Abstract

Coherent Gradient Sensor (CGS) system is presented for measurement of curvatures and nonuniform curvatures changes in film-substrate systems at cryogenic temperature. The influences of the interface of refrigerator and itself on the interferograms which are accounting for the temperature effect are successfully eliminated. Based on the measurement technique, the thermal stresses (including the radial stress, circumferential stress and shear stress) of superconducting YBCO thin-film are obtained by the extended Stoney’s formula during the heating process from 30K to 150K. Take the superconducting YBCO thin film as an example, the thermal stresses of which are gained successfully.

© 2013 OSA

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  1. P. A. Flinn, D. S. Gardner, and W. D. Nix, “Measurement and interpretation of stress in aluminum-based metallization as a function of thermal history,” IEEE Trans. Electron. Dev.34(3), 689–699 (1987).
    [CrossRef]
  2. E. Chason and B. W. Sheldon, “Monitoring stress in thin films during processing,” Surf. Eng.19(5), 387–391 (2003).
    [CrossRef]
  3. H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, “A coherent gradient sensor for crack tip deformation measurements: analysis and experimental results,” Int. J. Fract.48(3), 193–204 (1991).
    [CrossRef]
  4. H. V. Tippur, “Coherent gradient sensing: a Fourier optics analysis and applications to fracture,” Appl. Opt.31(22), 4428–4439 (1992).
    [CrossRef] [PubMed]
  5. A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore., “Full field measurements of curvature using coherent gradient sensing: application to thin film characterization,” Thin Solid Films325(1–2), 42–54 (1998).
    [CrossRef]
  6. M. A. Brown, T.-S. Park, A. Rosakis, E. Ustundag, Y. Huang, N. Tamura, and B. Valek, “A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems,” J. Appl. Mech.73(5), 723–729 (2006).
    [CrossRef]
  7. J. Tao, L. H. Lee, and J. C. Bilello, “Nondestructive evaluation of residual-stresses in thin-films via x-ray-diffraction topography methods,” J. Electron. Mater.20(7), 819–825 (1991).
    [CrossRef]
  8. T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, “Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry,” J. Mech. Phys. Solids51(11–12), 2191–2211 (2003).
    [CrossRef]
  9. M. D. Vaudin, E. G. Kessler, and D. M. Owen, “Precise silicon die curvature measurements using the NIST lattice comparator: comparisons with coherent gradient sensing interferometry,” Metrologia48(3), 201–211 (2011).
    [CrossRef]
  10. M. Budyansky, C. Madormo, J. L. Maciaszek, and G. Lykotrafitis, “Coherent gradient sensing microscopy (micro-CGS): A microscale curvature detection technique,” Opt. Lasers Eng.49(7), 874–879 (2011).
    [CrossRef]
  11. X. Dong, X. Feng, K. C. Hwang, S. Ma, and Q. Ma, “Full-field measurement of nonuniform stresses of thin films at high temperature,” Opt. Express19(14), 13201–13208 (2011).
    [CrossRef] [PubMed]
  12. G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character82(553), 172–175 (1909).
    [CrossRef]
  13. Y. Huang and A. J. Rosakis, “Extension of Stoney's formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry,” J. Mech. Phys. Solids53(11), 2483–2500 (2005).
    [CrossRef]
  14. X. Feng, Y. G. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, “The effect of thin film/substrate radii on the stoney formula for thin film/substrate subjected to nonuniform axisymmetric misfit strain and temperature,” J. Mech. Mater. Struct.1(6), 1041–1053 (2006).
    [CrossRef]
  15. D. Ngo, X. Feng, Y. Huang, A. J. Rosakis, and M. A. Brown, “Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: analysis for obtaining film stress from non-local curvature information,” Int. J. Solids Struct.44(6), 1745–1754 (2007).
    [CrossRef]
  16. M. A. Brown, A. J. Rosakis, X. Feng, Y. Huang, and E. Ustundag, “Thin film substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II: experimental validation of the non-local stress curvature relations,” Int. J. Solids Struct.44(6), 1755–1767 (2007).
    [CrossRef]
  17. X. Feng, Y. Huang, and A. J. Rosakis, “Stresses in a multilayer thin film/substrate system subjected to nonuniform temperature,” J. Appl. Mech.75(2), 021022 (2008).
    [CrossRef]
  18. X. F. Yao, H. Y. Yeh, and W. Xu, “Fracture investigation at V-notch tip using coherent gradient sensing (CGS),” Int. J. Solids Struct.43(5), 1189–1200 (2006).
    [CrossRef]
  19. R. P. Singh, J. Lambros, A. Shukla, and A. J. Rosakis, “Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity,” P Roy Soc A-Math Phy. 4532649–2667 (1997).
  20. L. T. Mao, C. P. Liu, K. Chen, L. Q. An, and X. X. Zhu, “Study on stress intensity factor of PMMA with double cracks using coherent gradient sensing(CGS) technique,” Appl. Mech. Mater.109, 114–119 (2011).
    [CrossRef]
  21. C. Liu, X. Zhang, J. Zhou, and Y. Zhou, “A general coherent gradient sensor for film curvature measurements: error analysis without temperature constraint,” Opt. Lasers Eng.51(7), 808–812 (2013).
    [CrossRef]
  22. J. Xiong, W. Qin, X. Cui, B. Tao, J. Tang, and Y. Li, “Effect of processing conditions and methods on residual stress in CeO2 buffer layers and YBCO superconducting films,” Physica C442(2), 124–128 (2006).
    [CrossRef]
  23. H. Lee, A. J. Rosakis, and L. B. Freund, “Full-field optical measurement of curvatures in ultra-thin-film–substrate systems in the range of geometrically nonlinear deformations,” J. Appl. Phys.89(11), 6122–6123 (2001).
    [CrossRef]
  24. R. Navarro, R. Rivera, and J. Aporta, “Representation of wavefronts in free-form transmission pupils with Complex Zernike Polynomials,” J. Opt.4(2), 41–48 (2011).
    [CrossRef]
  25. B. Gu, P. E. Phelan, and S. Mei, “Coupled heat transfer and thermal stress in high-Tc thin-film superconductor devices,” Cryogenics38(4), 411–418 (1998).
    [CrossRef]

