The effect of pitch on deformation behavior and the stretching-induced failure of a polymer-encapsulated stretchable circuit

The effect of pitch on deformation behavior and the stretching-induced failure of a polymer-

encapsulated stretchable circuit

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2010 J. Micromech. Microeng. 20 075036

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J. Micromech. Microeng. 20 (2010) 075036 (11pp) doi:10.1088/0960-1317/20/7/075036

The effect of pitch on deformationbehavior and the stretching-inducedfailure of a polymer-encapsulatedstretchable circuitYung-Yu Hsu1,2,4, Mario Gonzalez1, Frederick Bossuyt3, Fabrice Axisa3,Jan Vanfleteren3 and Ingrid De Wolf1,2

1 IMEC, Kapeldreef 75, 3001, Leuven, Belgium2 Department of Materials Engineering, K.U. Leuven, Belgium3 IMEC-CMST, Gent-Zwijnaarde, Belgium

E-mail: [email protected]

Received 21 December 2009, in final form 26 April 2010Published 17 June 2010Online at stacks.iop.org/JMM/20/075036

AbstractThe deformation behavior and failure mechanisms of parallel-aligned, horseshoe-patterned,stretchable conductors encapsulated in a polymer substrate were investigated by numerical andexperimental analyses. A design guideline for the optimal pitch between the conductors wasproposed through numerical analysis, and two extreme cases—fine and coarse pitches—wereinvestigated by in situ experimental observations. The experimental results demonstrate thatthe stretchable conductors enable elongation up to 123 and 135% without metal rupture for thefine and coarse pitches, respectively. The difference between these numbers is much smaller(12%) than expected from the simulations. It is found and confirmed by a modified simulationmodel that the reason for this is interfacial delamination, the onset of which depends on thepitch of the conductors and occurs before metal rupture of the conductors. The definition of‘stretchability of the electronic interconnects’ is discussed based on the facts that two differentfailure mechanisms occur: interfacial delamination and metal rupture.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Electronic systems with deformability such as bending,twisting and stretching have great potential for use inapplications which are hard to cover with conventionalstiff semiconductor microelectronics. One of the attractiveapplications is in the area of biomedical systems. Thesebiomedical systems, such as electroencephalographic (EEG),electrocardiographic (ECG), photodetector [1, 2] andimplantable devices [3], are usually composed of rigidelectrodes and metal wires for connecting or transmittingelectrical signals. However, their limited deformabilityis neither comfortable nor durable for long-term in situmonitoring, and therefore, an improvement of the

4 Author to whom any correspondence should be addressed.

deformability of such systems is needed. In order to achievehigh deformability, hybrid systems are proposed. These hybridsystems are usually composed of rigid or bendable elements(such as thinned silicon dies) connected through stretchableelectrical conductors, both embedded in a stretchablesubstrate for mechanical protection and chemical isolation.Since the stretchable conductors have to withstand most ofthe deformations, a reliable design is essential to avoid losingelectrical performance and structural integrity.

Several technologies for stretchable metal conductorshave been proposed in recent years, such as out-of-plane,wavy or wrinkling conductors [4–8] and coplanar-patternedmetal conductors [9, 10]. It has been reported that bydepositing a nanometer thick thin metal film on top of astretchable substrate, even a straight line remains conductivewhen stretching up to 50% elongation [11, 12]. However, this

0960-1317/10/075036+11$30.00 1 © 2010 IOP Publishing Ltd Printed in the UK & the USA

J. Micromech. Microeng. 20 (2010) 075036 Y-Y Hsu et al

nanometer thick metal film as well as the wrinkling conductorhas an unstable electrical resistance due to microcracking.

An alternative technology involving in-plane patternedbulk metal conductors has been proved to have a stableelectrical performance when stretching [13–17]. The ideaof this coplanar technology is to have the metal conductoracting like a spring while stretching. In this way, the inducedpermanent deformation in the metal is very low even when alarge deformation is applied to the circuit. In addition, currentconventional planar microfabrication technology can be easilyemployed for realization of these stretchable conductors. Thisallows reducing the cost, which is one of the major concernsin industry.

