Design strategy of porous elastomer substrate and encapsulation for inorganic stretchable electronics

ABSTRACT

The emergence of stretchable electronic technology has led to the development of many industries and facilitated many unprecedented applications, owing to its ability to bear various deformations. However, conventional solid elastomer substrates and encapsulation can severely restrict the free motion and deformation of patterned interconnects, leading to potential mechanical failures and electrical breakdowns. To address this issue, we propose a design strategy of porous elastomer substrate and encapsulation to improve the stretchability of serpentine interconnects in island-bridge structures. The serpentine interconnects are fully bonded to the elastomer substrate, while segments above circular pores remain suspended, allowing for free deformation and a substantial improvement in elastic stretchability compared to the solid substrates. The pores ensure unimpeded interconnect deformations, and moderate porosity provides support while maintaining the initial planar state. Compared to conventional solid configurations, finite element analysis (FEA) demonstrates a substantial enhancement of elastic stretchability (e.g. ≈9 times without encapsulation and ≈ 7 times with encapsulation). Uniaxial cyclic loading fatigue experiments validate the enhanced elastic stretchability, indicating the mechanical stability of the porous design. With its intrinsic advantages in permeability, the proposed strategy has the potential to offer insightful inspiration and novel concepts for advancing the field of stretchable inorganic electronics.

GRAPHICAL ABSTRACT

KEYWORDS:

• Stretchable inorganic electronics
• Island-bridge structures
• porous elastomer substrate
• encapsulation design
• serpentine interconnects

1. Introduction

The emerging stretchable electronic technology is sparking intense interest and widespread attention in recent years. Its excellent ability to accommodate mechanical deformations without causing electrical degeneration of rigid devices has facilitated various applications in many aspects, ranging from soft robotics [1–5], wireless communications [6–15], health monitoring [16–25], biomedicine [26–28], and electronic skin [29–36] to energy harvest/storage [36–41]. Stretchable inorganic electronics usually require integrating different materials and components into elastomer substrates to obtain flexible and stretchable hybrid systems with various functions. An effective strategy to achieve flexibility and stretchability relies on structural designs by combining rigid functional devices with special structures [42,43]. Island-bridge structure represents a widely employed structural design to make functional stretchable devices, where patterned interconnects (e.g. arc-shaped [44–46], serpentine [47,48], 3D helical [16,49], self-similar [50,51] and fractal-inspired [52–55]) between adjacent rigid islands can withstand nearly all deformations under stretching.

In many practical applications, interconnects need to be fully bonded to elastomer substrates to reconcile stretchability and reliability. Nevertheless, conventional solid elastomer substrates together with encapsulation layers tend to strictly constrain their out-of-plane motion and deformation, resulting in the decline of overall elastic stretchability for electrical devices [43,48,56–59]. To overcome this challenge, many strategies have been developed, including prestrain and spatial tailoring (such as pyramid [60], tripod [61], trapezoidal [62], toothed [63], and cellular [64–67] shapes) methods for the elastomer substrate. Additionally, fluid [60,68], microchannel [69,70], two-stage [16,71] methods, as well as network [72] and two-component [73,74] materials, have been proposed for encapsulation layer to address these limitations. The strategies mentioned here all exhibit a superior increase in elastic stretchability by relieving the free motion of interconnects, whether for elastomer substrates or encapsulation layers.

Notably, various strategic approaches in the structural design of elastomer materials highlight key concepts that offer distinct advantages. However, they also present their unique challenges. For instance, strategies employing surface structuring effectively mitigate delamination at the heterogeneous interface between the island and the soft substrate [61,62], and facilitate strain isolation for brittle islands [75,76]. Nonetheless, the necessity for substantial thickness to create such structures could constrain their integration into compact wearable multifunctional devices. This is due to the increased flexural rigidity potentially compromising the device’s ability to conform to curved surfaces. Alternatively, approaches that incorporate multiple materials are capable of precise regional strain control, yet they introduce higher costs and add complexity in the manufacturing process [77–79].

