Methods for determining piezoelectric properties of thin epitaxial films: Theoretical foundations

Abstract

An analytical method is developed to determine piezoelectric properties of a thin film directly from measurements of bilayer deflection. As a significant extension to previous approaches, we include here the effects of bilayer bending, differential thermal expansion, and epitaxial lattice mismatch which commonly arise in practical measurements. The formulation reported here thus relaxes restrictive assumptions made in previous models thereby enabling a more direct link with experimental conditions. The model, which has been validated by comparison with finite element analysis, is shown to reduce to the well-known Lefki-Dormans result as a limiting case for thin films when bending and in-plane deformations are neglected. If the curvature of a simply supported bilayer can be measured, then the model offers a methodology for measuring the piezoelectric properties (ε33T,d31,d33), the film elastic constant s11E+s12E, and lattice mismatch strains, provided a value of the elastic constant s13E can be determined or estimated. If curvature measurements are not available but lattice mismatch strains are known, then we find that it is still possible to measure these piezoelectric and elastic film properties. © 2014 Crown.