In this paper, we comprehensively investigate thedeformation behavior and failure mechanisms of planarhorseshoe-shaped stretchable electrical conductorsencapsulated in a stretchable polymer substrate throughboth numerical analysis and experiments. First, numericalanalysis of the metal conductors was done to provide designguidelines (design for reliability) based on an evaluation ofthe plastic strain in the metal. Two cases from the designguidelines were chosen for further modeling and experimentalstudies. To investigate the failure mechanisms, the stretchingbehavior of the metal conductor was recorded in situ andcorrelated with numerical analysis. A modified numericalmodel was implemented to understand the difference betweenthe experiments and the first numerical analysis’ results.These results lead to a discussion on the commonly useddefinition of ‘stretchability of the electronic interconnects’and a new definition is proposed.

2. Numerical modeling

Figure 1 illustrates the horseshoe-patterned metal conductorsencapsulated in an elastomeric substrate. The metalconductors are completely (above and below) encapsulated andreside in the center of the polymer substrate along the thicknessdirection. For visual clarification, only three parallel-alignedinterconnects are shown in the figure. The angle (θ ) of eachmeander of the patterned metal conductor is 120◦. The width(wCu), thickness (tCu), and radius (rCu) of the metal track are0.1, 0.018 and 0.75 mm, respectively. The substrate is a blockwith W sub = 20 mm width and Tsub = 1 mm thickness. Thelength of the substrate depends on the number of repeatingmeander units. Uniaxial elongation ‘u’ is applied to thesubstrate at one end and the other end is assumed to be asymmetrical plane (boundary condition for the simulations, seefigure 1), which corresponds to the experimental conditions.The commercial finite element code, MSC.MARC R©, wasused to simulate the deformation process and to calculate thedifferent stress and strain components. The metal used in thisresearch is copper and is modeled as a plastically deformablesolid, obeying the bi-linear isotropic hardening rule, with theelastic Young’s module E0 = 117 GPa, the yielding point atσy = 0.1723 GPa and the tangent module Et = 1.0342 GPa.The elastomeric substrate is modeled as an incompressible,hyperelastic Neo-Hookean solid [18] with C10 = 0.157.

Figure 1. Schematic illustration of horseshoe-patterned metallicconnectors encapsulated in a stretchable polymeric substrate.

3. Sample preparation

Polydimethylsiloxane (PDMS) (Sylgard 186 R©, Dow Corning)was chosen as the elastomeric substrate. A 0.018 mmthick, commercially available Cu foil was used for the metalconductor. This foil was used because of its low cost andstable, large area fabrication capabilities. Before adheringthe Cu to the PDMS, a potassium monopersulfate solutionwas used for microetching the copper surface. This is toincrease the Cu roughness and thus improve the otherwiseweak adhesion between the Cu foil and the PDMS.

The surface of the copper foil was 2 μm in roughness asmeasured by an optical interferometer. The prepared copperfoil was then temporarily adhered to a 0.5 mm thick Teflonmold, with an opening window for casting the PDMS ontop of the copper foil. The PDMS was prepared at roomtemperature in a 10:1 weight ratio of the polymer base andcuring agent. After degassing, the PDMS was poured inthe Teflon window and cured at 60 ◦C for 12 h. Then,the Cu/PDMS laminate was released from the Teflon mold,and placed on top of the ceramic carrier. Both conventionalphotolithography and wet etching processes were employedfor patterning the horseshoe structure in the Cu. Next, thesample was placed on a mold with the metal layer facing upand PDMS was poured in to encapsulate the horseshoe metallayer. A metal blade was used to squeeze out the excessPDMS. The PDMS/Cu/PDMS structure was then cured at60 ◦C for 12 h. In the final step, the structure was cut into20 × 70 mm strips. Each strip has five parallel-aligned, PDMS-encapsulated, horseshoe-patterned stretchableinterconnects. All interconnects are connected to tworectangular pads on both ends. In this way, only one channelfor in situ electrical resistance measurement is required, and,if there is any metal breakdown during stretching, the circuitsremain functional but the resistance increases step wise. Theelectrical resistance goes to infinite only when all the fivestretchable interconnects fail. Figures 2(a) and (b) show the

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(b)(a)

Figure 2. Horseshoe-patterned polymer-encapsulated stretchable interconnects with rectangular pads on two ends for electrical connection.(a) Fine pitch case, (b) coarse pitch case.

