Analytical solutions of electroelastic fields in piezoelectric thin-film multilayer: applications to piezoelectric sensors and actuators

Abstract

Analytical expressions are derived for the stresses and electric fields induced in a piezoelectric multilayer deposited on a substrate with lattice misfit and thermal expansion coefficient mismatch. The piezoelectric multilayer can be subjected to an externally applied force, moment and electric potential. The derived formulations can model any number of layers using recursive relations that minimize the computation time. A proper rotation matrix is utilized to generalize the derived expressions to accommodate various orientations allowing each layer to have hexagonal crystal symmetry. The influence of lattice misfit and thermal expansion coefficient mismatch in the presence of externally applied force, moment and electric potential on the state of the electroelastic fields in each layer is evaluated for various applications. Comparison with finite element analysis results shows excellent agreement. The analytical expressions developed here can be useful in designing electromechanical sensors, actuators and optoelectronic devices made from piezoelectric multilayers.