Elasticity of Fractal Inspired Interconnects

Abstract

The use of fractal-inspired geometric designs in electrical interconnects represents an important approach to simultaneously achieve large stretchability and high aerial coverage of active devices for stretchable electronics. The elastic stiffness of fractal interconnects is determined analytically in this paper. Specifically, the elastic energy and the tensile stiffness for an order n fractal interconnect of arbitrary shape are obtained, and are verified by the finite element analysis and experiments.

In‐Plane Deformation Mechanics for Highly Stretchable Electronics

“…Both experiments (Figure 3c) and FEA ( Figure S8 (Supporting Information) which shows the overall trend of stretchability vs thickness) confirm that the scissoring mode enhances the stretchabilitythin ribbons that respond to applied force by wrinkling fracture at an applied strain of ≈30% (Figure 3d, bottom frames), while thick bars involve scissoring and break at a much higher applied strain of ≈90% (Figure 3e, bottom frames). Scissoring can also be exploited with previously demonstrated approaches in stretchable electronics such as dielectric encapsulation, fractal designs, [20,21,26] and prestrain strategies, as is shown in Figure 3f. [22,26] The structures shown in Figure S9a (Supporting Information) are encapsulated by a 500-µm-thick layer of silicone (Ecoflex, Smooth-On, Inc.).…”

“…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%.…”

Mechanics and thermal management of stretchable inorganic electronics

“…The cross-section of the bridge has the width w and thickness t . The elastic stiffness of fractal interconnects could be determined by analytical models [61,62]. …”

Mechanical Designs for Inorganic Stretchable Circuits in Soft Electronics

“…A representative work that provides mechanical insights into this was reported in [48], in which the elasticity of an order- n fractal-inspired interconnects of arbitrary shape are determined analytically and verified experimentally. The analysis starts with a fractal shape given in the Cartesian coordinates Y = Y ( X ) (Fig.…”