#### Date of Award

Fall 2013

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Electrical and Computer Engineering

#### First Advisor

Josse, Fabien J.

#### Second Advisor

Heinrich, Stephen M.

#### Third Advisor

Lee, Chung Hoon

#### Abstract

Dynamically driven microcantilevers excited in the transverse (or out-of-plane) direction are widely used as highly sensitive chemical sensing platforms in various applications. While these devices work very well in air, their performance in liquids is not efficient because of the combination of increased viscous damping and effective fluid mass. In order to improve the characteristics of microcantilevers in liquid environments, some other vibration modes such as the torsional mode and lateral (or in-plane) flexural mode have been proposed.

In this work, the characteristics of torsionally vibrating rectangular microcantilevers with length L, width b and thickness h in viscous liquids are investigated taking into account the thickness effects. Finite element models are used to obtain the hydrodynamic loading (torque per unit length) and thus calculate values of the hydrodynamic function. An analytical expression of the hydrodynamic function in terms of the Reynolds number and aspect ratio, h/b, is then obtained by fitting the numerical results. This allows for the characteristics to be investigated as a function of both beam geometry and fluid properties, considering thickness effects on the torsional constant, the hydrodynamic function and the polar moment of area. For high aspect ratios, (h/b>0.16) microcantilevers vibrating in the 1st torsional mode, ignoring thickness effects could result in a minimum error of 9%, 5%, 20%, 7% for the resonance frequency, quality factor, mass sensitivity, and normalized mass limit of detection, respectively. Clearly, for many sensing applications based on analyzing the resonance frequency and mass sensitivity, thickness effects should be taken into account. The resonance frequency is found to be dependent on h/(bL) and the quality factor is found to be dependent on h/L1/2 for microcantilevers vibrating in the 1st torsional mode in viscous liquids. In comparison, for microcantilevers vibrating in the 1st lateral mode, the resonance frequency is dependent on b/L2 and the quality factor is dependent on hb1/2/L. Such different trends can be used to optimize device geometry and liquid property, thus maximizing quality factor and sensitivity in chemical sensing applications. Compared with microcantilevers in the 1st transverse mode, microcantilevers that vibrate in their first torsional mode have higher resonance frequency and quality factor. The increase in resonance frequency and quality factor results in higher sensitivity and reduced frequency noise, respectively. This will yield much lower limits of detection in liquid-phase chemical sensing applications.