Moreover, emphasizing the importance of breathability in flexible electronics is crucial. Ensuring adequate permeability and heat dissipation in these devices is vital for their comfort and performance, especially in some practical applications involving direct contact with the human body. The ability of flexible electronics to allow the free exchange of air facilitates improved comfort, wearability, and overall user experience. Integrating designs that prioritize both stretchability and breathability is essential for the continued advancement and widespread adoption of flexible electronic technologies. In the previous research, a promising cellular structural design for elastomer substrates has been introduced [64]. However, this similar design concept has not yet been applied to considerations of strain isolation and encapsulation layers. Therefore, a simple design strategy simultaneously possesses high elastic stretchability and good permeability, which can be applied to both substrates and encapsulation layers remains to be proposed.

Here, we introduce a design strategy of porous elastomer substrate and porous encapsulation to improve the stretchability of serpentine interconnects for island-bridge structures (Figure 1(a)). Serpentine interconnects are fully bonded to the elastomer substrate while the segments above round pores are suspended and can be freely deformed, thereby generating a substantial enhancement in elastic stretchability compared to the case of solid elastomer substrate. The pores are distributed uniformly at corresponding positions of substrate and encapsulation to guarantee ample space for the unconstrained deformation of interconnects. Moderate porosity can render adequate support to maintain the initial planar state of interconnects and achieve excellent permeability and heat dissipation. Quantitative finite element analysis (FEA) has been conducted to obtain optimal parameters and a notable increase in elastic stretchability with porous design is shown, e.g. ~9 times without encapsulation and ~ 7 times with encapsulation (Figure 1(b,c)). To validate the performance, uniaxial cyclic loading fatigue experiments have been implemented to define the approximate ranges of elastic stretchability (e.g. 5%–10% for the solid and 15%–20% for the porous), which also indicate mechanical stability and durability. This work can be of significance in providing enlightening ideas for the development of stretchable inorganic electronics.

Figure 1. Schematic illustration and analysis of the proposed porous elastomer substrate and porous encapsulation strategy for the island-bridge structure. (a) An exploded view of the island-bridge structure, featuring a porous partition elastomer substrate, a serpentine interconnect, two rigid devices, and a porous partition encapsulation layer. The rigid devices and the serpentine interconnect are fully bonded to the elastomer substrate. (b, c) FEA results comparing the elastic stretchability of solid and porous elastomer substrates without and with solid/porous encapsulation. The results indicate that the solid substrates exhibit elastic stretchability of 5% without solid encapsulation (b, top panel) and 4% with solid encapsulation (b, bottom panel). In contrast, the porous substrates demonstrate significantly higher stretchability of 45% without porous encapsulation (c, top panel) and 28% with porous encapsulation (c, bottom panel).

2. Results and discussion

2.1. Design of porous substrate and encapsulation

Figure 1(a) illustrates the exploded view of the island-bridge structure based on porous elastomer substrate and porous encapsulation (e.g. polydimethylsiloxane, PDMS), where the pores are uniformly distributed around the island, and the two layers are precisely aligned. The elastomer substrate features solid island adhesion area to ensure the strain isolation for rigid functional devices/components (i.e. islands), while square grooves in the soft porous encapsulation layers are designed to precisely accommodate the islands. Serpentine interconnects consist of polyimide (PI)/metal/PI along the cross-section, where the thicker PI layers (9 μm) provide enhanced physical protection for the thinner metal conductive layer (600 nm) against external chemical erosion and mechanical damage. The design minimizes mechanical failure in the interconnects, as the thin metal layer is strategically placed at the neutral mechanical plane within the sandwich structure. The thickness for the elastomer substrate, islands, and encapsulation layer is 1 mm, 0.5 mm, and 0.2 mm, respectively. Both the islands and interconnects are fully bonded to the porous elastomer substrate, while the segments of interconnects above pores are permitted to deform unencumbered, thereby significantly enhancing the elastic stretchability in contrast to the case of solid elastomer substrate.