2013 (1)

C. Liu, X. Zhang, J. Zhou, and Y. Zhou, “A general coherent gradient sensor for film curvature measurements: error analysis without temperature constraint,” Opt. Lasers Eng.51(7), 808–812 (2013).
[CrossRef]

2011 (5)

R. Navarro, R. Rivera, and J. Aporta, “Representation of wavefronts in free-form transmission pupils with Complex Zernike Polynomials,” J. Opt.4(2), 41–48 (2011).
[CrossRef]

L. T. Mao, C. P. Liu, K. Chen, L. Q. An, and X. X. Zhu, “Study on stress intensity factor of PMMA with double cracks using coherent gradient sensing(CGS) technique,” Appl. Mech. Mater.109, 114–119 (2011).
[CrossRef]

M. D. Vaudin, E. G. Kessler, and D. M. Owen, “Precise silicon die curvature measurements using the NIST lattice comparator: comparisons with coherent gradient sensing interferometry,” Metrologia48(3), 201–211 (2011).
[CrossRef]

M. Budyansky, C. Madormo, J. L. Maciaszek, and G. Lykotrafitis, “Coherent gradient sensing microscopy (micro-CGS): A microscale curvature detection technique,” Opt. Lasers Eng.49(7), 874–879 (2011).
[CrossRef]

X. Dong, X. Feng, K. C. Hwang, S. Ma, and Q. Ma, “Full-field measurement of nonuniform stresses of thin films at high temperature,” Opt. Express19(14), 13201–13208 (2011).
[CrossRef] [PubMed]

2008 (1)

X. Feng, Y. Huang, and A. J. Rosakis, “Stresses in a multilayer thin film/substrate system subjected to nonuniform temperature,” J. Appl. Mech.75(2), 021022 (2008).
[CrossRef]

2007 (2)

D. Ngo, X. Feng, Y. Huang, A. J. Rosakis, and M. A. Brown, “Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: analysis for obtaining film stress from non-local curvature information,” Int. J. Solids Struct.44(6), 1745–1754 (2007).
[CrossRef]

M. A. Brown, A. J. Rosakis, X. Feng, Y. Huang, and E. Ustundag, “Thin film substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II: experimental validation of the non-local stress curvature relations,” Int. J. Solids Struct.44(6), 1755–1767 (2007).
[CrossRef]

2006 (4)

X. Feng, Y. G. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, “The effect of thin film/substrate radii on the stoney formula for thin film/substrate subjected to nonuniform axisymmetric misfit strain and temperature,” J. Mech. Mater. Struct.1(6), 1041–1053 (2006).
[CrossRef]

M. A. Brown, T.-S. Park, A. Rosakis, E. Ustundag, Y. Huang, N. Tamura, and B. Valek, “A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems,” J. Appl. Mech.73(5), 723–729 (2006).
[CrossRef]

X. F. Yao, H. Y. Yeh, and W. Xu, “Fracture investigation at V-notch tip using coherent gradient sensing (CGS),” Int. J. Solids Struct.43(5), 1189–1200 (2006).
[CrossRef]

J. Xiong, W. Qin, X. Cui, B. Tao, J. Tang, and Y. Li, “Effect of processing conditions and methods on residual stress in CeO2 buffer layers and YBCO superconducting films,” Physica C442(2), 124–128 (2006).
[CrossRef]

2005 (1)

Y. Huang and A. J. Rosakis, “Extension of Stoney's formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry,” J. Mech. Phys. Solids53(11), 2483–2500 (2005).
[CrossRef]

2003 (2)

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, “Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry,” J. Mech. Phys. Solids51(11–12), 2191–2211 (2003).
[CrossRef]

E. Chason and B. W. Sheldon, “Monitoring stress in thin films during processing,” Surf. Eng.19(5), 387–391 (2003).
[CrossRef]

2001 (1)

H. Lee, A. J. Rosakis, and L. B. Freund, “Full-field optical measurement of curvatures in ultra-thin-film–substrate systems in the range of geometrically nonlinear deformations,” J. Appl. Phys.89(11), 6122–6123 (2001).
[CrossRef]

1998 (2)

B. Gu, P. E. Phelan, and S. Mei, “Coupled heat transfer and thermal stress in high-Tc thin-film superconductor devices,” Cryogenics38(4), 411–418 (1998).
[CrossRef]

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore., “Full field measurements of curvature using coherent gradient sensing: application to thin film characterization,” Thin Solid Films325(1–2), 42–54 (1998).
[CrossRef]

1992 (1)

1991 (2)

H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, “A coherent gradient sensor for crack tip deformation measurements: analysis and experimental results,” Int. J. Fract.48(3), 193–204 (1991).
[CrossRef]

J. Tao, L. H. Lee, and J. C. Bilello, “Nondestructive evaluation of residual-stresses in thin-films via x-ray-diffraction topography methods,” J. Electron. Mater.20(7), 819–825 (1991).
[CrossRef]

1987 (1)

P. A. Flinn, D. S. Gardner, and W. D. Nix, “Measurement and interpretation of stress in aluminum-based metallization as a function of thermal history,” IEEE Trans. Electron. Dev.34(3), 689–699 (1987).
[CrossRef]

1909 (1)

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character82(553), 172–175 (1909).
[CrossRef]

An, L. Q.

