Abstract

Coherence scanning interferometry is established as a powerful noncontact, three-dimensional, metrology technique used to determine accurate surface roughness and topography measurements with subnanometer precision. The helical complex field (HCF) function is a topographically defined helix modulated by the electrical field reflectance, originally developed for the measurement of thin films. An approach to extend the capability of the HCF function to determine the spectral refractive index of a substrate or absorbing film has recently been proposed. In this paper, we confirm this new capability, demonstrating it on surfaces of silicon, gold, and a gold/palladium alloy using silica and zirconia oxide thin films. These refractive index dispersion measurements show good agreement with those obtained by spectroscopic ellipsometry.

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References

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  1. D. Tentori-Santa-Cruz and J. Camacho, “Refractive index evaluation using reflectometry: accuracy analysis,” Proc. SPIE 1761, 316–324 (1993).
    [Crossref]
  2. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
    [Crossref]
  3. Horiba Jobin Yvon, Spectroscopic Ellipsometry User Guide (2008).
  4. International Organization for Standardization, “Geometrical Product Specifications (GPS)–Surface Texture: Areal–Part 604: Nominal Characteristics of Non-Contact (Coherence Scanning Interferometry) Instruments,” (2013).
  5. B. Maniscalco, P. M. Kaminski, and J. Walls, “Thin film thickness measurements using scanning white light interferometry,” Thin Solid Films 550, 10–16 (2014).
    [Crossref]
  6. D. Mansfield, “Apparatus for and a method of determining characteristics of thin-layer structures using low-coherence interferometry,” WO patent application PCT/GB2005/002,783 (19January2006).
  7. D. Mansfield, “Apparatus for and a method of determining a characteristic of a sample,” WO patent application PCT/GB2015/052,339 (18February2016).
  8. D. Mansfield, The distorted helix: thin film extraction from scanning white light interferometry, Proc. SPIE 6186, 61860O (2006).
    [Crossref]
  9. A. Bankhead and I. McDonnell, “Interferometric surface profiling,” G.B. patent application 2,390,676 (2008).
  10. R. Leach, L. Brown, X. Jiang, R. Blunt, M. Conroy, and D. Mauger, “Guide to the measurement of smooth surface topography using coherence scanning interferometry,” NPL Measurement Good Practice Guide 108, 2008.
  11. S.-W. Kim and G.-H. Kim, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38, 5968–5973 (1999).
    [Crossref]
  12. P. J. de Groot and X. C. de Lega, “Signal modeling for modern interference microscopes,” in Photonics Europe (International Society for Optics and Photonics, 2004), pp. 26–34.
  13. K. Palodhi, “Absolute surface topography measurement with polarisation sensitive coherence scanning interferometry,” Ph.D. thesis (Loughborough University (2013).
  14. S.-W. Kim and G.-H. Kim, “Method for measuring a thickness profile and a refractive index using white-light scanning interferometry and recording medium therefor,” U.S. patent application 6,545,763 B1 (8April2003).
  15. P. J. de Groot, “Interferometry method for ellipsometry, reflectometry, and scatterometry measurements, including characterization of thin film structures,” U.S. patent application 7,403,289 B2 (22July2008).
  16. H. Yoshino, R. Smith, J. M. Walls, and D. Mansfield, “The development of thin film metrology by coherence scanning interferometry,” Proc. SPIE 9749, 97490P (2016).
    [Crossref]
  17. H. Angus MacLeod, Thin-Film Optical Filters, 3rd ed., Series in Optics and Optoelectronics (Taylor & Francis, 2001).
  18. Taylor Hobson Ltd., “CCI System Specifications,” (2012).

2016 (1)

H. Yoshino, R. Smith, J. M. Walls, and D. Mansfield, “The development of thin film metrology by coherence scanning interferometry,” Proc. SPIE 9749, 97490P (2016).
[Crossref]

2014 (1)

B. Maniscalco, P. M. Kaminski, and J. Walls, “Thin film thickness measurements using scanning white light interferometry,” Thin Solid Films 550, 10–16 (2014).
[Crossref]

2006 (1)

D. Mansfield, The distorted helix: thin film extraction from scanning white light interferometry, Proc. SPIE 6186, 61860O (2006).
[Crossref]

1999 (1)

1993 (1)

D. Tentori-Santa-Cruz and J. Camacho, “Refractive index evaluation using reflectometry: accuracy analysis,” Proc. SPIE 1761, 316–324 (1993).
[Crossref]

1983 (1)

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[Crossref]

Angus MacLeod, H.

H. Angus MacLeod, Thin-Film Optical Filters, 3rd ed., Series in Optics and Optoelectronics (Taylor & Francis, 2001).

Bankhead, A.