Quantitative FEA can be utilized to study the uniaxial tensile mechanical behaviors of serpentine interconnects in the island-bridge structure of solid and porous cases. It’s worth noting that the elastic stretchability is defined as the applied strain when the maximum principal strain of the metal layer reaches its yield strain (e.g. Cu$\approx$0.3%). This threshold is set considering the significantly higher elastic limit of both PI (>8%) [80] and PDMS ($\approx$200%) [81,82]. When the applied strain does not exceed the elastic stretchability limit, the deformation remains linear and reversible, without any accumulation of plastic deformation. This aspect is crucial for ensuring that the interconnects are protected from fatigue fracture (e.g. the initiation of microcracks) [83,84] under cyclic loading conditions. Hence, elastic stretchability can also serve as a qualitative indicator of the fatigue limit and mechanical durability of stretchable systems to a certain extent. Stretchable electronic systems with enhanced elastic stretchability achieved by reasonable arrangements of pores and interconnects can better maintain original configurations after unloading, reducing residual deformation and damage, thereby prolonging the service life of the stretchable inorganic electronics.

Figure 1(b,c) illustrate the deformed configurations and strain distributions of the island-bridge structure on solid and porous elastomer substrates without and with solid/porous encapsulation, when uniaxially stretched to the elastic limit of the overall structure. The FEA results denote that the elastic stretchability of the island-bridge structure on the porous substrate achieves an elastic stretchability of 45%, which is eight times greater than that of its solid substrate counterpart (5%). Additionally, the use of soft porous encapsulation enhances elastic stretchability to 28%, representing a significant seven times improvement over solid encapsulation (4%). The design of porous substrate and encapsulation permits completely unconstrained out-of-plane bending and twisting of partial segments of interconnects, allowing them to respond to externally applied tension and effectively disperse strain energy. This helps considerably in reducing the probability of local plastic yielding in the metal layer. Serpentine interconnects with enhanced elastic stretchability can also better maintain original configurations after unloading, reducing residual deformation and damage, and consequently, prolonging the fatigue life and mechanical ductility of the stretchable inorganic electronics.

Moreover, regardless of encapsulation, the elastic failure of serpentine interconnects on solid substrates typically occurs on the inner sides of circular segments. In contrast, with porous substrates, the initial failure locations – near the island at the pore edges – shift to the linear segments post-encapsulation (see the contour maps in Figure 1(b,c). These segments experience significant free movement, thus altering the failure mechanism. The reduction in elastic stretchability after encapsulating can be mainly attributed to the restriction of out-of-plane wrinkling deformations in the fully bonded segments of the serpentine interconnects, leaving in-plane bending as the predominant mode of deformation.

2.2. Analysis of porous elastomer substrate with serpentine interconnects

To facilitate a systematic study of this design strategy, the analysis of the serpentine interconnects on a porous elastomer substrate within an island-bridge structure is firstly conducted. Figure 2(a) shows the schematic diagram of the island-bridge structure on the porous elastomer substrate featuring square rigid islands in size $2\mathit{a}$ and adjacent spacing in length $2\mathit{L}$. Round pores are uniformly distributed except in the island regions, and are placed on the center of a square unit cell (length $\mathit{l}$) with a diameter of $d_1$. Consequently, the porosity of the region between two adjacent islands (Region I) can be calculated using the formula $\mathrm{\Phi }=\frac{\pi d_1^2}{4l^2}$. Given that a equals L, the pores between the two adjacent islands present a regular $\mathit{n}\times \mathit{n}$ square array that denotes the density of pores. The two deterministic parameters Φ and n are extracted to characterize the tensile stiffness of porous substrates and the density of pores, respectively.

