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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

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Wrinkling of thin films on compliant substrates l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

Critical load:

Other equilibrium states: energetically unfavorable

Freestanding film: Euler buckling


Effect of an elastic substrate l.jpg

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 l.jpg

Elastic substrate

Linear analysis

0

Elastic substrate

Small perturbation:

Strain energy change per unit area:


Wrinkling stability l.jpg

Wrinkling Stability


Stability map l.jpg

Stability Map


Nonlinear analysis l.jpg

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.


Constrained equilibrium state l.jpg

Constrained Equilibrium State


Most unstable mode l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

s

Wrinkle-Induced Fracture

tension

compression

Tensile stress at the equilibrium state:


Wrinkle induced cracks l.jpg

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 l.jpg

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 l.jpg

Ratcheting-Induced Wrinkling

Elastic film

Plastic ratcheting

Metal layer

Cyclic temperature

Substrate

Amplitude growth per cycle:

Equilibrium amplitude:

Huang et al., in preparation.


Summary l.jpg

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.


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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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