Numerical Study of the Impact of Vibration Localization on the Motional Resistance of Weakly Coupled MEMS Resonators

This paper presents a numerical study of the impact of process-induced variations on the achievable motional resistance R_x of 1-D, 2-D, cyclic, and cross-coupled architectures of weakly coupled electrostatically transduced microelectromechanical resonators operating in the 250-kHz range. We use modal analysis to find the R_x of such coupled arrays and express it as a function of the eigenvectors of the specific mode of vibration. Monte Carlo numerical simulations, which accounted for up to 0.75% variation in critical resonator feature sizes, were initiated for different array sizes and coupling strengths for the four distinct coupling architectures. Improvements in the mean and standard deviation of the generated R_x distributions are reported when the resonators are implemented in a crosscoupled scheme, as opposed to the traditional 1-D chain. The 2-D coupling scheme proves to be a practical and scalable alternative to weakly coupled 1-D chains to improve the immunity to process variations. It is shown that a 75% reduction in both the mean and standard deviation of the Rx is achieved, as compared with the traditional 1-D chain for a normalized internal coupling κ > 10^-2.