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Review Article

Stretchable Thin Film Materials: Fabrication, Application, and MechanicsOPEN ACCESS

[+] Author and Article Information
Yu Wang, Zhengwei Li

Department of Mechanical Engineering,
Boulder, CO 80309-0427

Jianliang Xiao

Department of Mechanical Engineering,
Boulder, CO 80309-0427

1Corresponding author.

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received October 29, 2015; final manuscript received February 26, 2016; published online April 18, 2016. Assoc. Editor: Mehmet Arik.

J. Electron. Packag 138(2), 020801 (Apr 18, 2016) (22 pages) Paper No: EP-15-1122; doi: 10.1115/1.4032984 History: Received October 29, 2015; Revised February 26, 2016

Abstract

Stretchable thin film materials have promising applications in many areas, including stretchable electronics, precision metrology, optical gratings, surface engineering, packaging, energy harvesting, and storage. They are usually realized by engineering geometric patterns and nonlinear mechanics of stiff thin films on compliant substrates, such as buckling of thin films on soft substrates, prefabricated wavy forms of thin films, and mesh layouts that combine structured islands and bridges. This paper reviews fabrication, application, and mechanics of stretchable thin film materials. Methods and fabrication processes of realizing stretchability in different thin films, such as semiconductors, metals, and polymers, on compliant substrates are introduced. Novel applications that are enabled by stretchable thin films are presented. The underlying mechanics of stretchable thin film materials in different systems is also discussed.

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Introduction

Thin film materials have many advantages over their bulk counterparts, in terms of properties, applications, and economical considerations. One example is mechanical flexibility, i.e., bendability, when they are in freestanding forms or integrated with other thin film materials. Mechanics theory indicates that the strain in the thin film caused by bending is proportional to its thickness and the bending curvature [1]. For example, when a 100 nm thick Si thin film is integrated with a 20 μm thick plastic substrate and bended to a radius of curvature 10 mm, the maximum strain in the Si film is only 0.1%, which is ten times smaller than its fracture strain (∼1%) [2,3]. This type of mechanical robustness has enabled many applications, such as flexible electronics and micro/nanoelectromechanical systems [4,5].

However, the mechanical flexibility alone provided by thin film materials cannot meet the much more critical challenges posed by novel applications that require very large stretchability [6,7]. Examples range from stretchable electronics and tunable optical gratings to biomedical implants and stretchable energy harvesting and storage devices [814]. These applications require thin films to be extremely soft and stretchable, like a rubber band. The mechanical strains introduced in these applications can be as large as 100%, way beyond the failure strains of most thin film materials (typically ∼1%) [3]. To conquer this challenge, a lot of research efforts have been invested in the last two and half decades. Different strategies have been utilized to realize mechanically stretchable thin films without affecting their intrinsic functionalities, such as semiconducting properties, electrical conductance, and piezoelectricity [7,1520]. All these strategies take advantage of nonlinear mechanics associated with novel geometrical patterns and layouts to enable desired stretchabilities in otherwise inextensible thin film materials [1,1520].

A flexible electronic device with printed sensors (upper) and its bending performance (bottom) is shown in Fig. 1(a) [21]. As the bending radius reduces to 12.5 mm, the performance starts to degrade. Assume the thickness of the substrate is h, and the electronic device is much thinner than the substrate, the minimal bending radius Rm can be reached is limited by the failure strain of the electronics εf, Rm ∼ $h/εf$. Since the failure strain of most electronic materials is ∼1% or smaller, the minimal bending radius of the system is ∼100 h. To further improve the bendability, we can either reduce the thickness h or increase the failure strain εf. However, reducing the thickness of the substrate is always constrained by design, fabrication, handling, and packaging. To increase the failure strain εf, we have to make the electronics stretchable. With stretchable electronics, the minimal bending radius of the system can be reduced to an extreme level. Figure 1(b) shows an ultrathin, stretchable Si-CMOS circuit wrapped around the edge of a microscope cover slip (thickness ∼0.1 mm) [18]. The inset is a cross-sectional schematic view of the circuit. The circuit is bended to an extreme folding state, which is not achievable through conventional flexible electronics. In addition to improved bendability, stretchable electronics can enable other extreme deformation capabilities, as illustrated in Fig. 1(c) [22]. Top left frame shows a stretchable inorganic light-emitting diode (LED) array on a piece of paper, folded twice. Top right frame is an LED array on an aluminum foil, in a crumpled state. Bottom left is an LED array on an deflated catheter balloon. Bottom right shows an LED array integrated on a plastic tube (diameter ∼2.0 mm). The insets show the undeformed states of the LED arrays. A more direct demonstration of the deformability of stretchable electronics is exhibited in Fig. 1(d) [14]. The stretchable lithium-ion battery can be stretched by 300% while functioning.

The purpose of this paper is to review fabrication, application, and mechanics of stretchable thin films. Different fabrication methods and processes to realize mechanically stretchable thin film materials will be introduced, including buckling of stiff thin films on soft substrates, prefabricated wavy patterns, and mesh layouts that combine rigid islands and stretchable interconnectors. Interesting and novel applications enabled by stretchable thin films will be summarized, such as stretchable and tunable optical gratings, precision metrology, tunable surface properties, and stretchable and curvilinear electronics. The underlying mechanics of stretchable thin films in these systems will also be discussed.

Fabrication of Stretchable Thin Films

One feasible way to realize stretchable thin films is by transforming thin film materials into wavy structures, through nonlinear buckling, or wrinkling on soft substrates. The underlying mechanism is analogous to a spring, an extensible structure made of inextensible material. Different strategies have been utilized to induce buckling in thin films on soft substrates in order to fabricate stretchable thin films, such as mechanical strain (Sec. 2.1), thermal mismatch (Sec. 2.2), surface treatment by ultraviolet ozone (UVO) (Sec. 2.2), and focused ion beam (FIB) (Sec. 2.3) [2334]. Although these strategies are convenient and effective in making wavy, stretchable thin films, they share some common drawbacks. The wavy structures of the thin films, which determine the stretchability, are defined by the material and geometric properties of the thin films and the substrates [35]. This gives little freedom in designing the wavy structures once the thin films and substrates are specified. Two different methods were then introduced to resolve this issue: controlled buckling (Sec. 2.4) and prefabricated wavy thin films (Sec. 2.5) [19,35]. On the other hand, mesh layouts that combine rigid islands and stretchable interconnectors were also widely used in stretchable electronics. This strategy leaves the functional electronic elements in their flat, microscale formats but transforms the metal interconnectors into wavy, stretchable forms, in order to comply with the established manufacturing processes in semiconductor industry [1,3,4,6,1317,3645].

Buckling Induced Wrinkles Through Mechanical Strain Mismatch.

By applying mechanical strains to the substrates, strain mismatch between the thin film and substrate can be applied with precise control and with desired rate [32]. Mechanical strains can be applied on either substrate only or the bilayer system. For example, tensile strain can be applied to the compliant substrate, and then the thin film is introduced to the substrate surface. Releasing the strain in the substrate leads to wrinkling of the thin film if the compressive strain exceeds a critical value (Figs. 2(a) and 2(b)) [20]. Compressive strain can also be applied to the bilayer system directly to induce surface wrinkling [46]. However, this method may induce global system buckling instead of thin film wrinkling on the surface, depending on the material properties of the film and substrate and the ratio of their thicknesses [47].

