Effect of twisting fatigue on the electrical reliability of a metal interconnect on a flexible substrate

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To secure the reliability of flexible electronics, the effect of multicomponent stress on the device properties during complex mechanical deformation needs to be thoroughly understood. The electrical resistances of metal interconnects are investigated by in situ monitoring at different twisting angles and with different pattern positions. As the twisting angle increased, the electrical resistance increased earlier. Furthermore, in the line pattern located far from the central axis, severe electrical degradation and fatigue damage formation were observed. Multicomponent stress evolution during twisting was analyzed by the finite-element simulation method. For easy practical application for estimating the representative twisting strain, an analytic solution of twisting deformation was formulated and compared with the simulation. Using the equivalent strain, the fatigue lifetime was fitted, and the exponents were obtained for lifetime expectation. This systematic study provides the guidelines for highly reliable flexible devices and the tools for determining the expected fatigue lifetime.

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  1. 1.

    X. Huang, Y. Liu, H. Cheng, W-J. Shin, J.A. Fan, Z. Liu, C-J. Lu, G-W. Kong, K. Chen, D. Patnaik, S-H. Lee, S. Hage-Ali, Y. Huang, and J.A. Rogers: Materials and designs for wireless epidermal sensors of hydration and strain. Adv. Funct. Mater. 24, 3846–3854 (2014).

    CAS  Article  Google Scholar 

  2. 2.

    Q.C. Liu, J.J. Xu, D. Xu, and X.B. Zhang: Flexible lithium-oxygen battery based on a recoverable cathode. Nat. Commun. 6, 7892 (2015).

    CAS  Article  Google Scholar 

  3. 3.

    S. Kim, H.J. Kwon, S. Lee, H. Shim, Y. Chun, W. Choi, J. Kwack, D. Han, M. Song, S. Kim, S. Mohammadi, I. Kee, and S.Y. Lee: Low-power flexible organic light-emitting diode display device. Adv. Mater. 23, 3511–3516 (2011).

    CAS  Article  Google Scholar 

  4. 4.

    Y. Li, D-K. Lee, J.Y. Kim, B. Kim, N-G. Park, K. Kim, J-H. Shin, I-S. Choi, and M.J. Ko: Highly durable and flexible dye-sensitized solar cells fabricated on plastic substrates: PVDF-nanofiber-reinforced TiO2 photoelectrodes. Energy Environ. Sci. 5, 8950 (2012).

    CAS  Article  Google Scholar 

  5. 5.

    X. Zhu, B. Zhang, J. Gao, and G. Zhang: Evaluation of the crack-initiation strain of a Cu–Ni multilayer on a flexible substrate. Scr. Mater. 60, 178–181 (2009).

    CAS  Article  Google Scholar 

  6. 6.

    J-H. Lee, N-R. Kim, B-J. Kim, and Y-C. Joo: Improved mechanical performance of solution-processed MWCNT/Ag nanoparticle composite films with oxygen-pressure-controlled annealing. Carbon 50, 98–106 (2012).

    CAS  Article  Google Scholar 

  7. 7.

    B-J. Kim, H-A.S. Shin, J-H. Lee, T-Y. Yang, T. Haas, P. Gruber, I-S. Choi, O. Kraft, and Y-C. Joo: Effect of film thickness on the stretchability and fatigue resistance of Cu films on polymer substrates. J. Mater. Sci. 29, 2827–2834 (2014).

    CAS  Google Scholar 

  8. 8.

    Y-J. Lee, H-A.S. Shin, D-H. Nam, H-W. Yeon, B. Nam, K. Woo, and Y-C. Joo: Improvements of mechanical fatigue reliability of Cu interconnects on flexible substrates through MoTi alloy under-layer. Electron. Mater. Lett. 11, 149–154 (2015).

    CAS  Article  Google Scholar 

  9. 9.

    O. Glushko, A. Klug, E.J.W. List-Kratochvil, and M.J. Cordill: Relationship between mechanical damage and electrical degradation in polymer-supported metal films subjected to cyclic loading. Mater. Sci. Eng., A 662, 157–161 (2016).

    CAS  Article  Google Scholar 

  10. 10.

    D. Akinwande, N. Petrone, and J. Hone: Two-dimensional flexible nanoelectronics. Nat. Commun. 5, 5678 (2014).

    CAS  Article  Google Scholar 

  11. 11.

    P. Lee, J. Lee, H. Lee, J. Yeo, S. Hong, K.H. Nam, D. Lee, S.S. Lee, and S.H. Ko: Highly stretchable and highly conductive metal electrode by very long metal nanowire percolation network. Adv. Mater. 24, 3326–3332 (2012).

    CAS  Article  Google Scholar 

  12. 12.

    B.J. Kim, Y. Cho, M.S. Jung, H.A. Shin, M.W. Moon, H.N. Han, K.T. Nam, Y.C. Joo, and I.S. Choi: Fatigue-free, electrically reliable copper electrode with nanohole array. Small 8, 3300–3306 (2012).

    CAS  Article  Google Scholar 

  13. 13.

    G.D. Moon, G.H. Lim, J.H. Song, M. Shin, T. Yu, B. Lim, and U. Jeong: Highly stretchable patterned gold electrodes made of Au nanosheets. Adv. Mater. 25, 2707–2712 (2013).

    CAS  Article  Google Scholar 

  14. 14.

    Y. Zhang, H. Fu, Y. Su, S. Xu, H. Cheng, J.A. Fan, K-C. Hwang, J.A. Rogers, and Y. Huang: Mechanics of ultra-stretchable self-similar serpentine interconnects. Acta Mater. 61, 7816–7827 (2013).

    CAS  Article  Google Scholar 

  15. 15.

    Y-Y. Hsu, M. Gonzalez, F. Bossuyt, F. Axisa, J. Vanfleteren, and I. De Wolf: The effect of pitch on deformation behavior and the stretching-induced failure of a polymer-encapsulated stretchable circuit. J. Micromech. Microeng. 20, 075036 (2010).

    Article  Google Scholar 

  16. 16.

    M. Gonzalez, F. Axisa, M.V. Bulcke, D. Brosteaux, B. Vandevelde, and J. Vanfleteren: Design of metal interconnects for stretchable electronic circuits. Microelectron. Reliab. 48, 825–832 (2008).

    Article  Google Scholar 

  17. 17.

    R. Zhou, W. Guo, R. Yu, and C. Pan: Highly flexible, conductive and catalytic Pt networks as transparent counter electrodes for wearable dye-sensitized solar cells. J. Mater. Chem. A 3, 23028–23034 (2015).

    CAS  Article  Google Scholar 

  18. 18.

    S.G. Yoon, H.J. Koo, and S.T. Chang: Highly stretchable and transparent microfluidic strain sensors for monitoring human body motions. ACS Appl. Mater. Interfaces 7, 27562–27570 (2015).

    CAS  Article  Google Scholar 

  19. 19.

    D-Y. Cho, K. Eun, S-H. Choa, and H-K. Kim: Highly flexible and stretchable carbon nanotube network electrodes prepared by simple brush painting for cost-effective flexible organic solar cells. Carbon 66, 530–538 (2014).

    CAS  Article  Google Scholar 

  20. 20.

    S. Song, J. Jang, Y. Ji, S. Park, T-W. Kim, Y. Song, M-H. Yoon, H.C. Ko, G-Y. Jung, and T. Lee: Twistable nonvolatile organic resistive memory devices. Org. Electron. 14, 2087–2092 (2013).

    CAS  Article  Google Scholar 

  21. 21.

    N. Lu, Z. Suo, and J.J. Vlassak: The effect of film thickness on the failure strain of polymer-supported metal films. Acta Mater. 58, 1679–1687 (2010).

    CAS  Article  Google Scholar 

  22. 22.

    D.Y.W. Yu and F. Spaepen: The yield strength of thin copper films on Kapton. J. Appl. Phys. 95, 2991–2997 (2004).

