Estimating the effective quality factor of a rotary comb-drive microresonator based on a non-classical theory

Due to the considerable importance of viscous damping as a principal source of energy dissipation in microstructures, this manuscript presents a mathematical model to predict the thin film damping in a rotary comb-drive microresonator. The proposed model is for a silicon micro-finger which oscillates longitudinally as a rigid body. The gap between the fingers is filled with air, which typically plays a significant role in the damping of the vibrating structures. As the gap between the fingers is so small (in the range of micrometer), the equations governing the surrounding air are extracted based on micropolar theory, which is considered to be an expedient theory for analyzing the micro-scale fluid behavior. The governing equations are discretized and numerically solved by considering the slip and spin boundary conditions on the fluid–solid interface. By applying a complex frequency approach, the effective quality factor of the resonator is predicted. Investigating the profound effect of boundary conditions shows that considering the slip and spin boundary conditions lead to the decrement of the viscous damping ratio of the resonator.