L. T. Mao, C. P. Liu, K. Chen, L. Q. An, and X. X. Zhu, “Study on stress intensity factor of PMMA with double cracks using coherent gradient sensing(CGS) technique,” Appl. Mech. Mater.109, 114–119 (2011).
[CrossRef]

Aporta, J.

R. Navarro, R. Rivera, and J. Aporta, “Representation of wavefronts in free-form transmission pupils with Complex Zernike Polynomials,” J. Opt.4(2), 41–48 (2011).
[CrossRef]

Bilello, J. C.

J. Tao, L. H. Lee, and J. C. Bilello, “Nondestructive evaluation of residual-stresses in thin-films via x-ray-diffraction topography methods,” J. Electron. Mater.20(7), 819–825 (1991).
[CrossRef]

Brown, M. A.

D. Ngo, X. Feng, Y. Huang, A. J. Rosakis, and M. A. Brown, “Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: analysis for obtaining film stress from non-local curvature information,” Int. J. Solids Struct.44(6), 1745–1754 (2007).
[CrossRef]

M. A. Brown, A. J. Rosakis, X. Feng, Y. Huang, and E. Ustundag, “Thin film substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II: experimental validation of the non-local stress curvature relations,” Int. J. Solids Struct.44(6), 1755–1767 (2007).
[CrossRef]

M. A. Brown, T.-S. Park, A. Rosakis, E. Ustundag, Y. Huang, N. Tamura, and B. Valek, “A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems,” J. Appl. Mech.73(5), 723–729 (2006).
[CrossRef]

Budyansky, M.

M. Budyansky, C. Madormo, J. L. Maciaszek, and G. Lykotrafitis, “Coherent gradient sensing microscopy (micro-CGS): A microscale curvature detection technique,” Opt. Lasers Eng.49(7), 874–879 (2011).
[CrossRef]

Chason, E.

E. Chason and B. W. Sheldon, “Monitoring stress in thin films during processing,” Surf. Eng.19(5), 387–391 (2003).
[CrossRef]

Chen, K.

L. T. Mao, C. P. Liu, K. Chen, L. Q. An, and X. X. Zhu, “Study on stress intensity factor of PMMA with double cracks using coherent gradient sensing(CGS) technique,” Appl. Mech. Mater.109, 114–119 (2011).
[CrossRef]

Cui, X.

J. Xiong, W. Qin, X. Cui, B. Tao, J. Tang, and Y. Li, “Effect of processing conditions and methods on residual stress in CeO2 buffer layers and YBCO superconducting films,” Physica C442(2), 124–128 (2006).
[CrossRef]

Dong, X.

Feng, X.

X. Dong, X. Feng, K. C. Hwang, S. Ma, and Q. Ma, “Full-field measurement of nonuniform stresses of thin films at high temperature,” Opt. Express19(14), 13201–13208 (2011).
[CrossRef] [PubMed]

X. Feng, Y. Huang, and A. J. Rosakis, “Stresses in a multilayer thin film/substrate system subjected to nonuniform temperature,” J. Appl. Mech.75(2), 021022 (2008).
[CrossRef]

D. Ngo, X. Feng, Y. Huang, A. J. Rosakis, and M. A. Brown, “Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: analysis for obtaining film stress from non-local curvature information,” Int. J. Solids Struct.44(6), 1745–1754 (2007).
[CrossRef]

M. A. Brown, A. J. Rosakis, X. Feng, Y. Huang, and E. Ustundag, “Thin film substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II: experimental validation of the non-local stress curvature relations,” Int. J. Solids Struct.44(6), 1755–1767 (2007).
[CrossRef]

X. Feng, Y. G. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, “The effect of thin film/substrate radii on the stoney formula for thin film/substrate subjected to nonuniform axisymmetric misfit strain and temperature,” J. Mech. Mater. Struct.1(6), 1041–1053 (2006).
[CrossRef]

Flinn, P. A.

P. A. Flinn, D. S. Gardner, and W. D. Nix, “Measurement and interpretation of stress in aluminum-based metallization as a function of thermal history,” IEEE Trans. Electron. Dev.34(3), 689–699 (1987).
[CrossRef]

Freund, L. B.

H. Lee, A. J. Rosakis, and L. B. Freund, “Full-field optical measurement of curvatures in ultra-thin-film–substrate systems in the range of geometrically nonlinear deformations,” J. Appl. Phys.89(11), 6122–6123 (2001).
[CrossRef]

Gardner, D. S.

P. A. Flinn, D. S. Gardner, and W. D. Nix, “Measurement and interpretation of stress in aluminum-based metallization as a function of thermal history,” IEEE Trans. Electron. Dev.34(3), 689–699 (1987).
[CrossRef]

Gu, B.

