Cao Z. (Ed.) Thin Film Growth: Physics, materials science and applications

338 Thin ﬁlm growth

13.6 References

Audoly B (2003), ‘Self-similar structures near boundaries in strained systems’, Phys.

Rev. Lett., 91, 086105.

Colin J, Cleymand F, Coupeau C and Grilhé J (2000), ‘Worm-like delamination

patterns of thin stainless steel lms on polycarbonate substrates’, Philos. Mag. A,

80, 2559–2565.

Cordill M J, Moody N R and Bahr D F (2005), ‘The effects of plasticity on adhesion of

hard lms on ductile interlayers’, Acta Mater., 53, 2555–2562.

Coupeau C and Grilhé J (2001), ‘Atomic force microscopy observations of in situ

deformed materials: application to single crystals and thin lms on substrates’, J.

Micro., 203, 99–107.

Coupeau C, Naud J F, Cleymand F, Goudeau P and Grilhé J (1999a), ‘Atomic force

microscopy of in situ deformed nickel thin lms’, Thin Solid Films, 353, 194–200.

Coupeau C, Girard J C and Grilhé J (1999b), ‘Atomic force microscopy of single crystal

surfaces during plastic deformation’, Probe Mic., 1, 313–321.

Coupeau C, Cleymand F and Grilhé J (2000), ‘Atomic force microscopy of dislocation

locking effects at gold lm LiF substrate interface’, Scripta Mater., 43, 187–192.

Coupeau C, Girard J C and Rabier J (2004), ‘Scanning probe microscopy and dislocations’,

in Nabarro F R N and Hirth J P (eds), Dislocations in Solids, amsterdam, elsevier,

275–338.

Crosby K M and Bradley R M (1999), ‘Pattern formation during delamination and

buckling of thin lms’, Phys. Rev. E, 59, 2542–2545.

Föppl A (1907), Vorlesungen über Technische Mechanik, 5, 132.

Foucher F and Coupeau C (2007), ‘Effect of the dislocation emergence on the mechanical

behavior of coated materials: elastic energy relaxation or adhesion modication’, Surf.

Coat. Tech., 202, 1094–1097.

Foucher F, Coupeau C, Colin J, Cimetière A and Grilhé J (2006), ‘How does crystalline

substrate plasticity modify thin lm buckling?’, Phys. Rev. Lett., 97, 096101.

Hutchinson J W and Suo Z (1992), ‘Mixed mode cracking in layered materials’, Adv.

Appl. Mech., 29, 63–191.

Hutchinson J W, He M Y and Evans A G (2000), ‘The inuence of imperfections on

the nucleation and propagation of buckling driven delaminations’, J. Mech. Phys.

Sol., 48, 709–734.

Jagla E A (2006), ‘Morphologies of expansion ridges of elastic thin lms onto a substrate’,

Phys. Rev. E, 74, 036207.

Jagla E A (2007), ‘Modeling the buckling and delamination of thin lms’, Phys. Rev.

B, 75, 085405.

Junqua N and Grilhé J (1997), ‘Surface step-dislocation transition and dislocation

nucleation at a solid free surface’, Philos. Mag. Lett., 75, 125.

Matuda N, Baba S and Kinbara A (1981), ‘Internal stress, Young’s modulus and adhesion

energy of carbon lms on glass substrates’, Thin Solid Films, 81, 301–305.

Moon M W, Chung J W, Lee K R, Oh K H, Wang R and Evans A G (2002), ‘An

experimental study of the inuence of imperfections on the buckling of compressed

thin lms’, Acta Mater., 50, 1219–1227.

Parry G, Coupeau C, Colin J, Cimetière A and Grilhé J (2004), ‘Buckling and post-

buckling of stressed straight-sided wrinckles: experimental AFM observations of

bubbles formation and nite element simulations’, Acta Mater., 52, 3959–3966.

Parry G, Colin J, Coupeau C, Foucher F, Cimetière A and Grilhé J (2005), ‘Effect

ThinFilm-Zexian-13.indd 338 7/1/11 9:44:54 AM



339Understanding substrate plasticity and buckling of thin ﬁlms

of substrate compliance on the global unilateral post-buckling of coatings: AFM

observations and nite element calculations’, Acta Mater., 53, 441–447.

Parry G, Cimetière A, Coupeau C, Colin J and Grilhé J (2006), ‘Stability diagram of

unilateral buckling patterns of strip-delaminated lms’, Phys. Rev. E, 74, 066601.

