Analytical Modeling of the Mechanical Behavior of MEMS/NEMS-Multilayered Resonators With Variable Cross-Sections for Sensors and Energy Harvesters

Abstract

Resonators based on micro and nanoelectromechanical systems (MEMS/NEMS) are used in many applications, including biological and gas sensors, magnetic field sensors, RF switches, accelerometers, piezoelectric micro and nanogenerators, and viscosity sensors. The design of these resonators requires analytical models to predict their mechanical behavior and optimize the sensitivity and resolution. However, most of these models are only applied to resonators with rectangular and uniform cross-sections. In this paper, we present the analytical modeling to determine the first bending resonant frequency, out-of-plane deflections, and normal stresses of MEMS/NEMS-based multilayered resonators with variable cross-sections and multiple fixed supports. The proposed modeling is derived using the well-known Rayleigh and Macaulay methods, as well as the Euler-Bernoulli beam theory. This analytical modeling is applied to four multilayered resonators with different clamped supports and non-uniform cross-sections. The results of our analytical modeling agree well with respect to those of finite element method (FEM) models and experimental data reported in the literature. The proposed analytical modeling can be used to estimate the frequency shift of resonators due to variations of their geometric parameters, number of clamped-supports or mechanical properties of the materials. Furthermore, this modeling can be used to obtain optimal designs of resonators that ensure safe operations and enhanced performance for sensors and energy harvesters in telecommunications, automotive sector, aerospace industry, consumer electronics, non-destructive testing, and navigation.

Lateral Extensional Mode Piezoelectric ZnO-on-Nickel RF MEMS Resonators for Back-End-of-Line Integration

“…Due to the low deposition rates, the thickness of RF magnetron-sputtered ZnO films is often limited to a couple of micrometers or less. Moreover, the fabrication tolerance and yield of thin-film ZnO lateral-extensional mode resonators are affected by the releasing step, as the residual stress causes suspended ZnO structural layers to buckle or even fracture [ 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. To circumvent these issues, this work investigates the employment of a nickel thin film, which is deposited by a low-temperature electroplating process, as the acoustic structural material for the vibrating micromechanical resonator body.…”

“…Piezoelectric transduction mechanisms have been exploited for lowering a resonator's motional resistance [12][13][14][15][16][17]. By taking full advantage of the strong piezoelectric coefficient of sputtered c-axis-aligned ZnO thin films, this work investigates ZnO-on-nickel lateral-extensional mode resonators that are capable of realizing high electromechanical coupling (kt 2 ) and low motional impedances.…”