A numerical simulation for the stress effect in flexural micro/nano electromechanical resonators

Abstract

Resonance frequencies and quality factors of micro/nano electromechanical resonators are known to differ significantly from target values in the presence of intrinsic stresses. This stress effect is modeled for a two-port system with electrostatic actuation and capacitive read-out. A methodology is proposed to compute equivalent electrical parameters for a double-clamped beam resonator under stress. The model is verified with finite element analysis, and a number of case studies are conducted in addition. Increase in resonance frequency with increasing intrinsic tensile stress is observed under mechanical and electrical effects, while a deterioration of quality factor is evident in cases with pronounced parasitic effects. Related challenges associated with the transition to the nanoscale are computationally captured. Finally, a short formulation is provided with relevant error margins for the direct estimation of equivalent circuit parameters. The proposed approach serves as a useful tool for layout design, where all involved dimensions are considered in addition to operational variables such as bias voltage and unloaded quality factor.