Deformation of substrate by epitaxial piezoelectric film and implications for interferometry

Abstract

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 d33 piezoelectric modulus receives comparable contributions from the film and the substrate. Implications for the interferometric measurement of the converse piezoelectric response are discussed.