Experimental Mechanics

, Volume 59, Issue 1, pp 111–120 | Cite as

Residual Stresses in Cu/Ni Multilayer Thin Films Measured Using the Sin2ψ Method

  • I. G. McDonald
  • W. M. Moehlenkamp
  • D. Arola
  • J. WangEmail author


Residual stresses in multilayer thin films are of substantial importance to the service life of advanced engineering systems. In this investigation, the residual stresses in magnetron sputtered Cu/Ni multilayer thin films were characterized using x-ray diffraction (XRD) and the sin2ψ method. The influence of layer thickness on residual stress was explored for films with alternating Ni and Cu layers with equal layer thicknesses ranging from 10 nm to 100 nm. To address peak broadening and overlapping, the Gaussian Mixture Model (GMM) and Expectation Maximization (EM) algorithm were employed, and the peak position was determined using the Center of Gravity (CoG) method. Results showed tensile residual stress in both the Cu and Ni layers and a prominent layer thickness dependence. The stress in the Ni layers increased from roughly 880 MPa to 1550 MPa with decreasing layer thickness from 100 nm to 10 nm. In the Cu layers, the stress remained relatively constant at ~250 MPa and then substantially decreased for the 10 nm thickness. The findings confirm that the XRD-based approach can be applied for residual stress measurement in nanoscale multilayer thin films, provided that peak broadening and overlapping issues are addressed. Furthermore, the residual stress in metal multilayers is strongly dependent on layer thickness.


Residual stress Multilayer thin-films Nanolaminates sin2ψ method X-ray diffraction 



The authors acknowledge technical support from the Molecular Analysis Facility (MAF) of the University of Washington for the residual stress analysis. The MAF is a National Nanotechnology Coordinated Infrastructure site at the University of Washington, which is supported in part by the National Science Foundation (grant ECC-1542101), the University of Washington, the Molecular Engineering & Sciences Institute, the Clean Energy Institute, and the National Institutes of Health. Special thanks are extended to Liam Bradshaw for training and consultation on the use of XRD. The team would like to thank Yang Zhou of the UW for his assistance with SEM imaging, as well as Tyler Johnson of the UW for his consultation on classification algorithms.


