Effects of Ohmic Resistance on Dynamic Characteristics and Impedance of Micro/Nano Cantilever Beam resonators

Abstract

Effects of Ohmic resistance on MEMS/NEMS vibrating structures that have always been dismissed in some situations may cause important changes in resonance properties and impedance parameters of the MEMS/NEMS based circuits. In this paper it is aimed to present a theoretical model to precisely investigate the problem on a simple cantilever-substrate resonator. In this favor the Ohm’s current law and charge conservation law have been merged to find a differential Equation for voltage propagation on the beam and because mostly nano structures are expected as the scope of the problem, modified couple stress theory is used to formulate the dynamic motion of the beam. The two governing equations were coupled and both nonlinear that have been solved simultaneously using a Galerkin based state space formulation. The obtained results that are in exact agreement with previous works show that dynamic pull-in voltage, switching time, and impedance of structure as a MEMS capacitor especially in frequencies higher than natural resonance frequency strongly relay on electrical resistance of the beam and substrate material.