Effect of surface stress on the stiffness of cantilever plates: Influence of cantilever geometry

Abstract

Numerous measurements have indicated that surface stress can significantly modify the stiffness of cantilever sensors. In contrast, theoretical calculations using classical beam theory predict that stiffness is independent of surface stress. Using a three-dimensional analysis, we recently showed that surface stress does indeed have an effect within the framework of linear elasticity. However, only cantilevers of rectangular geometry were explored. Here, we vary cantilever geometry and find that it plays a critical role, with V-shaped cantilevers displaying greatly enhanced sensitivity in comparison to rectangular cantilevers. Tuning cantilever geometry therefore provides a sensitive route to controlling the effects of surface stress.