The Effect of Lattice Mismatch on the Piezoresponse of Barium Titanate (BaTiO{sub}3) Thin Films on Magnesium Oxide (MgO) Substrates

摘要

During the process of deposition of a thin piezoelectric film on a substrate, a difference in the in-plane lattice parameters of the two materials leads to internal stresses that may bias the film response under external mechanical or electric fields. While the lattice mismatch is expected to have a gradient along the thickness of the film, we investigate two extreme cases here: (i) the lattice mismatch is confined in a thin layer of the film at the film-substrate interface, (ii) the lattice mismatch spans the entire domain of the thin film. We propose a scalar, volume-averaged internal stress parameter as a metric to quantify the internal stress state of the thin film. An equivalent thermal strain approach is employed to model the mismatch and the effect of substrate and film dimensions on the average internal stress parameter, free film surface displacements and the potential drop across the film are studied computationally. In particular, it is seen that the effect of a smaller film thickness is to increase the potential drop when the lattice mismatch is confined to a thin layer at the interface whereas the potential drop decreases when the entire film has a uniform mismatch. In both cases, the effect of a larger substrate radius is to increase the potential drop.