Figure 2. Computational analysis on the elastic stretchability of porous elastomer substrate with serpentine interconnects. (a) Illustration of porous elastomer substrate strategy, showing the key geometric parameters for porous elastomer substrate with rigid islands: the porosity (Φ) and the number of pores (n), which indicate the tensile stiffness of substrates and the density of pores, respectively. (b) Illustration of key geometric parameters for serpentine interconnects: the height ratio $\mathit{\lambda }=\frac{l_2}{\mathit{w}}$ and unit cell number $\mathit{m}=\frac{2L}{l_1}$, where l₁, l₂, w and 2L are the unit cell length, the arm length and the width of the serpentine interconnects, and the length between two adjacent islands, respectively. (c) Elastic stretchability versus the porosity Φ for a range of pore numbers (n = 2, 4, 6, 8) with the same configuration of serpentine interconnects (λ = 17, m = 2). (d) Elastic stretchability versus the unit cell number m for a range of height ratio (λ = 11, 14, 17, 20) with the same porous elastomer substrate and islands (Φ = 56.7%, n = 4). (e) Plots of elastic stretchability against the metal layer thickness (Cu) in serpentine interconnects for both solid and porous elastomer substrate. (f) 2D scatter diagram illustrating the relationship between ε_{elastic-stretchability} and out-of-plane deformation area ratio (α). The points are all distributed in the region surrounded by two exponential dashed curves.

Figure 2(b) presents the 2D serpentine interconnects with the unit cell lengths $l_1$, the arm length $l_2$ and width w. The thickness of the PI and Cu layers are 9 μm and 600 nm, respectively. When the serpentine interconnects are bonded between the islands (Figure 2(b)), the unit cell number m can be calculated by the expression $\mathit{m}=\frac{L}{\mathit{l}1}$ and a normalized factor λ can be obtained by the expression $\mathit{\lambda }=\frac{{\mathit{l}}_2}{\mathit{w}}$, which can be extracted to determine the configurations of serpentine interconnects. This arrangement allows for a detailed analysis of how the pore design influences the mechanical properties and stretchability of the interconnects, providing critical insights into the optimization of the island-bridge structure for enhanced durability and performance.

On one hand, when bonding the same serpentine interconnects (λ = 17, m = 2) to substrate with consistent basic dimensions but varying the key design parameters Φ and n, we obtain porous substrates differing in tensile stiffness and pore density. It is observed that the curves of ${\epsilon }_{\mathit{elastic}-\mathit{stretchability}}$ increase with Φ, as shown in Figure 2(c), on account of more release of free deformation but decrease with n due to the more intense distribution. When n equals 4, 6, and 8, the values of ${\epsilon }_{\mathit{elastic}-\mathit{stretchability}}$ vary below 15%. It can be further speculated that serpentine interconnects are almost equivalent to bonding to a solid substrate as n approaches infinity, causing extremely low elastic stretchability below 10%. When n = 2, the abrupt decline at high porosity may mainly arise from the local extreme out-of-plane deformation. The special relative placement between periodical serpentine interconnects and circular pores is that long straight segments of interconnects are bonded to the narrowest cell wall region of the porous substrate. Furthermore, the irregular fluctuation of ${\epsilon }_{\mathit{elastic}-\mathit{stretchability}}$ is observed as the ratio $\mathit{\delta }/\mathit{\delta w}-\mathit{w}$ (the minimum cell wall width/the serpentine width) changed if they are keeping identical special relative positions (Figure S1(a)). In this scenario, only a fraction of the slender straight segments are bonded to the narrowest cell wall, bearing extreme local deformation. The remaining straight segments, suspended over pores, facilitate free deformations, leading to inconsistent variations in elastic stretchability due to the complex mechanics of deformation.

On the other hand, by maintaining a consistent porous substrate (Φ = 56.7%, n = 4), and setting the width of serpentine interconnects (w) at 0.2 mm, while varying the two deterministic factors λ and m, we obtain the results in Figure 2(d). Divergent and irregular changes of ${\epsilon }_{\mathit{elastic}-\mathit{stretchability}}$ that range from 6% to 45% are exhibited with different configurations of serpentine interconnects. Larger values of λ tend to cause higher levels of elastic stretchability (beyond 15%). However, slight variations (3%-6%) are shown even with larger slenderness (λ) and more cell units (m) for solid substrates (Figure S1(b)) [63,85,86].