Paumier F, Gaboriaud R J and Coupeau C (2003), ‘Buckling phenomena in Y

2

o

3

thin

lms on GaAs substrates’, Appl. Phys. Lett., 82, 2056–2058.

von Kármán T (1910), ‘Festigkeitsprobleme in maschinenbau’, Ency. der. Math.

Wissenschaften, IV/4C, 311–385.

ThinFilm-Zexian-13.indd 339 7/1/11 9:44:54 AM



340

14

Controlled buckling of thin films on compliant

substrates for stretchable electronics

J. Song, University of Miami, USA and J. WU, and

Y. HUAng, northwestern University, USA

Abstract: Electronic systems with large stretchability have many

applications. This chapter reviews the mechanics of a non-coplanar mesh

design whose stretchability can be up to 100%. Mechanics models for

non-coplanar mesh designs are developed and used to predict the maximum

strains. The models agree well with experiments and give the stretchability

of the system in terms of the geometric parameters and fracture strain of the

material.

Key words: buckling, interconnect, island, substrate, stretchable electronics.

14.1 Introduction

Stretchable electronics is electronics with performance equal to established

technologies that use rigid semiconductor wafers, but in formats that can

be stretched and compressed. It enables many new application possibilities.

Examples include exible displays (Crawford, 2005), electronic eye camera

(Jin et al., 2004; Ko et al., 2008; Shin et al., 2010), conformable skin sensors

(Lumelsky et al., 2001), smart surgical gloves (Someya et al., 2004), and

structural health monitoring devices (Nathan et al., 2000). Circuits that use

organic semiconductor materials can sustain large deformations (Garnier et

al., 1994; Baldo et al., 2000; Crone et al., 2000; Loo et al., 2002; Facchetti

et al., 2005; Sekitani et al., 2008), but their electrical performance is

relatively poor (several orders of magnitude lower than that of conventional

inorganic material such as silicon). Compatibility with well developed, high

performance inorganic electronic materials represents a key advantage in

this area. The main challenge here is to design inorganic materials (e.g.,

silicon) for stretchability, which might initially seem challenging since all

known inorganic semiconductor materials are brittle and fracture at strains

of the order of 1%.

one of the most intuitive approaches to avoid directly straining these brittle

materials exploits wavy shaped structures (Bowden et al., 1998; Khang et al.,

2006; Choi et al., 2007) to make these high-quality, single-crystal inorganic

semiconductor materials stretchable. Figure 14.1a illustrates one example

of this design, as applied to arrays of thin ribbons. The initially at ribbons

ThinFilm-Zexian-14.indd 340 7/1/11 9:45:14 AM



341Controlled buckling of thin ﬁ lms on compliant substrates

are bonded at all points on their bottom surfaces to a prestrained elastomeric

substrate. The prestrain can be induced by mechanical (or thermal) stretch

along the ribbon directions. When the prestrain is released, the ribbons are

subject to a compression that leads to a nonlinear buckling response and

forms a wavy pro le. The resulting wavy deformations have well-de ned

wavelengths and amplitudes that depend on the material properties and the level

of prestrain. Detailed theoretical analysis reveals all aspects of the mechanics

of formation of such structures. For small prestrain e

pre

, the wavelength l

0

= 2ph

f

[E

f

/(3E

s

)]

1/3

is independent of the prestrain. It is proportional to the

thickness of thin  lm h

f

, and depends only on the plane-strain moduli E

f

=

E

f

/(1 – n

f

2

) and E

s

= E

s

/(1 – n

s

2

) of the ribbon and substrate. The amplitude A

0

=

h

fp

re

c

/

c

/

c

1

ee

fp

ee

fp

re

ee

re

/

ee

/

–

increases with the prestrain e

pre

, where e

c

= (3E

s

/E

f

)

2/3

/4 is

the critical buckling strain (Huang et al., 2005; Khang et al., 2006). For large

prestrain e

pre

, both wavelength and amplitude depend on the prestrain e

pre

.

The wavelength given by l

0

/Î(1 + e

pre

)(1 + x)

1/3

˚ decreases with e

pre

while

the amplitude given by

A

0

/ 1 + (1 + )

pre

1/3

ex

Í

Î

˙

˚

increases with e

pre

(Song

et al., 2008b). The wavelengths and amplitudes of the waves can change

to accommodate strains in a way that involves small strain in the ribbons.

