Abstract

Spectrally resolved white-light phase-shifting interference microscopy can be used for rapid and accurate measurements of the thickness profile of transparent thin-film layers deposited upon patterned structures exhibiting steps and discontinuities. We examine the sensitivity of this technique and show that it depends on the thickness of the thin-film layer as well as its refractive index. The results of this analysis are also valid for any other method based on measurements of the spectral phase such as wavelength scanning or white-light interferometry.

© 2006 Optical Society of America

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References

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  1. P. Hariharan and M. Roy, "Interferometric surface profiling with white light: effect of surface films," J. Mod. Opt. 43, 1797-1800 (1996).
    [CrossRef]
  2. M. Roy, I. Cooper, P. Moore, C. J. R. Sheppard, and P. Hariharan, "White-light interference microscopy: effects of multiple reflections within a surface film," Opt. Express 13, 164-170 (2005).
    [CrossRef] [PubMed]
  3. 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]
  4. D. Kim, S. Kim, H. Kong, and Y. Lee, "Measurement of the thickness profile of a transparent thin film deposited upon a pattern structure with an acousto-optic tunable filter," Opt. Lett. 27, 1893-1895 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
    [CrossRef]
  8. S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
    [CrossRef]
  9. S. K. Debnath and M. P. Kothiyal, "Optical profiler based on spectrally resolved white light interferometry," Opt. Eng. 44, 013606 (2005).
    [CrossRef]
  10. J. Schmit and K. Creath, "Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry," Appl. Opt. 34, 3610-3619 (1995).
    [CrossRef] [PubMed]
  11. J. Schmit and K. Creath, "Window function influence on phase error in phase-shifting algorithms," Appl. Opt. 35, 5642-5649 (1996).
    [CrossRef] [PubMed]
  12. S. K. Debnath, M. P. Kothiyal, J. Schmit, and P. Hariharan, "Spectrally resolved white-light phase-shifting interference microscopy for thickness profile measurement of transparent thin-film layers on patterned substrates," Opt. Express 14, 4662-4667 (2006).
    [CrossRef] [PubMed]

2006

2005

2004

2002

2001

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
[CrossRef]

1999

1996

P. Hariharan and M. Roy, "Interferometric surface profiling with white light: effect of surface films," J. Mod. Opt. 43, 1797-1800 (1996).
[CrossRef]

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. 28, 485-489 (1996).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
[CrossRef]

J. Schmit and K. Creath, "Window function influence on phase error in phase-shifting algorithms," Appl. Opt. 35, 5642-5649 (1996).
[CrossRef] [PubMed]

1995

Calatroni, J.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. 28, 485-489 (1996).
[CrossRef]

Cooper, I.

Creath, K.

Debnath, S. K.

Escalona, R.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. 28, 485-489 (1996).
[CrossRef]

Guerrero, A. L.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. 28, 485-489 (1996).
[CrossRef]

Hariharan, P.

Helen, S. S.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
[CrossRef]

Kim, D.

Kim, G. H.

Kim, S.

Kim, S. W.

Kong, H.

Kothiyal, M. P.

S. K. Debnath, M. P. Kothiyal, J. Schmit, and P. Hariharan, "Spectrally resolved white-light phase-shifting interference microscopy for thickness profile measurement of transparent thin-film layers on patterned substrates," Opt. Express 14, 4662-4667 (2006).
[CrossRef] [PubMed]

S. K. Debnath and M. P. Kothiyal, "Optical profiler based on spectrally resolved white light interferometry," Opt. Eng. 44, 013606 (2005).
[CrossRef]

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
[CrossRef]

Lee, Y.

Moore, P.

Perrin, H.

P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
[CrossRef]

Roy, M.

Sainz, C.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. 28, 485-489 (1996).
[CrossRef]

Sandoz, P.

P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
[CrossRef]

Schmit, J.

Sheppard, C. J. R.

Sirohi, R. S.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
[CrossRef]

Tribillon, G.

P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

P. Hariharan and M. Roy, "Interferometric surface profiling with white light: effect of surface films," J. Mod. Opt. 43, 1797-1800 (1996).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
[CrossRef]

Opt. Eng.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, "Optical profiler based on spectrally resolved white light interferometry," Opt. Eng. 44, 013606 (2005).
[CrossRef]

Opt. Express

Opt. Laser Technol.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. 28, 485-489 (1996).
[CrossRef]

Opt. Lett.

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Figures (6)

Fig. 1
Fig. 1

Multiple reflection of light within a transparent thin film.

Fig. 2
Fig. 2

Nonlinear component of the spectral phase versus the wavenumber for SiO 2 films on Si for film thicknesses of (a) 56   nm , (b) 99   nm , (c) 183   nm , (d) 198   nm , (e) 239   nm , (f) 297   nm , (g) 375   nm , (h) 398   nm , (i) 466   nm , (j) 496   nm , (k) 534   nm , and (l) 599   nm .

Fig. 3
Fig. 3

Magnitude of the nonlinear phase for the range of wavenumbers from 2.0 to 1.4 μ m - 1 (wavelength range 500 700 nm ) for SiO 2 films on Si, plotted as a function of the film thickness.

Fig. 4
Fig. 4

Sensitivity as a function of the film thickness for films with refractive indices of (a) 1.5, (b) 1.8, (c) 2.0, (d) 2.3, and (e) 2.5, deposited on a Si substrate.

Fig. 5
Fig. 5

Sensitivity as a function of the optical thickness ( N 1 d ) for films with refractive indices of (a) 1.5, (b) 1.8, (c) 2.0, (d) 2.3, and (e) 2.5, deposited on a Si substrate.

Fig. 6
Fig. 6

Sensitivity as a function of the film thickness for SiO2 films on a Si substrate for measurements made over the spectral ranges from 1.4 to 2.0 μ m - 1 and 1.5 to 1.9 μ m - 1 .

Tables (1)

Tables Icon

Table 1 Variation of the Reflectances r 01 and r 12 with the Refractive Index ( N 1) of the Film

Equations (66)

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

2 π
1   nm
E i
E r = R E i
R = r 01 + r 12   exp ( i2 β ) 1 + r 01 r 12   exp ( i2 β ) ,
r 01
r 12
β = 2 π σ d N 1   cos   θ 1 ,
σ = 1 / λ
θ 1
N 1
N 1
N 1 = A + B σ 2 + C σ 4 ,
R = a + i b ,
ψ = arctan ( b / a ) .
cos   θ 1 = 1
sin   θ 1 = θ 1
ϕ ( σ , d , z ) = 4 π σ z + ψ ( σ , d ) .
4 π σ z
ψ ( σ , d )
( d 0 )
ψ ( σ , d )
ψ ( σ , d )
ϕ measured ( σ )
η ( z , d ) = σ c Δ σ / 2 σ c + Δ σ / 2 [ ϕ model ( σ , z , d ) ϕ measured ( σ ) ] 2 ,
σ c
Δ σ
ψ ( σ , d )
1.4 μ m - 1
0.700 μ m
1   nm
SiO 2
599   nm
532   nm
99   nm
56   nm
( N 1 d )
( N 1 d )
1.95
ψ ( σ , d )
SiO 2
100   nm
120 150   nm
ψ ( σ , 0 )
ψ ( σ , d )
r 01
r 12
SiO 2
56   nm
99   nm
183   nm
198   nm
239   nm
297   nm
375   nm
398   nm
466   nm
496   nm
534   nm
599   nm
1.4 μ m - 1
500 700 nm
SiO 2
( N 1 d )
2.0 μ m - 1
1.9 μ m - 1

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