## The coherent gradient sensor for film curvature measurements at cryogenic temperature |

Optics Express, Vol. 21, Issue 22, pp. 26352-26362 (2013)

http://dx.doi.org/10.1364/OE.21.026352

Acrobat PDF (1156 KB)

### 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

## 1. Introduction

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]

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. Solids **51**(11–12), 2191–2211 (2003). [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. Express **19**(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. Character **82**(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. Solids **53**(11), 2483–2500 (2005). [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]

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]

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]

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]

5. A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore Jr., “Full field measurements of curvature using coherent gradient sensing: application to thin film characterization,” Thin Solid Films **325**(1–2), 42–54 (1998). [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 C **442**(2), 124–128 (2006). [CrossRef]

## 2. Experimental setup and processes

_{1}and G

_{2}with the same density (40 lines/mm) separated by a distance

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. Express **19**(14), 13201–13208 (2011). [CrossRef] [PubMed]

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]

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]

**51**(7), 808–812 (2013). [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]

## 3. Experimental results and discussion

### 3.1 Substrate curvature measurement

### 3.2 Nonuniform stresses of the thin film

25. B. Gu, P. E. Phelan, and S. Mei, “Coupled heat transfer and thermal stress in high-Tc thin-film superconductor devices,” Cryogenics **38**(4), 411–418 (1998). [CrossRef]

## 4. Conclusions

## Acknowledgments

## References and links

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. |

2. | E. Chason and B. W. Sheldon, “Monitoring stress in thin films during processing,” Surf. Eng. |

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. |

4. | H. V. Tippur, “Coherent gradient sensing: a Fourier optics analysis and applications to fracture,” Appl. Opt. |

5. | A. J. Rosakis, R. P. Singh, Y. Tsuji, E. Kolawa, and N. R. Moore Jr., “Full field measurements of curvature using coherent gradient sensing: application to thin film characterization,” Thin Solid Films |

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. |

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. |

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. Solids |

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,” Metrologia |

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. |

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. Express |

12. | G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character |

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. Solids |

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. |

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. |

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. |

17. | X. Feng, Y. Huang, and A. J. Rosakis, “Stresses in a multilayer thin film/substrate system subjected to nonuniform temperature,” J. Appl. Mech. |

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. |

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. |

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. |

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 C |

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. |

24. | R. Navarro, R. Rivera, and J. Aporta, “Representation of wavefronts in free-form transmission pupils with Complex Zernike Polynomials,” J. Opt. |

25. | B. Gu, P. E. Phelan, and S. Mei, “Coupled heat transfer and thermal stress in high-Tc thin-film superconductor devices,” Cryogenics |

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.6780) Instrumentation, measurement, and metrology : Temperature

(240.0310) Optics at surfaces : Thin films

(310.4925) Thin films : Other properties (stress, chemical, etc.)

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: April 22, 2013

Revised Manuscript: June 17, 2013

Manuscript Accepted: July 8, 2013

Published: October 25, 2013

**Citation**

Cong Liu, Xingyi Zhang, Jun Zhou, Youhe Zhou, and Xue Feng, "The coherent gradient sensor for film curvature measurements at cryogenic temperature," Opt. Express **21**, 26352-26362 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26352

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### References

- 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]
- E. Chason and B. W. Sheldon, “Monitoring stress in thin films during processing,” Surf. Eng.19(5), 387–391 (2003). [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]
- H. V. Tippur, “Coherent gradient sensing: a Fourier optics analysis and applications to fracture,” Appl. Opt.31(22), 4428–4439 (1992). [CrossRef] [PubMed]
- 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]
- 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. 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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. 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]
- 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]
- 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).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]

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