Stretchability dependency on stiffness of soft elastomer encapsulation for polyimide-supported copper serpentine interconnects

For conventional flexible printed circuit board widely used in industry, jointing islands of electric components with polyimide-supported copper serpentine interconnects is an effective approach to ensure circuit stretchability. The stretchability of the interconnects varies significantly due to the soft elastomer encapsulating the interconnect, as the encapsulation essentially constrains the lateral buckling of the serpentine structure during stretching. Previous studies have indicated that thin encapsulation with a low Young’s modulus is required to maximize stretchability. However, extremely low modulus and thinness lead to the elimination of the encapsulation function, and the design criteria for maximizing stretchability while maintaining adequate modulus and thickness are still unclear. This study investigates the dependence of stretchability on encapsulation stiffness, an index that simultaneously considers modulus and thickness. The interconnects with core–shell and single-elastomer encapsulations, each with a different stiffness, were prepared. The relationships between the elongation to failure of the interconnect and the tensile and bending stiffness of the encapsulation were investigated through experiments and finite element method calculations. The results indicate that the tensile stiffness is a more useful index in encapsulation design than the bending stiffness because the elongation to failure monotonically decreases as the tensile stiffness increases. The results also indicate that the required tensile stiffness to maximize interconnect stretchability, essentially making the interconnect almost freely deformable, ranges from 5 to 34 N m−1 when the interconnects use an 18 μm thick copper and 50 μm thick polyimide.


Introduction
Stretchable electronics have attracted significant attention due to the massive potential for use in applications such as biological monitoring on human skin [1][2][3][4][5], human-machine interaction [6][7][8][9], and energy harvesting on complex surfaces [10][11][12][13].Although numerous related technologies have been developed, providing stretchability to circuits while maintaining their performance and functionality remains a challenge.Joining islands of electric components with serpentine interconnects is an effective approach to ensure stretchability to conventional flexible printed circuit boards based on copper and polyimide, which are widely used in industry [1-3, 14, 15].The stretchability of polyimide-supported copper serpentine interconnects is much differed by their buckling behavior during stretching.The buckling behavior exhibits several modes, including wrinkle (out-of-plane multi-waving) buckling, lateral (outof-plane coupled bending and twisting) buckling, and in-plane bending, depending on the geometric and material parameters [16,17].If the thickness of the copper and polyimide ranges from several tens to hundreds of nanometers, wrinkle buckling occurs in many cases.This study primarily focuses on conventional flexible printed circuit boards that use copper and polyimide with thickness in the range of several micrometers or more.Therefore, the primary areas of investigation are the lateral buckling and in-plane bending.
When such a serpentine structure experiences large lateral buckling, a relatively small internal strain occurs compared to cases of small lateral buckling or in-plane bending [18].Generally, interconnects are encapsulated in a sheet of soft elastomers, such as silicone and polyurethane elastomers, for protection against mechanical and chemical damages, shape support, and reversible response to applied stretching.Encapsulation directly affects the displacement of lateral buckling and essentially constrains the buckling.It has been reported that an encapsulation/substrate with a lower Young's modulus results in an increase in the interconnect stretchability in terms of elongation and the number of cycles to failure [7,[18][19][20].Some related studies have proposed core-shell encapsulation, wherein interconnects are encased in an ultra-low modulus elastomer such as a silicone gel (core elastomer) and subsequently enclosed in silicone elastomers (shell elastomer) [1][2][3]21].Additionally, the encapsulation thickness also affects stretchability, and previous studies have indicated that a thinner encapsulation/substrate is more suitable because lateral buckling is less constrained [22][23][24].Hence, the impact of each modulus and thickness on stretchability has been investigated independently in previous studies for both core-shell and single encapsulations.It has been found that thin encapsulation with a low modulus is required to maximize the stretchability.However, the extremely low modulus and thinness can lead to easy breaking, eliminating the encapsulation function.The design criteria for encapsulation to maximize stretchability while maintaining adequate modulus and thickness remain unclear.
This study focuses on the stiffness of soft elastomer encapsulation, which is an index that simultaneously considers the Young's modulus and thickness.When lateral buckling of a serpentine interconnect occurs during stretching, local stretching and bending are induced in the encapsulation around the interconnect, and wavy surface topography is observed [22,25].We considered that a lower stiffness leads to less constrained lateral buckling, eventually resulting in buckling behavior similar to that of the freely deformable interconnect if the stiffness is sufficiently small.Conversely, it is considered that a higher stiffness causes less displacement in lateral buckling, eventually leading to deformation of the in-plane constrained interconnect, that is, in-plane bending, if the stiffness is sufficiently high.
Therefore, this study investigates the dependency of serpentine interconnect stretchability on encapsulation stiffness by evaluating the variation in stretchability due to tensile and bending stiffness.The goal is to determine a sufficiently small stiffness that allows the interconnect to deform almost freely.In this study, experiments and finite element method (FEM) calculations were conducted.In the experiments, polyimide-supported copper serpentine interconnects encapsulated with elastomers having different stiffness were prepared, and the elongation to failure was measured.In the FEM calculation, the internal strain distributions of the freely deformable and in-plane constrained interconnects were computed, and the failure elongation of the interconnects with each buckling behavior was obtained.Then, the relationships between the elongation to failure and encapsulation stiffness were plotted to determine the stiffness value required to make the interconnect almost freely deformable.

