Verification of a 3D analytical model of multilayered piezoelectric systems using finite element analysis

Abstract

An approximate 3D analytical model of multilayered systems is developed that can be used to identify promising dimensions and property selection during the initial design of components needed for microscaled and nanoscaled devices. This paper is focused on the deformation of nanoscaled crystallographic systems of perfectly bonded multilayer materials forming the piezoelectric components of piezoelectronic transistor devices. The assembly includes two perfectly conducting electrodes adjacent to piezoelectric layer(s). The assembly of layers is assumed to be epitaxial so that atoms of the crystal are associated with a lattice defining a local displacement vector and strain tensor. Because of epitaxy, layers have their own lattice spacing and account is taken additional strains and stresses arising due to lattice mismatch effects. The multilayered system can be subject to complex mechanical loading characterized by biaxial in-plane, uniform through-thickness loading, and orthogonal biaxial bending. Any isothermal temperature can be considered, and the application of a voltage across the electrodes. The model estimates the effective properties of the multilayer, enabling predictions of stress and strain distributions when the system is subject to complex loading. Model verification considers a free-standing multilayer system subject to electrical loading. This challenging problem constrains boundary conditions to avoid edge effects, while accounting for clamping of the multilayer. The results are presented comparing model predictions with results of finite element analysis. Excellent agreement verifies that the analytical model and associated software are working correctly, and will apply to diverse applications, such as actuators and sensors, in addition to piezoelectronic transistor devices.