Cantilever unified theory and optimization for sensors andactuators

摘要

The deflection of a bilayered cantilever due to an externalstimulus can be utilized in novel microsensors and actuators. It can alsobe used to determine the material properties of the components. Existingmodels are limited to investigations of individual systems such asisotropic (thermal, piezoelectric etc) or anisotropic (magnetostrictive)driving stimuli. A unified theory is presented based on total energyminimization, allowing inclusion of all stimuli acting on the system.Current theory, including that of a magnetostrictive cantilever, also tendsto be related to a negligible film-to-substrate thickness ratio. Thisanalysis allows examination of all thickness ratios, is in agreement withfinite-element analysis, and also reduces to the thin-film limit. This isof increasing importance with the current drive to make micro devices.The data are examined for both sensor and actuator application. This ispresented in a novel form, particularly for actuators. It is assumed that acantilever actuator should deliver a given force at specific displacement.The full analysis of such systems allows, for the first time, quantitativeoptimization of device performance based on material properties anddimensions. The limitations on cantilever geometry given by thermal noiseare derived. This analysis shows that substantial improvements inmicromechanical sensor technology are still possible.