Abstract

We present an interferometry using a far-infrared light as a tool for surface topography measurement of rough reflective surfaces. The method is based on the optical configuration of classical Fizeau interferometry, but we achieve roughness tolerance by using a long-wavelength infrared light (λ = 10.6 µm). The method is called far-infrared Fizeau interferometry. We conducted a rigorous mathematical analysis to describe the true intensity distribution of fringe patterns while considering multiple reflections and surface roughness. The mathematical derivation is verified with experimental data obtained from specimens with various values of reflectivity and roughness. The effect of reflectivity and roughness on fringe contrast is discussed.

© 2001 Optical Society of America

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References

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  1. K. Verma, B. Han, “Warpage measurement on dielectric rough surfaces of microelectronics devices by far infrared Fizeau interferometry,” J. Electron. Packaging 122, 227–232 (2000).
    [CrossRef]
  2. P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).
  3. C. R. Munnerlyn, M. Latta, “Rough surface interferometry using CO2 laser source,” Appl. Opt. 7, 1858–1859 (1968).
    [CrossRef] [PubMed]
  4. O. Kwon, J. C. Wyant, C. R. Hayslett, “Rough surface interferometry at 10.6 µm,” Appl. Opt. 19, 1862–1869 (1980).
    [CrossRef] [PubMed]
  5. J. Lewandowski, B. Mongeau, M. Cormier, J. Lapierre, “Infrared interferometers at 10 µm,” J. Appl. Phys. 60, 3407–3413 (1986).
    [CrossRef]
  6. J. Sinha, H. Tippur, “Infrared interferometry for rough surface measurements: application to failure characterization and flaw detection,” Opt. Eng. 38, 2233–2239 (1997).
    [CrossRef]
  7. W. L. Wolfe, G. J. Zissis, eds., The Infrared Handbook (Infrared Information Analyses Center, Ann Arbor, Mich., 1985).
  8. J. Brossel, “Multiple-beam localized fringes. I. Intensity distribution and localization,” Proc. Phys. Soc. London 59, 224–234 (1947).
    [CrossRef]
  9. Y. H. Meyer, “Fringe shape with an interferential wedge,” J. Opt. Soc. Am. 71, 1255–1263 (1981).
    [CrossRef]
  10. T. T. Kajava, H. M. Lauranto, A. T. Friberg, “Interference pattern of the Fizeau interferometer,” J. Opt. Soc. Am. A 11, 2045–2054 (1994).
    [CrossRef]
  11. J. M. Bennett, L. Mattsson, eds., Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).
  12. D. L. Lide, ed., Handbook of Chemistry and Physics, 79th ed. (CRC Press, Boca Raton, Fla., 1998).
  13. K. Verma, “Development of far infrared Fizeau interferometry for real-time warpage measurement of rough surfaces,” Ph.D. dissertation (Clemson University, Clemson, S.C., 2000).

2000 (1)

K. Verma, B. Han, “Warpage measurement on dielectric rough surfaces of microelectronics devices by far infrared Fizeau interferometry,” J. Electron. Packaging 122, 227–232 (2000).
[CrossRef]

1997 (1)

J. Sinha, H. Tippur, “Infrared interferometry for rough surface measurements: application to failure characterization and flaw detection,” Opt. Eng. 38, 2233–2239 (1997).
[CrossRef]

1994 (1)

1986 (1)

J. Lewandowski, B. Mongeau, M. Cormier, J. Lapierre, “Infrared interferometers at 10 µm,” J. Appl. Phys. 60, 3407–3413 (1986).
[CrossRef]

1981 (1)

1980 (1)

1968 (1)

1947 (1)

J. Brossel, “Multiple-beam localized fringes. I. Intensity distribution and localization,” Proc. Phys. Soc. London 59, 224–234 (1947).
[CrossRef]

Beckmann, P.

P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

Brossel, J.

J. Brossel, “Multiple-beam localized fringes. I. Intensity distribution and localization,” Proc. Phys. Soc. London 59, 224–234 (1947).
[CrossRef]

Cormier, M.

J. Lewandowski, B. Mongeau, M. Cormier, J. Lapierre, “Infrared interferometers at 10 µm,” J. Appl. Phys. 60, 3407–3413 (1986).
[CrossRef]

Friberg, A. T.

Han, B.

K. Verma, B. Han, “Warpage measurement on dielectric rough surfaces of microelectronics devices by far infrared Fizeau interferometry,” J. Electron. Packaging 122, 227–232 (2000).
[CrossRef]

Hayslett, C. R.

Kajava, T. T.

Kwon, O.

Lapierre, J.

J. Lewandowski, B. Mongeau, M. Cormier, J. Lapierre, “Infrared interferometers at 10 µm,” J. Appl. Phys. 60, 3407–3413 (1986).
[CrossRef]

Latta, M.

Lauranto, H. M.

Lewandowski, J.

J. Lewandowski, B. Mongeau, M. Cormier, J. Lapierre, “Infrared interferometers at 10 µm,” J. Appl. Phys. 60, 3407–3413 (1986).
[CrossRef]

Meyer, Y. H.