Following the same procedure to generate stretchable nanoribbons (Khang

et al., 2006), Choi et al. (2007) generated 2D wavy Si nanomembrane as

shown in Fig. 14.1(b). The Si nanomembrane is chemically bonded to a heated

poly(dimethylsiloxane) (PDMS) substrate which induces a controlled degree

of isotropic thermal expansion. Cooling to room temperature released the

thermally induced prestrain in PDMS, and formed the 2D wavy patterns on the

surface. Recent work by Kim et al. (2008a) demonstrated high-performance,

stretchable, and foldable integrated circuits (e.g., silicon complementary

logic gates, ring oscillators, and different ampli ers) using this strategy.

In a related strategy, the ribbons can be designed to bond to the elastomeric

substrate only at certain locations (Sun et al., 2006). When the prestrain is

released, the ribbon on the non-bonded regions delaminates from the substrate

and forms the one-dimensional non-coplanar design (Fig. 14.1c). Compared

to Figs 14.1(a) and (b), this layout has the advantage that the wavelengths

can be de ned precisely with a level of engineering control to have a higher

stretchability.

The other strategy uses stretchable interconnect bridges such as metal

wires to link the rigid device islands (i.e., interconnect-island structure)

(Lacour et al., 2005; Kim et al., 2008b, 2008c). Mechanical response to

stretching or compression involves, primarily, deformations only in these

interconnects, thereby avoiding unwanted strains in the regions of the active

devices. Lacour et al.

(2005) developed coplanar mesh designs by using the

wavelike interconnect bridges, which are bonded with the substrate. The

deformation of the interconnect bridge is similar to that in Fig. 14.1(a).

ThinFilm-Zexian-14.indd 341 7/1/11 9:45:14 AM



342 Thin ﬁlm growth

Although such a coplanar mesh design can improve the stretchability to

around 40%, the stretchability is still too small for certain applications and

large-scale integration can be difcult.

Sosin et al. (2008) showed that free-

standing copper interconnects can be used for stretchable electronics and the

stretchability can be a few hundreds percent. By adopting the ‘free-standing’

idea, Kim et al. (2008c) developed a two-dimensional non-coplanar mesh

design (Fig. 14.1d) consisting of device islands linked by ‘popup’ interconnect

bridges for stretchable circuits, which can be stretched to rubber-like levels

of strain (e.g., up to 100%). Recent work by Ko et al. (2008) demonstrated

a hemispherical electronic eye camera based on this non-coplanar mesh

design.

The fundamental aspects of stretchable coplanar nanoribbons (Fig. 14.1a)

and nanomembranes (Fig. 14.1b) such as the edge effect (Koh et al., 2007),

nite width (Jiang et al., 2008a), nite deformation (Song et al., 2008a), local

versus global buckling modes (Wang et al., 2008), and biaxial stretchability

(Song et al., 2008b) have been well studied and reviewed by Jiang et al.

2 µm

10 µm

50 µm

100 µm

(a)

(c)

(b)

(d)

14.1 SEM images of (a) stretchable nanoribbons, (b) stretchable

nanomembranes, (c) one-dimensional non-coplanar mesh design,

and (d) two-dimensional non-coplanar mesh design. Reprinted

Institute of Physics.

ThinFilm-Zexian-14.indd 342 7/1/11 9:45:15 AM



343Controlled buckling of thin ﬁlms on compliant substrates

(2008b) and Song et al. (2009a). This chapter provides a review on the

mechanics of non-coplanar mesh designs (Figs 14.1c and d). Section 14.2

reviews the mechanics of one-dimensional non-coplanar mesh design (Fig.

14.1c) and Section 14.3 describes the mechanics of two-dimensional non-

coplanar mesh design (Fig. 14.1d).

14.2 Mechanics of one-dimensional non-coplanar

mesh design

Figure 14.2 schematically illustrates the fabrication of one-dimensional non-

coplanar mesh designs for stretchable electronics on compliant substrates

(Sun et al., 2006; Jiang et al., 2007), which combines lithographically

patterned surface bonding chemistry and a buckling process. The ribbons

are fabricated from SoI wafers, which are patterned by conventional

photolithography using AZ 5214 photoresist and etched with SF

6

plasma.

After the photoresist is washed away with acetone, the buried oxide layer

is then etched in HF (40%). More details can be found in the paper by Sun

et al. (2006). Figure 14.2(a) shows the photolithography process that denes

the bonding chemistry on a pre-stretched PDMS substrate with prestrain

e

pre

= DL/L along the ribbon direction to form periodic interfacial patterns.