The mechanical behavior of the staggered pores layout has also been studied, and the schematic diagram is shown in Figure S2(a). Merely altering the configurations of serpentine interconnects (i.e. m ranging from 2 to 5 and λ equaling 0, 10 and 20), approximate values of elastic stretchability are demonstrated when comparing the staggered with uniform layouts, which also manifests the effectiveness of staggered layout (Figure S2(b)). Regarding the thickness of the metal layer ($t_{\mathit{Cu}}$), ${\mathit{\epsilon }}_{\mathit{elastic}-\mathit{stretchability}}$ increases with $t_{\mathrm{Cu}}$ for both solid and porous substrates (Figure 2(e)).

As inferred from Figure 2(c,d), merely changing the design of pores on the substrate or configurations of serpentine interconnects does not result in significant or consistent effects on elastic stretchability, since the interplay of their relative positions is crucial or even predominant, leading to the non-monotonic changes in elastic stretchability according to various design parameters. The coupling of relative positions renders the distinction of two deformation configurations on the serpentine interconnects bounded by non-monotonic circular profiles. It means that fully bonded segments can only occur limited out-of-plane wrinkles, while those suspended above pores can occur almost completely free deformations (mainly in the forms of bending and torsion). The complex interaction of these deformation configurations makes accurate analysis challenging.

Therefore, considering the fundamental principles of the porous design strategy, we introduce the factor α that defines the area ratio of serpentine interconnects above pores where the out-of-plane deformation is unrestricted. An interesting observation has been revealed that the data points illustrating the relations between ${\epsilon }_{\mathit{elastic}-\mathit{stretchability}}$ and α are distributed within the region encircled by two exponential curves (Figure 2(f)). A specific α correlates to a consistent range of ${\mathit{\epsilon }}_{\mathit{elastic}-\mathit{stretchability}}$, which may guide the rational design of the interconnects and porous substrates.

2.3. Analysis of Island-bridge structures with porous encapsulation

Encapsulation is essential for the practical applications of flexible and stretchable electronics, as direct physical contact with the outside environment could result in the failure of fragile electronic device components and interconnects. Topically, the solid soft-encapsulated layer is used to protect interconnects and electronic devices from environmental corrosion or pollution, thereby improving the stability and reliability of flexible and stretchable electronic systems. However, the solid soft encapsulation layer limits the out-of-plane deformations of interconnects, which greatly restricts the stretchability of the whole system. Therefore, a highly stretchable and reliable encapsulation scheme is crucial for the design and manufacture of flexible and stretchable electronic devices.

The porous elastomer films can serve as encapsulation layers, achieving the protection of the interconnects while maintaining high stretchability (Figure 3(a)). The porous encapsulation layer is aligned and bonded to the porous elastomer substrate, allowing the interconnects sandwiched in between to freely deform within the pores, as shown in Figure 3(b), thereby ensuring high elastic stretchability.

Figure 3. Mechanical analysis of the porous encapsulation strategy. (a, b) Schematic illustration of the island-bridge structure with porous encapsulation layer on porous elastomer substrate: (a) initial state, and (b) stretched to 28% in uniaxial tension. (c) Top view schematic of the island-bridge structure with porous encapsulation for a representative region. (d) The normal strain distribution of the porous substrate ε_x at the surface along the x-axis under 28% uniaxial stretching for both unencapsulated and encapsulated cases. (e) The out-of-plane displacement of the porous substrate u_z at the surface along the x-axis under 28% uniaxial stretching for both unencapsulated and encapsulated cases, where the inset panel presents the out-of-plane deformation contour map of the area closest to the island side.

