An Analytical Formulation of the Radio-Frequency Response of Piezoelectric Contour-Mode MEMS Resonators Verified by Measurements

Mirco-electromechanical systems (MEMS) have already revolutionised the world of radio-frequency (RF) electronic circuits. Especially their small size and compatibility with semiconductor processes make MEMS devices advantageous for the use in integrated timing devices such as RF-MEMS oscillators. In addition to the wide-spread numerical simulations, analytical design aids remain to be of utmost relevance when it comes to optimising the performance of RF-MEMS circuits. In this paper, we present an extended analytical treatment of MEMS resonators that has not been considered before. Based on the wave equation, the mechanical stress is calculated for a contour-mode resonator, and the resulting trans-admittance and an equivalent-circuit model are derived in closed form. A comparison of the results with the state-of-the-art and measurement results underline the correctness and accuracy of this extended formulation.