Sample preparation
Figure 1(a) illustrates the geometric parameters of the polyimide-supported copper serpentine interconnects used in the experiments.The thicknesses of the copper and polyimide were 18 and 50 µm, respectively.A previous study reported the relationship between the stretchability and geometric parameters of serpentine interconnects [26], where stretchability was primarily determined by the ratios of geometric parameters: t inter /l 1 , w/l 1 , and l 2 /l 1 , where t inter , w, l 1 , and l 2 represent the thickness, width, space, and length of the serpentine straight line.In this study, t inter and w were determined to have similar values to those of conventional flexible printed circuit boards.l 1 and l 2 were determined to have similar values of w/l 1 and l 2 /l 1 as in previous studies (w/l 1 is approximately 0.3, and l 2 /l 1 is 1-3 [19,27]).Additionally, in a previous study [27], various shape interconnects, such as elliptical and horseshoe shapes, were investigated and compared with the serpentine shape.The findings suggest that elliptical and horseshoe shapes exhibit larger and smaller internal strains, respectively, compared to the serpentine interconnect under the same elongation.Whereas, horseshoe shapes have a longer total electrical path, resulting in a higher initial electrical resistance than the serpentine interconnect.
We studied serpentine interconnects with six types of soft elastomer encapsulations, labeled as types A-F, as listed in table 1. Core-shell (types A-D) and single (types E and F) encapsulations were examined based on previous studies [1][2][3]21].For the core-shell encapsulation, Ecoflex gel and Ecoflex 00-50/00-30 (Smooth-on) were used as the core and shell elastomers, respectively.For a single encapsulation, ecoflex 00-30 or 00-30 sponge [19] was used.The ecoflex 00-30 sponge has a lower Young's modulus owing to its open-cell structure.The thickness of the core, shell, and single elastomer, denoted as t core , t shell , and t single " respectively, as illustrated in  Figures 2(a)-(m) illustrate the fabrication process of the serpentine interconnects encapsulated with the core-shell and single encapsulations.First, a polyimide-laminated copper foil (Felios R-F770, Panasonic Industry) was adhered to a thermal-release adhesive sheet (Revalpha, Nitto Denko) (figure 2(a)), and patterned into a serpentine shape using a cutting plotter machine (CE6000-40, Graphtec) (figure 2

