Buckling shape of elastically constrained multi-layered micro-bridges

In this paper, an analytical model that characterizes the buckling shape of a multi-layered micro-bridge is presented. The model takes into account elastically constrained boundary conditions and residual moment at the supporting ends. Results are compared with Finite Element Analysis (FEA) using ANSYS simulation and measurements from fabricated micro-bridges. A novel structure which consists of a tri-layer micro-bridge supported by a pair of springs and legs at its two ends is employed to obtain elastically constrained boundary conditions. Four such structures have been analysed, simulated, fabricated and their buckled shapes were measured using SEM micrographs. Results from the model are in good agreement with those obtained from simulations and experimental measurements to within 7% error compared to 10-25% error for previously used models. It is also shown that by applying best fitting curve method between the fabricated or simulated result and the analytical model, the torsional stiffness of the supporting ends of the micro-bridges can be extracted.