Analysis and fabrication of curved multimorph transducers that undergo bending and twisting

Difference in strains in the layers of a multimorph beam causes it to curl, thereby leading to transduction. Straight multimorph beams have been widely used for thermal, piezoelectric, and shape-memory-alloy-based transducers that undergo out-of-plane bending, but curved multimorph beams have not been explored much. In this paper, we report thermal transducers based on curved multimorphs that have a nonzero curvature in the plane of the substrate. The distinguishing feature of curved multimorphs is that they undergo both out-of-plane bending and twisting deformations. We report the small-deformation analysis of curved multimorphs. The analytical expressions greatly expand the design space for microelectromechanical systems engineers and can lead to novel devices, including micromirrors and infrared sensors. The closed-form expressions were validated against finite-element (FE) simulation and experimental results. Experimental verification was done by monitoring a curved electrothermal multimorph beam at different temperatures. Good agreement between the analysis and experiments has been observed in the small-deformation range. At large deformations, in-plane displacement becomes significant. FE simulations and experiments are used to study large deformations.