Uniaxial and biaxial mechanical strains induce one-dimensional (1D) and two-dimensional (2D) wrinkling patterns, respectively. Figure 2(a) shows the fabrication processes of 1D wrinkling by uniaxial mechanical strain mismatch [20]. In this example, thin Si ribbons are fabricated from silicon on insulator wafer by photolithography and etching processes. After etching away the bonding layer of SiO2, Si ribbons are supported by, but not bonded to the mother wafer. Then Si ribbons are transferred to prestretched polydimethylsiloxane (PDMS) substrate. Releasing the prestretch in the PDMS substrate induces 1D wrinkling of the Si ribbons. As shown in Fig. 2(b), wrinkled Si ribbons show uniform wavy patterns. Inspired by this method, researchers fabricated stretchable electronics and curvilinear electronics systems [3844,4850].

Similar to the processes of realizing 1D Si ribbon wrinkling patterns in Fig. 2(a), Choi et al. produced 2D wrinkling in Si nanomembranes on PDMS substrates to provide biaxial stretchability for the electronics [51]. Fabrication processes are shown in Fig. 2(c) [51,52]. The difference from 1D wrinkling is that the PDMS substrate is biaxially stretched before transferring Si nanomembranes. Optical and atomic-force microscopy (AFM) images are shown in the left and right frames of Fig. 2(d), respectively. At different locations, the wrinkling shows different patterns. For example, 1D wrinkling is observed at the edges, and 2D herringbone patterns are present at the inner region.

Two-dimensional wrinkling can also be obtained on PDMS substrates with surfaces treated by plasma or UVO [2833]. Oxygen plasma or UVO treatment on PDMS leads to the formation of an oxidized, silicalike stiff thin layer on the surface of PDMS [28]. Lin et al. used a square-shaped PDMS strip, clamped and stretched equally in both directions [32]. Plasma treatment is performed on the surface of the stretched sample. Highly ordered zigzag herringbone patterns are observed when the strain in X direction is released before strain release in Y direction. They also observed disordered zigzag herringbone patterns form when the sample is stretched and released simultaneously in both directions with equal strains.

Buckling Induced Wrinkles Through Thermal Mismatch.

This method was first introduced by Bowden et al. in 1998 [23]. In this study, a thin layer of gold film is deposited onto PDMS by electron beam evaporation, as shown in Fig. 3(a) [23]. In the film deposition process, PDMS is heated by metal source, which leads to its volume expansion. Because the coefficient of thermal expansion of PDMS is much larger than that of gold, after the film-substrate system cools down, the film is compressed by the substrate, leading to wrinkled, wavy pattern on the surface. Figures 3(b) and 3(c) show wrinkling patterns induced by this method. Many other researchers have also realized wrinkling of different metal films, such as nickel, aluminum, titanium, and chromium, by adopting similar approaches [23,31].

Surface treatment using plasma or ozone is also a common approach to form stiff thin films on PDMS substrates for creating wrinkle patterns [24,2733]. It leads to substitution of carbon atoms by oxygen atoms at the surface of PDMS, which produces a thin and stiff silicalike layer [2730,45]. When the system cools down, thermal mismatch introduces compression into the stiff thin film, leading to thin film wrinkling at the surface.

The wrinkle patterns on the surface are also controllable. When a continuous, uniform stiff thin film is deposited, and the substrate is also heated uniformly, equibiaxial thermal mismatch strain induces 2D, herringbone wrinkle patterns (Fig. 3(b)) [23]. When ridges are introduced with appropriate spacing, guided 1D sinusoidal wrinkle patterns can be realized (Fig. 3(c)) [23]. The 2D, herringbone wrinkle patterns are caused by isotropic (equibiaxial) compressive stress induced by thermal expansion mismatch between the thin film and the substrate. But with ridges on the surface, the stress in the film is not isotropic or uniform anymore. The compressive stress perpendicular to the ridges is much smaller than the compressive stress along the ridge direction, causing the formation of ordered, 1D wavy patterns, as highlighted by the red box in the bottom right of Fig. 3(c). The top left red box shows a transition zone from the ordered, 1D pattern to 2D, herringbone pattern. Similar phenomena can also be seen in 1D buckling of narrow ribbons [53] and at the edges of 2D herringbone patterns [52].

Buckling Induced Wrinkles Through Other Methods.

In the previous discussion, wrinkling forms in the whole film simultaneously. Meanwhile, some researchers have used different methods, such as FIB or laser treatment, to modify the surface of substrate or the film in designed paths to induce surface wrinkling in desired areas [33,54]. Figure 4(a) shows the setup to form wrinkling patterns by FIB [33]. The material used here is a flat PDMS sheet. Upon exposing the surface to a FIB of Ga+ ions, wrinkling forms in desired paths. The resolution of this method is high and can produce complex wrinkling patterns with various widths by controlling movement of the sample. Figure 4(b) is a SEM image of the wrinkling pattern formed only in the area of the PDMS exposed to FIB (left to the yellow dashed line), the unexposed surface remains flat (right to the dashed line). Figure 4(c) shows a wrinkle pattern along an S-shaped path generated by controlling the relative motion of the substrate and ion beam. Inset shows a wrinkling pattern induced along a circular path. Similar to FIB, Guo et al. used laser direct writing technique to control wrinkling patterns in a gold/polystyrene (Au/PS) system [54]. When heated by laser, the mechanical properties of the gold film and the surface of the elastomer are locally modified, leading to patterned wrinkling along the path of laser.

Ohzono et al. combined lithography and self-organization to fabricate microwrinkle structures, as shown in Fig. 4(d) and 4(e) [55]. Two-dimensional arrays of PS microspheres are transferred to a bare PDMS surface by adhesion. After oxygen plasma treatment, the microspheres are removed. Next, a thin layer of Pt film is deposit on the PDMS surface by sputtering. In the deposition process, PDMS expands due to heating effect. After cooling down, wrinkling appears on the PDMS surface. In this approach, wrinkling patterns strongly depend on the sizes of the microspheres.

Swelling is another approach to introduce strain mismatch and thus to induce surface wrinkling in bilayer systems [56]. Figure 3(f) shows reversible surface wrinkling of UVO-treated PDMS in response to ethanol drop [56]. When UVO-treated PDMS is exposed to ethanol, the stiff top layer swells much more than the substrate [56]. This mismatch leads to an anisotropic stress field in the film and induces the formation of surface wrinkling patterns, as shown in Fig. 3(g). With the same approach, Chung and coworkers fabricated diffusion-controlled and self-organized symmetric wrinkling patterns on UVO-treated PS film [57]. The exposure time is critical for the surface morphologies. Different exposure time leads to different patterns, including spoke and target patterns, as shown in Fig. 4(h) [57]. A possible mechanism for the symmetric patterns is the defects in the film, as illustrated in Figs. 3(i) and 3(j). In Fig. 4(i), a glass bead is used as a mask to produce a defect in the UVO treatment. When the film is exposed to solvent vapor, a regular spokelike pattern forms by localized swelling through the predefined defect. The defect in Fig. 4(j) is formed by diamond tip. When the film meets the solvent, self-organized concentric ring pattern forms at the indent site spontaneously.

