Optimal design of self-similar serpentine interconnects embedded in stretchable electronics

The order-2 self-similar serpentine interconnects (SSIs) that joint rigid, functional devices can ensure mechanical integrity and stretchability in electronic systems under large deformations. However, the conventional design and analysis aim merely at the freestanding order-2 SSIs. The paper studies the design law and the stretchability of order-2 SSI that are bonded onto the polydimethylsiloxane (PDMS) substrate in stretchable electronics through analytical modeling, finite elementmethod (FEM), and experiments. The scale law formula is built to predict the stretchability of the order-2 SSI with geometry parameters based on FEM simulation results. The out-of-plane and in-plane bending strains during lateral postbuckling processes are proportional to the thickness andwidth of the order-2 SSI, respectively. The stretchability of order-2 SSI decreases with the increasing ratio beta of order-2 space L-2 to order-1 space L-1, and it would be approximate to the stretchability of order-1 serpentine interconnect when beta > 32. The optimized order-2 SSI is demonstrated in stretchable electronics application with high stretchability.