Reliability analysis of serpentine interconnects on soft elastomers for stretchable electronics

Serpentine layouts improve the deformability of metal interconnects on soft elastomers, but localised strain concentrations at the arc segments can end electrical function before any damage is visible. A probabilistic framework coupling finite element analysis with structural reliability methods is therefore proposed. The onset of plastic yielding of the copper layer, at an allowable strain of 0.003 taken from published work on serpentine microstructures, is adopted as a conservative lower bound of functional failure; an electromechanical measurement on a copper serpentine on Sylgard 184 gives a knee strain of 2.56%, reproducing that allowable strain in the finite element model to within 2%. An explicit limit state function is built by an iteratively updated response surface whose accuracy is quantified by leave-one-out cross-validation rather than by the coefficient of determination alone; the reliability index is obtained by the checking point method and verified by Monte Carlo simulation. Two examples are analysed. In the first, the line width and the metal thickness of the unencapsulated specimen are random with coefficients of variation of 0.075 and 0.111; at 2.2% applied strain the reliability is 91.15% by the checking point method and 91.64% by Monte Carlo sampling truncated at three standard deviations. In the second, an encapsulated polyimide–copper–polyimide interconnect under 15% applied strain, the reliability is 92.51% with random elastic moduli and 90.54% once the scatter of the allowable strain is included. Sobol analysis identifies the substrate modulus as dominant, with a first-order index of 0.51 and a total-effect index of 0.56.