Ultra-Tuning of nonlinear drumhead MEMS resonators by Electro-Thermoelastic buckling

Nonlinear micro-electro-mechanical systems (MEMS) resonators open new opportunities in sensing and signal manipulation compared to their linear counterparts by enabling frequency tuning and increased bandwidth. Here, we design, fabricate and study drumhead resonators exhibiting strongly nonlinear dynamics and develop a reduced order model (ROM) to capture their response accurately. The resonators undergo electrostatically-mediated thermoelastic buckling, which tunes their natural frequency from 4.7 to 11.3 MHz, a factor of 2.4× tunability. Moreover, the imposed buckling switches the nonlinearity of the resonators between purely stiffening, purely softening, and even softening-to-stiffening. Accessing these exotic dynamics requires precise control of the temperature and the DC electrostatic forces near the resonator's critical-buckling point. To explain the observed tunability, we develop a one-dimensional physics-based ROM that predicts the linear and nonlinear response of the fundamental bending mode of these drumhead resonators. The ROM captures the dynamic effects of the internal stresses resulting from three sources: The residual stresses from the fabrication process, the mismatch in thermal expansion between the constituent layers, and lastly, the applied electrostatic forces. The novel ROM developed in this article not only replicates the observed tunability of linear (within 5.5 % error) and nonlinear responses even near the states of critical buckling but also provides insightful intuition on the interplay among the softening and stiffening, which is invaluable for the precise design of similar devices. This remarkable nonlinear and large tunability of the natural frequency are valuable features for on-chip acoustic devices in broad applications such as signal manipulation, filtering, and MEMS waveguides.