Reliability Assessment of Stretchable Interconnects Yung-Yu Hsu1,3, Biljana Dimcic1,3, Mario Gonzalez1, Frederick Bossuyt2, Jan Vanfleteren2, and Ingrid De Wolf1,3 1 IMEC, Kapeldreef 75, 3001, Leuven, Belgium 2 IMEC-CMST, Gent-Zwijnaarde, Belgium 3 K.U.Leuven, Dept. MTM, Leuven, Belgium Phone: +32 (0) 16 28 11 16, E-mail: hsu@imec.be ABSTRACT In this paper, we comprehensively investigate the fatigue life and the failure modes of horseshoe-patterned stretchable interconnects, through both experimental and numerical analysis. The experimental results demonstrate that the fatigue life of a horseshoe-patterned stretchable interconnect embedded into a silicone matrix is able to resist up to 3000 cycles for a uniaxial elongation of 10%. By increasing the magnitude of the uniaxial elongation up to 30%, the lifetime drops rapidly to 85 cycles. A power law curve fitting relating the elongation versus the number of stretching cycles (E-N curve) is proposed based on the abovementioned experimental results. Moreover, combining the numerical modeling with the experimental results, a modified Coffin-Manson equation for fatigue life prediction is proposed for further evaluation of reliability performance. Micrographs and the correlated numerical simulations of the nonencapsulated stretchable intereconnects provide the experimental evidences and numerical explanations of the three-step failure processes. INTRODUCTION Electronic systems with flexibility and stretchability have great potential in biomedical applications, such as implantable devices, artificial skin and wearable health monitoring systems. An emerging application that highly relies on the device stretchability and reliability is the “phototherapy by textile”. The idea of this “lighting” textile is to integrate light sources, ex. OLED, with electronic devices supported by a flexible and stretchable elastomeric substrate adhering on the surface of the textile. Because of the rigidity of the lighting sources and electronic devices which are bendable but not stretchable, a hybrid system combining stretchable interconnects together with rigid components was proposed recently in order to fulfill the demands of extreme deformation. Several technologies for stretchable interconnects have been proposed in recent years in order to achieve a certain level of stretchability. One of the possible effective ways with controllable stretchability is using the idea of an out-of-plane structure [1, 2]. This out-of-plane structure can be realized through depositing a nanometer scale thin conductor on top of a “pre-stretched” substrate. As soon as this “pre-stretched” substrate is released back to its original position, the deposited thin conductor buckles periodically forming a wavy surface and thus, the stretchability can be controlled by the amplitude of the buckling waves. However, it is observed that microcracks in the conductor are accompanied with elongation and therefore, the electrical resistance is unstable upon stretching [2]. Due to this instability of the electrical resistance, the application of this technology is limited to certain applications. An alternative technology which uses a co-planar patterned conductor has been proposed in recent years [3, 4]. This co-planar technology has several advantages such as stability of the electrical resistance upon stretching, compatibility with conventional microfabrication technology, and feasibility for large area fabrication. Although both the abovementioned out-of-plane and coplanar technologies have been realized and proved the possibility to have stretchable systems, all the up-to-date studies on the reliability performance of these two kinds of technologies are still limited to the so-called “one-time stretching”. In this paper, we comprehensively investigate the reliability performance of the co-planar, horseshoe-patterned stretchable interconnect through both experimental and numerical analysis. A fatigue life prediction model of the encapsulated stretchable interconnect is proposed. In order to visualize the occurring failure, non-encapsulated interconnects were studied and the results are correlated to numerical analysis. This combination allows explaining the building-up processes of mechanics and failure mechanisms. FATIGUE LIFE PREDICTION MODEL Two types of horseshoe-patterned stretchable interconnects were fabricated using the same process steps as discussed in our previous publications [3, 4]. The first type is sample with encapsulation (fully embedded), and the second type consists of a two-layer system without encapsulation (metal exposed). The first type, fully embedded stretchable interconnect, was used for a fatigue life study, whereas the second type, metal exposed sample, was used for visualization of metal failure after cyclic stretching in a scanning electron microscope (SEM). Figure 1 (a) shows a completed horseshoe-patterned polymer-encapsulated sample. Two square pads on two ends of the sample are designed for the four-probe resistance measurement. The dash lines mark one repeated unit of a horseshoepatterned stretchable