We have produced a stretchable form of silicon that consists of submicrometer single-crystal elements structured into shapes with microscale, periodic, wavelike geometries. When supported by an elastomeric substrate, this "wavy" silicon can be reversibly stretched and compressed to large levels of strain without damaging the silicon. The amplitudes and periods of the waves change to accommodate these deformations, thereby avoiding substantial strains in the silicon itself. Dielectrics, patterns of dopants, electrodes, and other elements directly integrated with the silicon yield fully formed, high-performance "wavy" metal oxide semiconductor field-effect transistors, p-n diodes, and other devices for electronic circuits that can be stretched or compressed to similarly large levels of strain.

We present detailed experimental and theoretical studies of the mechanics of thin buckled films on compliant substrates. In particular, accurate measurements of the wavelengths and amplitudes in structures that consist of thin, single-crystal ribbons of silicon covalently bonded to elastomeric substrates of poly(dimethylsiloxane) reveal responses that include wavelengths that change in an approximately linear fashion with strain in the substrate, for all values of strain above the critical strain for buckling. Theoretical reexamination of this system yields analytical models that can explain these and other experimental observations at a quantitative level. We show that the resulting mechanics has many features in common with that of a simple accordion bellows. These results have relevance to the many emerging applications of controlled buckling structures in stretchable electronics, microelectromechanical systems, thin-film metrology, optical devices, and others.buckling ͉ stiff thin film ͉ compliant substrate ͉ stretchable electronics

Stretchable electronic devices, such as p-n diodes, [1] photovoltaic devices, [2,3] transistors, [4,5] and functional electronic eyes, [6] have been fabricated using buckled single-crystal (e.g., Si, GaAs) thin films supported by elastomeric substrates. Recently, carbon nanotube (CNT)-based highly conducting elastic composites [7,8] and stretchable graphene films [9] have been reported, which are suitable as interconnects in stretchable electronic devices. As an indispensable component of stretchable electronics, a stretchable power-source device should be able to accommodate large strains while retaining intact function. Of various power-source devices, supercapacitors have attracted great interest in recent years due to their high power and energy densities compared with lithium-ion batteries and conventional dielectric capacitors, respectively. The most active research in supercapacitors is the development of new electrode materials. Recently, CNTs have been studied as good candidates for electrode materials [10][11][12][13][14][15][16] because of several advantages, including a high surface area, nanoscale dimensions, and excellent electrical conductivity.Here, we report stretchable supercapacitors based on periodically sinusoidal single-walled carbon nanotube (SWNT) macrofilms (a 2D network of randomly oriented SWNTs). The stretchable supercapacitors comprise two sinusoidal SWNT macrofilms as stretchable electrodes, an organic electrolyte, and a polymeric separator. Electrochemical tests were performed and the fabricated stretchable supercapacitors are found to possess energy and power densities comparable with those of supercapacitors using pristine SWNT macrofilms as electrodes. Remarkably, the electrochemical performance of the stretchable supercapacitors remains unchanged even under 30% applied tensile strain.The preparation of the periodically sinusoidal SWNT macrofilms is of primary importance for stretchable supercapacitors. The synthesis of high-quality, purified, and functionalized SWNT macrofilms is, thus, an important preprocess, which has been presented elsewhere.[17] The purified SWNT macrofilm was then shaped to a sinusoidal form by following the steps shown in Figure 1a. The procedure introduced here (step i in Fig. 1a) involves the uniaxial prestretching (e pre ) of an elastomeric substrate of a poly(dimethylsiloxane) (PDMS) slab (e pre ¼ DL/L for length changed from L to L þ DL), followed by a chemical surface treatment to form a hydrophilic surface (see Experimental Section). The exposure of UV light introduces atomic oxygen, an activated species that reacts with PDMS and, thus, changes the Figure 1. Fabrication steps of a buckled SWNT macrofilm on an elastomeric PDMS substrate. a) Illustration of the fabrication flow comprising surface treatment, transfer, and relaxation of the prestrained PDMS substrate. b) Optical microscopy image of a 50-nm-thick, buckled SWNT macrofilm on a PDMS substrate with 30% prestrain, where the well-defined periodic buckling structure is shown. c) SEM image of ...

Control over the composition, shape, spatial location and/or geometrical configuration of semiconductor nanostructures is important for nearly all applications of these materials. Here we report a mechanical strategy for creating certain classes of three-dimensional shapes in nanoribbons that would be difficult to generate in other ways. This approach involves the combined use of lithographically patterned surface chemistry to provide spatial control over adhesion sites, and elastic deformations of a supporting substrate to induce well-controlled local displacements. We show that precisely engineered buckling geometries can be created in nanoribbons of GaAs and Si in this manner and that these configurations can be described quantitatively with analytical models of the mechanics. As one application example, we show that some of these structures provide a route to electronics (and optoelectronics) with extremely high levels of stretchability (up to approximately 100%), compressibility (up to approximately 25%) and bendability (with curvature radius down to approximately 5 mm).

There are significant challenges in developing deformable devices at the system level that contain integrated, deformable energy storage devices. Here we demonstrate an origami lithium-ion battery that can be deformed at an unprecedented high level, including folding, bending and twisting. Deformability at the system level is enabled using rigid origami, which prescribes a crease pattern such that the materials making the origami pattern do not experience large strain. The origami battery is fabricated through slurry coating of electrodes onto paper current collectors and packaging in standard materials, followed by folding using the Miura pattern. The resulting origami battery achieves significant linear and areal deformability, large twistability and bendability. The strategy described here represents the fusion of the art of origami, materials science and functional energy storage devices, and could provide a paradigm shift for architecture and design of flexible and curvilinear electronics with exceptional mechanical characteristics and functionalities.

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This Letter introduces a biaxially stretchable form of single crystalline silicon that consists of two dimensionally buckled, or "wavy", silicon nanomembranes on elastomeric supports. Fabrication procedures for these structures are described, and various aspects of their geometries and responses to uniaxial and biaxial strains along various directions are presented. Analytical models of the mechanics of these systems provide a framework for quantitatively understanding their behavior. These classes of materials might be interesting as a route to high-performance electronics with full, two-dimensional stretchability.

A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically.