A new dimension for piezo actuators: Free-form out-of-plane displacement of single piezo layers

We present a controlled mode of "topological" displacement of homogeneous piezo films that arises solely from an inhomogeneous in-plane strain due to an inhomogeneous polarization. For the rotationally symmetric case, we develop a theoretical model that analytically relates the shape of the displacement to the polarization for the cases of in-plane and out-of-plane polarization. This is verified for several examples, and we further demonstrate controlled asymmetric deformations.