A mechanics and electromagnetic scaling law for highly stretchable radio frequency electronics

Many classes of flexible and stretchable bio-integrated electronic systems rely on mechanically sensitive electromagnetic components, such as various forms of antennas for wireless communication and for harvesting energy through coupling with external power sources. This efficient wireless functionality can be important for body area network technologies and can enable operation without the weight and bulky size of batteries for power supply. Recently, antenna designs have received increased attention because their mechanical and electromagnetic properties significantly influence the wireless performance of bio-integrated electronics, particularly under excessive mechanical loads. These mechanical factors are critical for skin-integrated electronics during human motion, as complex skin deformations can damage the conductive traces of antennas, such as those used for near-field communication (NFC), leading to yield or fracture and affecting their electromagnetic stability. Serpentine interconnects have been proposed as a geometric alternative to in-plane circular or rectangular spiral antenna designs to improve the elastic stretchability of the metallic traces in NFC antennas and prevent mechanical fractures. Despite the use of serpentine interconnects within the physiologically relevant strain range for skin (<20 %), the electromagnetic stability of the antennas decreases. This instability, reflected by shifts in resonance frequency and scattering parameters due to inductance changes, reduces the antennas' wireless power transfer efficiency and readout range. Therefore, maintaining the electromagnetic stability of antennas, specifically NFC antennas, under various mechanical deformations has become a critical challenge in practical wireless skin-integrated applications, such as sensing and physiological monitoring. Here, we establish a new mechanics and electromagnetic scaling law that quantifies the inductance changes under strain in a rectangular-loop serpentine structure typically used for NFC wireless communication in stretchable electronics. We present a systematic analysis of the antenna's geometric parameters, material properties of the antenna and substrate, and the applied strain on the inductance change. Our findings demonstrate that the relative change of inductance is solely influenced by the serpentine structure's width-radius ratio, arc angle, aspect ratio of the NFC antennas, and the applied strain. Additionally, under physiological strain conditions for the skin, the relative change of inductance can be minimized to preserve the NFC antenna's performance and prevent mechanical fracture and electromagnetic stability loss.