Highly tunable electrothermally actuated arch resonator

This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of electrothermally actuated MEMS arch beams. The beams are made of silicon and are intentionally fabricated with some curvature as inplane shallow arches. Analytical results based on the Galerkin discretization of the Euler Bernoulli beam theory are generated and compared to the experimental data and results of a multiphysics finite-element model. A good agreement is found among all the results. The electrothermal voltage is applied between the anchors of the clamped-clamped MEMS arch beam, generating a current that passes through the MEMS arch beam and controls its axial stress caused by thermal expansion. When the electrothermal voltage increases, the compressive stress increases inside the arch beam. This leads to increase in its curvature, thereby increases the resonance frequencies of the structure. We show here that the first resonance frequency can increase up to twice its initial value. We show also that after some electro-thermal voltage load, the third resonance frequency starts to become more sensitive to the axial thermal stress, while the first resonance frequency becomes less sensitive. These results can be used as guidelines to utilize arches as wide-range tunable resonators.