Figure 3(c) presents the top view of a representative volume element (RVE) featuring periodically aligned islands (size 2a) on the substrate, with a center-to-center distance of 2L between the adjacent islands. As shown in Figure 3(d), it’s evident that the strain concentration around rigid islands has been alleviated, with ${\epsilon }_x$ decreasing from 0.28 to 0.14 when $\frac{x}{\mathit{a}+\mathit{L}}\approx 0.5$, navigating to the boundary area of the heterogeneous interface, which is usually considered as the extreme area of strain concentration after encapsulation. Moreover, the excessive out-of-plane displacement $u_z$ caused by the drag of serpentine interconnects has been lessened (Figure 3(e)). The out-of-plane deformation contour map of the area closest to the island side indicates that the encapsulation layer can alleviate local extreme out-of-plane movements caused by the deformation of the interconnects. Therefore, it can be inferred that the encapsulation compensates for the reduction in strength of the porous elastomer substrate. Furthermore, the restriction of out-of-plane motion helps prevent extreme deformation of the serpentine interconnects attached to it, thereby lowering the risk of mechanical fracture.

Considering the geometries of interconnects and the porosity, two representative cases, P₁ and P₂, were chosen for detailed analysis, as illustrated in Figure 4(a). Both P₁ and P₂ exhibit identical porosity (Φ = 50%). P₂ corresponds to more slender serpentine interconnects bonded to a relatively sparse porous region. This configuration tends to generate a larger out-of-plane deformation area ratio α (α₂ = 65%). In contrast, P₁ demonstrates a reduced ratio (α₁ = 27%), owing to its different structural arrangement. In the analysis of the unencapsulated state, it was observed that the center points (α, ${\epsilon }_{\mathit{elastic}-\mathit{stretchability}}$) are all distributed within the region surrounded by two exponential dashed curves (Figure 2(f)). Similarly, in the encapsulated state, as depicted in Figure 2(b), the data points were also found to exhibit a comparable distribution. Moreover, the deformed configuration in the case of P₂ when stretched to the elastic stretchability limit was shown in Figure S3(a). Figure S3(b) also verified the almost consistent deformed configurations of serpentine interconnects between experimental observations and FEA predictions, with strain distribution of metal layer clearly revealed.

Figure 4. Mechanics analysis of the porous encapsulation strategy for serpentine interconnects. (a) Schematic illustration of two representative layouts (P₁ and P₂) of island-bridge structure with porous substrate and porous encapsulation. (b) 2D scatter diagram illustrating the relationship between ${\epsilon }_{\mathit{elastic}-\mathit{stretchability}}$ and out-of-plane deformation area ratio α for both unencapsulated and encapsulated cases, highlighting the two cases of P₁ (α = 0.27) and P₂ (α = 0.65) in (a). (c) Plots of elastic stretchability varying with the relative size of concentric pores in the encapsulation layer and substrate (d₂/d₁) for the two cases in (a). (d) Plots of elastic stretchability varying with the thickness ratio of the porous encapsulation layer and island (t_enc/t_island) for the two cases in (a).

Upon a more detailed examination of P₁ and P₂ scenarios, it was observed that the elastic stretchability remains relatively consistent across varying relative diameters of encapsulation ($d_2/d_1)$. More precisely, an enhancement in stretchability of approximately 1%-2% was noted with larger pores, as evidenced in Figures 4(c) and S4). Besides, variations in the thickness of the encapsulation layer, whether below or beyond island thickness (t_encap/t_island), have exerted negligible influence on the elastic stretchability (Figures 4(d) and S5). If the thickness of the encapsulation layer doesn’t exceed the island (t_encap/t_island ≤1), the primary function of the encapsulation is to protect the interconnecting conductors, which endure significant deformation. The top surfaces of rigid devices remain exposed to the external environment, facilitating energy or material exchange, which is particularly relevant for the design of chemical sensors. Conversely, when rigid devices are completely encapsulated, they are isolated from external effects, aligning with the requirements of the vast majority of circuits and systems. This suggests that porous encapsulation can be a universal design strategy, accommodating various needs of functional devices, whether partially exposed to external environments or not, with minor impact on overall stretchability.

