Abstract

Using a phase-shifting technique with an atomic force microscope (AFM), we propose a phase-shifting AFM scanning moiré method. The phase shifting is realized in four steps from 0 to 2π by a piezoscanner in the AFM. The measurement method and experimental techniques are described in detail. For demonstration this method is applied to determine the phase distribution in the AFM moiré of a 1200-line/mm holographic grating used to measure the thermal deformation in a Quad FlatPack electronic package.

© 2001 Optical Society of America

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References

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  1. J. M. Huntely, “Automatic fringe pattern analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105–125 (1998).
    [CrossRef]
  2. J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 14.
  3. R. S. Sirohi, F. S. Chau, Optical Methods of Measurement: Wholefield Techniques (Marcel Dekker, New York, 1999), Chap. 3.
  4. H. Chen, D. Liu, A. Lee, “Moiré in atomic force microscope,” Exp. Tech. 24(1), 31–32 (2000).
    [CrossRef]
  5. H. Xie, S. Kishimoto, A. Asundi, G. B. Chai, N. Shinya, J. Yu, B. K. A. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
    [CrossRef]
  6. F.-P. Chiang, “Moiré methods of strain analysis,” in Manual on Experimental Stress Analysis, 5th ed., J. F. Doyle, J. W. Philips, ed. (Society for Experimental Mechanics, Bethel, Conn., 1989).
  7. H. Xie, C. G. Boay, A. Asundi, “Thermal deformation measurement of electronic package using advanced moiré methods,” in The Third Electronics Packaging Technology Conference, 5–7 December 2000, Singapore, IEEE Catalog 00EX456 (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 163–168.
  8. D. Post, B. Han, P. Ifju, High Sensitivity Moiré (Springer-Verlag, New York, 1994), Appendix B.
    [CrossRef]
  9. M. V. Salapaka, H. S. Bergh, J. Lai, A. Majumdar, E. Mcforland, “Multimode noise analysis of cantilevers for the scanning probe microscope,” J. Appl. Phys. 71, 2480–2487 (1997).
    [CrossRef]

2000 (2)

H. Chen, D. Liu, A. Lee, “Moiré in atomic force microscope,” Exp. Tech. 24(1), 31–32 (2000).
[CrossRef]

H. Xie, S. Kishimoto, A. Asundi, G. B. Chai, N. Shinya, J. Yu, B. K. A. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[CrossRef]

1998 (1)

J. M. Huntely, “Automatic fringe pattern analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105–125 (1998).
[CrossRef]

1997 (1)

M. V. Salapaka, H. S. Bergh, J. Lai, A. Majumdar, E. Mcforland, “Multimode noise analysis of cantilevers for the scanning probe microscope,” J. Appl. Phys. 71, 2480–2487 (1997).
[CrossRef]

Asundi, A.

H. Xie, S. Kishimoto, A. Asundi, G. B. Chai, N. Shinya, J. Yu, B. K. A. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[CrossRef]

H. Xie, C. G. Boay, A. Asundi, “Thermal deformation measurement of electronic package using advanced moiré methods,” in The Third Electronics Packaging Technology Conference, 5–7 December 2000, Singapore, IEEE Catalog 00EX456 (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 163–168.

Bergh, H. S.

M. V. Salapaka, H. S. Bergh, J. Lai, A. Majumdar, E. Mcforland, “Multimode noise analysis of cantilevers for the scanning probe microscope,” J. Appl. Phys. 71, 2480–2487 (1997).
[CrossRef]

Boay, C. G.

H. Xie, C. G. Boay, A. Asundi, “Thermal deformation measurement of electronic package using advanced moiré methods,” in The Third Electronics Packaging Technology Conference, 5–7 December 2000, Singapore, IEEE Catalog 00EX456 (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 163–168.

Bruning, J. H.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 14.

Chai, G. B.

H. Xie, S. Kishimoto, A. Asundi, G. B. Chai, N. Shinya, J. Yu, B. K. A. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[CrossRef]

Chau, F. S.

R. S. Sirohi, F. S. Chau, Optical Methods of Measurement: Wholefield Techniques (Marcel Dekker, New York, 1999), Chap. 3.

Chen, H.

H. Chen, D. Liu, A. Lee, “Moiré in atomic force microscope,” Exp. Tech. 24(1), 31–32 (2000).
[CrossRef]

Chiang, F.-P.

F.-P. Chiang, “Moiré methods of strain analysis,” in Manual on Experimental Stress Analysis, 5th ed., J. F. Doyle, J. W. Philips, ed. (Society for Experimental Mechanics, Bethel, Conn., 1989).