B. Gu, P. E. Phelan, and S. Mei, “Coupled heat transfer and thermal stress in high-Tc thin-film superconductor devices,” Cryogenics38(4), 411–418 (1998).
[CrossRef]

Huang, Y.

X. Feng, Y. Huang, and A. J. Rosakis, “Stresses in a multilayer thin film/substrate system subjected to nonuniform temperature,” J. Appl. Mech.75(2), 021022 (2008).
[CrossRef]

D. Ngo, X. Feng, Y. Huang, A. J. Rosakis, and M. A. Brown, “Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: analysis for obtaining film stress from non-local curvature information,” Int. J. Solids Struct.44(6), 1745–1754 (2007).
[CrossRef]

M. A. Brown, A. J. Rosakis, X. Feng, Y. Huang, and E. Ustundag, “Thin film substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II: experimental validation of the non-local stress curvature relations,” Int. J. Solids Struct.44(6), 1755–1767 (2007).
[CrossRef]

M. A. Brown, T.-S. Park, A. Rosakis, E. Ustundag, Y. Huang, N. Tamura, and B. Valek, “A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems,” J. Appl. Mech.73(5), 723–729 (2006).
[CrossRef]

Y. Huang and A. J. Rosakis, “Extension of Stoney's formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry,” J. Mech. Phys. Solids53(11), 2483–2500 (2005).
[CrossRef]

Huang, Y. G.

X. Feng, Y. G. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, “The effect of thin film/substrate radii on the stoney formula for thin film/substrate subjected to nonuniform axisymmetric misfit strain and temperature,” J. Mech. Mater. Struct.1(6), 1041–1053 (2006).
[CrossRef]

Hwang, K. C.

Jiang, H. Q.

X. Feng, Y. G. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, “The effect of thin film/substrate radii on the stoney formula for thin film/substrate subjected to nonuniform axisymmetric misfit strain and temperature,” J. Mech. Mater. Struct.1(6), 1041–1053 (2006).
[CrossRef]

Kessler, E. G.

M. D. Vaudin, E. G. Kessler, and D. M. Owen, “Precise silicon die curvature measurements using the NIST lattice comparator: comparisons with coherent gradient sensing interferometry,” Metrologia48(3), 201–211 (2011).
[CrossRef]

Kolawa, E.

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore., “Full field measurements of curvature using coherent gradient sensing: application to thin film characterization,” Thin Solid Films325(1–2), 42–54 (1998).
[CrossRef]

Krishnaswamy, S.

H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, “A coherent gradient sensor for crack tip deformation measurements: analysis and experimental results,” Int. J. Fract.48(3), 193–204 (1991).
[CrossRef]

Lambros, J.

R. P. Singh, J. Lambros, A. Shukla, and A. J. Rosakis, “Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity,” P Roy Soc A-Math Phy. 4532649–2667 (1997).

Lee, H.

H. Lee, A. J. Rosakis, and L. B. Freund, “Full-field optical measurement of curvatures in ultra-thin-film–substrate systems in the range of geometrically nonlinear deformations,” J. Appl. Phys.89(11), 6122–6123 (2001).
[CrossRef]

Lee, L. H.

J. Tao, L. H. Lee, and J. C. Bilello, “Nondestructive evaluation of residual-stresses in thin-films via x-ray-diffraction topography methods,” J. Electron. Mater.20(7), 819–825 (1991).
[CrossRef]

Li, Y.

J. Xiong, W. Qin, X. Cui, B. Tao, J. Tang, and Y. Li, “Effect of processing conditions and methods on residual stress in CeO2 buffer layers and YBCO superconducting films,” Physica C442(2), 124–128 (2006).
[CrossRef]

Liu, C.

C. Liu, X. Zhang, J. Zhou, and Y. Zhou, “A general coherent gradient sensor for film curvature measurements: error analysis without temperature constraint,” Opt. Lasers Eng.51(7), 808–812 (2013).
[CrossRef]

Liu, C. P.

L. T. Mao, C. P. Liu, K. Chen, L. Q. An, and X. X. Zhu, “Study on stress intensity factor of PMMA with double cracks using coherent gradient sensing(CGS) technique,” Appl. Mech. Mater.109, 114–119 (2011).
[CrossRef]

Lykotrafitis, G.

M. Budyansky, C. Madormo, J. L. Maciaszek, and G. Lykotrafitis, “Coherent gradient sensing microscopy (micro-CGS): A microscale curvature detection technique,” Opt. Lasers Eng.49(7), 874–879 (2011).
[CrossRef]

Ma, Q.

Ma, S.

Maciaszek, J. L.

M. Budyansky, C. Madormo, J. L. Maciaszek, and G. Lykotrafitis, “Coherent gradient sensing microscopy (micro-CGS): A microscale curvature detection technique,” Opt. Lasers Eng.49(7), 874–879 (2011).
[CrossRef]

Madormo, C.

M. Budyansky, C. Madormo, J. L. Maciaszek, and G. Lykotrafitis, “Coherent gradient sensing microscopy (micro-CGS): A microscale curvature detection technique,” Opt. Lasers Eng.49(7), 874–879 (2011).
[CrossRef]

Mao, L. T.

L. T. Mao, C. P. Liu, K. Chen, L. Q. An, and X. X. Zhu, “Study on stress intensity factor of PMMA with double cracks using coherent gradient sensing(CGS) technique,” Appl. Mech. Mater.109, 114–119 (2011).
[CrossRef]

Mei, S.

B. Gu, P. E. Phelan, and S. Mei, “Coupled heat transfer and thermal stress in high-Tc thin-film superconductor devices,” Cryogenics38(4), 411–418 (1998).
[CrossRef]

Moore, N. R.

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore., “Full field measurements of curvature using coherent gradient sensing: application to thin film characterization,” Thin Solid Films325(1–2), 42–54 (1998).
[CrossRef]

Navarro, R.

R. Navarro, R. Rivera, and J. Aporta, “Representation of wavefronts in free-form transmission pupils with Complex Zernike Polynomials,” J. Opt.4(2), 41–48 (2011).
[CrossRef]

Ngo, D.

D. Ngo, X. Feng, Y. Huang, A. J. Rosakis, and M. A. Brown, “Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: analysis for obtaining film stress from non-local curvature information,” Int. J. Solids Struct.44(6), 1745–1754 (2007).
[CrossRef]

X. Feng, Y. G. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, “The effect of thin film/substrate radii on the stoney formula for thin film/substrate subjected to nonuniform axisymmetric misfit strain and temperature,” J. Mech. Mater. Struct.1(6), 1041–1053 (2006).
[CrossRef]

Nix, W. D.

P. A. Flinn, D. S. Gardner, and W. D. Nix, “Measurement and interpretation of stress in aluminum-based metallization as a function of thermal history,” IEEE Trans. Electron. Dev.34(3), 689–699 (1987).
[CrossRef]

Owen, D. M.

M. D. Vaudin, E. G. Kessler, and D. M. Owen, “Precise silicon die curvature measurements using the NIST lattice comparator: comparisons with coherent gradient sensing interferometry,” Metrologia48(3), 201–211 (2011).
[CrossRef]

Park, T.-S.

M. A. Brown, T.-S. Park, A. Rosakis, E. Ustundag, Y. Huang, N. Tamura, and B. Valek, “A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems,” J. Appl. Mech.73(5), 723–729 (2006).
[CrossRef]

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, “Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry,” J. Mech. Phys. Solids51(11–12), 2191–2211 (2003).
[CrossRef]

Phelan, P. E.

B. Gu, P. E. Phelan, and S. Mei, “Coupled heat transfer and thermal stress in high-Tc thin-film superconductor devices,” Cryogenics38(4), 411–418 (1998).
[CrossRef]

Qin, W.

J. Xiong, W. Qin, X. Cui, B. Tao, J. Tang, and Y. Li, “Effect of processing conditions and methods on residual stress in CeO2 buffer layers and YBCO superconducting films,” Physica C442(2), 124–128 (2006).
[CrossRef]

Rivera, R.

R. Navarro, R. Rivera, and J. Aporta, “Representation of wavefronts in free-form transmission pupils with Complex Zernike Polynomials,” J. Opt.4(2), 41–48 (2011).
[CrossRef]

Rosakis, A.

M. A. Brown, T.-S. Park, A. Rosakis, E. Ustundag, Y. Huang, N. Tamura, and B. Valek, “A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems,” J. Appl. Mech.73(5), 723–729 (2006).
[CrossRef]

Rosakis, A. J.

X. Feng, Y. Huang, and A. J. Rosakis, “Stresses in a multilayer thin film/substrate system subjected to nonuniform temperature,” J. Appl. Mech.75(2), 021022 (2008).
[CrossRef]

D. Ngo, X. Feng, Y. Huang, A. J. Rosakis, and M. A. Brown, “Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: analysis for obtaining film stress from non-local curvature information,” Int. J. Solids Struct.44(6), 1745–1754 (2007).
[CrossRef]

M. A. Brown, A. J. Rosakis, X. Feng, Y. Huang, and E. Ustundag, “Thin film substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II: experimental validation of the non-local stress curvature relations,” Int. J. Solids Struct.44(6), 1755–1767 (2007).
[CrossRef]

X. Feng, Y. G. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, “The effect of thin film/substrate radii on the stoney formula for thin film/substrate subjected to nonuniform axisymmetric misfit strain and temperature,” J. Mech. Mater. Struct.1(6), 1041–1053 (2006).
[CrossRef]

Y. Huang and A. J. Rosakis, “Extension of Stoney's formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry,” J. Mech. Phys. Solids53(11), 2483–2500 (2005).
[CrossRef]

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, “Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry,” J. Mech. Phys. Solids51(11–12), 2191–2211 (2003).
[CrossRef]

H. Lee, A. J. Rosakis, and L. B. Freund, “Full-field optical measurement of curvatures in ultra-thin-film–substrate systems in the range of geometrically nonlinear deformations,” J. Appl. Phys.89(11), 6122–6123 (2001).
[CrossRef]

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore., “Full field measurements of curvature using coherent gradient sensing: application to thin film characterization,” Thin Solid Films325(1–2), 42–54 (1998).
[CrossRef]

H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, “A coherent gradient sensor for crack tip deformation measurements: analysis and experimental results,” Int. J. Fract.48(3), 193–204 (1991).
[CrossRef]

R. P. Singh, J. Lambros, A. Shukla, and A. J. Rosakis, “Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity,” P Roy Soc A-Math Phy. 4532649–2667 (1997).

Ryu, J.

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, “Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry,” J. Mech. Phys. Solids51(11–12), 2191–2211 (2003).
[CrossRef]

Sheldon, B. W.

