Deformation of substrate by epitaxial piezoelectric film and implications for interferometry.

• A theory is provided for piezoelectricity of a film on a flexible substrate with isotropic lattice mismatch. • Attribution of DBLI signal to thickness change of the thin film only is erroneous. • Contributions of the substrate and the film to piezoelectric response are comparable in magnitude. • Piezoelectric response is calculated for relevant ferroelectrics depending on substrate thickness. Advanced micro- and nano-electro-mechanical systems benefit from single-crystal-type epitaxial piezoelectric films, whose high crystal quality ensures excellent performance. Strong mechanical coupling in such films to non-piezoelectric substrates defines a difference in their operation with respect to purely piezoelectric counterparts. This is often described by a limiting case of a thick non-deformable substrate, whereas the film has out-of-plane deformations only. Here we consider a general practically relevant case, when converse piezoelectric effect in the film causes bending of the substrate. We provide a thermodynamic description and deliver analytical expressions for curvature, stress release, and thickness changes in a stack of the parallel-plate thin-film capacitor coherent to the substrate. It is shown that substrate deformations cannot be neglected and the d 33 piezoelectric modulus receives comparable contributions from the film and the substrate. Implications for the interferometric measurement of the converse piezoelectric response are discussed. [ABSTRACT FROM AUTHOR]