interconnect, corresponding to the finite element model (FEM) as shown in figure 1 (b). Taking the advantage of symmetry, only one unit of the horseshoe-patterned interconnect was simulated. The detail dimensions of the horseshoe-patterned interconnect and the non-linear material properties used for FEM in this paper can be found in our publication [4]. It is noted that in this investigation, the two end surfaces of the FEM model are stretched in opposite directions for five different magnitudes of elongation: 10, 15, 20, 25, and 30% elongation, which correspond to the fatigue experiments. The maximum accumulated plastic strain per cycle in the horseshoe-patterned conductor was recorded and used as the failure criteria for further analysis of fatigue life prediction. Symmetrical surface Symmetrical surface Stretching direction for 10, 15, 20, 25, 30% elongation 1 mm (a) (b) FIGURE 1. (a) The horseshoe-patterned stretchable interconnect embedded in an elastomeric substrate; (b) one repeat unit of the stretchable interconnect corresponding to the middle area in (a). Figure 2 (a) shows the plastic strain distribution of one horseshoe meander at 30% elongation. The plastic strain concentrates on the crest of the meander, with highest value at the inner corner, which indicates the possible location to initiate the metal fracture. In figure 2 (b), it is observed that the horseshoe meander breaks at the crests where the maximum plastic strain was applied. Comparing figure 2 (a) and (b), a good agreement is found between simulation and experiment. It should be noted that the simulation and the metal failure in figure 2 (a) and (b) are from the sample with encapsulation, In order to experimentally observe the fracture initiation and propagation in a SEM, samples without encapsulation are used and will be discussed in the later section. This is required because samples with encapsulation charge-up in the SEM, disturbing the images. 30% elongation Before stretching numbers of the accumulated plastic strain per cycle are acquired from the 5th stretching cycle which reaches steady state. The empirical Coffin-Manson relationship is adopted as N f = C ⋅ (∆ε pl ) −n where Nf denotes the mean cycle to failure; C is the fatigue ductility coefficient; n is the reciprocal of the fatigue ductility exponent; and Δεpl is the accumulated plastic strain per cycle, which is defined as ( Number of stretching cycle to electrical failure Plastic strain concentration (a) (b) FIGURE 2. (a) Plastic strain distribution at 30% elongation; (b) the typical failure on the crest of the stretchable interconnect. Relative elongation of the substrate (%) Figure 3 shows the power law fitting of elongation versus number of stretching cycles to failure (E-N curve). Five different magnitudes of elongation (10, 15, 20, 25, and 30%) were applied experimentally to stretchable interconnects with 0.5%/sec strain rate. Every data point in this figure indicates the average number of five repeated experiments. The average experimental deviation is 6% for every data point and the power law fitting has R2 of 0.98. The error bars are hard to see in this figure due to the log-log scale. It is observed that the horseshoe-patterned stretchable interconnect survives for more than 3000 cycles at 10% elongation. As the elongation increases to 30%, the number of stretching cycle to failure drops rapidly to 85 cycles. This phenomenon can be explained by the accumulated plastic strain in the metal. A higher elongation results in more accumulated plastic strain. As soon as the accumulated plastic strain in the metal reaches the intrinsic fracture strain, the metal initiates cracks and eventually, the metal ruptures. Number of stretching cycle to failure Power law fitting 30 20 ( ) ) + (∆ε 2 pl z ) 2 − ∆ε xpl  2  (2)   1 1000 10000 Number of stretching cycle to electrical failure FIGURE 3. Power law fitting of elongation versus number of stretching cycles (E-N curve). Figure 4 shows the number of stretching cycle to failure (Nf) obtained from the experiments versus the accumulated plastic strain per cycle (Δεpl) obtained from the FEM simulation (figure 1 (b)). The 3500 Stretching cycle from 10 to 30% elongation Fitting (Coffin-Manson) N f = 0.1512 ⋅ (∆ε pl ) −1.82 3000 2500 2000 1500 1000 500 0 0.005 0.010 0.015 0.020 0.025 Accumulated plastic strain per stretching cycle FIGURE 4. Coffin-Manson equation for fatigue life prediction. CYCLIC STRETCHING INDUCED FAILURE In order to analyze the failure mechanism of the stretchable interconnect, a modified horseshoe-patterned configuration was designed. In this case, the metal is deposited on top of an elastomeric substrate without encapsulation, allowing the possibility to acquire high resolution images in a scanning electron microscope (SEM). The stretchable interconnects were stretched separately for 50 and 100 cycles at 30% elongation, following by in-situ observation on the home-build tensile stage in the SEM at 30% elongation. The SEM micrographs of the “non-encapsulated” stretchable interconnect show that there are three sequential steps for growing fracture: 1. 