Design Method to Achieve High Frequency Stability of Electrostatically Actuated Doubly-Clamped Nano-Oscillators

Abstract

Frequency stability is a desirable property for micro- and nanoelectromechanical system oscillators used in reference and timing applications. In case of doubly-clamped oscillators, resonant frequencies are highly sensitive to the operating temperature because of development of internal stresses due to thermal expansion under the restraint of fixed boundary conditions. In this paper, we present a design procedure to reduce the variation of resonant frequency with respect to change in operating temperature, in other words improve the frequency stability, by exploiting the interaction between electrostatic and geometric nonlinearities in electrostatically actuated doubly-clamped nano-oscillators. We have modeled the nano-oscillators using Euler-Bernoulli beam theory and Galerkin based reduced order modeling technique. We have examined first natural frequency variation due to temperature change for different carbon nanotube oscillators and an optimization based design procedure has been devised for improving the frequency stability.