Abstract

A new method for the measurement of anisotropic stress in thin films based on 2-D fast Fourier transform (FFT) is presented. A modified Twyman-Green interferometer was used for surface topography measurement. A fringe normalization technique was also used to improve the phase extraction technique efficiently. The measurement of anisotropic stress in obliquely deposited MgF2 thin film was demonstrated.

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References

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  1. M. Ohring, Materials Science of Thin Films: Deposition and Structure, 2nd ed. (Academic Press, 2004).
  2. A. J. Perry, J. A. Sue, and P. J. Martin, “Practical measurement of the residual stress in coatings,” Surface Coatings Technol. 8l, 17–28 (l996).
  3. W. D. Nix, “Mechanical properties of thin films,” Metall. Trans. A 20A, 2217–2245 (1989).
  4. C. L. Tien, C. C. Lee, Y. L. Tsai, and W. S. Sun, “Determination of the mechanical properties of thin films by digital phase shifting interferometry,” Opt. Commun. 198(4-6), 325–331 (2001).
    [CrossRef]
  5. L. B. Freund, and S. Suresh, Thin Films:Materials: Stress, Defect Formation and Surface Evolution (Cambridge University Press, 2003).
  6. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
    [CrossRef]
  7. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
    [CrossRef] [PubMed]
  8. W. W. Macy., “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22(23), 3898–3901 (1983).
    [CrossRef] [PubMed]
  9. G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 82(553), 172–175 (1909).
    [CrossRef]
  10. A. Brenner and S. Senderoff, “Calculation of stress in electrodeposits from the curvature of a plated strip,” J. Res. Nat’l. Bur. Stand. 42, 105–123 (1949).
  11. E. van de Riet, “Deflection of a substrate induced by an anisotropic thin-film stress,” J. Appl. Phys. 76(1), 584–586 (1994).
    [CrossRef]
  12. C. L. Tien, S. S. Jyu, and H. M. Yang, “A method for fringe normalization by Zernike polynomial,” Opt. Rev. 16(2), 173–175 (2009).
    [CrossRef]

2009

C. L. Tien, S. S. Jyu, and H. M. Yang, “A method for fringe normalization by Zernike polynomial,” Opt. Rev. 16(2), 173–175 (2009).
[CrossRef]

2001

C. L. Tien, C. C. Lee, Y. L. Tsai, and W. S. Sun, “Determination of the mechanical properties of thin films by digital phase shifting interferometry,” Opt. Commun. 198(4-6), 325–331 (2001).
[CrossRef]

1994

E. van de Riet, “Deflection of a substrate induced by an anisotropic thin-film stress,” J. Appl. Phys. 76(1), 584–586 (1994).
[CrossRef]

1989

W. D. Nix, “Mechanical properties of thin films,” Metall. Trans. A 20A, 2217–2245 (1989).

1983

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
[CrossRef] [PubMed]

W. W. Macy., “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22(23), 3898–3901 (1983).
[CrossRef] [PubMed]

1982

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
[CrossRef]

1949

A. Brenner and S. Senderoff, “Calculation of stress in electrodeposits from the curvature of a plated strip,” J. Res. Nat’l. Bur. Stand. 42, 105–123 (1949).

1909

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 82(553), 172–175 (1909).
[CrossRef]

Brenner, A.

A. Brenner and S. Senderoff, “Calculation of stress in electrodeposits from the curvature of a plated strip,” J. Res. Nat’l. Bur. Stand. 42, 105–123 (1949).

Ina, H.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
[CrossRef]

Jyu, S. S.

C. L. Tien, S. S. Jyu, and H. M. Yang, “A method for fringe normalization by Zernike polynomial,” Opt. Rev. 16(2), 173–175 (2009).
[CrossRef]

Kobayashi, S.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
[CrossRef]

Lee, C. C.

C. L. Tien, C. C. Lee, Y. L. Tsai, and W. S. Sun, “Determination of the mechanical properties of thin films by digital phase shifting interferometry,” Opt. Commun. 198(4-6), 325–331 (2001).
[CrossRef]

Macy, W. W.

W. W. Macy., “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22(23), 3898–3901 (1983).
[CrossRef] [PubMed]

Mutoh, K.

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
[CrossRef] [PubMed]

Nix, W. D.

W. D. Nix, “Mechanical properties of thin films,” Metall. Trans. A 20A, 2217–2245 (1989).

Senderoff, S.

A. Brenner and S. Senderoff, “Calculation of stress in electrodeposits from the curvature of a plated strip,” J. Res. Nat’l. Bur. Stand. 42, 105–123 (1949).

Stoney, G. G.

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 82(553), 172–175 (1909).
[CrossRef]

Sun, W. S.

C. L. Tien, C. C. Lee, Y. L. Tsai, and W. S. Sun, “Determination of the mechanical properties of thin films by digital phase shifting interferometry,” Opt. Commun. 198(4-6), 325–331 (2001).
[CrossRef]

Takeda, M.