Controlled Buckling.

The approaches discussed previously demonstrated effective methods to create ordered wrinkling patterns in bilayer systems; however, it is difficult to control the geometries of the patterns directly once the thin films and substrates are selected, which limits the freedom in designing the wavy structures for applications. To solve this issue, Sun et al. developed a method to control the wrinkling geometries precisely [19], as illustrated in Fig. 5(a). The fabrication starts with making a mask for patterning surface chemical adhesion sites on PDMS substrate. The mask is brought in conformal contact with the PDMS. The surface of untreated PDMS is dominated by –OSi(CH3)2O– groups. After UVO treatment, they are converted to –OnSi(OH)4-n, which are highly polar and reactive. The –OnSi(OH)4-n groups allow condensation reaction with similar surface groups to form strong siloxane (–O–Si–O–) bonding [19]. When Si or GaAs ribbons (coated with thin SiO2) are transferred onto the prestretched, treated PDMS, strong chemical bonding forms between Si ribbons and the reactive sites. For the other inactive areas, only weak van der Waals interactions exist between ribbons and the PDMS [58]. When the prestrain is released, wavy shapes form through the separation of the nanoribbons from the inactive regions of the PDMS. The bulked nanoribbon structures can also be encapsulated by applying another layer of PDMS. Nanoribbons formed in this way offer both high strechability and compressibility for the system, as illustrated in Fig. 5(b), with potential applications in stretchable electronics. The top frame of Fig. 5(c) shows a SEM image of buckled GaAs nanoribbons on PDMS. As shown in the figure, nanoribbons show uniform, periodic pattern with common geometries and spatially coherent phases [19]. Since the patterns is solely controlled by the selection of activation sites during exposure to UVO treatment, nonperiodic and nonuniform patterns and incoherent phases can be easily realized, as shown in the middle and bottom frames in Fig. 5(c) [19].

More recently, Xu and coworkers extended this method to assemble the micro/nanomaterials, including device-grade silicon, into three-dimensional (3D) architectures by mechanical compressive bulking, as shown in Fig. 5(d) [39]. Two-dimensional planar filamentary serpentine silicon ribbons are treated by ultraviolet (UV) light to create precisely controlled patterns of surface hydroxyl terminations at desired locations. Treated silicon ribbons are then transferred onto the surface of prestretched, UV-treated PDMS. Strong covalent bonding between Si ribbons and PDMS forms in selected locations, marked by red dots and dashed lines in the left frame (one site is also highlighted by a red square). Relaxing the strain in the substrate, compressive force leads to out-of-plane buckling, twisting, and translational motions, leading to formation of 3D mesostructures. This method offers many possibilities for the fabrication of complicated 3D electronics and devices.

Prefabricated Wavy Patterns.

Prefabricated wavy patterns can also provide an effective method to fabricate wavy thin films with controlled geometries. To fabricate a wavy substrate, a series of molding and smoothing processes from a rigid silicon template are involved [34]. Figure 6(a) is the saw tooth structure after the anisotropic etching of the Si (100) in an isopropyl alcohol buffered KOH solution. After a few steps of smoothing and molding, a PDMS substrate with sinusoidal wavy shaped surface is obtained. Then, depositing a layer of gold thin film on top yields a bilayer system with wavy surface relief, as shown in Fig. 6(b). The thin film obtained through this method offers both high stretchability and compressibility (the maximum compressive strain can be reached without failure) for the thin films because of the initial wavy shape. Furthermore, the surface wavy geometries can be easily controlled by designing different surface relief features.

Mesh Layouts That Combine Rigid Islands and Stretchable Interconnectors.

Mesh layouts that combine rigid islands and stretchable interconnectors offers extremely high compressibility and stretchability and, therefore, are widely used in stretchable electronics [16,40,42,43]. Figure 7(a) shows the fabrication processes of a noncoplanar mesh design for stretchable, integrated circuits [16]. As shown in the top frame, the circuit with a mesh layout is first fabricated on a mother wafer through photolithography, deposition, and etching processes. The circuit itself is a mesh with isolated active device islands. These islands are connected by straight, narrow metal interconnectors (encapsulated by polyimide) to offer electrical and mechanical connections. Then, the circuit is transfer printed onto a prestretched PDMS substrate (middle and bottom frames, Fig. 7(a)). A thin layer of SiO2 is coated on the surfaces of the islands, which form strong, covalent –O–Si–O– bonding with UVO-treated PDMS surface after transfer printing. However, the interconnectors only have weak van der Waals interaction with the PDMS substrate. Upon release of the prestrain in PDMS, the interconnectors buckle into arc shapes to absorb most of the compressive strain in the mesh, while the brittle, active device islands remain intact (bottom frame, Fig. 7(a)). Bottom frame of Fig. 7(b) shows a SEM image of the as-fabricated noncoplanar mesh structure of stretchable, integrated circuits. The arc-shaped interconnectors provide huge stretchability and deformability to the mesh structure. When the system is stretched, the arc-shaped interconnectors are flattened out to absorb most of the strain, as shown in the top frame of Fig. 7(b). When subject to other types of deformation, the interconnectors can also easily bend and twist due to their narrow and thin geometries to protect the active devices from breaking.

To further improve system stretchability, serpentine designs were adopted for the interconnectors, as shown in Fig. 7(c) [16]. The fabrication processes is similar to Fig. 7(a), but the straight interconnectors are replaced by serpentine interconnectors. Upon transfer printing and release of prestretch, serpentine interconnectors buckle in a much more complicated manner, which includes bending and twisting deformation (top left frame, Fig. 7(c)). This complex deformation mode, together with the increased effective length, provide much larger stretchability to the interconnectors when the system is deformed, as shown in Fig. 7(c). Another advantage provided by the serpentine interconnector design is that prestretching PDMS substrate is not required during the transfer printing process. The nonbuckled, flat serpentine interconnectors can also provide very large stretchability, since serpentine shapes, when stretched (or compressed), can adopt lateral buckling modes that combine bending and twisting deformation to effectively reduce strains. More advanced developments that utilize fractal designs can offer even better compressibility and stretchability to the system [59].

Application of Stretchable Thin Films

Optical Gratings.

Ordered nanoscale thin film wrinkles on soft substrate have many potential applications. Figure 8 is an example showing fabrication and performance of a tunable optical grating based on thin film wrinkling [10]. Prestretched PDMS is treated by oxygen plasma and then an ultrathin gold and palladium film is sputtered on top of the surface. When the strain in PDMS is released, sinusoidal wrinkling forms with submicron period, which can provide grating effect to light, as shown in Fig. 8(b). As the system is stretched, the period of the sinusoidal wrinkles increases, leading to the shift of the peak wavelength (Fig. 8(b)). Stretch of the system also causes decrease of the amplitude of the wrinkles, resulting in decrease of the diffraction intensity, as plotted in Fig. 8(c). This optical grating based on thin film buckling has also been used to amplify small strain signals to orders of magnitude larger signals of change in diffraction angles, for measurement of very small strains [60].

