Measurement of Internal Stresses via the Polarization in Epitaxial Ferroelectric Films

Abstract

The relations between electrical and mechanical properties of constrained ferroelectric films are analyzed. It is shown that the internal stresses and the elastic constants can be determined through the measurement of the electrical response. The change in the polarization is proportional to internal stresses due to film-substrate misfit, whereas the linear electrical and electromechanical responses to external field do not depend on the misfit and are determined by the film constraint. The theoretical results are successfully applied to $\mathrm{PbZr}{}_{0.2}\mathrm{Ti}{}_{0.8}\mathrm{O}{}_3$ films on (001) $\mathrm{LaAlO}{}_3$ substrate which exhibit a considerable increase in the saturation polarization due to epitaxial stresses. Significant recovery in the piezoelectric constant and susceptibility is theoretically predicted and experimentally verified for specific film configurations which reduce the degree of constraint. The concept presented in this Letter can be expanded to constrained ferromagnetic and superconductor films.