Design strategies for controlling damping in micromechanical and nanomechanical resonators

Damping is a critical design parameter for miniaturized mechanical resonators used in microelectromechanical systems (MEMS), nanoelectromechanical systems (NEMS), optomechanical systems, and atomic force microscopy for a large and diverse set of applications ranging from sensing, timing, and signal processing to precision measurements for fundamental studies of materials science and quantum mechanics. This paper presents an overview of recent advances in damping from the viewpoint of device design. The primary goal is to collect and organize methods, tools, and techniques for the rational and effective control of linear damping in miniaturized mechanical resonators. After reviewing some fundamental links between dynamics and dissipation for systems with small linear damping, we explore the space of design and operating parameters for micromechanical and nanomechanical resonators; classify the mechanisms of dissipation into fluid–structure interactions (viscous damping, squeezed-film damping, and acoustic radiation), boundary damping (stress-wave radiation, microsliding, and viscoelasticity), and material damping (thermoelastic damping, dissipation mediated by phonons and electrons, and internal friction due to crystallographic defects); discuss strategies for minimizing each source using a combination of models for dissipation and measurements of material properties; and formulate design principles for low-loss micromechanical and nanomechanical resonators.