Hardening, Softening, and Linear Behavior of Elastic Beams in MEMS: An Analytical Approach

This paper investigates different topologies of springs used to couple the orthogonal translational motion of proof masses in Micro-Electro-Mechanical Systems (MEMS). This type of coupling is a key issue, since the dynamic response, and hence, the performance of various devices (e.g., MEMS gyroscopes) critically depends on the mechanical behavior of such deformable components. We first analytically investigate the problem through a model based on a modified second-order Timoshenko beam theory developed for both compact and built-up section beams. Its predictions inspire the design of three test structures, whose purpose is to highlight, through different spring topologies, the transition from a hardening behavior to a softening behavior, with possible intermediate optimum conditions for linear response at large displacements. The structures are characterized in detail, with variable forced displacements at resonance (25 kHz) up to about 10 μm. Experiments validate the model predictions in all the considered situations.