(b)).
A cutting plotter machine was used due to its processability without causing chemical or thermal damage [18,19,[27][28][29][30]. Subsequently, excess areas of copper and polyimide were manually peeled off using tweezers (figure 2(c)), and the patterned interconnect was released from the thermal-release adhesive sheet by baking at 120 • C for 1 min in a hot oven (figure 2(d)).The released interconnect is self-standing and can be handled using tweezers, as it has sufficient thicknesses of copper and polyimide.For the fabrication process of core-shell encapsulation, pre-cured shell elastomer (Ecoflex 00-50 or 00-30) was first poured into a 3Dprinted mold (Agilista AR-H1, Keyence) and cured at 90 • C for 90 min in a hot oven (figure 2(e)).To improve mold releasability, the mold was coated with a 2 µm thick layer of parylene C and a release agent (Ease Release 205, Smooth-on).The shell elastomer was then removed from the mold and a pre-cured core elastomer (Ecoflex gel with 0.5 wt.% of black pigment (Silc Pig, Smooth-on)) was poured into the shell elastomer (figure 2(f)).The thickness of the core elastomer was controlled by measuring its wight during pouring.The core elastomer was cured at 90 • C for 30 min in a hot oven, and the interconnect was then mounted on it using tweezers (figure 2(g)).The interconnect was adhered to the core elastomer using the adhesive properties of the Ecoflex gel itself.Finally, the core and shell elastomers layers were formed on the interconnect using a similar process (figures 2(h) and (i)).For the fabrication process of a single encapsulation, sheets of Ecoflex 00-30 or 00-30 sponge were first fabricated using a 3D-printed mold (figure 2(j)).The sponge sheets were prepared using the sugar templating process described in a previous study [19].Subsequently, pre-cured Ecoflex 00-30 was coated on one side of the elastomer sheets (the thickness of pre-cured Ecoflex 00-30 was approximately less than 50 µm) (figure 2(k)), and the interconnect was sandwiched between them using tweezers (figure 2(l)).Finally, the pre-cured Ecoflex 00-30 was cured at 90 • C for 30 min in a hot oven (figure 2(m)).The fabricated interconnects with each type of encapsulation are shown in figure 3.

Experimental conditions
The elongation-to-failure of the fabricated samples was determined through resistance measurements under stretching.Figure 4 shows the experimental setup for the resistance measurements.The fabricated serpentine interconnect was clamped at the contact pads with a tensile testing machine (AGS-X, Shimadzu), and stretching was applied to the interconnect at an elongation speed of 10 mm min −1 .The elongation speed corresponds to an elongation of 25% per minute, which is not excessively slow when compared to previous studies (e.g. an elongation of 50% per minute [18]).In this study, viscoelastic effects were not considered.The resistances of the interconnects were measured using the four-probe method.A constant current of 100 mA was applied to the interconnect using a constant-current power supply (PA600-0.1B,Texio Technology), and the voltage was measured using a data logger (GL900, Graphtec).The power supply and data logger were electrically connected to the contact pads of the interconnect.The stretching deformation was stopped when electrical failure was observed.The point where the resistance suddenly increased to approximately 100 times its initial value was determined as the point of elongation to failure.

Condition of FEM calculations
The FEM calculations were performed using Ansys software.The internal strain of the serpentine interconnect was determined through a post-buckling analysis to replicate the lateral buckling behavior of the freely deformable serpentine interconnect.In the post-buckling analysis, the buckling displacement in the elastic region was first calculated under small stretching, and then it was used as the initial irregularity to simulate buckling deformation in the plastic region under large stretching.
The internal strain in the elastic region of the copper was initially computed in the linear static analysis, where an elongation of 1% was applied.Subsequently, the buckling displacement was determined using eigenvalue buckling analysis, which obtains the displacement by utilizing the computed internal strain   distribution.The calculated buckling displacement served as the initial irregularity, and the internal strain (von Mises strain) was then computed in the plastic region based nonlinear static analysis.For the in-plane constrained interconnect, the bottom of the polyimide support was constrained to a plane.The dimensions of the serpentine structure were identical to those used in the experiments.An interconnect length of 8.5 mm, instead of 40 mm, was used for the calculation to reduce the computation time.The material properties used in these calculation are listed in table 2.