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
[CrossRef] [PubMed]

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
[CrossRef]

Tien, C. L.

C. L. Tien, S. S. Jyu, and H. M. Yang, “A method for fringe normalization by Zernike polynomial,” Opt. Rev. 16(2), 173–175 (2009).
[CrossRef]

C. L. Tien, C. C. Lee, Y. L. Tsai, and W. S. Sun, “Determination of the mechanical properties of thin films by digital phase shifting interferometry,” Opt. Commun. 198(4-6), 325–331 (2001).
[CrossRef]

Tsai, Y. L.

C. L. Tien, C. C. Lee, Y. L. Tsai, and W. S. Sun, “Determination of the mechanical properties of thin films by digital phase shifting interferometry,” Opt. Commun. 198(4-6), 325–331 (2001).
[CrossRef]

van de Riet, E.

E. van de Riet, “Deflection of a substrate induced by an anisotropic thin-film stress,” J. Appl. Phys. 76(1), 584–586 (1994).
[CrossRef]

Yang, H. M.

C. L. Tien, S. S. Jyu, and H. M. Yang, “A method for fringe normalization by Zernike polynomial,” Opt. Rev. 16(2), 173–175 (2009).
[CrossRef]

Appl. Opt.

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
[CrossRef] [PubMed]

W. W. Macy., “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22(23), 3898–3901 (1983).
[CrossRef] [PubMed]

J. Appl. Phys.

E. van de Riet, “Deflection of a substrate induced by an anisotropic thin-film stress,” J. Appl. Phys. 76(1), 584–586 (1994).
[CrossRef]

J. Opt. Soc. Am.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
[CrossRef]

J. Res. Nat’l. Bur. Stand.

A. Brenner and S. Senderoff, “Calculation of stress in electrodeposits from the curvature of a plated strip,” J. Res. Nat’l. Bur. Stand. 42, 105–123 (1949).

Metall. Trans. A

W. D. Nix, “Mechanical properties of thin films,” Metall. Trans. A 20A, 2217–2245 (1989).

Opt. Commun.

C. L. Tien, C. C. Lee, Y. L. Tsai, and W. S. Sun, “Determination of the mechanical properties of thin films by digital phase shifting interferometry,” Opt. Commun. 198(4-6), 325–331 (2001).
[CrossRef]

Opt. Rev.

C. L. Tien, S. S. Jyu, and H. M. Yang, “A method for fringe normalization by Zernike polynomial,” Opt. Rev. 16(2), 173–175 (2009).
[CrossRef]

Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 82(553), 172–175 (1909).
[CrossRef]

Other

L. B. Freund, and S. Suresh, Thin Films:Materials: Stress, Defect Formation and Surface Evolution (Cambridge University Press, 2003).

M. Ohring, Materials Science of Thin Films: Deposition and Structure, 2nd ed. (Academic Press, 2004).

A. J. Perry, J. A. Sue, and P. J. Martin, “Practical measurement of the residual stress in coatings,” Surface Coatings Technol. 8l, 17–28 (l996).

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of the experimental setup.

Fig. 2
Fig. 2

Flow chart of the stress measurement.

Fig. 3
Fig. 3

Principal axes and their directions.

Fig. 4
Fig. 4

Interferogram with carrier frequency

Fig. 5
Fig. 5

Proposed method used for: (a) Fourier transform spectrum; (b) wrapped phase obtained by IFFT.

Fig. 6
Fig. 6

3-D surface contour map: (a) before film deposition; (b) after film deposition.

Fig. 7
Fig. 7

Curvature radius fitting: (a) in the x-axis direction for finding Rx; (b) in the y-axis direction for finding Ry.

Tables (1)

Tables Icon

Table 1 Stress measuring results for three obliquely deposited MgF2 thin films

Equations (9)

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i ( x , y ) = a ( x , y ) + b ( x , y ) cos [ 2 π f 0 x + ϕ ( x , y ) ] ,
i ( x , y ) = a ( x , y ) + c ( x , y ) exp ( 2 π i f 0 x ) + c ( x , y ) exp ( 2 π i f 0 x ) ,
I ( u , v ) = A ( u , v ) + C ( u , v ) + C * ( u , v ) ,
ϕ ( x , y ) = t a n 1 ( Im [ c ( x , y ) ] Re [ c ( x , y ) ] ) ,
h ( x , y ) = λ 4 π Φ ( x , y ) ,
σ = E s t s 2 6 ( 1 ν s ) t f ( 1 R 2 1 R 1 ) = E s t s 2 6 ( 1 ν s ) t f R ,
σ x = 1 6 E s 1 ν s 2 ( 1 R x + ν s R y ) t s 2 t f ,
σ y = 1 6 E s 1 ν s 2 ( 1 R y + ν s R x ) t s 2 t f ,
Δ σ σ = ( Δ t f t f ) 2 + ( Δ ϕ ϕ ) 2 + ( Δ T T ) 2 + ( Δ n n ) 2 ,

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