(a) (b)

Figure 3. Finite element meshes before stretching. (a) Fine pitch case, (b) coarse pitch case.

flexibility of the samples with two different pitches. The line-to-line pitch corresponds to the two cases in the numericalmodeling, which are 1.8 mm (fine pitch) in figure 2(a) and3.0 mm (coarse pitch) in figure 2(b).

4. Result and discussion

4.1. Mechanical modeling on pitch effect

The effect of the pitch on the mechanical behavior ofthe parallel-aligned stretchable interconnects is investigatedthrough numerical modeling. Figures 3(a) and (b) show thefinite element meshes with fine and coarse pitches in therelaxed state (i.e. non-stretched). The part shown correspondsto the middle block of the real horseshoe-patterned stretchablesample in the experiment. The Cu interconnect is fullyembedded in the substrate at its center, along the thicknessdirection. A displacement (u) of up to 50% elongation isapplied at one end surface in the numerical models, and thesimulated maximum equivalent plastic strain in the metal isused for further analysis. Figure 4 shows the maximumplastic strain in the Cu interconnect as a function of therelative elongation. Seven models with different line-to-linepitches starting from 1.8 mm up to infinity were simulated.It is found that the maximal plastic strain in the metalinterconnect remains approximately zero when stretching upto 3% elongation. This point is defined as the onset point of

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plastic strain, which starts accumulating in the metal. Beyondthis onset point, the plastic strain goes nonlinearly up to 6.8%when the line-to-line pitch is 1.8 mm and the elongation is 50%.The mechanical behavior and the plastic strain for the sevenmodels follow a similar trend; only the magnitude of the plastic

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Figure 5. Maximum equivalent plastic on the metal as a function ofline-to-line pitch of stretchable circuits. Two insets indicate themasks of the two study cases for further analysis and fabrication.

strain is different. Figure 5 shows the maximum plastic strainat 50% elongation as a function of line-to-line pitch. It is foundthat the maximal plastic strain drops drastically in the rangeof line-to-line pitch from 1.8 to 3.0 mm and after the 3.0 mmline-to-line pitch, the plastic strain in the metal is not modifiedvery much. Thus, this curve can be divided into two sections,zone I and zone II. Zone I represents the zone where theplastic strain goes from a high to a steady state. Zone II is thesteady state zone. In other words, zone I indicates the highlyrisky zone in terms of plastic strain, i.e. permanent damage inthe metal for parallel-aligned stretchable circuits. Therefore,to have high stretchability of such interconnects, one has toavoid a line-to-line pitch within zone I but design the circuits

Figure 6. Geometrical opening and plastic strain distribution on the deformed horseshoe-patterned stretchable interconnect.

with the line-to-line pitch in zone II. This consideration andanalysis provide an important design guideline for the futuredevelopment of these particular stretchable circuits.

Figure 6 shows the shape of one horseshoe of the metalconductor. It shows the in-plane geometrical opening as wellas the plastic strain distribution in the metal when stretchingto 50% elongation. The plastic strain accumulates in the crestof the horseshoe-patterned metal conductor, which is for thisreason the expected failure location when stretching up tothe rupture strain. The maximum plastic strain resides at theinner part of the crest. This plastic strain concentration comesfrom the in-plane geometrical opening. In figure 6, lines Aand B indicate distances before stretching, while lines A′ andB′ indicate distances at the same position of the metal afterstretching to 50%. The calculated distance change at thesetwo positions as a function of the line-to-line pitch is givenin figure 7. It is found that A increases by 81% while Bincreases by 26% at the maximum investigated line-to-linepitch of 20 mm. This indicates that the elongation mainlycomes from the in-plane geometrical opening of the meandersand that the position of line A plays a major role, especially atthe opening. Moreover, this distance increase can be dividedinto two sections which correspond to zone I and zone II asdefined in figure 5. In zone I, i.e. the highly risky zone, thedistance A increases with increasing line-to-line pitch whereasdistance B decreases. This is because the small line-to-linepitch induces a constraint interaction between parallel-alignedmetal lines, and as a result, the distance A has less freedom,with a geometrical opening in zone I compared to zone II. Sincethe elongation mainly comes from an in-plane geometricalopening and line A is constrained between parallel-alignedmetal lines, line B has to accommodate more geometricalopening in zone I than in zone II. Consequently, a higherplastic strain is introduced due to longitudinal elongation onthe crest of each repeating meander. This is confirmed in

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Figure 7. Geometrical opening percentage as a function ofline-to-line pitch of one single stretchable interconnect subjected to50% elongation. The inset indicates two lines of interest, A and B,for further analysis.

figure 8, in which the maximum plastic strain along the metalinterconnect is plotted as a function of the curve length of oneunit meander. Because of longitudinal (tensile) elongationon the crest of the meander, positions (a), (d) and (g) havea higher plastic strain concentration than positions (b), (c),(e) and (f), where the plastic strain is mainly from the localbending. In order to understand the difference in plastic straindistribution between the most critical case and the ‘normal’case, the plastic strain distributions in the 1.8 mm line-to-line pitch (LtLP18) sample and the 3.0 mm line-to-line pitch(LtLP30) sample are compared in this figure. It is foundthat the plastic strain distribution for the two above-mentionedpitches follows a similar pattern with a difference only inthe magnitude of the plastic strain. A difference of 22% isobserved between the peaks of plastic strain (regions (a), (d)and (g)). This corresponds to what was shown and discussedin figure 5. Combining the analyses of figures 5, 6 and 8, onecan expect that the potential failure due to plastic strain in theCu interconnects is initiated at the inner part of every crest ofthe meanders and moreover, a small line-to-line pitch designhas a higher possibility to cause an early failure due to theconstraint interaction.

Besides metal breakdown, interfacial delaminationinduced by in-plane shear stress has been reported as one ofthe major failure modes of stretchable interconnects [16]. Topredict the possible interfacial failure location, figure 9 plotsthe in-plane shear stress contour in the substrate of a 50%stretched LtLP30 sample. It is found that the in-plane shearstress in the substrate concentrates alongside the horseshoe-patterned interconnect, and consequently, creates potentialinterfacial failure at the location where the highest in-planeshear stress is.

4.2. In situ observation of deformation behaviors

In order to experimentally investigate the effect of the pitchon the failure onset of stretchable circuits, one ‘critical’ case

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sample with 1.8 mm line-to-line pitch (LtLP18) and one‘normal’ case sample with 3.0 mm line-to-line pitch (LtLP30)were fabricated and tested. These two cases are depicted infigure 5, in which the two insets illustrate the masks usedfor sample fabrication and indicate the predicted maximumplastic strain level in the metal circuits when stretching to50% elongation. The deformation processes and failuremechanisms of these samples subjected to uniaxial stretchingwere investigated using a home-built tensile tester andin situ monitored by a high-resolution Hirox KH-7700 opticalmicroscope. All tests were performed at room temperaturewith a constant strain rate of 2.5 × 10−4 s−1. During tensiletesting, the electrical resistance of the patterned metal circuitswas recorded every 0.5 s by an Agilent 34420A multimeter.A four-point resistance measuring technique was employed inthe testing so that the resistance of the connecting wires canbe neglected. Since the deformation and failure mechanismsare similar between LtLP18 and LtLP30 samples, only imagesfrom the LtLP18 sample will be shown in the later analysis.