Precision Metrology.

Due to the strong correlation between the wrinkle formation and the mechanical properties of the bilayer system, the thin film wrinkling has shown applications in precision metrology, for example, measurement of elastic moduli of polymeric thin film and microstrain sensing (Fig. 9) [61]. Stafford and coworkers developed an efficient method for the measurement of moduli of nanoscale polymer films [61,62]. In this method, thin polymer films wrinkle on PDMS substrate with wavy, sinusoidal profiles. The optical and atomic force microscopy images are shown in Figs. 9(a) and 9(b), respectively. According to thin film bulking theory, the modulus of the film can be precisely determined once the wavelength of the wrinkling, the thickness of the film, and the modulus of the substrate are known (Fig. 9(c)).

Surface roughness and chemistry determine the adhesion between two surfaces [32,63,64]. Lin et al. developed a new method to regulate adhesion by varying the strain applied to the wrinkled film, which leads to the change of the surface roughness (Fig. 10(a)) [32]. Wrinkle pattern is produced on UV-treated PDMS sample by releasing tensile prestrain and completely disappears after the system is stretched to the same magnitude of prestrain. Surface roughness increases as wrinkle amplitude increases due to the increase of applied prestrain, as shown in Fig. 10(a), which leads to monotonic decrease of adhesion [32]. As shown in Fig. 10(b), the pull-off force drops by more than ten times from flat surface to a wrinkled surface due to applied prestrain of 22.4% [32]. Another study, however, demonstrated that wrinkled surface could lead to increase in adhesion, due to increasing contact perimeters [65]. In this latter study, the wrinkle pattern shows 2D, short features. When in contact with a flat test probe, the interface forms small enclosed perimeters. The edge constraints are different from the long, 1D wrinkles as in work of Lin et al. study.

Stretchable Electronics and Optoelectronic Systems.

In addition to the previous applications, thin film winkling induced by strain mismatch is a promising way to realize stretchable thin films that can be used in stretchable electronics and optoelectronic systems. The approach of mechanical strain mismatch allows application of desired strain levels to the bilayer system to induce desired surface patterns. Wrinkled nanoribbons and nanomembranes on PDMS offer stretchability to the brittle, inextensible semiconductor materials. Based on this method, stretchable electronics and optoelectronic systems are realized [6,18,3744,6673]. A silicon-based integrated circuit that is stretchable, twistable, and foldable is shown in Fig. 11 [18]. In this study, a thin layer of silicon circuit covered by PI film is transferred onto PDMS substrate to form wrinkled, “wavy” structures of logic gates, ring oscillators, and differential amplifiers (Fig. 11(a)). This form of silicon circuit offers good stretchability and foldability. Figures 11(b) and 11(c) show optical microscope images of functional units at the center and edge of the circuit in the twisted configuration, respectively.

To further improve stretchability, serpentine and self-similar designs of interconnects were also developed. Figure 12(a) shows an epidermal electronic system (EES) that can be mounted on human skin [12]. This system consists of multifunctional sensors, microscale LED, active/passive circuit elements, wireless power coils, and devices for radio frequency communication. These components are designed in the form of filamentary serpentine nanoribbons and are integrated on the surface of a thin elastomeric sheet. Such thin serpentine geometries offer elastic responses to large strains beyond 100%. The great stretchability and flexibility of this system guarantee conformal contact and adequate adhesion after it is attached to human skin. Figure 12(b) shows a fractal design of interconnect that can offer even better stretchability, which was investigated by experiment and FEA [59].

More examples of stretchable electronic and optoelectronic systems are presented in Fig. 13. Figure 13(a) shows an electronic eye camera with semiconductor pixel elements distributed on a hemispherical surface [6]. Pixel elements made of single crystalline Si are connected by thin, narrow bridges, consisting of thin layers of patterned metal encapsulated by thin layers of polyimide. This design enables elastic compressibility in the system, via buckling of the bridges. Figure 13(b) exhibits a dynamically tunable electronic eye camera, with the curvatures of both the lens and imaging plane adjustable to achieve zoom capability [37]. The electrical and mechanical interconnects between adjacent functional units are serpentine structures, which allow the system to work reliably under large dynamical deformation. Similar designs of interconnects and pixel elements were also adopted to create artificial compound eye cameras that were inspired by arthropod eyes, as shown in Fig. 13(c) [38]. This artificial compound eye camera is consisted of an optical subsystem and an optoelectronic subsystem and can provide very wide field of view and nearly infinite depth of field. Both subsystems are design to sustain very large deformation induced by the geometric transformation from planar to hemispherical shapes during the fabrication processes, so that their optical and electrical properties are not affected.

With the fractal design, Xu et al. fabricated a three-dimensional multifunctional integumentary membrane [66]. As shown in Fig. 13(d), this device is integrated on a Langendorff-perfused rabbit heart. Fractal design is used for the electrodes to enable large area coverage and high filling fraction for electrically active surfaces. Figure 13(e) demonstrates a multifunctional balloon catheter integrated with sensors, actuators, and other components [67]. Such catheter is a new type of surgical tool that can provide versatile modes of operation, such as angioplasty, septostomy, and other standard procedures. Figure 13(f) is an EES with near-field communication (NFC) [68]. Copper coils in this device are in filamentary serpentine shapes to provide large stretchability. This device can be integrated with the skin seamlessly to offer wireless interface with any standard, NFC-enabled devices, even under extreme deformation.

A few studies have been conducted to investigate the system reliability under mechanical deformation. Stretching cycles ranging from 1000 to 105 have been applied to different systems [16,22,74]. Mechanical strains used in these studies range from 22% to 75%. The results showed very stable electronic performances. The packaging in these systems was done through polymer and elastomer encapsulation to provide protection and mechanical stretchability.

Mechanics of Stretchable Thin Films

Mechanics of 1D Wrinkling.

The pattern of thin film wrinkling is determined by the material properties of the thin film and the substrate, as well as the thickness of the film. Long wavelength is preferred for the stiff film, while substrate favors short wavelength [75]. Formation of wrinkling is the process to balance the bending energy of the film and the deformation energy of the substrate [76]. Total system energy is minimized in the form of wrinkling with specific wavelength and amplitude [76].

Small Deformation Theory.

