In the island-interconnect design, the device islands connected by interconnects are mounted on a soft elastomeric substrate. The out-of-plane motion of interconnects accommodates the deformation applied to the system, enabling stretchable feather in electronics. The areal coverage, however, decreases due to the presence of interconnects. This problem is difficult to address for many important applications where high areal coverage is desired. By minimizing the interfacial stress between the device islands and substrate, a structured substrate introduces surface relief in the substrate and this design offers a desired level of stretchability with a relatively large areal coverage. Theoretical and numerical investigations give the strain levels in both the substrate and interconnect, providing design guidance on the optimization of the geometric and material parameters in the experiment.