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Wrinkling of thin films on compliant substrates. Rui Huang Center for Mechanics of Solids, Structures and Materials The University of Texas at Austin. Au films on PDMS (Bowden et al., Nature 393, 146, 1998). SiO 2 on Si (Courtesy of David Cahill). Wrinkling of thin films.

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wrinkling of thin films on compliant substrates

Wrinkling of thin films on compliant substrates

Rui Huang

Center for Mechanics of Solids, Structures and Materials

The University of Texas at Austin

wrinkling of thin films

Au films on PDMS

(Bowden et al., Nature 393, 146, 1998)

SiO2 on Si

(Courtesy of David Cahill)

Wrinkling of thin films
more wrinkling thin films

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
outline
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
freestanding film euler buckling

Critical load:

Other equilibrium states: energetically unfavorable

Freestanding film: Euler buckling
effect of an elastic substrate

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
linear analysis

Elastic substrate

Linear analysis

0

Elastic substrate

Small perturbation:

Strain energy change per unit area:

nonlinear analysis
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.

most unstable mode
Most unstable mode

Kinetics effect: growth rate depends on the driving force

Other nonlinear effects: plasticity, large deformation of substrate

effect of a viscous underlayer

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.
wrinkling kinetics

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).

kinetically constrained equilibrium wrinkles

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).

simultaneous expansion and wrinkling

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).

wrinkle induced fracture

s

Wrinkle-Induced Fracture

tension

compression

Tensile stress at the equilibrium state:

wrinkle induced cracks
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)

thin film ratcheting

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).

ratcheting induced wrinkling
Ratcheting-Induced Wrinkling

Elastic film

Plastic ratcheting

Metal layer

Cyclic temperature

Substrate

Amplitude growth per cycle:

Equilibrium amplitude:

Huang et al., in preparation.

summary
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.
acknowledgement
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)

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