Based on plane strain, small deformation theory, energy method was used to determine the buckling geometry of the thin film with 1D sinusoidal profile [20,77,78]. In a bilayer system, a stiff thin film with thickness $hf$, Poisson's ratio $νf$, and elastic modulus $Ef$ is attached to a prestretched thick compliant substrate with Young's modulus $Es$, and Poisson's ratio $νs$. The substrate is assumed to be much more compliant than the thin film, and thus, $Es≪Ef$. Upon release of the prestrain $εpre$, the thin film wrinkles with wavelength $λ0$ and amplitude A0. Figure 14(a) shows an optical microscope image of wrinkled Si nanoribbons on PDMS [20]. The wrinkle profile can be fitted very well by a sinusoidal function, as demonstrated in Fig. 14(b) [20]. The out-of-plane displacement of the wrinkled film can be expressed as

Display Formula

(1)$w=A0 cos(kx1)=A0 cos(2πx1λ0)$

where $x1$ is the coordinate along the film length direction. The total energy per unit length of the film-substrate system consists of three parts, the membrane energy $Um$ and bending energy $Ub$ in the thin film, and the strain energy $Us$ in the substrate, and is obtained as Display Formula

(2)$Utot=Ub+Um+Us=π4E¯fhf3A023λ04+12E¯fhf(π2A02λ02−εpre)2+π4λ0E¯sA02$

where $E¯f=Ef/(1−νf2)$ and $E¯s=Es/(1−νs2)$ are the plane strain moduli of the film and substrate, respectively. Minimizing the total energy with respect to buckling amplitude and wavelength, i.e., $∂Utot/∂A0=∂Utot/∂λ0=0$, gives buckling wavelength $λ0$ and amplitude $A0$ as [77] Display Formula

(3)$λ0=2πhf(E¯f3E¯s)1/3,A0=hfεpreεc−1$

where $εc=(1/4)(3E¯s/E¯f)2/3$ is the critical buckling strain. If the prestrain applied to the substrate is smaller than $εc$, buckling does not occur. The buckling wavelength and amplitude of a Si thin film given by Eq. (3) versus Si film thickness are presented in the top and bottom frames of Fig. 14(c), respectively [20]. Both show good agreement with experiment.

For small deformation buckling theory, the membrane strain $εm=−εc$ keeps constant after buckling, and the maximum bending strain $εb=2π2Ahf/λ2$ increases with the deformation of the system. When the film is much stiffer than the substrate ($Ef$$≫$$Es$), the membrane strain (i.e., the critical buckling strain) is negligibly small. Then, the peak strain in the thin film is approximately obtained as Display Formula

(4)$εpeak≈2εpreεc$

For an Si film-PDMS substrate system, with material properties $Ef=130 GPa$, $νf=0.27$, $Es=1.8 MPa$, and $νs=0.48$ [79,80], the critical buckling strain is 0.034%. The prestrain can be as high as 23.8% before the peak strain in Si film reaches the fracture value 1.8% [78]. This means the stretchability of the bilayer system can reach 25.6%, which is 14.2 times of the fracture strain of Si.

The small deformation theory of thin film wrinkling has also been extended to study buckling of carbon nanotubes and nanowires on elastomeric substrates [8184]. These studies are helpful for understanding of the mechanical behaviors of nanowires and nanotubes and can provide theoretical basis for designing nanowire/nanotube-based stretchable devices. To account for the viscoelastic behavior of the elastomeric substrate, Huang and Suo have also studied wrinkling mechanics of thin films on viscos and viscoelastic substrates [8588]. The kinetics of the wrinkle formation and growth are illustrated.

Finite Deformation Theory.

In the above theoretical model based on small deformation theory, buckling wavelength is independent of the prestrain. However, when large strains are applied, experiments show that the wavelength decreases with the prestrain [89,90], as shown in Fig. 14(d). To understand this phenomenon, a finite deformation thin film wrinkling theory was established [89,90]. By using energy method, the buckling wavelength and amplitude can be obtained as Display Formula

(5)$λ=λ0(1+εpre)(1+ξ)1/3,A=A01+εpre(1+ξ)1/3$

where $λ0$ and $A0$ are the wavelength and amplitude in Eq. (3), and $ξ=5εpre(1+εpre)/32$. As shown in Fig. 14(e), both amplitude and wavelength show good agreement with experimental results [89]. For a very stiff thin film on a compliant substrate, the membrane strain is negligibly small [89]. The peak strain in the thin film can be approximately obtained as Display Formula

(6)$εpeak≈2εpreεc(1+ξ)1/31+εpre$

when an external strain $εapplied$ is applied to the wrinkled system, the wavelength and amplitude become Display Formula

(7)$λ=λ0(1+εapplied)(1+εpre)(1+εapplied+ζ)1/3,A=h(εpre−εapplied)/εc−11+εpre(1+εapplied+ζ)1/3$
where $ζ=5(εpre−εapplied)(1+εpre)/32$. The peak strain of the film is Display Formula
(8)$εpeak=2(εpre−εapplied)εc(1+εapplied+ζ)1/31+εpre$

Figure 14(f) shows that the theoretically predicted wavelength and amplitude agree very well with experiment, for a wrinkled Si thin film on PDMS substrate with prestrain 16.2% [89].

Mechanics of 2D Wrinkling.

When 2D strain mismatch is introduced to the bilayer system, stiff thin films wrinkle with 2D patterns, which are much more complex than the 1D sinusoidal patterns, observed in 1D wrinkling. Typically, three types of surface morphological patterns can show up, i.e., 1D sinusoidal wavy pattern, checkerboard pattern, and herringbone pattern, as shown in Figs. 15(a)15(c) [52]. To study 2D wrinkling of stiff thin films on compliant substrates, Huang et al. adopted spectral method and demonstrated that the surface morphology shows checkerboard pattern when the prestrain is slightly above the critical buckling strain and evolves to herringbone pattern as the prestrain increases [91]. Chen and Hutchinson developed a finite element model to study energetics of 2D wrinkling, and the results showed that the herringbone pattern has the lowest energy [92,93].

Using energy method, Song et al. systematically investigated the 1D, checkerboard and herringbone buckling modes for 2D wrinkling [51,52]. Analytical solutions for all three modes were obtained for biaxial prestrains $ε11pre$ and $ε22pre$. The results are briefly reviewed here.

One-Dimensional Mode.

The out-of-plane displacement and buckling wavelength are the same to those in 1D wrinkling mechanics, given by Eqs. (1) and (3), respectively. The amplitude is given as Display Formula

(9)$A=hfε11pre+νfε22pre(1/4)(3E¯s/E¯f)2/3−1$
For $ε22pre=0$, i.e., plane strain condition, the amplitude is the same to the one given by Eq. (3). For equibiaxial prestrains ($ε11pre=ε22pre=εpre$), amplitude $A$ becomes Display Formula
(10)$A=hfεpreε1Dc−1$

where $ε1Dc=(3E¯s/E¯f)2/3/4(1+νf)$ is the critical strain for the 1D buckling mode.

Checkerboard Mode.

The out-of-plane displacement is described by Display Formula

(11)$w=A cos(k1x1)cos(k2x2)$

For equibiaxial prestrains $ε11pre=ε22pre=εpre$, the wave number and amplitude are [52] Display Formula

(12)$k1=k2=121hf(3E¯sE¯f)1/3,A=hf1(3−νf)(1+νf)(εpreεcheckerboardc−1)$

where $εcheckerboardc=(3E¯s/E¯f)2/3/4(1+νf)$ is the critical strain for checkerboard buckling mode, the same to that in 1D mode. For general biaxial prestrain states, $ε11pre≠ε22pre$, analytical solutions are also obtained but are not reviewed here [52].

Herringbone Mode.