2.4. Fatigue experiments

Cycle fatigue experiments have been performed to estimate the elastic stretchability of both solid and porous encapsulation strategies. Metallurgical microscopes were employed to observe microcracks under the unloading state, enabling accurate monitoring of initiation microscale cracks. Figure 5 presents the optical images of the strained island-bridge structures with solid (Figure 5(a)) and porous (Figure 5(b)) substrates and encapsulation layers after 1200 cycles of uniaxial tensile fatigue tests. For solid substrate and encapsulation, serpentine interconnects suffered mechanical fracture with initiation of microcracks under the applied strain of 10% while remaining undamaged under the strain of 5%, indicating that the corresponding elastic stretchability can be determined in the range of 5%~10% approximately. In contrast, porous substrates demonstrated significantly larger elastic stretchability in the range of 15%~20%. A microcrack was captured at the arc segment of serpentine interconnects after 800 cycles of uniaxial tension. Accumulation of cycles caused the initiation and propagation of cracks to be seen under the metallurgical microscope.

Figure 5. Fatigue experimental results. (a) Optical images of the island-bridge structures on a solid elastomer substrate with the solid encapsulation: the unfractured state after 1200 cycles at 5% uniaxial tensile (I) and the fractured state with a microcrack after 800 cycles at 10% uniaxial tensile (II). (b) Optical images of the island-the bridge structures on a porous elastomer substrate with the porous encapsulation: the unfractured state after 1200 cycles at 15% uniaxial tensile (I) and the fractured state with a microcrack after 800 cycles at 20% uniaxial tensile (II). (c) Comparison results between experiment images and FEA predictions focusing on the deformed configurations and strain distribution of fully bonded serpentine interconnects when stretched to the elastic limits for the encapsulated solid (I) and porous (II) substrates. Notably, the FEA images were captured with serpentine interconnects displayed on the top layer (with the encapsulation layer hidden), to clearly reveal the deformations and strain distribution in the metal layer.

The specific elastic stretchability of solid and porous systems acquired by FEA predictions are 7% and 16%, respectively, which are in good agreement with the fatigue results (Figure 5(c)). The generally consistent deformed configurations in both FEA predictions and experiment images could be observed, and the minor deviation may arise from the environmental disturbance and assembly errors. Though not completely precisely aligned, the distinction of deformed configurations, i.e. local wrinkles for the solid substrate and out-of-plane deformation for the porous substrate, can be both observed in FEA predictions and experiment images.

Furthermore, the fatigue experiments together with simulation predictions highlighted that the enhanced elastic stretchability observed with porous design is attributed to the serpentine interconnects’ ability to produce out-of-plane deformations, e.g. bending and torsion, to a significant extent during stretching. This mechanism effectively releases cumulative strain energy and mitigates mechanical failure.

3. Conclusion

In summary, our proposed design strategy, featuring the porous elastomer substrate and encapsulation, has been proven to be highly effective in enhancing the stretchability of serpentine interconnects for the island-bridge structure in stretchable inorganic electronics. The serpentine interconnects are fully bonded to the elastomer substrate, while segments above pores remain suspended, allowing for free deformation and a substantial improvement in elastic stretchability compared to the solid substrates. The pores ensure unimpeded interconnect deformations, and moderate porosity provides support while maintaining the initial planar state. FEA was employed to thoroughly examine this design concept and its key parameters. In comparison to the conventional solid elastomer substrate and encapsulation, a substantial enhancement of elastic stretchability has been proven (e.g. $\approx 9.0$ times without encapsulation and$\approx 7.0$ times with encapsulation). Moreover, the mechanical stability of the proposed design strategy has been validated through uniaxial cyclic loading fatigue experiments. Fatigue experiments without microcracks defined the ranges of elastic stretchability for both solid and porous encapsulation, and the porous systems exhibit a remarkable 15%–20% elastic stretchability, which is two to three times higher than the 5%–10% observed in solid systems. This underscores the effectiveness of our approach in not only improving stretchability but also ensuring the mechanical integrity and stability of the stretchable electronic components. Beyond stretchability, the intrinsic advantages of the proposed strategy, including permeability and heat dissipation, could serve as a promising avenue for advancing the field of stretchable inorganic electronics. The results gained from this study open new possibilities for innovative applications and contribute to the ongoing development of stretchable electronic technology.

