Lateral buckling mechanics in silicon nanowires on elastomeric substrates.

We describe experimental and theoretical studies of the buckling mechanics in silicon nanowires (SiNWs) on elastomeric substrates. The system involves randomly oriented SiNWs grown using established procedures on silicon wafers, and then transferred and organized into aligned arrays on prestrained slabs of poly(dimethylsiloxane) (PDMS). Releasing the prestrain leads to nonlinear mechanical buckling processes that transform the initially linear SiNWs into sinusoidal (i.e., "wavy") shapes. The displacements associated with these waves lie in the plane of the substrate, unlike previously observed behavior in analogous systems of silicon nanoribbons and carbon nanotubes where motion occurs out-of-plane. Theoretical analysis indicates that the energy associated with this in-plane buckling is slightly lower than the out-of-plane case for the geometries and mechanical properties that characterize the SiNWs. An accurate measurement of the Young's modulus of individual SiNWs, between approximately 170 and approximately 110 GPa for the range of wires examined here, emerges from comparison of theoretical analysis to experimental observations. A simple strain gauge built using SiNWs in these wavy geometries demonstrates one area of potential application.

Materials and noncoplanar mesh designs for integrated circuits with linear elastic responses to extreme mechanical deformations.

Electronic systems that offer elastic mechanical responses to high-strain deformations are of growing interest because of their ability to enable new biomedical devices and other applications whose requirements are impossible to satisfy with conventional wafer-based technologies or even with those that offer simple bendability. This article introduces materials and mechanical design strategies for classes of electronic circuits that offer extremely high stretchability, enabling them to accommodate even demanding configurations such as corkscrew twists with tight pitch (e.g., 90 degrees in approximately 1 cm) and linear stretching to "rubber-band" levels of strain (e.g., up to approximately 140%). The use of single crystalline silicon nanomaterials for the semiconductor provides performance in stretchable complementary metal-oxide-semiconductor (CMOS) integrated circuits approaching that of conventional devices with comparable feature sizes formed on silicon wafers. Comprehensive theoretical studies of the mechanics reveal the way in which the structural designs enable these extreme mechanical properties without fracturing the intrinsically brittle active materials or even inducing significant changes in their electrical properties. The results, as demonstrated through electrical measurements of arrays of transistors, CMOS inverters, ring oscillators, and differential amplifiers, suggest a valuable route to high-performance stretchable electronics.

Stretchable and foldable silicon integrated circuits.

We have developed a simple approach to high-performance, stretchable, and foldable integrated circuits. The systems integrate inorganic electronic materials, including aligned arrays of nanoribbons of single crystalline silicon, with ultrathin plastic and elastomeric substrates. The designs combine multilayer neutral mechanical plane layouts and "wavy" structural configurations in silicon complementary logic gates, ring oscillators, and differential amplifiers. We performed three-dimensional analytical and computational modeling of the mechanics and the electronic behaviors of these integrated circuits. Collectively, the results represent routes to devices, such as personal health monitors and other biomedical devices, that require extreme mechanical deformations during installation/use and electronic properties approaching those of conventional systems built on brittle semiconductor wafers.

Molecular scale buckling mechanics in individual aligned single-wall carbon nanotubes on elastomeric substrates.

We have studied the scaling of controlled nonlinear buckling processes in materials with dimensions in the molecular range (i.e., approximately 1 nm) through experimental and theoretical studies of buckling in individual single-wall carbon nanotubes on substrates of poly(dimethylsiloxane). The results show not only the ability to create and manipulate patterns of buckling at these molecular scales, but also, that analytical continuum mechanics theory can explain, quantitatively, all measurable aspects of this system. Inverse calculation applied to measurements of diameter-dependent buckling wavelengths yields accurate values of the Young's moduli of individual SWNTs. As an example of the value of this system beyond its use in this type of molecular scale metrology, we implement parallel arrays of buckled SWNTs as a class of mechanically stretchable conductor.

Biaxially stretchable "wavy" silicon nanomembranes.

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.

Controlled buckling of semiconductor nanoribbons for stretchable electronics.

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).

Stamp collapse in soft lithography.

We have studied the so-called roof collapse in soft lithography. Roof collapse is due to the adhesion between the PDMS stamp and substrate, and it may affect the quality of soft lithography. Our analysis accounts for the interactions of multiple punches and the effect of elastic mismatch between the PDMS stamp and substrate. A scaling law among the stamp modulus, punch height and spacing, and work of adhesion between the stamp and substrate is established. Such a scaling law leads to a simple criterion against the unwanted roof collapse. The present study agrees well with the experimental data.