  1. 1.
    Wang J, Zhou Q, Shao S, Misra A (2016) Strength and plasticity of nanolaminated materials. Mater Res Lett 5(1):1–19. CrossRefGoogle Scholar
  2. 2.
    Yang Z, Wang J (2014) Orientation-dependent hardness in as-deposited and low-temperature annealed Ti/Ni multilayer thin films. J Appl Mech 82(1):011008. CrossRefGoogle Scholar
  3. 3.
    Yang Z, Wang J (2016) Coupled annealing temperature and layer thickness effect on strengthening mechanisms of Ti/Ni multilayer thin films. J Mech Phys Solids 88:72–82. CrossRefGoogle Scholar
  4. 4.
    Misra A, HK TEM, Nastasi M (1999) Residual stresses in polycrystalline cu/Cr multilayered thin films. J Mater Res 15(03):756–763. CrossRefGoogle Scholar
  5. 5.
    Zheng S, Beyerlein IJ, Carpenter JS, Kang K, Wang J, Han W, Mara NA (2013) High-strength and thermally stable bulk nanolayered composites due to twin-induced interfaces. Nat Commun 4:1696. CrossRefGoogle Scholar
  6. 6.
    Misra A, Hoagland RG, Kung H (2004) Thermal stability of self-supported nanolayered cu/Nb films. Philos Mag 84(10):1021–1028. CrossRefGoogle Scholar
  7. 7.
    Khan MI, Bhatti KA, Qindeel R, Althobaiti HS, Alonizan N (2017) Structural, electrical and optical properties of multilayer TiO 2 thin films deposited by sol–gel spin coating. Results Phys 7:1437–1439. CrossRefGoogle Scholar
  8. 8.
    Nix WD, Clemens BM (1999) Crystallite coalescence: a mechanism for intrinsic tensile stresses in thin films. J Mater Res 14(08):3467–3473. CrossRefGoogle Scholar
  9. 9.
    Chason E, Engwall A, Pei F, Lafouresse M, Bertocci U, Stafford G, Murphy JA, Lenihan C, Buckley DN (2013) Understanding residual stress in electrodeposited cu thin films. J Electrochem Soc 160(12):D3285–D3289. CrossRefGoogle Scholar
  10. 10.
    Drory MD, Thouless MD, Evans AG (1988) On the decohesion of residually stressed thin films. Acta Metall 36(8):2019–2028. CrossRefGoogle Scholar
  11. 11.
    Czerwinski F, Kedzierski Z (1997) On the mechanism of microcrack formation in nanocrystalline Fe–Ni electrodeposits. J Mater Sci 32(11):2957–2961. CrossRefGoogle Scholar
  12. 12.
    Ghosh SK, Limaye PK, Swain BP, Soni NL, Agrawal RG, Dusane RO, Grover AK (2007) Tribological behaviour and residual stress of electrodeposited Ni/cu multilayer films on stainless steel substrate. Surf Coat Technol 201(8):4609–4618. CrossRefGoogle Scholar
  13. 13.
    Stoney GG (1909) The tension of metallic films deposited by electrolysis. Royal Society of London A 82:4Google Scholar
  14. 14.
    Freund LB, Suresh S (2004) Thin film materials: stress, defect formation, and surface evolution. Cambridge University Press, Cambridge. CrossRefzbMATHGoogle Scholar
  15. 15.
    Abadias G, Chason E, Keckes J, Sebastiani M, Thompson GB, Barthel E, Doll GL, Murray CE, Stoessel CH, Martinu L (2018) Review article: stress in thin films and coatings: current status, challenges, and prospects. J Vac Sci Technol A 36(2):020801. CrossRefGoogle Scholar
  16. 16.
    Shull AL, Spaepen F (1996) Measurements of stress during vapor deposition of copper and silver thin films and multilayers. J Appl Phys 80(11):6243–6256. CrossRefGoogle Scholar
  17. 17.
    Noyan IC, Cohen JB (1987) Residual stress: measurement by diffraction and interpretation. Springer-Verlag, New YorkCrossRefGoogle Scholar
  18. 18.
    He BB (2009) Two-dimensional X-ray diffraction. John Wiley & Sons, Hoboken, New JerseyCrossRefGoogle Scholar
  19. 19.
    He K, Chen N, Wang C, Wei L, Chen J (2018) Method for determining crystal grain size by X-ray diffraction. Cryst Res Technol 53(2).
  20. 20.
    Sedighi M, Nazemnezhad R (2013) Effect of peak positioning method on accuracy of X-ray diffraction residual stress measurement. Exp Tech 40:295–302. CrossRefGoogle Scholar
  21. 21.
    Luo Q, Yang S (2017) Uncertainty of the X-ray diffraction (XRD) sin2 ψ technique in measuring residual stresses of physical vapor deposition (PVD) hard coatings. Coatings 7(8).
  22. 22.
    Swanson HE, Tatge E (1953) Standard X-ray diffraction powder patterns, vol 1. U. S. Dept. of Commerce, National Bureau of Standards, WashingtonGoogle Scholar
  23. 23.
    Duda RO, Hart PE, Stork DG (2012) Pattern classification. John Wiley & Sons, HobokenzbMATHGoogle Scholar
  24. 24.
    Bousquet O, von Luxburg U, Rätsch G (2011) Advanced lectures on machine learning: ML summer schools 2003, Canberra, Australia, February 2–14, 2003, Tübingen, Germany, august 4–16, 2003, revised lectures, vol 3176. Springer-Verlag Berlin, HeidelbergzbMATHGoogle Scholar
  25. 25.
    Mitra R, Hoffman RA, Madan A, Weertman JR (2011) Effect of process variables on the structure, residual stress, and hardness of sputtered nanocrystalline nickel films. J Mater Res 16(04):1010–1027. CrossRefGoogle Scholar
  26. 26.
    Zhang X, Misra A (2004) Residual stresses in sputter-deposited copper/330 stainless steel multilayers. J Appl Phys 96(12):7173–7178. CrossRefGoogle Scholar
  27. 27.
    Stoudt MR, Ricker RE, Cammarata RC (2001) The influence of multilayered metallic caoting on fatigue crack nucleation. Int J Fatigue 23:S125–S223CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2018

Authors and Affiliations

  • I. G. McDonald
    • 1
  • W. M. Moehlenkamp
    • 2
  • D. Arola
    • 1
    • 2
  • J. Wang
    • 1
    Email author
  1. 1.Department of Mechanical EngineeringUniversity of WashingtonSeattleUSA
  2. 2.Department of Material Science and EngineeringUniversity of WashingtonSeattleUSA

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