Mongeau, B.

J. Lewandowski, B. Mongeau, M. Cormier, J. Lapierre, “Infrared interferometers at 10 µm,” J. Appl. Phys. 60, 3407–3413 (1986).
[CrossRef]

Munnerlyn, C. R.

Sinha, J.

J. Sinha, H. Tippur, “Infrared interferometry for rough surface measurements: application to failure characterization and flaw detection,” Opt. Eng. 38, 2233–2239 (1997).
[CrossRef]

Spizzichino, A.

P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

Tippur, H.

J. Sinha, H. Tippur, “Infrared interferometry for rough surface measurements: application to failure characterization and flaw detection,” Opt. Eng. 38, 2233–2239 (1997).
[CrossRef]

Verma, K.

K. Verma, B. Han, “Warpage measurement on dielectric rough surfaces of microelectronics devices by far infrared Fizeau interferometry,” J. Electron. Packaging 122, 227–232 (2000).
[CrossRef]

K. Verma, “Development of far infrared Fizeau interferometry for real-time warpage measurement of rough surfaces,” Ph.D. dissertation (Clemson University, Clemson, S.C., 2000).

Wyant, J. C.

Appl. Opt. (2)

J. Appl. Phys. (1)

J. Lewandowski, B. Mongeau, M. Cormier, J. Lapierre, “Infrared interferometers at 10 µm,” J. Appl. Phys. 60, 3407–3413 (1986).
[CrossRef]

J. Electron. Packaging (1)

K. Verma, B. Han, “Warpage measurement on dielectric rough surfaces of microelectronics devices by far infrared Fizeau interferometry,” J. Electron. Packaging 122, 227–232 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

J. Sinha, H. Tippur, “Infrared interferometry for rough surface measurements: application to failure characterization and flaw detection,” Opt. Eng. 38, 2233–2239 (1997).
[CrossRef]

Proc. Phys. Soc. London (1)

J. Brossel, “Multiple-beam localized fringes. I. Intensity distribution and localization,” Proc. Phys. Soc. London 59, 224–234 (1947).
[CrossRef]

Other (5)

W. L. Wolfe, G. J. Zissis, eds., The Infrared Handbook (Infrared Information Analyses Center, Ann Arbor, Mich., 1985).

P. Beckmann, A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

J. M. Bennett, L. Mattsson, eds., Introduction to Surface Roughness and Scattering (Optical Society of America, Washington, D.C., 1989).

D. L. Lide, ed., Handbook of Chemistry and Physics, 79th ed. (CRC Press, Boca Raton, Fla., 1998).

K. Verma, “Development of far infrared Fizeau interferometry for real-time warpage measurement of rough surfaces,” Ph.D. dissertation (Clemson University, Clemson, S.C., 2000).

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Figures (8)

Fig. 1
Fig. 1

Fringe patterns produced by FIFI. The specimen was a microelectronics device subjected to a thermal excursion, and the measurements were made on a silicon surface with a rms roughness of 0.21 µm.

Fig. 2
Fig. 2

Optical path for multiple-beam interference in FIFI.

Fig. 3
Fig. 3

Illustration of the randomly varying local height and the mean topography of a rough surface.

Fig. 4
Fig. 4

Optical configuration of FIFI.

Fig. 5
Fig. 5

Fringe patterns obtained from aluminum specimens with different values of surface roughness. The intensity distributions obtained from the fringe patterns are compared with the mathematical predictions.

Fig. 6
Fig. 6

Fringe patterns obtained from silicon specimens with different values of surface roughness. The intensity distributions obtained from the fringe patterns are compared with the mathematical predictions.

Fig. 7
Fig. 7

Fringe patterns obtained from Plexiglas specimens with different values of surface roughness. The intensity distributions obtained from the fringe patterns are compared with the mathematical predictions.

Fig. 8
Fig. 8

Fringe contrast as a function of (a) reflectivity and (b) roughness.

Tables (2)

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Table 1 Properties at 10.6 µma

Tables Icon

Table 2 Measured rms Roughness of the Specimens

Equations (10)

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δn=PN1-PNn=POsin θ1-sin θn,
ϕn=2πδnλ=2πWx, yλ tan α-sin θn+sin θ1,
AR=A0r+t2rrsn=2rrsn exp iϕn+2n-3π.
IR=I0RR2+ρ2τ2-R2R21-ρ2-2τρRn=2ρn cosϕn+2τ2ρ2R2i=j+1j=2ρi+j cosϕij,
Wx, y=w1+wx, y+hx, y.
ph=1σ2πexp-h22σ2,
I=- phIhdh.
I=I0RR2+ρ2τ2-R2R21-ρ2-2τρRn=2ρn×exp-2Kn2σ2cosϕn+2τ2ρ2R2i=j+1j=2ρi+j exp-2Kij2σ2cosϕij,
RE=Rs exp-4πσ cos θλ2.
fringe contrast%=Imax-IminImax×100.

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