Figures 10(a) to (f ) show a sequence of in situobservations on stretched LtLP18 samples, starting at 0%up to 100% elongation. By examining these images, twodeformation mechanisms can be observed.

(1) Localized substrate thinning identified by a growinglight/gray color in the area near the crests of the meanders.

(2) Uniaxial geometrical opening of the meanders in thestretching direction, evidenced by the changing lengthof LA and LB to L′

A and L′B .

In order to verify the first deformation mechanismmentioned above, change in reflecting light because ofthe localized substrate thinning instead of an out-of-plane deformation of the metal, both optical interferometry(figure 11(a) top-view and bottom right; figure 11(b) cross-sectional view) and finite element simulation (bottom leftfigure 11(b)) were used to obtain the surface topography ofa LtLP18 sample stretched to 100% elongation. The colorsof the finite element meshes indicate the deformation gradient

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Figure 9. In-plane shear stress contour in the substrate of the LtLP30 sample subjected to 50% elongation.

(a) (b) (c)

(d) (e) ( f )

Figure 10. Optical images taken in situ while stretching to (a) 0%, (b) 20%, (c) 40%, (d) 60%, (e) 80%, (f ) 100%.

in the thickness direction. It is found that the surface has aregularly parallel-arranged wavy profile. The hills representthe areas where the crests of each meander reside and thevalleys indicate the local thinning of the PDMS substrate. Theamplitude indicates the height difference between the substrateand the crests. This surface topography can be explained by thedifferent Poisson’s ratio of the materials. When the substrateis stretched in the longitudinal direction, the PDMS materialcontracts not only in the transversal direction, i.e. along thewidth, but also in the thickness direction. However, the metalinterconnects do not contract in the thickness direction butconstrain the substrate thinning alongside them and thereforecreate thickness variations, which is observed as the lightreflection changes in the optical images, as shown in figure 10.It is also observed that the more the elongation, the more the

significance of the substrate thinning, and as a result, the morepronounced the height differences.

4.3. In situ electromechanical behavior and failuremechanism analysis of the stretchable circuits

To observe the failure mechanism of these polymer-encapsulated stretchable conductors, a home-built tensiletester along with an electrical measurement setup was mounteddirectly under a high-resolution Hirox KH-7700 digitalmicroscope. Uniaxial stretching was applied to the stretchabledevices and in situ resistance and images were continuouslyrecorded until metal rupture (infinite resistance). Figure 12shows the normalized resistance (R/R0) obtained from theelectrical measurements, and the onset point of the interfacialdelamination obtained from optical images, as a function of

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(b)

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Figure 11. Surface topography of the LtLP18 sample stretching to 100% elongation obtained from optical interferometry and finite elementmodeling: (a) top view, (b) 3D cross section view of deformed finite element meshes and surface topography.

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relative elongation. It is shown that the LtLP18 and LtLP30samples have a maximum elongation to break (MEB) of 123and 135%, respectively. The electrical resistivity in the twocases remains constant, i.e. un-changed relative to the initial

resistance, until electrical failure. Furthermore, it is foundthat all the five parallel-aligned stretchable circuits on eachone of the LtLP18 and LtLP30 samples failed at the samemoment and the same location, as shown in figure 13. Theinset shows a magnified view of the fracture. If the stretchablecircuits would fail one by one, the resistance will have a gradualincrease, instead of one infinite jump as seen in figure 12.

It is also noted from figure 12 that there is only a 12%difference in elongation until metal rupture between the finepitch (LtLP18) and coarse pitch (LtLP30) cases. This smalldifference is rather unexpected. According to the numericalresults, a larger difference in ultimate relative elongation isexpected since there is 22% difference in plastic strain in themetal when stretching to 50% (see figure 5). The reason forthis difference between experimental results and numericalsimulations is interfacial delamination. As shown in figure 10,and more clearly in figure 13, the Cu breaks but there isalso delamination between the PDMS substrate and the Cu.This delamination takes place before the Cu breaks, as shownin figures 14 and 15. It is believed that this interfacialdelamination contributes to the overall relative elongationand thus reduces the plastic strain in the metal. In order toprove this assumption, the numerical models were adoptedand interfacial delamination was introduced at the side wallsof the meanders, corresponding to the delaminated location as

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Figure 13. Metal breakdown at 123% elongation of the LtLP18 sample. The inset shows the enlarged metal fracture.