Experimental results
The resistance changes of the serpentine interconnects under stretching for each encapsulation type are depicted in figures 5(a)-(f).The resistance change rate was calculated using (R-R 0 )/R 0 , where R and R 0 represent the resistance and initial resistance of the interconnect, respectively.Here, R 0 was typically 0.22-0.23Ω. Elongation was determined by dividing the displacement by the initial interconnect length of 40 mm.For each encapsulation type, the resistance change rate remained almost constant at zero until electrical failure occurred.Basically, the resistance increases as a crack propagates in the copper at the semicircular serpentine segment [18,19].A sudden increase in the resistance means that the crack propagates much faster when the elongation reaches the failure point.Therefore, figures 5(a)-(g) indicate that the behavior of crack propagation did not vary significantly, even when the encapsulation differs for these experimental conditions.The average values of the elongation to failure are

Results of FEM calculations
Figures 6(a) and (b) depict the internal strain distributions computed in the FEM calculations up to an elongation of 50%.For a freely deformable interconnect, the behavior of lateral buckling closely resembles that of the free-standing serpentine interconnect examined in previous studies [18,29].A comparison of figures 6(a) and (b) revealed that the internal strain was significantly smaller in the freely deformable interconnect.The internal strain at the semicircular serpentine segment.In particular, the internal strain at the semicircular serpentine segment exhibited higher values in the in-plane-constrained interconnect.The maximum internal strain determined by the elongation is shown in figure 6(c).For the freely deformable interconnect, the maximum internal strain increased slightly and then significantly as the elongation increased.A previous study that examined free-standing serpentine interconnects reported similar curves, where the maximum strain increased in proportion to the square root of the elongation and then increased in proportion to the squared elongation [26].That is because the internal strain resulting from out-of-plane deformation dominates in the initial stage of buckling, and the internal strain due to in-plane deformation takes effect only when the elongation is relatively large.In contrast, for the in-plane constrained interconnect, the maximum internal strain increased almost proportionally with the elongation.Hence, figures 6(a)-(c) indicate that the internal strain varies significantly owing to the buckling behavior, especially between lateral buckling and in-plane bending, in the serpentine structure.
When the failure strain of copper was 10% [31], the obtained elongation to failure were 129% and 59% for the freely deformable and in-plane constrained interconnects, respectively.

Relationships between elongation to failure and encapsulation stiffness
For a composite beam with multiple layers, the effective tensile and bending stiffness per unit width, K tensile and K bending , are given by [32] where the summation is for all n layers, with i = 1 being the bottom layer, E i and t i are the Young's modulus and thickness of ith layer, respectively.Here, t neutral is the distance from the bottom to the neutral mechanical plane, and is given by This study mainly focused on the local stretching and bending induced in the encapsulation around the interconnect; therefore, the K tensile and K bending values for one side of the encapsulation with the interconnect layers as the boundary plane were obtained using equations ( 1)- (3).The obtained values were K tensile = 45, 43, 38, 36, 34, and 5 N m −1 and K bending = 3.2 × 10 −6 , 1.4 × 10 −6 , 3.1 × 10 −6 , 1.2 × 10 −6 , 7.2 × 10 −7 , and 1.0 × 10 −7 N m for encapsulation types A-F, respectively.The calculations were performed using the modulus and thickness values provided in table 1, disregarding the interconnect thickness for simplicity.
Figures 7(a) and (b) illustrate the relationship between the elongation to failure and K tensile and K bending of the encapsulation, respectively, as obtained through experiments and FEM calculation.Regarding K tensile , the elongation to failure monotonically decreased as K tensile increased, and it sharply decreased when K tensile was equal to or greater than 34 N m −1 .On the other hand, for K bending , the elongation to failure did not decrease monotonically as K bending increased.This indicates that K tensile is a more useful index in the design of the encapsulation than K bending .The encapsulations with K tensile values of 5 and 34 N m −1 (types F and E) exhibited elongation to failure (133 and 126%, respectively) close to that predicted by the FEM calculation for freely deformable interconnects (129%).Hence, this indicates that a sufficient value of K tensile for making the interconnect freely deformable ranges from 5 to 34 N m −1 , in the case of the interconnect with 18 µm thick copper and 50 µm thick polyimide.Whereas, for interconnect with type F encapsulation, the force for reversible response to applied stretching was insufficient, and the serpentine structure did not recover to its initial state after stretching several tens of percent, as shown in figure 8.In total, the encapsulation of type E was functionally superior to that of type F. The elongation to failure of the encapsulation with 45 N m −1 (type A) was 67%, which was close to that predicted using the FEM calculation for the in-plane constrained interconnect (59%).On the other hand, experiments with optical observation confirmed that even the interconnect with type A encapsulation, which possesses the highest encapsulation stiffness, exhibits lateral buckling when the elongation is relatively low.This indicates that the stretchability of the serpentine interconnect can be significantly degraded even when the buckling behavior does not perfectly transition from lateral buckling to in-plane bending.The relationship between the elongation to failure and K tensile is considered to follow an S-shaped curve, such as a logistic function, approaching 129% and 59% when K tensile is sufficiently small (less than 34 N m −1 ) and large (greater than 45 N m −1 ), respectively.On the other hand, for the relationship between the elongation to failure and K bending , although the elongation to failure is considered to be approaching 129% and 59% with sufficiently small and large K bending , respectively, it increases once at K bending = 3.1 × 10 −6 N m (type C).This is because type C encapsulation exhibits a greater K bending than type B in figure 7(b), resulting in the reversal of the order of types B and C compared to figure 7(a) in terms of the stiffness magnitude.This indicates that the magnitude relationship of stiffness is not necessarily the same for K tensile and K bending in core-shell encapsulation.
This study focused on the variation in stretchability under single stretching.For cyclic stretching, a previous study [18] reported the relationship between the elongation ε appl and cycle number to failure N f : , where A is the coefficient determined by the material properties, geometric parameters, and constrained condition of serpentine structure.The fatigue ductility exponent of copper is denoted by c.A serpentine interconnect under a less constrained condition exhibits a higher value of A, indicating that an interconnect with a smaller encapsulation stiffness exhibits greater stretchability even under repeated stretching.