10 100 ) (  ∆ε pl − ∆ε pl 2 + ∆ε pl − ∆ε pl y y z 2 x ∆ε pl = 2 2 2 3  3 + ∆γ pl + ∆γ pl + ∆γ pl xy yz zx  2 In this investigation, the coefficients of “C” and “n” are fitted and proposed as 0.1512 and 1.82, respectively. The fitting has R2 of 0.99. It is noted that these two fitting coefficients (C and n) along with Eq. (1) are useful for future fatigue life prediction of this particular type of stretchable interconnect through numerical modeling. After stretching 40 (1) Microcracks initiate at the inner corner of the crest as well as in the interface between the metal and the substrate, as shown in figure 5 (a). The sample was tilted for 30 degree in order to see the interface. It is noted that the stretchable interconnect in figure 5 (a) experienced 50 stretching cycles at 30% elongation. This crack initiation is valid only for the stretchable interconnect without encapsulation. For the fully encapsulated stretchable interconnect, it is believed that the crack initiate at the side wall of the inner corner of the crest, instead of initiating at the bottom interface. The details of 2. The microcracks propagate through the thickness of the metal at the inner corner of the crests, as shown in figure 5 (b), forming so-called “channel crack”. The stretchable interconnect in figure 5 (b) experienced 100 stretching cycles at 30% elongation. This failure formation is valid only for the interconnect without encapsulation. 3. The channel cracks propagate through the metal in the width direction, followed by metal breakdown, as shown in the top view of figure 6 (a) and (b), respectively. It should be noted that, for the stretchable interconnect “with encapsulation”, the channel crack initiates at the side wall of the metal, as explained in the first step, following by the crack propagation, as shown in figure 6 (a). The final metal breakdown is similar for both cases (with and without encapsulation). (b), the fully encapsulated stretchable interconnect has the plastic strain uniformly distributed (no plastic strain gradient) along the thickness direction, whereas in the width direction of the metal, it is found that the highest plastic strain is located at the inner corner of the crest. Moreover, the plastic strain is occurring at the outer edge of the metal as well, even for the small elongation. This plastic strain distribution (fig. 7 (b)), different than the distribution in figure 7 (a), can be explained by the constraint of the out-of-plane deformation from the encapsulation, resulting in more in-plane geometrical opening. The detail explanations on the effect of encapsulation can be found in the reference [5]. 18 16 Cu height (um) this failure mechanism can be explained by FEM simulation and will be discussed in the later section. 14 12 Sample with Cu exposed Plastic strain in Cu 1.250E-05 2.500E-05 10 3.750E-05 8 5.000E-05 6 6.250E-05 4 7.500E-05 2 8.750E-05 0 3% elongation 0.000 Cu height 1.000E-04 Cu width 0 10 20 30 40 50 60 70 80 90 100 Cu width (mm) Crack initiation (inner circle; Cu/PDMS interface) (a) Channel crack 18 Cu height (um) 16 14 12 1.250E-04 1.875E-04 2.500E-04 6 3.125E-04 4 3.750E-04 2 4.375E-04 Cu height 5.000E-04 Cu width 0 10 20 30 40 50 60 70 80 90 100 Cu width (mm) (b) FIGURE 7. Plastic strain initiation at the cross section of the crest stretching for 3% elongation (a) non-encapsulated sample; (b) encapsulated sample. Cu height (um) 16 Metal breakdown 6.250E-05 8 18 Channel crack 3% elongation 0.000 10 0 (a) (b) FIGURE 5. Sample tilted for 30 degree in order to see the interface (a) crack initiation at the inner corner of the crest and interface between metal and substrate; (b) crack propagation through the thickness direction of the metal interconnect. Sample with Cu embedded Plastic strain in Cu 14 12 Sample with Cu exposed Plastic strain in Cu 0.005000 0.01000 10 0.01500 8 0.02000 0.02500 6 0.03000 4 0.03500 2 0.04000 0 30% elongation Cu height 0.04500 Cu width 0 10 20 30 40 50 60 70 80 90 100 Cu width (mm) (a) (b) FIGURE 6. Top view of (a) channel crack formation through the width of the metal interconnect; (b) completed failed stretchable interconnect. LOCAL STRESS/STRAIN BUILDING-UP PROCESS 18 16 14 Cu height (um) (a) 12 30% elongation 0.005000 0.01062 0.01625 10 0.02187 8 0.02750 6 0.03312 4 0.03875 2 0.04437 0 The crack growing steps discussed in the previous section can be verified and explained by the plastic strain building-up processes upon stretching. The first stretching step from 0 to 30% elongation was simulated and analyzed. Figure 7 and 8 demonstrate the plastic strain distribution at the cross section of the crest which is identified as the failure location in the SEM. Figure 7 (a) indicates the interconnect without encapsulation stretching for 3% elongation, whereas figure 7 (b) shows the encapsulated interconnect stretched for the same amount of elongation. Figure 8 shows the same but for 30% elongation. Comparing (a) and (b) in both figure 7 and 8, it is found that the plastic strain distribution in the metal is different. In figure 7 (a), the non-encapsulated