E. Chason and B. W. Sheldon, “Monitoring stress in thin films during processing,” Surf. Eng.19(5), 387–391 (2003).
[CrossRef]

Shukla, A.

R. P. Singh, J. Lambros, A. Shukla, and A. J. Rosakis, “Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity,” P Roy Soc A-Math Phy. 4532649–2667 (1997).

Singh, R. P.

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore., “Full field measurements of curvature using coherent gradient sensing: application to thin film characterization,” Thin Solid Films325(1–2), 42–54 (1998).
[CrossRef]

R. P. Singh, J. Lambros, A. Shukla, and A. J. Rosakis, “Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity,” P Roy Soc A-Math Phy. 4532649–2667 (1997).

Stoney, G. G.

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character82(553), 172–175 (1909).
[CrossRef]

Suresh, S.

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, “Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry,” J. Mech. Phys. Solids51(11–12), 2191–2211 (2003).
[CrossRef]

Tamura, N.

M. A. Brown, T.-S. Park, A. Rosakis, E. Ustundag, Y. Huang, N. Tamura, and B. Valek, “A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems,” J. Appl. Mech.73(5), 723–729 (2006).
[CrossRef]

Tang, J.

J. Xiong, W. Qin, X. Cui, B. Tao, J. Tang, and Y. Li, “Effect of processing conditions and methods on residual stress in CeO2 buffer layers and YBCO superconducting films,” Physica C442(2), 124–128 (2006).
[CrossRef]

Tao, B.

J. Xiong, W. Qin, X. Cui, B. Tao, J. Tang, and Y. Li, “Effect of processing conditions and methods on residual stress in CeO2 buffer layers and YBCO superconducting films,” Physica C442(2), 124–128 (2006).
[CrossRef]

Tao, J.

J. Tao, L. H. Lee, and J. C. Bilello, “Nondestructive evaluation of residual-stresses in thin-films via x-ray-diffraction topography methods,” J. Electron. Mater.20(7), 819–825 (1991).
[CrossRef]

Tippur, H. V.

H. V. Tippur, “Coherent gradient sensing: a Fourier optics analysis and applications to fracture,” Appl. Opt.31(22), 4428–4439 (1992).
[CrossRef] [PubMed]

H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, “A coherent gradient sensor for crack tip deformation measurements: analysis and experimental results,” Int. J. Fract.48(3), 193–204 (1991).
[CrossRef]

Tsuji, Y.

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore., “Full field measurements of curvature using coherent gradient sensing: application to thin film characterization,” Thin Solid Films325(1–2), 42–54 (1998).
[CrossRef]

Ustundag, E.

M. A. Brown, A. J. Rosakis, X. Feng, Y. Huang, and E. Ustundag, “Thin film substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II: experimental validation of the non-local stress curvature relations,” Int. J. Solids Struct.44(6), 1755–1767 (2007).
[CrossRef]

M. A. Brown, T.-S. Park, A. Rosakis, E. Ustundag, Y. Huang, N. Tamura, and B. Valek, “A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems,” J. Appl. Mech.73(5), 723–729 (2006).
[CrossRef]

Valek, B.

M. A. Brown, T.-S. Park, A. Rosakis, E. Ustundag, Y. Huang, N. Tamura, and B. Valek, “A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems,” J. Appl. Mech.73(5), 723–729 (2006).
[CrossRef]

Vaudin, M. D.

M. D. Vaudin, E. G. Kessler, and D. M. Owen, “Precise silicon die curvature measurements using the NIST lattice comparator: comparisons with coherent gradient sensing interferometry,” Metrologia48(3), 201–211 (2011).
[CrossRef]

Xiong, J.

J. Xiong, W. Qin, X. Cui, B. Tao, J. Tang, and Y. Li, “Effect of processing conditions and methods on residual stress in CeO2 buffer layers and YBCO superconducting films,” Physica C442(2), 124–128 (2006).
[CrossRef]

Xu, W.

X. F. Yao, H. Y. Yeh, and W. Xu, “Fracture investigation at V-notch tip using coherent gradient sensing (CGS),” Int. J. Solids Struct.43(5), 1189–1200 (2006).
[CrossRef]

Yao, X. F.

X. F. Yao, H. Y. Yeh, and W. Xu, “Fracture investigation at V-notch tip using coherent gradient sensing (CGS),” Int. J. Solids Struct.43(5), 1189–1200 (2006).
[CrossRef]

Yeh, H. Y.

X. F. Yao, H. Y. Yeh, and W. Xu, “Fracture investigation at V-notch tip using coherent gradient sensing (CGS),” Int. J. Solids Struct.43(5), 1189–1200 (2006).
[CrossRef]

Zhang, X.

C. Liu, X. Zhang, J. Zhou, and Y. Zhou, “A general coherent gradient sensor for film curvature measurements: error analysis without temperature constraint,” Opt. Lasers Eng.51(7), 808–812 (2013).
[CrossRef]

Zhou, J.

C. Liu, X. Zhang, J. Zhou, and Y. Zhou, “A general coherent gradient sensor for film curvature measurements: error analysis without temperature constraint,” Opt. Lasers Eng.51(7), 808–812 (2013).
[CrossRef]

Zhou, Y.

C. Liu, X. Zhang, J. Zhou, and Y. Zhou, “A general coherent gradient sensor for film curvature measurements: error analysis without temperature constraint,” Opt. Lasers Eng.51(7), 808–812 (2013).
[CrossRef]

Zhu, X. X.