Figure 14. Onset of the interfacial delamination at 35% elongation of the LtLP18 sample.

observed in reality. The detailed modeling analysis will bediscussed in a later section.

From the optical images it was deduced that the onset ofthe interfacial delamination on LtLP18 and LtLP30 samplesis at 35 and 68% elongation, respectively, as indicated infigure 12. It is noted that at these two values of elongation,the stretchable samples were still fully functional (no Cubreakage), i.e. no resistance change was detected. Thedifference of the onset point of the delamination betweenthe two samples is mainly caused by the local stiffnessand constraint effect from parallel-aligned meanders. Sincethe LtLP18 sample has less substrate material in the areawhere meanders are close to each other, the local stiffness

is higher and the constraint effect is more significant thanfor the LtLP30 case. Therefore, the LtLP18 sample has anearlier onset of the interfacial delamination at stretching to35% elongation. Figure 14 shows the image taken at theonset of the interfacial delamination of the LtLP18 samplewhen subjected to 35% stretching. It is observed that theinterfacial delamination indeed initiated at the closest locationbetween the metal interconnects and delaminated mostly inthe mode I opening. When stretching to a higher elongation,the interfacial delamination propagated along the interfacebetween the meanders and substrate, and at that moment, notonly the mode I but also the mode II shear fracture becameinvolved in the delaminating process. A more quantitative

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(b)(a)

Empty chamber

Figure 15. (a) Optical image of deformation behavior and the failure mechanism of the LtLP18 sample. (b) Three-dimensional schematicillustration of creation of empty chambers by severe interfacial delamination.

analysis in fracture mechanics will be carried out in futurework.

Figure 15(a) shows an optical image of the LtLP18sample stretched to 100% elongation. It is clearly shownthat there is a severe interfacial delamination deforming in anS-shape between the metal interconnects and the substrate.Moreover, by looking in more detail, one can find thatfibrillation is involved in the delamination process. Thisfibrillation is a proof that the delamination not only occursat the interface but also involves material cratering. As aresult of this, ‘empty chambers’, as indicated in figure 15(b),are created within this particular device. Because of thesedelamination and ‘empty chambers’ observations, one shouldquestion the commonly used definition of the so-calledstretchability of the electronic interconnects. While themajority of researchers in this field define electrical failureas the failure criteria, one may overestimate the ‘stretchabilityof the electronic interconnects’ of a stretchable device. Indeed,once the interfacial delamination is initiated in the deviceand thus empty chambers are introduced, this part is nolonger protected by the polymer, and will form a weak linkin the sample. Consequently, humidity, salt corrosion andmany other environmental effects might diffuse through thesubstrate [19] and cause early metal failure on the stretchabledevices. From this practical point of view, we redefine thestretchability of the LtLP18 and LtLP30 samples as 35 and68%, respectively, which are the onset points of the interfacialdelamination.

4.4. Interfacial delamination modeling

From the discussion in the previous section, it is foundthat the interfacial delamination contributes to the overallstretchability. Consequently, the plastic strain in the metalis different than expected if no delamination takes place. Thisphenomenon suggests that not only the plastic strain in themetal has to be taken into account during the stretching processbut also possible interfacial delamination. To study this, a‘pre-existing’ interfacial delamination was applied in the finiteelement models. With ‘pre-existing’, we mean delamination

that was there even before stretching. This assumption isdone because simulation of the delamination process is verycomplicated and needs further study.

