Extended lamb´s model application to high-order resonances of micromachined circular membranes with integrated actuation and sensing capabilities

Chips (5mm×5mm) containing 5 self-actuated/self sensed membranes have been fabricated by standard micromachining techniques starting with a Silicon-On-Insulator wafer and their dynamic behavior in liquid media was thoroughly considered by means of analytical modeling. An extended theoretical model on the basis of H. Lamb´s seminal work is validated at the microscale and allows calculating resonant frequencies in liquid media using analytical formulation. Despite the complex multilayered structure of the circular membranes, the model allows further estimating mass sensing specifications such as mass sensitivity and minimum detectable mass. Moreover, being purely analytical, the main advantage of the extended Lamb´s model consists on its ability to build close-form expressions which can be used as design rules for bioMEMS designers in order to enhance the performances of circular micromembranes-based sensors.