stretchable interconnect has the plastic strain initiation at the inner corner of the crest and at the interface between metal and substrate. No plastic strain on the outer edge of the metal is observed for small elongation (3%). In figure 7 Sample with Cu embedded Plastic strain in Cu 0.05000 0 10 20 30 40 50 60 70 80 90 100 Cu height Cu width Cu width (mm) (b) FIGURE 8. Plastic strain distribution at the cross section of the crest stretching for 30% elongation (a) non-encapsulated sample; (b) encapsulated sample. Figure 8 (a) and (b) show the plastic strain distribution at 30% elongation of the non-encapsulated and encapsulated stretchable interconnect, respectively. Both figure 8 (a) and (b) indicate the same cross section as shown in figure 7. In figure 8 (a), although the stretchable interconnect is subjected to a large elongation (30%), there is still a plastic strain gradient in both thickness and width direction. In figure 8 (b), the plastic strain distribution follows the same trend as explained in figure 7 (b). It should be noted that there is a neutral area where the plastic strain approaches to zero for both non-encapsulated and encapsulated interconnects, as shown in both figure 7 and 8. The more elongation, the narrower the neutral area that is observed. This phenomenon can be explained by the discrete stress components in the metal upon stretching. Figure 9 and 10 show examples of the longitudinal (σxx) and transversal (σyy) stress components of the encapsulated interconnect subjected to 30% elongation, respectively. When the stretchable interconnect is subjected to elongation, not only tensile stress but also a bending moment is generated in the metal, as shown in figure 9 right. The tensile stress is mainly from the longitudinal stretching, and the bending moment is from the geometrical opening. It has been proven that the geometrical opening contributes to the majority of the elongation [4, 5]. Consequently, the bending moment contributes more to the local tensile and compressive stress than the tensile stress solely from the longitudinal elongation. M σxx x σxx y M compressive stress Tensile stress stress. No transversal stress (σyy) is observed at the crest. Moreover, it is found that the neutral line resides at the center of the arms in width direction. This stress distribution can be explained by the bending moment in the arms due to the contraction of the substrate in transversal direction (Poisson’s ratio) when stretching. CONCLUSIONS In summary, the reliability of the horseshoe-patterned stretchable interconnect was analyzed through both experimental and numerical investigations. A power low fitting of elongation versus number of stretching cycles (E-N curve) is proposed. According to this E-N curve, one can estimate the life time of the stretchable interconnect through the designated magnitude of elongation, and vice versa. Moreover, an empirical Coffin-Manson equation is proposed by correlating the experiments with simulations. Based on this equation, one can effectively predict the fatigue life of the stretchable interconnect through numerical modeling. Our experiments shown that the non-encapsulated stretchable interconnect follows three failure steps, which are different than the encapsulated stretchable interconnect. However, through numerical simulations, it is concluded that the root cause (tensile stress induced plastic strain) and the metal breakdown location at the inner corner of the crest are the same. In future, further studies will focus on metal ductility, and the mechanics of fatigue failure. This will allow us to further understand, and to improve, the reliability of the horseshoe-patterned stretchable interconnect. FIGURE 9. Stress (σxx) distribution in longitudinal direction (stretching direction). ACKNOWLEDGEMENT This work was supported by the European Commission, under the PLACE-it research project (Contract Number 0248048). Inner radius REFERENCES M Outer radius x y [1] [2] [3] FIGURE 10. Stress (σyy) distribution in transversal direction (vertical to stretching direction). Combing the tensile and compressive stress from both bending moment and longitudinal elongation, it is found that there is a neutral line which resides in the width direction close (shifted from the center) to the outer edge of the crest, as shown in figure 9. The area above the neutral line in the width direction has compressive stress whereas the area below the neutral line has tensile stress. This stress distribution explains the plastic strain distribution in figure 8 (b). The highest plastic strain at the inner corner of the crest is mainly due to the tensile stress, and the plastic strain at the outer edge of the crest is mainly due to the compressive stress. In addition, the neutral line in figure 9 represents the area where the neutral area is (figure 8 (b)). This stress distribution (figure 9) combining with the plastic strain distribution (figure 8 (b)) indicate that the root cause for metal fracture is the tensile stress at the inner corner of the crest. 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