    CAS  Article  Google Scholar 

  23. 23.

    S. Suresh: Fatigue of Materials, 2nd ed. (Cambridge University Press, Cambridge, 1999); pp. 133–222.

    Google Scholar 

  24. 24.

    G.E. Dieter: Mechanical Metallurgy (McGraw-Hill Book Company, London, 1988); pp. 381–419.

    Google Scholar 

  25. 25.

    B-J. Kim, H-A.S. Shin, S-Y. Jung, Y. Cho, O. Kraft, I-S. Choi, and Y-C. Joo: Crack nucleation during mechanical fatigue in thin metal films on flexible substrates. Acta Mater. 61, 3473–3481 (2013).

    CAS  Article  Google Scholar 

  26. 26.

    Y. Li, X-S. Wang, and X-K. Meng: Buckling behavior of metal film/substrate structure under pure bending. Appl. Phys. Lett. 92, 131902–131903 (2008).

    Article  Google Scholar 

  27. 27.

    F. Toth, F.G. Rammerstorfer, M.J. Cordill, and F.D. Fischer: Detailed modelling of delamination buckling of thin films under global tension. Acta Mater. 61, 2425–2433 (2013).

    CAS  Article  Google Scholar 

  28. 28.

    I.H. Shames and J.M. Pitarresi: Introducion to Solid Mechanics, 3rd ed. (Pearson Education, New Delhi, 2000); pp. 513–554.

    Google Scholar 

  29. 29.

    R. Gupta and T.S. Siller: Stress distribution in structural composite lumber under torsion. For. Prod. J. 55, 51–56 (2005).

    Google Scholar 

  30. 30.

    H. Huang and F. Spaepen: Tensile testing of free-standing Cu, Ag, and Al thin films and Ag/Cu multilayers. Acta Mater. 48, 3261–3269 (2000).

    CAS  Article  Google Scholar 

  31. 31.

    Y. Xiang and J.J. Vlassak: Bauschinger effect in thin metal films. Scr. Mater. 53, 177–182 (2005).

    CAS  Article  Google Scholar 

  32. 32.

    N.S. Trahair: Nonlinear elastic nonuniform torsion. J. Struct. Eng. 131, 1135–1142 (2005).

    Article  Google Scholar 

  33. 33.

    L.F. Coffin: A study of the effects of cyclic thermal stresses on a ductile metal. Trans. ASME. 76, 931–950 (1954).

    CAS  Google Scholar 

  34. 34.

    S.S. Manson: Behavior of Materials Under Conditions of Thermal Stress; Report 1170; Lewis Flight Propulsion Laboratory: Cleveland, OH, 1954.

    Google Scholar 

  35. 35.

    O. Kraft, R. Schwaiger, and P. Wellner: Fatigue in thin films: Lifetime and damage formation. Mater. Sci. Eng., A 319–321, 919–923 (2001).

    Article  Google Scholar 

  36. 36.

    X.J. Sun, C.C. Wang, J. Zhang, G. Liu, G.J. Zhang, X.D. Ding, G.P. Zhang, and J. Sun: Thickness dependent fatigue life at microcrack nucleation for metal thin films on flexible substrates. J. Phys. D: Appl. Phys. 41, 195404 (2008).

    Article  Google Scholar 

  37. 37.

    O.H. Basquin: The exponential law of endurance tests. Proc. ASTM 10, 625–630 (1910).

    Google Scholar 

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This research was supported by “Development of Interconnection System and Process for Flexible Three Dimensional Heterogeneous Devices” funded by MOTIE (Ministry of Trade, Industry and Energy) and National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP; Ministry of Science, ICT & Future Planning) (No. 2017R1C1B5017889) in Korea.

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Correspondence to Byoung-Joon Kim or Young-Chang Joo.

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Yang, JK., Lee, YJ., Yi, SM. et al. Effect of twisting fatigue on the electrical reliability of a metal interconnect on a flexible substrate. Journal of Materials Research 33, 138–148 (2018). https://doi.org/10.1557/jmr.2017.422

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