The patterning process creates selected regions with activated sites where

chemical bonding occurs between the ribbons (e.g., GaAs or Si) and the

PDMS substrate, as well as inactivated sites where there are only weak van

der Waals interactions. Let W

act

and W

in

denote the widths of activated and

inactivated sites, respectively (Fig. 14.2a). Thin ribbons are then attached to

the prestrained and patterned PDMS substrate (Fig. 14.2b) with the ribbon

direction parallel to the prestreched direction. The relaxation of the prestrain

in PDMS leads to the separation of the ribbons from the inactivated sites

on the PDMS (Fig. 14.2c). The wavelength of the buckled structures is

then given by 2L

1

= W

in

/(1 + e

pre

) due to the geometrical constrain, and the

amplitude A will depend on the geometries of the interfacial patterns (W

act

and W

in

) and the prestrain.

Jiang et al. (2007) developed an analytical model to study the buckling

behavior of such systems and to predict the maximum strain in the ribbons

as a function of interfacial pattern. The energy method is used to determine

the buckling geometry. The thin lm is modeled as an elastic nonlinear

von Kármán beam since the lm thickness is much smaller than the other

characteristic lengths and the strain in the lm is negligibly small (to be

shown later). The substrate is modeled as a semi-innite elastic solid because

its thickness (~mm) is much larger than the thickness of the lm (~mm).

The total energy of the system consists of the bending energy U

bending

due to

thin lm buckling, membrane energy U

membrane

in the thin lm and substrate

energy U

substrate

.

ThinFilm-Zexian-14.indd 343 7/1/11 9:45:15 AM



344 Thin ﬁlm growth

W

act

W

in

Inactivated

region

Activated

region

PDMS

(a)

(b)

(c)

L + DL

Thin

ﬁlm

x

2

x

1

A

2L

1

2L

2

L

14.2 Processing steps for precisely controlled thin ﬁlm buckling on

elastomeric substrate. (a) Prestrained PDMS with periodic activated

and inactivated patterns. L is the original length of PDMS and DL

is the extension. The widths of activated and inactivated sites are

denoted as W

act

and W

in

, respectively. (b) A thin ﬁlm parallel to the

prestrain direction is attached to the prestrained and patterned PDMS

substrate. (c) The relaxation of the prestrain e

pre

in PDMS leads to

buckles of thin ﬁlm. The wavelength of the buckled ﬁlm is 2L

1

, and

its amplitude is A. 2L

2

is the sum of activated and inactivated regions

after relaxation. Reprinted with permission from Jiang et al. (2007),

ThinFilm-Zexian-14.indd 344 7/1/11 9:45:15 AM



345Controlled buckling of thin ﬁ lms on compliant substrates

The buckling pro le of the ribbon can be expressed as

w

wA

x

L

Lx

L

w

=

wA =wA

1

wA

1

wA

2

wA

2

wA

1 + cos

,

Lx, Lx

1

wA

1

wA

1

2

p

1

11

Lx

11

Lx

,

11

,

Lx, Lx

11

Lx, Lx

11

Lx Lx

11

Lx Lx

1

Ê

Ë

Ê

Ë

Ê

Á

Ê

Ë

Á

Ë

Ê

Ë

Ê

Á

Ê

Ë

Ê

ˆ

¯

ˆ

¯

ˆ

˜

ˆ

¯

˜

¯

ˆ

¯

ˆ

˜

ˆ

¯

ˆ

-<

Lx-<Lx

, -<,

Lx, Lx-<Lx, Lx

Lx

11

Lx-<Lx

11

Lx

Lx, Lx

11

Lx, Lx-<Lx, Lx

11

Lx, Lx

<

= 0,

== 0,=

12

Lx

12

Lx

12

Lx

12

Lx

12

L

12

L

12

<<

12

<<

12

<<

12

Lx<<Lx

12

Lx

12

<<

12

Lx

12

Lx

12

<<

12

Lx

12

Ï

Ì

Ô

Ï

Ô

Ï

Ì

Ô

Ì

Ó

Ô

Ì

Ô

Ì

Ó

Ô

Ó

Ô

Ó

Ô

Ó

Ô

Ó

Ô

Ó

12112

12

<<

12112

<<

12

[14.1]

where A is the buckling amplitude to be determined, 2L

1

= W

in

/(1 + e

pre

)

