Cantilever unified theory and optimization for sensors and actuators

The deflection of a bilayered cantilever due to an external stimulus can be utilized in novel microsensors and actuators. It can also be used to determine the material properties of the components. Existing models are limited to investigations of individual systems such as isotropic (thermal, piezoelectric etc) or anisotropic (magnetostrictive) driving stimuli. A unified theory is presented based on total energy minimization, allowing inclusion of all stimuli acting on the system. Current theory, including that of a magnetostrictive cantilever, also tends to be related to a negligible film-to-substrate thickness ratio. This analysis allows examination of all thickness ratios, is in agreement with finite-element analysis, and also reduces to the thin-film limit. This is of increasing importance with the current drive to make micro devices. The data are examined for both sensor and actuator application. This is presented in a novel form, particularly for actuators. It is assumed that a cantilever actuator should deliver a given force at specific displacement. The full analysis of such systems allows, for the first time, quantitative optimization of device performance based on material properties and dimensions. The limitations on cantilever geometry given by thermal noise are derived. This analysis shows that substantial improvements in micromechanical sensor technology are still possible.