A. Bankhead and I. McDonnell, “Interferometric surface profiling,” G.B. patent application 2,390,676 (2008).

Blunt, R.

R. Leach, L. Brown, X. Jiang, R. Blunt, M. Conroy, and D. Mauger, “Guide to the measurement of smooth surface topography using coherence scanning interferometry,” NPL Measurement Good Practice Guide 108, 2008.

Brown, L.

R. Leach, L. Brown, X. Jiang, R. Blunt, M. Conroy, and D. Mauger, “Guide to the measurement of smooth surface topography using coherence scanning interferometry,” NPL Measurement Good Practice Guide 108, 2008.

Camacho, J.

D. Tentori-Santa-Cruz and J. Camacho, “Refractive index evaluation using reflectometry: accuracy analysis,” Proc. SPIE 1761, 316–324 (1993).
[Crossref]

Conroy, M.

R. Leach, L. Brown, X. Jiang, R. Blunt, M. Conroy, and D. Mauger, “Guide to the measurement of smooth surface topography using coherence scanning interferometry,” NPL Measurement Good Practice Guide 108, 2008.

de Groot, P. J.

P. J. de Groot and X. C. de Lega, “Signal modeling for modern interference microscopes,” in Photonics Europe (International Society for Optics and Photonics, 2004), pp. 26–34.

P. J. de Groot, “Interferometry method for ellipsometry, reflectometry, and scatterometry measurements, including characterization of thin film structures,” U.S. patent application 7,403,289 B2 (22July2008).

de Lega, X. C.

P. J. de Groot and X. C. de Lega, “Signal modeling for modern interference microscopes,” in Photonics Europe (International Society for Optics and Photonics, 2004), pp. 26–34.

Jiang, X.

R. Leach, L. Brown, X. Jiang, R. Blunt, M. Conroy, and D. Mauger, “Guide to the measurement of smooth surface topography using coherence scanning interferometry,” NPL Measurement Good Practice Guide 108, 2008.

Kaminski, P. M.

B. Maniscalco, P. M. Kaminski, and J. Walls, “Thin film thickness measurements using scanning white light interferometry,” Thin Solid Films 550, 10–16 (2014).
[Crossref]

Kim, G.-H.

S.-W. Kim and G.-H. Kim, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38, 5968–5973 (1999).
[Crossref]

S.-W. Kim and G.-H. Kim, “Method for measuring a thickness profile and a refractive index using white-light scanning interferometry and recording medium therefor,” U.S. patent application 6,545,763 B1 (8April2003).

Kim, S.-W.

S.-W. Kim and G.-H. Kim, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38, 5968–5973 (1999).
[Crossref]

S.-W. Kim and G.-H. Kim, “Method for measuring a thickness profile and a refractive index using white-light scanning interferometry and recording medium therefor,” U.S. patent application 6,545,763 B1 (8April2003).

Leach, R.

R. Leach, L. Brown, X. Jiang, R. Blunt, M. Conroy, and D. Mauger, “Guide to the measurement of smooth surface topography using coherence scanning interferometry,” NPL Measurement Good Practice Guide 108, 2008.

Maniscalco, B.

B. Maniscalco, P. M. Kaminski, and J. Walls, “Thin film thickness measurements using scanning white light interferometry,” Thin Solid Films 550, 10–16 (2014).
[Crossref]

Mansfield, D.

H. Yoshino, R. Smith, J. M. Walls, and D. Mansfield, “The development of thin film metrology by coherence scanning interferometry,” Proc. SPIE 9749, 97490P (2016).
[Crossref]

D. Mansfield, The distorted helix: thin film extraction from scanning white light interferometry, Proc. SPIE 6186, 61860O (2006).
[Crossref]

D. Mansfield, “Apparatus for and a method of determining characteristics of thin-layer structures using low-coherence interferometry,” WO patent application PCT/GB2005/002,783 (19January2006).

D. Mansfield, “Apparatus for and a method of determining a characteristic of a sample,” WO patent application PCT/GB2015/052,339 (18February2016).

Mauger, D.

R. Leach, L. Brown, X. Jiang, R. Blunt, M. Conroy, and D. Mauger, “Guide to the measurement of smooth surface topography using coherence scanning interferometry,” NPL Measurement Good Practice Guide 108, 2008.

McDonnell, I.

A. Bankhead and I. McDonnell, “Interferometric surface profiling,” G.B. patent application 2,390,676 (2008).

Palodhi, K.

K. Palodhi, “Absolute surface topography measurement with polarisation sensitive coherence scanning interferometry,” Ph.D. thesis (Loughborough University (2013).

Smith, R.

