Modeling and Characterization of Cantilever-Based MEMS Piezoelectric Sensors and Actuators

Piezoelectric materials are used in a number of applications including those in microelectromechanical systems. These materials offer characteristics that provide unique advantages for both sensing and actuating. Common implementations of piezoelectric transduction involve the use of a cantilever with several layers, some of which are piezoelectric. Although most analyses of such a cantilever assume small piezoelectric coupling (SPC), the validity of this assumption has not been fully investigated. This paper presents closed-form expressions for the voltage developed across a piezoelectric layer in an N-layer cantilever used as a sensor (e.g., as a microphone) and for the displacement profile of an N-layer cantilever used as an actuator. This represents the first time these closed-form expressions have been presented without making the SPC assumption and are used to determine the validity of the this assumption. Furthermore, a new, more robust experimental technique for identifying the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">d₃₁</tex></formula> piezoelectric coefficient is demonstrated using an aluminum nitride (AlN) cantilever beam. The developed expressions are also used to predict the voltage across a piezoelectric layer in a beam containing AlN layers in response to a pressure excitation and are shown to be in close agreement with experimental results. <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"></tex></formula> [2011-0107]