is the buckling wavelength, and 2L

2

= W

in

/(1 + e

pre

) + W

act

is the sum of

activated and inactivated regions after relaxation (Fig. 14.2c). The bending

energy in the thin  lm can be obtained as

U

Eh

dw

dx

f

bending

L

f

Eh

f

Eh

3

2

dw

2

dw

1

2

1

=

1

21

2

=

2

–

Ú

–

Ú

–

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

2

4

p

96

9969

f

32

1

3

Eh

f

Eh

f

A

32

A

32

L

3

L

3

[14.2]

where h

f

is the  lm thickness, and E

f

= E

f

/(1 – n

f

2

) is the plane-strain modulus

of the  lm.

The membrane strain e

11

is related to the out-of-plane displacement w

and the in-plane displacement u

1

by e

1

= du

1

/dx

1

+ (dw/dx)

2

/2 – e

pre

. Huang

et al. (2005) showed that the shear stress at the  lm/substrate interface is

negligibly small. The force equilibrium gives a constant membrane force,

which requires a constant membrane strain e

11

given by

e

11

= p

2

A

2

/(16L

1

L

2

) – e

pre

[14.3]

Then we have the membrane energy in the  lm as

UE

h

A

LL

L

memb

UE

memb

UE

ra

UE

ra

UE

ne

UE

ne

UE

ff

UE

ff

UE

h

ff

h

pr

e

prepr

UE = UE

–

p

e

22

A

22

A

12

LL

12

LL

2

16

Ê

Ë

Ê

Ë

Ê

Á

Ê

Ë

Á

Ë

Ê

Ë

Ê

Á

Ê

Ë

Ê

ˆ

¯

ˆ

¯

ˆ

˜

ˆ

¯

˜

¯

ˆ

¯

ˆ

˜

ˆ

¯

ˆ

[14.4]

The relaxed PDMS has vanishing energy

U

substrate

= 0 [14.5]

because the substrate has zero displacement at the interface where remains

intact and vanishing stress traction at the long and buckled portion.

The buckling amplitude A is determined by energy minimization as

AL

L

AL =AL

4

AL

4

AL

(

)

, f

or

, for, f

or or

pr

ec

precpr

pr

ec

precpr

p

ee

–

ee

–

pr

ee

pr

ec

ee

ec

–

ec

–

ee

–

ec

–

precpr

ee

precpr

ee

pr

ee

pr

ee

pr

ec

ee

ec

ee

ec

precpr

ee

precpr

pr

ec

pr

ee

pr

ec

pr

12

L

12

L

>

ee

>

ee

ec

ee

ec

>

ec

ee

ec

[14.6]

where

ep

c

f

2

1

2

= /(12)hL

2

is the critical strain for buckling, which is identical to

the Euler buckling strain for a doubly clamped beam with length 2L

1

. When

e

pre

< e

c

, the  lm does not buckle and remains  at. Once the prestrain exceeds

the critical strain (i.e., e

pre

> e

c

), the  lm buckles to form the sinusoidal

waves. The critical strain e

c

is very small in most practical applications. For

ThinFilm-Zexian-14.indd 345 7/1/11 9:45:16 AM



346 Thin ﬁ lm growth

example, for the buckling wavelength 2L

1

~ 200 mm and ribbon thickness h

f

~ 0.1 mm, e

c

is on the order of 10

–6

. The buckling amplitude A in Eq. 14.6

then can be approximately by

AL

LW

WW

AL AL

4

AL

4

AL

LW =LW

(

LW (LW

WW +WW

)

WW )WW

/(

1 +

pr

LW

pr

LW

ei

LW

ei

LW

LW =LW

ei

LW =LW

(

ei

(

ei

(

LW (LW

ei

LW (LW

ei

LW (LW

ei

LW (LW

preipr

LW

pr

LW

ei

LW

pr

LW

ni

WW

ni

WW

(

ni

(

n

WW

n

WW

act

)

act

)

WW )WW

act

WW )WW

pr

ep

/(

ep

/(

preppr

r

ALªAL

p

e

LW

e

LW

p

ei

p

ei

(

ei

(

p

(

ei

(

ee

/(

ee

/(

1 +

ee

1 +

pr

ee

pr

ep

ee

ep

/(

ep

/(

ee

/(

ep

/(

1 +

ep

1 +

ee

1 +

ep

1 +

preppr

ee

preppr

12

LW

12

LW

2

(

2

(

LW (LW

2

LW (LW

eee

rererer

)

[14.7]

which is completely determined by the interfacial patterns (W

in

and W

act

) and

the prestrain. Figure 14.3 shows the pro les (dashed lines) of buckled GaAs

ribbons given by Eqs 14.1 and 14.6 for different prestrain levels for W

act

= 10 mm and W

in

= 190 mm. The experimental images are also shown for

comparison. Both wavelength and amplitude agree well with experiments.

