Electrothermally Tunable Arch Resonator

This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of electrothermally actuated microelectromechanical arch beams. The beams are made of silicon and are intentionally fabricated with some curvature as in-plane shallow arches. An electrothermal voltage is applied between the anchors of the beam generating a current that controls the axial stress caused by thermal expansion. When the electrothermal voltage increases, the compressive stress increases inside the arch beam. This leads to an increase in its curvature, thereby increasing its resonance frequencies. We show here that the first resonance frequency can increase monotonically up to twice its initial value. We show also that after some electrothermal 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. Analytical results based on the nonlinear Euler Bernoulli beam theory are generated and compared with the experimental data and the results of a multi-physics finite-element model. A good agreement is found among all the results.