Stress-Induced Wrinkling in Thin Films

1. Stress-Induced Wrinkling in Thin Films Rui Huang Center for Mechanics of Solids, Structures and Materials Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin

2. Wrinkles “Wrinkles occur on scales varying from a few nanometers (in thin films) to hundreds of kilometers (on the surface of the earth), in a variety of natural phenomena (see above).” (From http://www.deas.harvard.edu/softmat/)

3. Wrinkling in Thin Films

4. Applications of Wrinkling - Stretchable interconnects/electrodes for flexible electronics - Optical scattering, grating, and waveguide structures - Mechanical characterization of polymer thin films - Reliability of integrated devices containing soft organic materials (Jones et al., MRS Symp. Proc. 769, H6.12, 2003 )

5. Mechanics of Wrinkling • Elastic film on elastic substrate • Equilibrium and Energetics • Elastic film on viscous substrate • Non-equilibrium and Kinetics • Elastic film on viscoelastic substrate • Evolution of wrinkle patterns

6. Other equilibrium states: energetically unfavorable Freestanding film: Euler buckling Critical load: • Buckling relaxes compressive stress • Bending energy minimizes at long wavelength

7. Elastic substrate On elastic substrates • Deformation of the substrate disfavors wrinkling of long wavelengths and competes with bending to select an intermediate wavelength Wrinkling: short wavelength, on soft substrates, no delamination Buckling: long wavelength, on hard substrates, with delamination

8. Critical Condition for Wrinkling Thick substrate (hs >> hf): The critical strain decreases as the substrate stiffness decreases. In general, the critical strain depends on the thickness ratio and Poisson’s ratios too. In addition, the interface must be well bonded.

9. Equilibrium Wrinkle Wavelength Thick substrate (hs >> hf): Measure wavelength to determine film stiffness The wrinkle wavelength is independentof compressive strain. The wavelength increases as the substrate stiffness decreases. In general, the wavelength depends on thickness ratio and Poisson’s ratios too.

10. Equilibrium Wrinkle Amplitude Thick substrate (hs >> hf): Measure amplitude to determine film stress/strain. The wrinkle amplitude increases as the compressive strain increases. For large deformation, however, nonlinear elastic behavior must be considered.

11. Equilibrium Wrinkle Patterns In an elastic system, the equilibrium state minimizes the total strain energy. However, it is extremely difficult to find such a state for large film areas. More practically, one compares the energy of several possible patterns to determine the preferred pattern. How does the pattern emerge? How to control wrinkle patterns?

12. Fastest mode GrowthRate s sm Viscous layer Rigid substrate 0 c m  Euler buckling Kinetics: on a viscous substrate (For hs >> hf) • Viscous flow controls the growth rate: long-wave wrinkling grows slowly, and an intermediate wavelength is kinetically selected.

13. 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).

14. 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).

15. Wrinkle Amplitude Rubbery State Glassy State 0 Compressive Strain Wrinkling on Viscoelastic Substrates Cross-linked polymers • Evolution of wrinkles: • Viscous to Rubbery • Glassy to Rubbery

16. (Lee at al., 2004)

17. Wrinkling Kinetics I: Wrinkles of intermediate wavelengths grow exponentially; The fastest growing mode dominates the initial growth. GrowthRate Fastest mode 0 m  For hs >> hf : The kinetically selected wavelength is independent of substrate!

18. Wrinkling Kinetics II: Instantaneous wrinkle at the glassy state: Kinetic growth at the initial stage: Long-term evolution:

19. Numerical Simulation t = 0 Growing wavelengths t = 1104 Coarsening t = 1105 Equilibrium wavelength t = 1107

20. Evolution of Wrinkle Wavelength Initial stage: kinetically selected wavelengths Intermediate stage: coarsening of wavelength Final stage: equilibrium wavelength at the rubbery state

21. Evolution of Wrinkle Amplitude Initial stage: exponential growth Intermediate stage: slow growth Final stage: saturating

22. 2D Wrinkle Patterns I t = 0 t = 104 t = 105 t = 107 t = 106

23. 2D Wrinkle Patterns II t = 0 t = 105 t = 106 t = 5X106 t = 2X107

24. 2D Wrinkle Patterns III t = 5X105 t = 0 t = 104 t = 107 t = 106

25. On a Patterned Substrate t = 0 t = 104 t = 105 t = 107 t = 106

26. Circular Perturbation t = 0 t = 104 t = 105 t = 107 t = 5105 t = 106

27. Evolution of Wrinkle Patterns • Symmetry breaking in isotropic system: • from spherical caps to elongated ridges • from labyrinth to herringbone. • Symmetry breaking due to anisotropic strain • from labyrinth to parallel stripes • Controlling the wrinkle patterns • On patterned substrates • By introducing initial defects

28. What else? • Ultra-thin films • Effect of surface energy and surface stress • Effect of thickness-dependent modulus • Effect of temperature, molecular weight, cross-linking • Other effect at nanoscale? • Nonlinear elastic/viscoelastic behavior • Nested wrinkles?