H. Yoshino, R. Smith, J. M. Walls, and D. Mansfield, “The development of thin film metrology by coherence scanning interferometry,” Proc. SPIE 9749, 97490P (2016).
[Crossref]

Swanepoel, R.

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[Crossref]

Tentori-Santa-Cruz, D.

D. Tentori-Santa-Cruz and J. Camacho, “Refractive index evaluation using reflectometry: accuracy analysis,” Proc. SPIE 1761, 316–324 (1993).
[Crossref]

Walls, J.

B. Maniscalco, P. M. Kaminski, and J. Walls, “Thin film thickness measurements using scanning white light interferometry,” Thin Solid Films 550, 10–16 (2014).
[Crossref]

Walls, J. M.

H. Yoshino, R. Smith, J. M. Walls, and D. Mansfield, “The development of thin film metrology by coherence scanning interferometry,” Proc. SPIE 9749, 97490P (2016).
[Crossref]

Yoshino, H.

H. Yoshino, R. Smith, J. M. Walls, and D. Mansfield, “The development of thin film metrology by coherence scanning interferometry,” Proc. SPIE 9749, 97490P (2016).
[Crossref]

Appl. Opt. (1)

J. Phys. E (1)

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
[Crossref]

Proc. SPIE (3)

D. Mansfield, The distorted helix: thin film extraction from scanning white light interferometry, Proc. SPIE 6186, 61860O (2006).
[Crossref]

H. Yoshino, R. Smith, J. M. Walls, and D. Mansfield, “The development of thin film metrology by coherence scanning interferometry,” Proc. SPIE 9749, 97490P (2016).
[Crossref]

D. Tentori-Santa-Cruz and J. Camacho, “Refractive index evaluation using reflectometry: accuracy analysis,” Proc. SPIE 1761, 316–324 (1993).
[Crossref]

Thin Solid Films (1)

B. Maniscalco, P. M. Kaminski, and J. Walls, “Thin film thickness measurements using scanning white light interferometry,” Thin Solid Films 550, 10–16 (2014).
[Crossref]

Other (12)

D. Mansfield, “Apparatus for and a method of determining characteristics of thin-layer structures using low-coherence interferometry,” WO patent application PCT/GB2005/002,783 (19January2006).

D. Mansfield, “Apparatus for and a method of determining a characteristic of a sample,” WO patent application PCT/GB2015/052,339 (18February2016).

Horiba Jobin Yvon, Spectroscopic Ellipsometry User Guide (2008).

International Organization for Standardization, “Geometrical Product Specifications (GPS)–Surface Texture: Areal–Part 604: Nominal Characteristics of Non-Contact (Coherence Scanning Interferometry) Instruments,” (2013).

P. J. de Groot and X. C. de Lega, “Signal modeling for modern interference microscopes,” in Photonics Europe (International Society for Optics and Photonics, 2004), pp. 26–34.

K. Palodhi, “Absolute surface topography measurement with polarisation sensitive coherence scanning interferometry,” Ph.D. thesis (Loughborough University (2013).

S.-W. Kim and G.-H. Kim, “Method for measuring a thickness profile and a refractive index using white-light scanning interferometry and recording medium therefor,” U.S. patent application 6,545,763 B1 (8April2003).

P. J. de Groot, “Interferometry method for ellipsometry, reflectometry, and scatterometry measurements, including characterization of thin film structures,” U.S. patent application 7,403,289 B2 (22July2008).

H. Angus MacLeod, Thin-Film Optical Filters, 3rd ed., Series in Optics and Optoelectronics (Taylor & Francis, 2001).

Taylor Hobson Ltd., “CCI System Specifications,” (2012).

A. Bankhead and I. McDonnell, “Interferometric surface profiling,” G.B. patent application 2,390,676 (2008).

R. Leach, L. Brown, X. Jiang, R. Blunt, M. Conroy, and D. Mauger, “Guide to the measurement of smooth surface topography using coherence scanning interferometry,” NPL Measurement Good Practice Guide 108, 2008.

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Figures (12)