For this first estimation, the delaminated location isdefined corresponding to the experimental image. Figure 16(a)illustrates a schematic diagram of the pre-existing interfacialdelamination at the meanders. The ‘Ldel’ denotes the length ofone single interfacial delamination. Next, uniaxial elongationwas applied for 10% on the two end surfaces, and thedeformation process and plastic strain in the metal wererecorded. It is found that when applying 10% stretching in thefinite element models, the pre-existing interfacial delaminationopened, and thus, created empty chambers, as shown infigure 16(b).

Figure 17 plots the maximum plastic strain in the metal at10% stretching as a function of the percentage of pre-existinginterfacial delamination, calculated by Ldel/L0 × 100%, whereL0 is the length of one unit meander. The percentage of pre-existing interfacial delamination starts from zero, which meansno interfacial delamination occurred during the stretchingprocess, and reaches a maximum of 63%. It is found thatif there is no interfacial delamination and the meander isstretched for 10% elongation, there is a 22% difference inthe maximum plastic strain between the LtLP18 and LtLP30cases, which can also be deduced from figure 5. This ideal casesuggests that the LtLP18 sample should have a significantlyearlier electrical failure than the LtLP30 case. However, byapplying the pre-existing interfacial delamination, it is foundthat as the length of the interfacial delamination grows, themaximum plastic strain reduces and eventually approaches thesame value for the two samples when 63% of the meander isdelaminated. This phenomenon is explained by the releasinglocal constraint in the position of line A from figures 6 and7, particularly for the LtLP18 case. It is noted that themore the delaminated length along the meander, the less theconstraint effect between parallel-aligned stretchable circuits.In other words, the interfacial delamination contributes theelongation, resulting in empty chambers and compromisingthe plastic strain concentration on each crest of the meanders.Consequently, the LtLP18 and LtLP30 cases have only a 12%

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Figure 16. (a) Schematic illustration of the pre-existing interfacial delamination. (b) Finite element meshes stretching for 10% elongation.

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Figure 17. Maximum equivalent plastic strain on a metal as afunction of length of the pre-existing interfacial delamination. Twocases (LtLP18 and LtLP30) are shown here corresponding to theexperimental cases.

difference in their maximum elongation, as measured by theelectrical failure as shown in figure 12.

5. Conclusions

In summary, the deformation behavior and failuremechanisms of horseshoe-patterned, parallel-aligned andpolymer-encapsulated stretchable conductors were analyzedby numerical simulations and experimental investigations. Bychanging the line-to-line pitch from the minimum 1.8 mm toinfinity, the maximum plastic strain in the Cu interconnectdrops by 22% and therefore creates a transition from a highlyrisky zone to a steady state zone. A design guideline wasproposed based on the transition zones. The simulation resultsindicated that the crest of the meander is the weakest pointwhere potential metal failure will occur during stretching.This was confirmed by in situ electromechanical observations.

Our experiments showed that the 1.8 mm and 3.0 mm line-to-line pitch sample could be stretched up to 123 and 135%without electrical failure, respectively. However, before theelectrical failure due to the breaking of the Cu meander at thecrest, interfacial delamination took place. This new failuremechanism made us question the definition of ‘stretchabilityof the electronic interconnects’, which is commonly based onelectrical resistance changes. If the onset of the delaminationis taken as a definition of stretchability, the LtLP18 and LtLP30samples can be stretched to 35 and 68%, respectively, whichare much lower numbers than the electrically measured 123and 135% elongation.

It is confirmed through numerical analysis thatthe interfacial delamination contributes to the maximumelongation and reduces the maximal equivalent plastic strainin the Cu meander at a certain elongation. By applying thepre-existing interfacial delamination, the maximum plasticstrain indeed drops as the length of the pre-existing interfacialdelamination grows.

The above analysis and results show that not only thepitch effect but also the interfacial delamination have to betaken into consideration when evaluating the performanceof stretchable devices. Future studies will focus on thisdelamination behavior. This will allow us to further understandand improve the reliability of the horseshoe-patterned andpolymer-encapsulated stretchable circuits.

Acknowledgement

This work was supported by the European Commission, underthe STELLA research project (contract number 028026).

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