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) SiO 2 on Si (Courtesy of David Cahill)

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, , 2003)

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

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 Elastic substrate

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

Wrinkling Stability

Stability Map

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

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

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

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). 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). Viscous layer Rigid substrate

Wrinkle-Induced Fracture Tensile stress at the equilibrium state:  tension compression

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

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

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 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)