Fig. 1.
Fig. 1. Schematic diagram of the thin film assembly consisting of a number of layers (L). The incident angle is θ. The multilayer structure is defined by the thickness vector d={d1,,dL}.
Fig. 2.
Fig. 2. Interference signal with respect to the scanning direction Z [μm] of (a) the Si substrate and (b) a 560 nm SiO2 layer deposited on Si.
Fig. 3.
Fig. 3. Spectral amplitude of the Fourier transform of the Si reference substrate and the film assembly of 560 nm SiO2 deposited on Si.
Fig. 4.
Fig. 4. Curve fitting between HCFs and HCFd corresponding to Fig. 2(b).
Fig. 5.
Fig. 5. Two separate measurements are required for the determination of the refractive index of the test sample.
Fig. 6.
Fig. 6. Potential refractive indices for gold. Some of the refractive index candidates Nt with respect to ΔzHCF1 are shown (top: n, bottom: κ).
Fig. 7.
Fig. 7. Refractive index of Si determined using a sample of 520 nm SiO2 deposited on Si. {n,κ} determined by the HCF-based method, and {n,κ} determined by spectroscopic ellipsometry.
Fig. 8.
Fig. 8. Refractive index of Si determined using a sample of 314 nm ZrO2 deposited on Si. {n,κ} determined by the HCF-based method, and {n,κ} determined by spectroscopic ellipsometry.
Fig. 9.
Fig. 9. Refractive index of gold determined using a sample of 305 nm ZrO2 deposited on gold. {n,κ} determined by the HCF-based method, and {n,κ} determined by spectroscopic ellipsometry.
Fig. 10.
Fig. 10. Refractive index of AuPd determined using a sample of 306 nm ZrO2 deposited on AuPd. {n,κ} determined by the HCF-based method, and {n,κ} determined by spectroscopic ellipsometry.
Fig. 11.
Fig. 11. Sample #2. Logarithm of absolute values of the derivatives of the candidate refractive indices for the Si substrate with a deposited ZrO2 thin film (top: n, bottom: κ).
Fig. 12.
Fig. 12. Sample #3. Logarithm of absolute values of the derivatives of the candidate refractive indices for the gold substrate with a deposited ZrO2 thin film (top: n, bottom: κ).

Tables (5)

Tables Icon

Table 1. Specifications of CCI HD

Tables Icon

Table 2. Test Materials and Their Thin Filmsa

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Table 3. Number of the Reference Measurement and the Number of the Measurements for Each Material

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Table 4. Root Mean Square Error between n and κ Determined with the HCF Method and Spectroscopic Ellipsometry in the Bandwidth (430 to 730 nm) and Their Ratios to Representative n and κ at 550 nm Wavelength, the Best Values are Emphasized

Tables Icon

Table 5. Correlation Coefficients between n and κ Determined by the HCF Method and Spectroscopic Ellipsometry, the Best Values are Emphasized

Equations (15)

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

N(ν)=n(ν)jκ(ν),where  n,κ0.
ηp=NYcosθ,ηs=NYcosθ,
r(ν,d,θ)=12{rp(ν,d,θ)+rs(ν,d,θ)},rp,s(ν,d,θ)=ηp,sairYp,sηp,sair+Yp,s,where  d={d1,,dL}.
Yp,s(d)=Cp,sBp,s,where[Bp,sCp,s]=i=1L[cosδijsinδi/ηp,sijηp,sisinδicosδi][1ηp,ssub],
δi=2πνNidicosθi,cosθi=1NiNi2sin2θ.
r¯(ν,d)=θminθmaxr(ν,d,θ)·w(θ)dθ,whereθminθmaxw(θ)dθ=1.
θ¯=θminθmaxθ·w(θ)dθ.
rsRM(ν,θ)rpRM(ν,θ).
HCFd(ν)=r¯ref(ν)·F[I(Z)]SB+F[Iref(Z)]SB+,HCFs(ν,d)=r¯(ν,d)·exp(+j4πνΔzHCFcosθ¯),
minimizeΔzHCF,dJHCF=ν|HCFd(ν)HCFs(ν,d)|2dνsubject to2ΔZstep<ΔzHCF<2ΔZstep,
HCF1d(ν)=rref(ν)·F[I1(Z)]SB+F[Iref(Z)]SB+,HCF1s(ν,0)=1Nt(ν)1+Nt(ν)·exp(+j4πνΔzHCF1),where2ΔZstep<ΔzHCF1<2ΔZstep.
N^t(ν,ΔzHCF1)=exp(+j4πνΔzHCF1)HCF1dexp(+j4πνΔzHCF1)+HCF1d,where2ΔZstep<ΔzHCF1<2ΔZstep.
HCF2d(ν)=rref(ν)·F[I2(Z)]SB+F[Iref(Z)]SB+,HCF2s(ν,d|N^t)=r2(ν,d|Nf,N^t)·exp(+j4πνΔzHCF2),where2ΔZstep<ΔzHCF2<2ΔZstep.
minimizeΔzHCF1,2,dJ=ν|HCF2d(ν)HCF2s(ν,d|N^t)|2dνsubject to2ΔZstep<ΔzHCF1,2<2ΔZstep.
NtΔzHCF1=j8πν·HCF1d·exp(+j4πνΔzHCF1){exp(+j4πνΔzHCF1)+HCF1d}2.

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