The out-of-plane displacement is described by Display Formula

(13)$w=A cos {k1[x1+B cos(k2x2)]}$

where $k1=2π/λ1$, $k2=2π/λ2$, A is the out-of-plane amplitude, and B is the in-plane jog amplitude. These parameters are illustrated in Figs. 15(d) and 15(e) [52]. The thin film membrane energy, bending energy, and the substrate strain energy can all be obtained analytically. Summation of these three energies gives the total system energy, which can be minimized with respect to $A$, $B$, $k1$, and $k2$ to give the governing equations. These governing equations can be solved numerically to obtain the solutions. For each $k2$, there are multiple local minima for the large range of initial values of $A$, $B$, and $k1$. The global minimum is obtained by comparing all local minima in the range [52].

Figure 15(f) shows the total energy $Utotal$ of all three buckling modes normalized by the energy in the unbuckled state $U0=E¯fhf(1+νf)εpre2$ versus the prestrain [52]. The herringbone mode gives the lowest energy, therefore, it's energetically favorable mode in 2D buckling. The underlying mechanism is that the herringbone mode significantly decreases the thin film membrane energy at the expense of slightly increasing thin film bending energy and substrate strain energy, as comparing to the other modes.

Mechanics of Controlled Buckling.

The precisely controlled wrinkling strategy developed by Sun et al. offers a good approach to control the wrinkling geometries and to improve the stretchability of the system [19]. Using energy method, Jiang et al. developed a theoretical model to study the wrinkling behavior of this system [94]. The processes to realize the controlled buckling is illustrated in Fig. 16(a) and described in Sec. 2.4 [94]. As shown in Fig. 16(a), the prestrain of the PDMS substrate is $εpre=ΔL/L$, and the widths of activated and inactivated sites are $Wact$ and $Win$, respectively. After the prestrain in the substrate is released, the thin film over the inactivated region deforms via Euler buckling, while the thin film bonded to the activated region remains flat. The profile of the buckled thin film is described as

Display Formula

(14)$w={w1=12A(1+cos πxL1),−L1

where A is the buckling amplitude, $2L1=Win/(1+εpre)$ is the buckling wavelength, and $2L2=Win/(1+εpre)+Wact$. The amplitude $A$ is determined by minimization of total energy with respect to amplitude Display Formula

(15)$A=4πL1L2(εpre−εc)$

where $εc=hf2π2/12L12$ is critical buckling strain. For typical system setup, thin film thickness hf is much smaller than $L1$; therefore, the critical buckling strain is extremely small and is negligible in Eq. (15). This gives the amplitude as Display Formula

(16)$A≈4πL1L2εpre=2πWin(Win+Wact)εpre/(1+εpre)$

which only depends on the interfacial pattern ($Wact$ and $Win$) and the prestrain. Figure 16(b) shows the profile comparison of a GaAs nanoribbon under different prestrains between experimental results and theoretical predictions (red lines) [94].

In typical system setup, the membrane strain is negligibly small comparing to the bending strain. Thus, the peak strain in the ribbon is approximately the maximum bending strain Display Formula

(17)$εpeak=hf2max(d2wdx12)=hfπL12L1L2εpre$

when the inactive region is much larger than the active region, the peak strain can be approximated by $εpeak≈(hfπ/L1)εpre$. For a system with $hf=0.3$μm, $Wact=10$μm, $Win=400$μm, and $εpre=60%$, the peak strain in the thin film is only 0.6%. The controlled buckling approach reduces the maximum strain in the film and leads to improvement of the system strechability.

Mechanics of Prefabricated Wavy Patterns.

Thin films deposited onto prefabricated wavy patterns can also provide freedom in designing the wavy structures and good stretchability and compressibility for the system. For the structure in Fig. 17(a), the profile of the wavy film can be expressed as $y=A0 cos kx$, where $A0$ is the initial amplitude, $k=2π/λ$, and $λ$ is the wavelength [34]. When a strain $εa$ is applied to the system, the total system energy consists of three parts, the bending energy membrane energy of the thin film, and the substrate strain energy, and can be obtained analytically. Minimization of the total system energy with respect to the amplitude gives

Display Formula

(18)$A=A0[1−6εa(E¯s+2E¯fkh)6E¯s+E¯fkh(k2h2+6k2A02)]$

where $h$ is the thickness of the film, $E¯f$ and $E¯s$ are plane strain moduli of the film and substrate, respectively. The maximum strain in the system is the sum of the membrane strain and bending strain Display Formula

(19)$εmax=εa3E¯s(2−k2A02+k2A0h)+E¯fk3h2(6A0+h)6E¯s+E¯fk3h(6A02+h2)$

The ratio of $εa/εmax$ versus the ratio of $A0/λ$ for different ratios of $A0/h$ is plotted in Fig. 17(b). The plateau indicates the maximum stretchability can be achieved for each ratio of $A0/h$. When the film is very stiff and thin, the plateau is well approximated by $A0/h$. Therefore, the system stretchability of the system can be expressed as $A0εc/h$. For Au thin films with fracture strain of 0.46% [95], the stretchabilities of the system are 4.6%, 23%, and 46% for $A0/h$  = 10, 50, and 100, respectively. These results are also valid for compression.

Mechanics of Noncoplanar Mesh Design and Serpentine Interconnects.

For the circuit with noncoplanar mesh design, the width of interconnects is much smaller than the size of islands, which leads to a very small rotation at the ends [35]. Therefore, in Song et al. model, the interconnects are modeled as beams with clamped ends [35]. Fabrication and mechanics model of such circuit is illustrated in Fig. 18(a). In this theoretical model, $X$ denotes the initial configuration and $x$ denotes the deformed configuration (Fig. 18(b)) [35]. After deformation, the distance between islands changes from $Lbridge0$ to $Lbridge$. The out-of-plane displacement of the interconnect can be represented by

Display Formula

(20)$w=A2(1+cos 2πxLbridge)=A2(1+cos 2πXLbridge0)$

The total strain energy in an interconnect consists of the bending energy and membrane energy, both of which are obtained analytically. Minimization of the total energy gives amplitude as Display Formula

(21)$A=2Lbridge0πLbridge0−LbridgeLbridge0−εc$

where $εc=π2hbridge2/[3(Lbridge0)2]$ is the critical buckling strain for a beam with both ends clamped.

For thin and long interconnects, the membrane strain due to buckling is very small. Therefore, the maximum strain in the interconnect is approximately equal to the maximum bending strain and can be written as Display Formula

(22)$εbridgemax=2πhbridgeLbridge0εpre1+εpre$

where $hbridge$ is the thickness of the interconnect. The maximum strain in the island is also obtained as Display Formula

(23)$εislandmax=(1−νisland2)Ebridgehbridge2Eislandhisland2εbridgemax$

where $Ebridge$ is the Young's modulus of the interconnect, $Eisland$, $νisland$, and $hisland$ are the Young's modulus, Poisson's ratio, and thickness of the island, respectively. The stretchability of the system is defined as the maximum tensile strain can be applied before the buckled interconnects return to flat and is obtained as Display Formula

(24)$εstretchability=Lbridge0−LbridgeLbridge+Lisland0=εpre1+(1+εpre)Lisland0Lbridge0$

where $Lisland0$ is the original length of the island. The compressibility is defined as the maximum compressive strain can be applied before the failure of the interconnect or the island, or the contact of neighbor islands, and is given as Display Formula

(25)$εcompressibility=min[(1+εpre)a2−εpre1+(1+εpre)Lisland0Lbridge0,11+(1+εpre)Lisland0Lbridge0]$

where

$a=(Lisland02πhbridge)min[εbridgefailure,Eislandhisland2(1−νisland2)Ebridgehbridge2(εislandfailure)]$
$εbridgefailure$, and $εislandfailure$ are the failure strains of the bridge and the island, respectively.