Materials and methods

Finite element analysis

Finite element simulations were performed using commercial software ABAQUS to analyze the island-bridge structure with porous elastomer substrate and encapsulation. Four-node shell elements (S4R) were adopted to simulate the serpentine interconnects and eight-node solid elements (C3D8R) for other parts. Serpentine interconnects and encapsulation were tied to the elastomer substrate regardless of interface delamination or fracture. The meshes at the contact area were refined to ensure accuracy and convergence. Minor damping and perturbation were introduced to induce the configuration transformation from the initial state. The elastic stretchability corresponds to the point at which the maximum principal strain of the metal layer reaches its yield strain (e.g. ${\epsilon }_{\mathit{Cu}}\approx 0.3\mathrm{\%}$) across half the width of any section of the interconnects. Hyperelastic constitutive called the Mooney-Rivlin law captured the properties of elastomer substrate ($E_{\mathit{PDMS}}$ = 2 MPa, ${\mathit{\nu }}_{\mathit{PDMS}}$ = 0.48) and the converted parameters are C₁₀ = 0.27027 MPa, C₀₁ = 0.067568 MPa, and D = 0.12 MPa⁻¹. Other material parameters include $E_{\mathit{Si}}$ = 150 GPa, ${\mathit{\nu }}_{\mathit{Si}}$ = 0.27 for islands and $E_{\mathit{Cu}}$ = 130 GPa, ${\mathit{\nu }}_{\mathit{Cu}}$ = 0.34 for metal layers.

Fabrication of the porous elastomer substrate and encapsulation layer

The fabrication began with 3D printing of the pouring mold (for elastomer substrate: 1 mm in thickness, for encapsulation layer: 0.2 mm in thickness). Subsequently, silica gel (PDMS, Sylgard 184, Dow Corning) mixed by 10:1 was poured into the molds and cured at 80 ${\hspace{0.17em}}_{\hspace{0.17em}}^{\circ }\mathrm{C}$ for 4 h. Finally, ultraviolet laser cutting was then used to fabricate the porous substrate and porous encapsulation layers.

Fabrication of the serpentine interconnects for fatigue experiments

The preparation of serpentine interconnects began with spin-coating an ultrathin sacrificial layer of polymethyl methacrylate (~200 nm, PMMA 495 A4; MicroChem) on a silicon wafer. Following the curing of the PMMA layer, a layer of PI (9 µm, paa1002; Furunte) was applied via spin-coating. Subsequently, a layer of copper with a thickness of ~600 nm was deposited using electron-beam evaporation, followed by spin-coating another layer of PI (9 µm), and defining the serpentine interconnects (PI/Cu/PI) by ultraviolet laser cutting. The underlying PMMA layer was then dissolved by immersing in acetone, resulting in the release of the serpentine interconnects on a water-soluble tape (polyvinyl alcohol; Aquasol Co.). Following the removal of the water-soluble tape by immersing in hot water, the serpentine interconnects were meticulously aligned and transferred onto a porous elastomer substrate (1 mm, PDMS). Finally, the encapsulation layer was aligned and transferred onto the top surface.

Acknowledgments

Z.X. acknowledges support from the National Natural Science Foundation of China (Grant No. 12172027) and the Fundamental Research Funds for the Central Universities. X.M. acknowledges support from the National Natural Science Foundation of China (Grant Nos. 12272023 and U23A20111). Numerical computations were performed on the Hefei Advanced Computing Center.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/19475411.2024.2342871

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12172027, 12272023, and U23A20111) and the Fundamental Research Funds for the Central Universities.