Mechanics of ultra-stretchable self-similar serpentine interconnects

Electrical interconnects that adopt self-similar, serpentine layouts offer exceptional levels of stretchability in systems that consist of collections of small, non-stretchable active devices in the so-called island–bridge design. This paper develops analytical models of flexibility and elastic stretchability for such structures, and establishes recursive formulae at different orders of self-similarity. The analytic solutions agree well with finite element analysis, with both demonstrating that the elastic stretchability more than doubles when the order of the self-similar structure increases by one. Design optimization yields 90% and 50% elastic stretchability for systems with surface filling ratios of 50% and 70% of active devices, respectively.