Dimensional considerations in achieving large quality factors for resonant silicon cantilevers in air

Abstract

This work aims to provide guidelines for designing rectangular silicon cantilever beams to achieve maximum quality factors for the fundamental flexural resonance at atmospheric pressure. The methodology of this work is based on experimental data acquisition of resonance characteristics of silicon cantilevers, combined with modification of analytical damping models to match the captured data. For this purpose, rectangular silicon cantilever beams with thicknesses of 5, 7, 8, 11, and 17 μm and lengths and widths ranging from 70 to 1050 μm and 80 to 230 μm, respectively, have been fabricated and tested. Combining the three dominant damping mechanisms, i.e., the air damping, support loss, and thermoelastic damping, the variation in the measured Q-factors with the cantilever geometrical dimensions is predicted. Also to better describe the experimental data, modified models for air damping have been developed. These modified models can predict the optimum length and thickness of a resonant cantilever to achieve the maximum quality factor at the fundamental flexural resonance mode in air.

Geometrical considerations for the design of liquid-phase biochemical sensors using a cantilever's fundamental in-plane mode

“…The frequency stability is correlated with the quality factor, Q, of the resonance mode. For this reason, several recent studies have measured and modeled the Q-factors of cantilevers vibrating in out-ofplane bending modes in air [4], [5], [6], [7] and [8]. While Q-factors up to 1500 have been measured for the first out-of-plane bending mode in air [4], liquid operation becomes challenging because of the substantial viscous damping by the fluid.…”

“…For this reason, several recent studies have measured and modeled the Q-factors of cantilevers vibrating in out-ofplane bending modes in air [4], [5], [6], [7] and [8]. While Q-factors up to 1500 have been measured for the first out-of-plane bending mode in air [4], liquid operation becomes challenging because of the substantial viscous damping by the fluid. Besides low Q-factors, typically not exceeding 10-20 in water [2], a substantial reduction of the out-of-plane resonance frequency (typically in the range of 30-50%) is observed in liquid due to the large effective mass of the fluid.…”

A xylophone bar magnetometer for micro/pico satellites

“…In this section, we follow an approach similar to the work of Naeli & Brand (2009). Four sources of dampings are considered : air damping, support damping, thermoelastic damping and surface damping.…”

“…At higher pressure, in the viscous regime, the air acts as a viscous fluid that brakes the displacement of the bar. The bar is then modeled as a string of resonant spheres for which the quality factor does not depend anymore on P (Hosaka et al 1995, Naeli & Brand 2009). Of course, in space, the contribution of air damping will be negligible but for other potential groundbased applications, we keep it as a possible loss source.…”

Resonant characteristics of rectangular hammerhead microcantilevers vibrating laterally in viscous liquid media

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