.

Cheng, W.

Choi, E. S.

Choi, H. Y.

Cremer, S.

Cristoloveanu, S.

G. K. Celler and S. Cristoloveanu, “Frontiers of silicon-on-insulator,” J. Appl. Phys. 93(9), 4955–4978 (2003).
[Crossref]

Daio, H.

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1), 38–39 (1999).
[Crossref]

Doležal, M.

Eom, T. B.

Fere, M.

Hernández-Romano, I.

Jin, J.

J. Jin, “Dimensional metrology using the optical comb of a mode-locked laser,” Meas. Sci. Technol. 27(2), 1–17 (2016).
[Crossref]

Joo, K.-N.

Kang, C.-S.

Kim, J. W.

Kim, J.-A.

Kimura, M.

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1), 38–39 (1999).
[Crossref]

Kren, P.

Le Maitre, P.

Lee, B. H.

Lee, C.

Lee, H.

Lee, S.

Liu, J.

Maeng, S.

Maggi, L.

Mašika, P.

Masini, G.

Mekis, A.

Monzón-Hernández, D.

Moreno-Hernández, C.

Na, J.

O, B.

Park, J.

Petiton, H.

Pinguet, T.

Saito, Y.

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1), 38–39 (1999).
[Crossref]

Shaw, M.

Tao, L.

Temporiti, E.

Traldi, M.

Trotter, D. C.

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18(23), 23598–23607 (2010).
[Crossref] [PubMed]

Villatoro, J.

Vulliet, N.

Wan Kim, J.

Watts, M. R.

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18(23), 23598–23607 (2010).
[Crossref] [PubMed]

Yakushiji, K.

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1), 38–39 (1999).
[Crossref]

Zhang, K.

Zilio, S. C.

S. C. Zilio, “Simultaneous thickness and group index measurement with a single arm low-coherence interferometer,” Opt. Express 22(22), 27392–27397 (2014).
[Crossref] [PubMed]

Zortman, W. A.

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18(23), 23598–23607 (2010).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. Appl. Phys. (1)

G. K. Celler and S. Cristoloveanu, “Frontiers of silicon-on-insulator,” J. Appl. Phys. 93(9), 4955–4978 (2003).
[Crossref]

J. Lightwave Technol. (2)

Jpn. J. Appl. Phys. (1)

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1), 38–39 (1999).
[Crossref]

Meas. Sci. Technol. (3)

J. Jin, “Dimensional metrology using the optical comb of a mode-locked laser,” Meas. Sci. Technol. 27(2), 1–17 (2016).
[Crossref]

Opt. Commun. (1)

Opt. Express (8)

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18(23), 23598–23607 (2010).
[Crossref] [PubMed]

S. C. Zilio, “Simultaneous thickness and group index measurement with a single arm low-coherence interferometer,” Opt. Express 22(22), 27392–27397 (2014).
[Crossref] [PubMed]

Other (1)

BIPM, “Guide to the expression of uncertainty in measurement,” (JCGM 100:2008), http://www.bipm.org/en/publications/guides/gum.html .

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Fig. 1 Schematic diagram of the total physical thickness measurement of a multi-layered specimen.

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Fig. 2 Measurement system of the total physical thickness of a SOG wafer: (a) optical configuration, (b) a photo of the experimental setup, (c) a cross-sectional image of a two-layered SOG wafer, and (d) a cross-sectional image of a three-layered SOG wafer (CL: collimating lens; BS1, BS2: beam splitter; M1, M2: mirror; FL: focusing lens).

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Fig. 3 Examples of the interference spectra and amplitude information in the Fourier domain: (a) interference spectrum obtained without a wafer, (b) interference spectrum obtained with a two-layered SOG wafer, (c) interference spectrum obtained with a three-layered SOG wafer, (d) Fourier transform of the interference spectrum (a), (e) Fourier transform of the interference spectrum (b), and (f) Fourier transform of the interference spectrum (c).

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Fig. 4 Measurement result of the total physical thickness of two SOG wafers: (a) repeated measurement result of the physical thickness of a two-layered SOG wafer at fixed point, (b) repeated measurement result of the physical thickness of a three-layered SOG wafer at a fixed point, and (c) total physical thickness distribution of the three-layered SOG wafer.

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Fig. 5 Comparative measurement results of the total physical thickness of the two SOG wafers studied here.