Conculusions
We investigated the stretchability dependence on both the tensile and bending stiffness of soft elastomer encapsulations for serpentine interconnects.In the experiments, interconnects with different encapsulation stiffness (from 5 to 45 N m −1 in K tensile and 1.0 × 10 −7 -3.2 × 10 −6 N m in K bending ) were prepared, and the elongation to failure was measured.In the FEM calculation, the internal strain distribution of the freely deformable and in-plane constrained interconnects were computed, and the elongation to failure of each buckling behavior was obtained.The relationship between the elongation to failure and encapsulation stiffness indicates that K tensile is a more useful index in the design of the encapsulation because the elongation to failure monotonically decreases as K tensile increases.The encapsulations with K tensile values of 5 and 34 N m −1 exhibited elongation to failure (133 and 126%, respectively) close to that predicted by FEM calculation for freely deformable interconnects (129%).Therefore, this suggests that the sufficient value of K tensile to maximize interconnect stretchability, essentially making the interconnect almost freely deformable, ranges from 5 to 34 N m −1 , in the case of the interconnect with 18 µm thick copper and 50 µm thick polyimide.

Figure 1 .
Figure 1.(a) Geometric parameters of polyimide-supported copper serpentine interconnect.(b), (c) Top and cross-sectional views of interconnects with core-shell and single encapsulations of soft elastomers.

Figure 3 .
Figure 3. (a)-(f) Optical images of fabricated serpentine interconnects with type A-F of soft elastomer encapsulations.

Figure 4 .
Figure 4. Experimental setup for resistance measurement under stretching.

Figure 5 .
Figure 5. (a)-(f) Resistance changes of serpentine interconnect with types A-F encapsulation.(g) Elongation to failure of interconnect with each encapsulation type.

Figure 6 .
Figure 6.strain distribution of (a) freely deformable and (b) in-plane constrained interconnects.(c) Maximum internal strain determined by elongation.

Figure 7 .
Figure 7. Relationship between the elongation to failure and (a) tensile and (b) bending stiffness of encapsulation.

Figure 8 .
Figure 8. Optical image of serpentine interconnect with type F encapsulation (single elastomer of Ecoflex 00-30 sponge) after stretching several tens of percent.

Table 1 .
Properties for six types of soft elastomer encapsulations.
figures 1(b) and (c), correspond to the thickness values listed in table 1.

Table 2 .
Material properties for FEM calculations.