L. T. Mao, C. P. Liu, K. Chen, L. Q. An, and X. X. Zhu, “Study on stress intensity factor of PMMA with double cracks using coherent gradient sensing(CGS) technique,” Appl. Mech. Mater.109, 114–119 (2011).
[CrossRef]

Appl. Mech. Mater. (1)

L. T. Mao, C. P. Liu, K. Chen, L. Q. An, and X. X. Zhu, “Study on stress intensity factor of PMMA with double cracks using coherent gradient sensing(CGS) technique,” Appl. Mech. Mater.109, 114–119 (2011).
[CrossRef]

Appl. Opt. (1)

Cryogenics (1)

B. Gu, P. E. Phelan, and S. Mei, “Coupled heat transfer and thermal stress in high-Tc thin-film superconductor devices,” Cryogenics38(4), 411–418 (1998).
[CrossRef]

IEEE Trans. Electron. Dev. (1)

P. A. Flinn, D. S. Gardner, and W. D. Nix, “Measurement and interpretation of stress in aluminum-based metallization as a function of thermal history,” IEEE Trans. Electron. Dev.34(3), 689–699 (1987).
[CrossRef]

Int. J. Fract. (1)

H. V. Tippur, S. Krishnaswamy, and A. J. Rosakis, “A coherent gradient sensor for crack tip deformation measurements: analysis and experimental results,” Int. J. Fract.48(3), 193–204 (1991).
[CrossRef]

Int. J. Solids Struct. (3)

D. Ngo, X. Feng, Y. Huang, A. J. Rosakis, and M. A. Brown, “Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: analysis for obtaining film stress from non-local curvature information,” Int. J. Solids Struct.44(6), 1745–1754 (2007).
[CrossRef]

M. A. Brown, A. J. Rosakis, X. Feng, Y. Huang, and E. Ustundag, “Thin film substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II: experimental validation of the non-local stress curvature relations,” Int. J. Solids Struct.44(6), 1755–1767 (2007).
[CrossRef]

X. F. Yao, H. Y. Yeh, and W. Xu, “Fracture investigation at V-notch tip using coherent gradient sensing (CGS),” Int. J. Solids Struct.43(5), 1189–1200 (2006).
[CrossRef]

J. Appl. Mech. (2)

X. Feng, Y. Huang, and A. J. Rosakis, “Stresses in a multilayer thin film/substrate system subjected to nonuniform temperature,” J. Appl. Mech.75(2), 021022 (2008).
[CrossRef]

M. A. Brown, T.-S. Park, A. Rosakis, E. Ustundag, Y. Huang, N. Tamura, and B. Valek, “A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems,” J. Appl. Mech.73(5), 723–729 (2006).
[CrossRef]

J. Appl. Phys. (1)

H. Lee, A. J. Rosakis, and L. B. Freund, “Full-field optical measurement of curvatures in ultra-thin-film–substrate systems in the range of geometrically nonlinear deformations,” J. Appl. Phys.89(11), 6122–6123 (2001).
[CrossRef]

J. Electron. Mater. (1)

J. Tao, L. H. Lee, and J. C. Bilello, “Nondestructive evaluation of residual-stresses in thin-films via x-ray-diffraction topography methods,” J. Electron. Mater.20(7), 819–825 (1991).
[CrossRef]

J. Mech. Mater. Struct. (1)

X. Feng, Y. G. Huang, H. Q. Jiang, D. Ngo, and A. J. Rosakis, “The effect of thin film/substrate radii on the stoney formula for thin film/substrate subjected to nonuniform axisymmetric misfit strain and temperature,” J. Mech. Mater. Struct.1(6), 1041–1053 (2006).
[CrossRef]

J. Mech. Phys. Solids (2)

T.-S. Park, S. Suresh, A. J. Rosakis, and J. Ryu, “Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry,” J. Mech. Phys. Solids51(11–12), 2191–2211 (2003).
[CrossRef]

Y. Huang and A. J. Rosakis, “Extension of Stoney's formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry,” J. Mech. Phys. Solids53(11), 2483–2500 (2005).
[CrossRef]

J. Opt. (1)

R. Navarro, R. Rivera, and J. Aporta, “Representation of wavefronts in free-form transmission pupils with Complex Zernike Polynomials,” J. Opt.4(2), 41–48 (2011).
[CrossRef]

Metrologia (1)

M. D. Vaudin, E. G. Kessler, and D. M. Owen, “Precise silicon die curvature measurements using the NIST lattice comparator: comparisons with coherent gradient sensing interferometry,” Metrologia48(3), 201–211 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (2)

M. Budyansky, C. Madormo, J. L. Maciaszek, and G. Lykotrafitis, “Coherent gradient sensing microscopy (micro-CGS): A microscale curvature detection technique,” Opt. Lasers Eng.49(7), 874–879 (2011).
[CrossRef]

C. Liu, X. Zhang, J. Zhou, and Y. Zhou, “A general coherent gradient sensor for film curvature measurements: error analysis without temperature constraint,” Opt. Lasers Eng.51(7), 808–812 (2013).
[CrossRef]

Physica C (1)

J. Xiong, W. Qin, X. Cui, B. Tao, J. Tang, and Y. Li, “Effect of processing conditions and methods on residual stress in CeO2 buffer layers and YBCO superconducting films,” Physica C442(2), 124–128 (2006).
[CrossRef]

Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character (1)

G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character82(553), 172–175 (1909).
[CrossRef]

Surf. Eng. (1)

E. Chason and B. W. Sheldon, “Monitoring stress in thin films during processing,” Surf. Eng.19(5), 387–391 (2003).
[CrossRef]

Thin Solid Films (1)

A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore., “Full field measurements of curvature using coherent gradient sensing: application to thin film characterization,” Thin Solid Films325(1–2), 42–54 (1998).
[CrossRef]

Other (1)

R. P. Singh, J. Lambros, A. Shukla, and A. J. Rosakis, “Investigation of the mechanics of intersonic crack propagation along a bimaterial interface using coherent gradient sensing and photoelasticity,” P Roy Soc A-Math Phy. 4532649–2667 (1997).