From Eq. (24), to increase the stretchability of the system, long interconnects, short islands, and large prestrain should be adopted. However, large prestrain offers higher stretchability but reduces compressibility. Figure 18(c) shows the system stretchability and compressibility versus the prestrain for the system with $Lisland0=20$μm, $hisland=50$ nm, $Lbridge0=20$μm, $hbridge=50$ nm, and the width of the bridge $wbridge=4$μm. Figure 18(d) shows the system stretchability and compressibility versus the initial bridge length with 50% prestrain, for $Lisland0=20$μm, $hisland=50$ nm, $hbridge=50$ nm, and $wbridge=4$μm. Both stretchability and compressibility increase with the length of interconnects.

The design of serpentine interconnects improves the stretchability of the system further. Figure 18(e) shows an SEM image of the mesh layout design with serpentine interconnects [16]. Figure 18(f) presents the FEA results for the system formed by 35% prestrain (upper) and stretched by 70% applied strain (bottom) [16]. Results demonstrate that the peak strain in silicon is 0.15% and the peak strains in metal layers in the bridges and islands are 0.2% and 0.5%, respectively. The serpentine interconnects can accommodate much larger strains than the straight ones, because they are much longer than straight interconnects, and their twisting and lateral buckling deformation can effectively release large strains.

The mechanics models of the systems discussed above are summarized in Table 1.

Conclusions and Outlook

We have reviewed fabrication, application, and mechanics of stretchable thin films on compliant substrates. Different approaches and strategies can be utilized to create wavy, stretchable thin films, including wrinkling induced by thermal strain, mechanical strain and swelling, controlled buckling, prefabricated wavy surface reliefs, and mesh layouts that combine rigid islands and stretchable interconnects. Stretchable thin films have been shown to have promising applications in optical gratings, precision metrology, smart adhesion, and stretchable electronics. Mechanics has been playing a central role in the development of stretchable thin films. Results from mechanics analyses provide important information to relate the wavy morphologies and stretchability to the material and geometrical properties of the system. These results offer important tools for guiding system prediction, design, and optimization.

Among all the interesting applications, stretchable electronics perhaps represents the most exciting one for stretchable form of thin film materials. Stretchable electronics opens up many new opportunities and possibilities in design and application of otherwise rigid, noncompliant electronic technologies. One of the most exciting opportunities is in biomedical area, such as fully integrated, biocompatible electronic systems, to meet surgical and diagnostic needs [9699]. The rubberlike compliance and deformability of stretchable electronics provide excellent shape conformability to complex biological tissues, which offers accurate and continuous monitoring of biological and electrical signals. Another exciting area of application is wearable electronics, which can be directly worn by people or can be integrated with fabrics [100]. Wearable electronics can greatly change people's lives in many ways, including health care, social activities, and sports. Challenges associated with these novel applications that have not been fully addressed include reliability, biocompatibility, and manufacturability. Probably most of these challenges are somewhat related to packaging [101104]. In most, if not all, of the stretchable systems discussed previously, packaging was realized through polymer encapsulation, which can provide both adequate protection to the devices inside and mechanical stretchability. However, for some applications that require hermetic sealing, polymer encapsulation may not be reliable over long period of time go prevent transmission of water vapor and oxygen. Therefore, it is necessary to develop reliable and stretchable packaging technique that utilizes inorganic thin film materials for hermetic sealing. Another issue associated with packaging is that polymer encapsulation can significantly reduce the stretchability of stretchable interconnectors, because the encapsulation material restricts the lateral, noncoplanar motion of the interconnectors. One recent study developed a core/shell packaging strategy to solve this challenge [105]. In this study, a layer of extremely soft silbione was used to surround the serpentine interconnectors, in order to minimize the constraint over their deformation and thus can retain most of the stretchability. Then, another layer of harder ecoflex was used to encapsulate and protect the inside structures. Even though this study has shown to be effective in retaining system stretchability when packaging is introduced, more research needs to be done on reliability and manufacturability.

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Figures

Fig. 1

(a) Flexible electronics with printed sensors (upper) and its bending performance (bottom). GMR is the abbreviation of giant magnetoresistance. (Reproduced with permission from Karnaushenko et al. [21]. Copyright 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.) (b) Optical image of stretchable, ultrathin Si-CMOS circuit in folded state. The inset shows a schematic view of the cross section. (Reprinted with permission from Kim et al. [18]. Copyright 2008 by American Association for the Advancement of Science.) (c) Optical images of inorganic LEDs integrated on unusual substrates. Upper left is an LED array on a piece of paper. Its flat state is shown in the inset. Upper right is an LED array on a sheet of aluminum foil in a crumpled state. The inset shows the device in its flat state. Bottom left is the array on a catheter balloon in its deflated and inflated (inset) states. Bottom right shows images of a strip of LEDs on a rigid plastic tube (diameter ∼2.0 mm, left). Inset shows the magnified view of a single pixel. (Reproduced with permission from Kim et al. [22]. Copyright 2010 by Nature Publishing Group.) (d) A stretchable battery under large deformation. (Reprinted with permission from Xu et al. [14]. Copyright 2013 by Macmillan Publishers Ltd).

Fig. 2

(a) Processes to fabricate stretchable single crystalline Si ribbons on elastomeric substrates. (b) Scanning electron microscope (SEM) image of wrinkled Si ribbons on PDMS substrate. (Reproduced with permission Khang et al. [20]. Copyright 2006 by American Association for the Advancement of Science.) (c) Schematic illustration of the fabrication processes for 2D wavy Si nanomembranes on PDMS substrate. (d) Optical microscope image (left) and AFM image (right) of wrinkled Si nanomembrane. (Reproduced with permission Song et al. [52]. Copyright 2008 by American Institute of Physics).

Fig. 3

(a) Fabrication processes of wrinkling of metal thin film on PDMS substrate via thermal strain mismatch. (b) and (c) Optical microscope image of wrinkling patterns produced from (a). (Reproduced with permission from Bowden et al. [23]. Copyright 1998 by Macmillan Publishers Ltd).

Fig. 4

(a) Method to induce wrinkling on PDMS surface by FIB. (b) Boundary of the wrinkling formed by FIB. (c) The wrinkling can be induced along desired path with specific width. (Reproduced with permission from Moon et al. [33]. Copyright 2007 by National Academy of Sciences.) (d) Fabrication processes of microwrinkle structures coupled to lithographic patterns. (e) AFM image (10 × 10 μm2) of the wrinkling pattern formed by method in (d). (Reproduced with permission from Ohzono et al. [55]. Copyright 2005 by The Royal Society of Chemistry 2005.) (f) Schematic illustration of reversible surface wrinkling on UVO-treated PDMS surface in response to solvent. (g) Optical microscope image of surface wrinkling of UVO-treated PDMS induced by solvent. (Reproduced with permission from Kim et al. [56]. Copyright 2011 by Wiley-VCH Verlag GmbH & Co. KGaA.) (h) Optical microscope images of spoke wrinkling pattern and target pattern. Possible mechanism for the formation of spoke pattern (i) and target pattern (j). (Reproduced with permission from Chung [57]. Copyright 2009 by Wiley-VCH Verlag GmbH & Co. KGaA).

