Modeling of the intrinsic stress effect on the resonant frequency of NEMS resonators integrated by beams with variable cross-section

Nano-electro-mechanical systems (NEMS) resonators integrated by a double clamped beam with variable cross-section are used in several applications such as chemical and biological detectors, high-frequency filters, and signal processing. The structure of these resonators can experience intrinsic stresses produced during their fabrication process. We present an analytical model to estimate the first bending resonant frequency of NEMS resonators based on a double clamped beam with three cross-sections, which considers the intrinsic stress effect on the resonant structure. This model is obtained using the Rayleigh and Macaulay methods, as well as the Euler–Bernoulli beam theory. We applied the analytical model to a silicon carbide (SiC) resonator of 186 nm thickness reported in the literature. This resonator has a total length ranking from 80 to 258 μm and is subjected to a tensile intrinsic stress close to 110 MPa. Results from this model show good agreement with experimental results. The analytic frequencies have a maximum relative difference less than 6.3% respect to the measured frequencies. The tensile intrinsic stress on the resonant structure causes a significantly increase on its bending resonant frequency. The proposed model provides an insight into the study of the intrinsic stress influence on the resonant frequency of this nanostructure. In addition, this model can estimate the frequency shift due to the variations of the resonator geometrical parameters.