Fractal design concepts for stretchable electronics

Abstract

Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

Extremely Stretchable Strain Sensors Based on Conductive Self‐Healing Dynamic Cross‐Links Hydrogels for Human‐Motion Detection

“…Stretchable, wearable, flexible, and human friendly soft electronic devices are of significance to meet the escalating requirements of increasing complexity and multifunctionality of modern electronics 1, 2, 3, 4, 5, 6. Strain sensors can generate repeatable electrical changes upon mechanical deformations.…”

In‐Plane Deformation Mechanics for Highly Stretchable Electronics

“…Structure designs for stretchable interconnects have evolved from straight [13,16] to curvilinear interconnects, [17] from those bonded to or embedded in the supporting substrate [11,18] to free-standing designs housed in microfluidic enclosures, [19] and from simple structures [17] to fractal/self-similar designs. [15,[20][21][22] All such cases, including a broad variety of shapes, sizes, and geometric arrangements, share the same underlying mechanisms, i.e., out-of-plane buckling of thin structures (metals, insulators, or semiconductors with thickness typically between ≈100 nm and ≈1 µm) provides the basis for elastic stretchability. The most advanced interconnects achieve elastic (reversible) stretchability as high as ≈190%, [15] which corresponds only to ≈40% system stretchability when the areal coverage ratio is ≈60%.…”

“…Transition from Wrinkling to Buckling: The mechanics of wrinkling of a thin metal film on an elastomer substrate gives [22,26,27] the wavelength at the onset of wrinkling as…”

Recent Progress in Electronic Skin

“…The non‐coplanar structures associated with deformable interconnecting structures, including straight ribbons and serpentine traces, allowed the device to undergo complex deformations, such as rotation and twisting. Recently, fractal layouts with self‐similarity served as alternative interconnectors, such as Peano and Vicsek curves, were proposed for stretchable devices for further adaption to various deformations (Figure 3c) 45. Three types of contact modes between the interconnector and the soft substrate were employed, including nonbonded, partially bonded, and completely bonded contacts, to accommodate the practical demands required by different applications.…”

“…c) Fractal design. Reproduced with permission 45. Copyright 2014, Macmillan Publishers Ltd. d) 3D architectures via compressive buckling.…”