Greivenkamp, J. E.

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 14.

Han, B.

D. Post, B. Han, P. Ifju, High Sensitivity Moiré (Springer-Verlag, New York, 1994), Appendix B.
[CrossRef]

Huntely, J. M.

J. M. Huntely, “Automatic fringe pattern analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105–125 (1998).
[CrossRef]

Ifju, P.

D. Post, B. Han, P. Ifju, High Sensitivity Moiré (Springer-Verlag, New York, 1994), Appendix B.
[CrossRef]

Kishimoto, S.

H. Xie, S. Kishimoto, A. Asundi, G. B. Chai, N. Shinya, J. Yu, B. K. A. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[CrossRef]

Lai, J.

M. V. Salapaka, H. S. Bergh, J. Lai, A. Majumdar, E. Mcforland, “Multimode noise analysis of cantilevers for the scanning probe microscope,” J. Appl. Phys. 71, 2480–2487 (1997).
[CrossRef]

Lee, A.

H. Chen, D. Liu, A. Lee, “Moiré in atomic force microscope,” Exp. Tech. 24(1), 31–32 (2000).
[CrossRef]

Liu, D.

H. Chen, D. Liu, A. Lee, “Moiré in atomic force microscope,” Exp. Tech. 24(1), 31–32 (2000).
[CrossRef]

Majumdar, A.

M. V. Salapaka, H. S. Bergh, J. Lai, A. Majumdar, E. Mcforland, “Multimode noise analysis of cantilevers for the scanning probe microscope,” J. Appl. Phys. 71, 2480–2487 (1997).
[CrossRef]

Mcforland, E.

M. V. Salapaka, H. S. Bergh, J. Lai, A. Majumdar, E. Mcforland, “Multimode noise analysis of cantilevers for the scanning probe microscope,” J. Appl. Phys. 71, 2480–2487 (1997).
[CrossRef]

Ngoi, B. K. A.

H. Xie, S. Kishimoto, A. Asundi, G. B. Chai, N. Shinya, J. Yu, B. K. A. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[CrossRef]

Post, D.

D. Post, B. Han, P. Ifju, High Sensitivity Moiré (Springer-Verlag, New York, 1994), Appendix B.
[CrossRef]

Salapaka, M. V.

M. V. Salapaka, H. S. Bergh, J. Lai, A. Majumdar, E. Mcforland, “Multimode noise analysis of cantilevers for the scanning probe microscope,” J. Appl. Phys. 71, 2480–2487 (1997).
[CrossRef]

Shinya, N.

H. Xie, S. Kishimoto, A. Asundi, G. B. Chai, N. Shinya, J. Yu, B. K. A. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[CrossRef]

Sirohi, R. S.

R. S. Sirohi, F. S. Chau, Optical Methods of Measurement: Wholefield Techniques (Marcel Dekker, New York, 1999), Chap. 3.

Xie, H.

H. Xie, S. Kishimoto, A. Asundi, G. B. Chai, N. Shinya, J. Yu, B. K. A. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[CrossRef]

H. Xie, C. G. Boay, A. Asundi, “Thermal deformation measurement of electronic package using advanced moiré methods,” in The Third Electronics Packaging Technology Conference, 5–7 December 2000, Singapore, IEEE Catalog 00EX456 (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 163–168.

Yu, J.

H. Xie, S. Kishimoto, A. Asundi, G. B. Chai, N. Shinya, J. Yu, B. K. A. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[CrossRef]

Exp. Tech. (1)

H. Chen, D. Liu, A. Lee, “Moiré in atomic force microscope,” Exp. Tech. 24(1), 31–32 (2000).
[CrossRef]

J. Appl. Phys. (1)

M. V. Salapaka, H. S. Bergh, J. Lai, A. Majumdar, E. Mcforland, “Multimode noise analysis of cantilevers for the scanning probe microscope,” J. Appl. Phys. 71, 2480–2487 (1997).
[CrossRef]

J. Strain Anal. (1)

J. M. Huntely, “Automatic fringe pattern analysis in experimental mechanics: a review,” J. Strain Anal. 33, 105–125 (1998).
[CrossRef]

Nanotechnology (1)

H. Xie, S. Kishimoto, A. Asundi, G. B. Chai, N. Shinya, J. Yu, B. K. A. Ngoi, “In-plane deformation measurement using the atomic force microscope moiré method,” Nanotechnology 11(1), 24–29 (2000).
[CrossRef]

Other (5)

F.-P. Chiang, “Moiré methods of strain analysis,” in Manual on Experimental Stress Analysis, 5th ed., J. F. Doyle, J. W. Philips, ed. (Society for Experimental Mechanics, Bethel, Conn., 1989).

H. Xie, C. G. Boay, A. Asundi, “Thermal deformation measurement of electronic package using advanced moiré methods,” in The Third Electronics Packaging Technology Conference, 5–7 December 2000, Singapore, IEEE Catalog 00EX456 (Institute of Electrical and Electronics Engineers, New York, 2000), pp. 163–168.

D. Post, B. Han, P. Ifju, High Sensitivity Moiré (Springer-Verlag, New York, 1994), Appendix B.
[CrossRef]

J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), Chap. 14.

R. S. Sirohi, F. S. Chau, Optical Methods of Measurement: Wholefield Techniques (Marcel Dekker, New York, 1999), Chap. 3.

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Figures (13)

Fig. 1
Fig. 1

Principle of the AFM scanning moiré.

Fig. 2
Fig. 2

AFM moiré pattern in a 55 µm × 55 µm square with a scan range of 100 µm and M = 128. The specimen grating pitch is 1200 lines/mm, and the corresponding reference-grating pitch is 1280 lines/mm.

Fig. 3
Fig. 3

Schematic of the AFM measurement principle.

Fig. 4
Fig. 4

Shift of the reference grating on the y axis: δ = 0, δ = π/2, δ = π, δ = 3π/2.

Fig. 5
Fig. 5

AFM phase-shifting moiré patterns (size: 38.5 µm × 19.9 µm).

Fig. 6
Fig. 6

Wrapped phase diagram.

Fig. 7
Fig. 7

Unwrapped phase diagram.

Fig. 8
Fig. 8

Fringe-order function in the measured area (1 pixel = 176 nm).

Fig. 9
Fig. 9

Schematic diagram of the measured section in the QFP electronic package: δ = 0, δ = π/2, δ = π, δ = 3π/2.

Fig. 10
Fig. 10

AFM scanning moiré patterns at the measured point O in the QFP package (size: 50.4 µm × 40 µm).

Fig. 11
Fig. 11

Wrapped phase diagram.

Fig. 12
Fig. 12

Unwrapped phase diagram.

Fig. 13
Fig. 13

Distribution of strain component ∊ y in the Y′ direction.

Equations (21)

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f ra = 1 p ra = M L ,
y = | p s - p ra | p ra = p s L ,
L = p s M 1 .
L = p s M N - 1 .
I i x ,   y = I 0 x ,   y 1 + b x ,   y cos φ x ,   y + δ i , i   =   1 ,   2 ,     ,
I 1 x ,   y = I 0 x ,   y 1 + b x ,   y cos φ x ,   y ,
I 2 x ,   y = I 0 x ,   y 1 + b x ,   y cos φ x ,   y + 1 2   π ,
I 3 x ,   y = I 0 x ,   y 1 + b x ,   y cos φ x ,   y + π ,
I 4 x ,   y = I 0 x ,   y 1 + b x ,   y cos φ x ,   y + 3 2   π .
φ x ,   y = arctan I 4 x ,   y - I 2 x ,   y I 1 x ,   y - I 3 x ,   y ,
b x ,   y = I 4 x ,   y - I 2 x ,   y 2 + I 1 x ,   y - I 3 x ,   y 2 1 / 2 2 I 0 x ,   y .
t r y = A 0 + A 1   cos 2 π p ra   y ,
t s x ,   y = B 0 + B 1   cos 2 π p ra y - v x ,   y ,
t x ,   y = t r y t s x ,   y = A 0 B 0 + A 0 B 1   cos 2 π p ra y - v x ,   y + B 0 A 1   cos 2 π p ra   y + A 1 B 1   cos 2 π p ra   y   cos 2 π p ra y - v x ,   y .
t x ,   y = A 0 2 + A 0 A 1   cos 2 π p ra y - v x ,   y + A 0 A 1   cos 2 π p ra   y + A 1 2 2 cos 2 π p ra 2 y - v x ,   y + A 1 2 2 cos 2 π p ra   v x ,   y .
t x ,   y A 1 2 2 cos 2 π p ra   v x ,   y .
Δ h = DV ,
φ x ,   y = 2 π p ra   v x ,   y ,
y = v y = p ra 2 π φ x ,   y y .
Δ y y < 2 %     Ref .   5 .
p s = L max M ± N - 1 .

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