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic of the CGS for cryogenic temperature, (b) photo of the measurement system, in which the number 1 denotes the closed cycle refrigerator (G-M).

Fig. 2
Fig. 2

(a) schematic of the lean of transparent windows, θ is the angle between the window and the horizontal plane, l denotes the width of the beam splitter, and h is the distance between the project plane of the transparent window and the bottom surface of the beam splitter, and while the thickness of quartz window is neglected, (b) Schematic of the effects of the quartz window on the interferogram, the dotted lines denote the normal of the window’s surface.

Fig. 3
Fig. 3

Interferogram fringes at 30K and their wrapped phase maps: (a) interferogram obtained by shearing laterally, (b) wrapped phase map for Fig. 3(a), (c) interferogram obtained by shearing vertically, (d) wrapped phase map for Fig. 3(c).

Fig. 4
Fig. 4

The substrate curvatures measured at 30K, (a) curvature κ xx in lateral direction, (b) curvature κ yy in vertical direction, (c) twist curvature κ xy .

Fig. 5
Fig. 5

The thermal expansion coefficients of the YBCO thin-film and MgO substrate vs. temperature.

Fig. 6
Fig. 6

The nonuniform stresses of the thin film measured at 30K: (a) stress σ rr in radial direction, (b) stress σ θθ in circumferential direction, (c) shear stress σ rθ , (d) interfacial shear stress τ r in radial direction, (e) interfacial shear stress τ θ in circumferential direction.

Fig. 7
Fig. 7

The film stresses in radial, circumferential directions (a) and the shear stress (b) at the central point of the specimen vs. temperature.

Equations (18)

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

1+ tan 2 θ 2tanθ = h l .
d=α e x +β e y +γ e z = n 1 n 2 d'+( n 2 2 (1+ | f | 2 ) 2 n 1 2 4 | f | 2 n 2 (1+ | f | 2 ) n 1 n 2 1 | f | 2 1+ | f | 2 ) e z ,
dd'.
I= I c +εμ a 1 a 2 cos( kΔβθ γ 2 ),
δ (x) (x,y)= 4πΔ p f x ,
δ (y) (x,y)= 4πΔ p f y ,
κ xx = 2 f( x,y ) x 2 = p 4πΔ δ (x) (x,y) x ,
κ yy = 2 f( x,y ) x 2 = p 4πΔ δ (y) (x,y) x ,
κ xy = 2 f( x,y ) xy = p 4πΔ δ (x) (x,y) y ,
I(x,y)=a(x,y)+b(x,y)cosδ(x,y),
I(x,y)=a(x,y)+c(x,y)c*(x,y),
I( ω (x) , ω (y) )=A( ω (x) , ω (y) )+C( ω (x) , ω (y) )+ C * ( ω (x) , ω (y) ).
δ(x,y)= tan 1 Im[ C(x,y) ] Re[ C(x,y) ] ,
σ rr (f) + σ θθ (f) = E s h s 2 6(1 ν s ) h f { κ rr + κ θθ ¯ + ( 1+ ν f )[ ( 1+ ν s ) α s 2 α f ] ( 1+ ν s )[ ( 1+ ν s ) α s ( 1+ ν f ) α f ] ( κ rr + κ θθ κ rr + κ θθ ¯ ) +[ 3+ ν s 1+ ν s 2 ( 1+ ν f )[ ( 1+ ν s ) α s 2 α f ] ( 1+ ν s )[ ( 1+ ν s ) α s ( 1+ ν f ) α f ] ] × m=1 ( m+1 ) ( r R ) m ( C m cosmθ+ S m sinmθ ) },
σ rr (f) σ θθ (f) = E s h s 2 α s ( 1 ν f ) 6(1 ν s ) h f 1 ( 1+ ν s ) α s ( 1+ ν f ) α f ×{ κ rr κ θθ m=1 ( m+1 )[ m ( r R ) m (m1) ( r R ) m2 ] ×( C m cosmθ+ S m sinmθ ) },
σ rθ f = E s h s 2 α s ( 1 ν f ) 6(1 ν s ) h f 1 ( 1+ ν s ) α s ( 1+ ν f ) α f ×{ κ rθ + 1 2 m=1 ( m+1 )[ m ( r R ) m (m1) ( r R ) m2 ]×( C m cosmθ S m sinmθ ) },
τ r = E s h s 2 6(1 ν s 2 ) { r ( κ rr + κ θθ ) 1 ν s 2R m=1 m( m+1 ) ( r R ) m1 ( C m cosmθ+ S m sinmθ ) },
τ θ = E s h s 2 6(1 ν s 2 ) { 1 r θ ( κ rr + κ θθ )+ 1 ν s 2R m=1 m( m+1 ) ( r R ) m1 ( C m cosmθ S m sinmθ ) },

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