Energy Losses in MEMS and Equivalent Viscous Damping

Energy losses change the behavior of mechanical microsystems and limit their performance. The response of a single degree-of-freedom (DOF) mechanical system, for instance, is conditioned by a damping term (force in translatory motion and torque in rotary motion), which can be formulated as a viscous damping agent whose magnitude is proportional to velocity. The damping coefficient is the proportionality constant and various forms of energy losses can be expressed as viscous damping ones, either naturally or by equivalence so that a unitary formulation is obtained. For oscillatory micro/nanoelectro mechanical systems (MEMS/NEMS), losses can be quantified by means of the quality factor (Q-factor), which is the ratio of the energy stored to the energy lost during one cycle of vibration, and the damping coefficient can be expressed in terms of the Q-factor. Energy losses in MEMS/NEMS are the result of the interaction between external and internal mechanisms. Fluid- structure interaction (manifested as squeeze- or slide-film damping), anchor (connection to substrate) losses, thermoelastic damping (TED), surface/volume losses and phonon-mediated damping are the most common energy loss mechanisms discussed in this chapter.