The maximum strain in the  lm is the sum of membrane strain and bending

strain. Since the membrane strain e

11

is negligible (~10

–6

), the maximum

strain in the ribbon can be approximated by the bending strain which is given

by

e

p

e

peak

f

1

2

f

1

2

pr

e

prepr

=

m

f

m

f

ax

=

h

dw

dx

h

L

2

L

2

LL

2

m

2

m

2

dw

2

dw

12

LL

12

LL

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

[14.8]

The maximum strain is much smaller than the prestrain. For example, for h

f

= 0.3 mm, W

act

= 10 mm, W

in

= 400 mm, and e

pre

= 60%, e

peak

is only 0.6%,

100 µm

W

act

= 10 mm, W

in

= 190 mm

Prestrain

11.3%

25.5%

33.7%

56.0%

14.3 Buckled GaAs thin ﬁ lms on patterned PDMS substrate with

W

act

= 10 mm and W

in

= 190 mm for different prestrain levels, 11.3%,

25.5%, 33.7%, and 56.0% (from top to bottom). The dashed lines are

the proﬁ les of the buckled GaAs thin ﬁ lm predicted by the analytical

solution. Reprinted with permission from Jiang et al. (2007)

ThinFilm-Zexian-14.indd 346 7/1/11 9:45:17 AM



347Controlled buckling of thin ﬁ lms on compliant substrates

which is two orders of magnitude smaller than the 60% prestrain. Therefore,

the one-dimensional non-coplanar mesh design can signi cantly reduce

the maximum strain in thin ribbon, and improve the system stretchability.

Moreover, this small strain ensures that the von Kármán beam assumption

for the  lm is always valid in this study. For much smaller active region

(i.e., W

act

<< W

in

), the maximum strain in Eq. (14.8) can be approximated

by

e

p

e

peak

f

1

pr

e

prepr

ª

h

L

.

It should be pointed out that, for very long inactivated region, buckling

pro les different from Eq. 14.1 have been observed in experiments. For

example, two or three short waves with wavelength about 100 mm, instead

of a long wavelength 2L

1

= W

in

/(1 + e

pre

) = 586 mm, have been observed in

experiments for W

in

= 760 mm and e

pre

= 33.7%. The thin  lm and substrate

remain bonded between the short waves. The analysis of this different

buckling mode can be found in the paper by Wang et al. (2008).

14.3 Mechanics of two-dimensional non-coplanar

mesh design

Figure 14.4 schematically illustrates the fabrication of a two-dimensional

non-coplanar mesh design for stretchable electronics on compliant substrates

(Kim et al., 2008c). The silicon (or other semiconductor material) islands,

on which the active devices are fabricated, are chemically bonded to a

prestrained (e.g., 50%) elastometric substrate poly(dimethylsiloxane)

(PDMS). The interconnect bridges between islands are loosely bonded to

the substrate. Releasing the prestrain leads to compression, which causes

the interconnect bridges to buckle out of the substrate surface and form

arc-shaped structures. The out-of-plane deformation localizes only to the

interconnect bridges because of their poor adhesion (to PDMS), narrow

geometries and low stiffness (compared to device islands). This gives

very small strain in islands, which leads to stretchability of the system of

device islands and interconnect bridges. The practical use of the non-coplanar

mesh design requires an additional encapsulation layer on the top surface

to provide mechanical and environmental protection (Kim et al., 2009).

A compliant encapsulation layer must be used in order not to restrict free

motion of the buckled interconnects, and therefore not to reduce the

stretchability.

Song et al. (2009b) and Wu et al. (2010) established mechanics models to

understand the underlying physics and to guide the design of such systems.

The analysis for pre-encapsulation is presented in Section 14.3.1 and the

analysis for post-encapsulation is discussed in Section 14.3.2.

ThinFilm-Zexian-14.indd 347 7/1/11 9:45:18 AM



Cao Z. (Ed.) Thin Film Growth: Physics, materials science and applications

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