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Tables (2)

Table 1 Uncertainty budget for the total thickness measurement of a two-layered SOG wafer.

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Table 2 Uncertainty budget for the total thickness measurement of a three-layered SOG wafer.

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Equations (5)

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I (f, l) = I_{0} (f) \cdot {1 + \cos (2 π f \cdot \frac{l}{c})} .

{OPD}_{1} = L_{1} - L_{2},

{OPD}_{2} = \sum_{i = 1}^{n} 2 \cdot (T_{i} \cdot N_{i}),

{OPD}_{3} = L_{1} - \sum_{i = 1}^{n} T_{i} + \sum_{i = 1}^{n} T_{i} \cdot N_{i} - L_{2},

T_{t o t a l} = \sum_{i = 1}^{n} T_{i} = \frac{{OPD}_{2}}{2} - {OPD}_{3} + {OPD}_{1}

Source of Uncertainty	Value	Type	Value for T_total = 551.729 μm
Optical path difference, OPD₃ = 1850.345 μm			24 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	23 nm
Measurement repeatability	33 nm	A	7 nm
Refractive index of air	10⁻⁶	B	2 nm
Optical path difference, OPD₂ = 1829.363 μm			23 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	23 nm
Measurement repeatability	20 nm	A	4 nm
Optical path difference, OPD₃ = 2213.297 μm			30 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	27 nm
Measurement repeatability	55 nm	A	12 nm
Refractive index of air	10⁻⁶	B	2 nm
Uncertainty of geometrical thickness, T_total			17 nm (k = 1)
Uncertainty of optical path differences, OPD₁, OPD₂, and OPD₃			40 nm
Uncertainty of coupling between OPD₁, OPD₂, and OPD₃			36 nm

Source of Uncertainty	Value	Type	Value for T_total = 1497.461 μm
Optical path difference, OPD1 = 1850.305 μm			24 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	23 nm
Measurement repeatability	23 nm	A	5 nm
Refractive index of air	10⁻⁶	B	2 nm
Optical path difference, OPD₂ = 7778.600 μm			97 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	96 nm
Measurement repeatability	46 nm	A	10 nm
Optical path difference, OPD₃ = 4242.144 μm			53 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	53 nm
Measurement repeatability	21 nm	A	5 nm
Refractive index of air	10⁻⁶	B	4 nm
Uncertainty of geometrical thickness, T_total			20 nm (k = 1)
Uncertainty of optical path differences, OPD₁, OPD₂, and OPD₃			76 nm
Uncertainty of coupling between OPD₁, OPD₂, and OPD₃			73 nm

Source of Uncertainty	Value	Type	Value for T_total = 551.729 μm
Optical path difference, OPD₃ = 1850.345 μm			24 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	23 nm
Measurement repeatability	33 nm	A	7 nm
Refractive index of air	10⁻⁶	B	2 nm
Optical path difference, OPD₂ = 1829.363 μm			23 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	23 nm
Measurement repeatability	20 nm	A	4 nm
Optical path difference, OPD₃ = 2213.297 μm			30 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	27 nm
Measurement repeatability	55 nm	A	12 nm
Refractive index of air	10⁻⁶	B	2 nm
Uncertainty of geometrical thickness, T_total			17 nm (k = 1)
Uncertainty of optical path differences, OPD₁, OPD₂, and OPD₃			40 nm
Uncertainty of coupling between OPD₁, OPD₂, and OPD₃			36 nm

Source of Uncertainty	Value	Type	Value for T_total = 1497.461 μm
Optical path difference, OPD1 = 1850.305 μm			24 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	23 nm
Measurement repeatability	23 nm	A	5 nm
Refractive index of air	10⁻⁶	B	2 nm
Optical path difference, OPD₂ = 7778.600 μm			97 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	96 nm
Measurement repeatability	46 nm	A	10 nm
Optical path difference, OPD₃ = 4242.144 μm			53 nm
DFT algorithm & wavelength accuracy of OSA	1.24 × 10⁻⁵	B	53 nm
Measurement repeatability	21 nm	A	5 nm
Refractive index of air	10⁻⁶	B	4 nm
Uncertainty of geometrical thickness, T_total			20 nm (k = 1)
Uncertainty of optical path differences, OPD₁, OPD₂, and OPD₃			76 nm
Uncertainty of coupling between OPD₁, OPD₂, and OPD₃			73 nm