Fig. 5

(a) Fabrication procedure of controlled buckling. (b) Buckled GaAs ribbons under stretch and compression. (c) SEM image of the buckled ribbons formed by the procedure described in (a). (Reprinted with permission from Sun et al. [19]. Copyright 2006 by Nature Publishing Group.) (d) Process for deterministic assembly of 3D mesostructures from 2D precursors and strain distribution results from finite element analysis (FEA). (Reprinted with permission from Xu et al. [39]. Copyright 2015 by American Association for the Advancement of Science).

Fig. 6

(a) Sawtooth pattern of silicon by anisotropic etching. (b) Final wavy PDMS substrate with a layer of 300 μm gold film. (Reprinted with permission from Xiao et al. [34]. Copyright 2008 by American Institute of Physics).

Fig. 7

(a) Fabrication processes of an array of functional units with noncoplanar mesh design. (b) SEM images showing deformed (upper) and released (lower) states of the mesh structure. (c) Serpentine interconnector design for stretchable electronics. (Reprinted with permission from Kim et al. [16]. Copyright 2008 by National Academy of Sciences.).

Fig. 8

(a) Schematic illustration of the fabrication of tunable optical gratings. (b) Light wavelength shift with the change of the prestrain. (c) Peak wavelength and intensity as a function of applied strain. (Reprinted with permission from Yu et al. [10]. Copyright 2007 by American Institute of Physics).

Fig. 9

(a) Experimental setup for measuring elastic modulus of thin films via buckling. (b) AFM image of buckled thin film. (c) Calculated Young's modulus (closed circles) and wrinkling wavelength (open circles) versus the thickness of the thin film (Reprinted with permission from Stafford et al. [61]. Copyright 2004 by Nature Publishing Group).

Fig. 10

(a) Three-dimensional surface contours of the wrinkled surfaces with different strains. (b) Pull-off force versus strain from experiments and theoretical predictions. (Reprinted with permission from Lin et al. [32]. Copyright 2008 by The Royal Society of Chemistry).

Fig. 11

(a) Si-CMOS circuit under twisting and bending (bottom inset). Optical microscope images of functional units at the center (b) and edge (c) of the circuit sample in the twisted configuration. (Reprinted with permission from Kim et al. [18]. Copyright 2008 by American Association for the Advancement of Science).

Fig. 12

(a) Optical image of multifunctional stretchable electronic system. (Reprinted with permission from Kim et al. [12]. Copyright 2011 by American Association for the Advancement of Science.) (b) Experimental and FEA simulation results of a fractal layout design for stretchable interconnects under different tensile strains. (Reprinted with permission from Fan et al. [59]. Copyright 2014 by Macmillan Publishers Ltd).

Fig. 13

Applications of stretchable thin films to electronics and optoelectronics system. (a) Photograph of a hemispherical electronic eye camera. (Reprinted with permission from Ko et al. [6]. Copyright 2008 by Macmillan Publishers Ltd.) (b) Photograph of a hemispherical electronic eye camera system with dynamically tunable zoom. (Reprinted with permission from Jung et al. [37]. Copyright 2011 by the National Academy of Sciences of the United States of America, Washington, DC.) (c) Image of a digital camera system with designs inspired by the arthropod eye. (Reprinted with permission from Song et al. [38]. Copyright 2013 by Macmillan Publishers Ltd.) (d) Image of a 3D multifunctional integumentary membrane integrated on a Langendorff-perfused rabbit heart. (Reprinted with permission from Xu et al. [66]. Copyright 2014 by Wiley-VCH Verlag GmbH & Co. KGaA.) (e) A multifunctional balloon catheter in its inflated state. (Reprinted with permission Kim et al. [67]. Copyright 2011 by Macmillan Publishers Ltd.) (f) Epidermal electronics with NFC under deformation. (Reprinted with permission from Kim et al. [68]. Copyright 2014 by Wiley-VCH Verlag GmbH & Co. KGaA).

Fig. 14

(a) Optical image of wrinkled Si ribbons on PDMS. (b) The profile of a wrinkled Si ribbon in (a). (c) Wrinkling wavelength and amplitude versus Si ribbon thickness. (Reprinted with permission from Khang et al. [20]. Copyright 2006 by American Association for the Advancement of Science.) (d) AFM images of wrinkled Si ribbons induced by different prestrains. Triangles mark the change of wavelength. (e) Wavelength and amplitude of buckled Si ribbons with 100 nm thickness on PDMS substrate versus the prestrain. (f) Wavelength and amplitude of the same system to (e) as a function of the applied strain. (Reprinted with permission from Jiang et al. [89]. Copyright 2007 by National Academy of Sciences.).

Fig. 15

Mechanics of 2D buckling of thin films on compliant substrates. Schematic illustrations of three buckling modes: (a) 1D mode, (b) checkerboard mode, and (c) herringbone mode. (d) and (e) Herringbone mode and its parameters. (f) Ratio of total energy in the buckled bilayer system to that in the unbuckled state versus the prestrain for three different buckling modes. (Reprinted with permission from Song et al. [52]. Copyright 2008 by American Institute of Physics).

Fig. 16

Mechanics of controlled buckling. (a) Fabrication procedure and parameters of the controlled buckling. (b) Comparison between experimental and theoretical results (dashed lines) at different prestrains. (Reprinted with permission from Jiang et al. [94]. Copyright 2007 by American Institute of Physics).

Fig. 17

Mechanics of stretchable thin films on prefabricated wavy patterns. (a) Optical image of a wavy gold film created by using prefabricated wavy patterns. (b) Ratio of applied strain to the maximum film strain versus the ratio of initial amplitude to wavelength for different ratios of amplitude to film thickness. (Reprinted with permission from Xiao et al. [34]. Copyright 2008 by American Institute of Physics).

Fig. 18

(a) Fabrication processes of electronics on a complaint substrate with noncoplanar mesh design. (b) Diagram of mechanics model for interconnects in (a). (c) Stretchability and compressibility as a function of prestrain for the system with noncoplanar mesh design. (d) Stretchability and compressibility as a function of the length of interconnects for the system with noncoplanar mesh design. Here, the prestrain is 50%. (Reprinted with permission from Song et al. [35]. Copyright 2009 by American Institute of Physics.) (e) SEM image of a stretchable electronic system with mesh layout and serpentine interconnects. (f) FEA simulation results of a representative unit in (e) in initial state (35% prestrain, upper) and under 70% tensile strain. (Reprinted with permission from Kim et al. [16]. Copyright 2008 by National Academy of Sciences.).

Tables

Table 1 Summarization of mechanics models of different systems