Fracture, Delamination and Buckling of
Elastic Thin Films on Compliant Substrates
Rui Huang
Center for Mechanics of Solids, Structures and Materials
Department of Aerospace Engineering and Engineering Mechanics
The University of Texas at Austin
Collaborators:
Christopher M. Stafford (NIST)
Hong-Hui Yu (CCNY)
Se Hyuk Im (UT Austin)
Haixia Mei (UT Austin)
Yaoyu Pang (UT Austin)
Large-Area Electronics:
flexible, stretchable, compressible
Wagner, et al, 2005.
σ >0
Ahn, et al, 2006
σ <0
• Not always possible (or practical) to put all the devices on the neutral plane.
• Being flexible requires being both stretchable and compressible!
Mechanics of Thin Films:
Stretch and Compress
Soft substrate
Stretchability
• A brittle thin film on a soft substrate
2
Dimensionless energy release rate, (GSSE1*)/(σ0h)
40
35
Beuth [21]
XFEM
β =α /4
30
25
20
15
10
5
0
-1
GSS = Z (α , β )
ε appl <
σ 02 h
Ef
-0.5
(
0
= Z (α , β )E f h ε appl + ε res
Γf
Z (α , β )E f h
− ε res
0.5
1
Elastic mismatch, α
)2
• Stretchability decreases with
increasing elastic mismatch
• Stretchability increases with a
compressive residual strain
Effect of interface delamination
1.5
α=−0.6
α=0
α=0.6
1.4
eff
Z /Z
1.3
1.2
1.1
1
Geff = Z eff (Γi , α , β )
ε appl <
Γf
σ 02 h
0.9
1
1.5
Interface toughness, Γi/Σ
Ef
Z eff (Γi , α , β )E f h
0.5
− ε res
• Stretchability decreases with
decreasing interface toughness
Tsui et al., JMR, 20, 2266 (2005).
Compressibility: buckling
Soft substrate
Wrinkling: enhance stretchability, but may fail under compression
Buckle-Delamination: lose interface integrity, may lead to film fracture
Mechanics of buckle-delamination
Hutchinson and Suo (1992):
• 1D buckle (plane strain cross section of a straight blister)
• Assume fixed edges (good for rigid substrates)
π ⎛h⎞
2
2
Critical strain for buckling:
εc =
Interfacial fracture
energy release rate:
⎡ Ef h
G=⎢
2
2
1
ν
−
⎢⎣
f
Compressibility 2:
⎜ ⎟
12 ⎝ b ⎠
(
G < Γi
Compressibility 1
⎤
⎥ (ε − ε c )(ε + 3ε c )
⎥⎦
)
ε<
2Γi
+ 4ε c2 − ε c
Ef h
• Compressibility strongly depends on interface defects and toughness
• No effect of elastic mismatch?
Effect of compliant substrates
Yu and Hutchinson (2002):
• 1D buckle (plane strain cross section of a straight blister)
• Elastic substrate
• Numerical solutions from a finite element model
2.2
0.9
simulation result
theoretical result for rigid substrate
0.8
simulation result
theoretical result for rigid substrate
2
1.8
0.7
α=0.9835
β=0.1628
1.6
2
G (J/m )
0.6
σcr (GPa)
0.5
α=0.9835
β=0.1628
1.4
1.2
0.4
1
0.3
0.8
0.2
0.6
0.1
0.4
0
20
25
30
35
40
45
50
55
60
65
0.2
20
25
30
35
εc =
2
⎜ ⎟ ξ (b / h, α , β )
12 ⎝ b ⎠
45
50
55
b/h
b/h
π2 ⎛h⎞
40
G=
E f ε 2h
(
2 1 −ν 2f
)
⎛ b
⎞
g⎜ ε , ,α , β ⎟
⎝ h
⎠
60
65
Wrinkling: Analytical Solutions
For thick, elastic substrates (hs >> hf):
Critical strain:
1 ⎛⎜ 3Es ⎞⎟
εc = ⎜
4 ⎝ E f ⎟⎠
Equilibrium wavelength:
Equilibrium amplitude:
For arbitrary thickness: Huang,
J. Mech. Phys. Solids 53, 63 (2005).
2/3
Es << E f
Small strain!
1/ 3
⎛ Ef ⎞
⎟⎟
λeq = 2πh f ⎜⎜
⎝ 3E s ⎠
1/ 2
⎞
⎛ε
Aeq = h f ⎜⎜ − 1⎟⎟
⎠
⎝εc
Measure wavelength to determine film stiffness;
Measure amplitude to determine film stress/strain.
Ultrathin PS Film on PDMS
Applied strain: ε = 2.5%
Stafford et al., Macromolecules 39, 5095 (2006).
Wrinkling vs Buckling
2b
σB =
π2 ⎛h⎞
2
⎜ ⎟ E f ξ (α , β )
12 ⎝ b ⎠
Soft substrate
σW
32 / 3 ⎛ 1 − α ⎞
=
⎜
⎟
4 ⎝1+α ⎠
2/3
Ef
Transition of buckling mode!
Mei et al., Appl. Phys. Lett. 90, 151902 (2007).
PS thin film on PDMS
• 1st cycle: small defects, wrinkling followed by buckle-delamination
• 2nd cycle: large defects, buckle-delamination followed by wrinkling
Mei et al., Appl. Phys. Lett. 90, 151902 (2007).
Wrinkle-induced fracture
σ eq =
SiGe film on glass
Yin, et al., J. Appl. Phys. 94, 6875 (2003).
E (kh )
2 1 −ν 2
2
(
)
2
⎡ ⎡
⎤
⎤
k
1
1
⎛
⎞
⎢ ⎢⎜ c ⎟ − 1⎥ − ⎥
⎢ 3 ⎢⎣⎝ k ⎠
⎥⎦ 6 ⎥⎦
⎣
Liang, et al., Acta Mater 50, 2933 (2002).
Summary
• Large-area electronics requires flexible,
stretchable, and compressible design.
• Stretchability is limited by film fracture.
• Compressibility may be limited by buckledelamination or wrinkle-induced fracture.
• Flexibility requires both!