Dynamics of oscillating piezoelectric micro resonators : hydrodynamic loading effect and intrinsic damping

Abstract

Micro resonators are important components in many micro electro mechanical system (MEMS) applications. The quality factor is a key parameter for MEMS resonators and is determined by the system damping of the devices. Aluminum nitride (AlN) based piezoelectric Si micro resonators with different geometries are fabricated and measured with an all-electrical excitation and detection method, to study the energy dissipation mechanisms. The dynamic behavior of these resonators is analyzed in gases as well as in high vacuum by developing and applying specific experimental, computational and analytical tools. We investigate the hydrodynamic loading in detail by exploring how factors, such as ambient pressure, the nature of the surrounding gas, the resonator geometry, higher mode operation and the presence of a nearby surface, effect the resonance behaviour of micro resonators. The resonator fluid interaction can be broadly divided into: i) resonators vibrating in an unbounded fluid, and ii) resonators vibrating close to a surface. For the first case, we systematically investigate the performance in different resonant modes. Incompressible flow is expected for the first few resonant modes. However, as the resonant mode number increases, the acoustic wavelength reduces and the energy loss is found to be diluted through mixing of viscous and acoustic effects. For the second case, most prior efforts to investigate this hydrodynamic loading have focused on squeeze film damping with very narrow gaps. In this research we investigate the case that a resonator vibrates close to a surface with a moderate distance. When a resonator is operated in high vacuum, intrinsic damping inside the solid materials dominates the quality factor. We focus on the three major intrinsic damping effects, which are thermoelastic damping (TED), anchor losses and coating losses. TED and anchor losses are investigated by using a combination of both analytical and numerical methods, while the coating loss mechanism is explored by measuring a series of cantilevers with a piezoelectrode stack coverage varying from 20%-100% of the beam length. Experimental validations are conducted on different structures of piezoelectric micro resonators, showing that the analysis yields qualitative matches with measurements and the contributions of the three mechanisms can be separated to a reasonable extent.