Mechanics of curvilinear electronics

Advanced methods are now available for conformally wrapping planar, silicon-based electronics circuits onto complex, curvilinear surfaces. Here, buckling physics of circuits configured into mesh geometries consisting of silicon islands interconnected by narrow ribbons leads to out of plane displacements across different parts of the curvilinear surface, in a way that accommodates strains associated with wrapping. The mechanisms for different buckling patterns are identified in this paper. A simple and robust method is established via the following steps to predict the buckling patterns of interconnect bridges for arbitrarily axisymmetric curvilinear surfaces: step 1, obtain analytically the strain distribution on the curvilinear surface; step 2, use the strain distribution from step 1 to determine the buckling patterns of interconnect bridges along different directions and at different locations on the curvilinear surface; and step 3, use the strain distribution from step 1 and buckling pattern from step 2 to obtain analytically the maximum strains in interconnect bridges and device islands. This method is useful to the design and optimization of curvilinear electronics against mechanical and electrical failure.