Wrinkling of thin films on compliant substrates

1. Wrinkling of thin films on compliant substrates Rui Huang Center for Mechanics of Solids, Structures and Materials The University of Texas at Austin

2. Au films on PDMS (Bowden et al., Nature 393, 146, 1998) SiO2 on Si (Courtesy of David Cahill) Wrinkling of thin films

3. Stretchable interconnects for large-area flexible electronics (Jones et al., MRS Symp. Proc. 769, H6.12, 2003 ) Wrinkling of skins (Cerda and Mahadevan, PRL 90, 074302, 2003) More wrinkling thin films

4. Outline • Elastic film on elastic substrate • linear and nonlinear analyses • Elastic film on viscous substrate • Kinetic process of wrinkling • Elastic film on plastic substrate • Ratcheting-induced wrinkling

5. Critical load: Other equilibrium states: energetically unfavorable Freestanding film: Euler buckling

6. Elastic substrate Effect of an elastic substrate • Wrinkling relaxes compressive strain • Bending energy prohibits wrinkling of short wavelengths • Deformation of the elastic substrate penalizes wrinkling of long wavelength

7. Elastic substrate Linear analysis 0 Elastic substrate Small perturbation: Strain energy change per unit area:

8. Wrinkling Stability

9. Stability Map

10. Nonlinear Analysis Nonlinear effect: large deflection of the film Energy minimization leads to the energetically favored wave number and the corresponding equilibrium amplitude: The energetically favored mode is independent of the compressive strain.

11. Constrained Equilibrium State

12. Most unstable mode Kinetics effect: growth rate depends on the driving force Other nonlinear effects: plasticity, large deformation of substrate

13. Viscous layer Rigid substrate Effect of a viscous underlayer • Wrinkling relaxes compressive strain; • Bending energy prohibits wrinkling of short wavelengths; • Viscous flow controls the growth rate: wrinkling of long wavelength is kinetically constrained.

14. Linear perturbation analysis: Fastest growing mode Euler buckling Growth rate, s Slow growing long-wave mode Wave number, kh Wrinkling Kinetics Huang and Suo, Int. J. Solids Struct. 39, 1791 (2002).

15. Viscous layer Rigid substrate Kinetically Constrained Equilibrium Wrinkles Infinitely many:each wavelength (  > c) has an equilibrium state Energetically unstable: longer wavelength  lower energy Kinetically constrained: flow is very slow near the equilibrium state • Elastic film is bent in equilibrium. • Viscous layer stops flowing. Huang and Suo, J. Appl. Phys. 91, 1135 (2002).

16. Viscous layer Rigid substrate Simultaneous Expansion and Wrinkling Expansion starts at the edges and propagates toward center Wrinkle grows before expansion relaxes the strain Long annealing removes wrinkles by expansion Liang et al., Acta Materialia 50, 2933 (2002).

17. s Wrinkle-Induced Fracture tension compression Tensile stress at the equilibrium state:

18. Wrinkle-induced cracks A 200m by 200m SiGe island on BPSG annealed for 90 minutes at 790°C. Huang et al., Acta Mechanica Sinica 18, 441, (2002)

19. Uni-directional shear cyclic stress metal film cyclic temperature substrate Ratching-creep analogy: Strain per cycle Thin Film Ratcheting Huang, Suo, Ma, Acta Materialia 49, 3039-3049 (2001).

20. Ratcheting-Induced Wrinkling Elastic film Plastic ratcheting Metal layer Cyclic temperature Substrate Amplitude growth per cycle: Equilibrium amplitude: Huang et al., in preparation.

21. Summary • Wrinkling of a compressed thin film on an elastic substrate is constrained: a critical strain exists; the wavelength of the equilibrium state is independent of the strain. • Flow of a viscous underlayer control the wrinkling kinetics: a fastest growing mode exists, and the equilibrium state is kinetically constrained. • Plastic ratcheting of a metal layer subject to cyclic temperatures can induce wrinkling of a compressed cap layer.

22. Acknowledgement Zhigang Suo (Harvard University) Zhenyu Huang (Harvard University) Haizhou Yin (Princeton University) James C. Sturm (Princeton University) Jim Liang (Intel Corp.) Se Hyuk Im (University of Texas-Austin)