Piezoelectric thin-film superlattices without using piezoelectric materials

In this paper we show that experimentally realizable apparently piezoelectric thin-film superlattices can be created from nonpiezoelectric materials provided an odd-order (e.g., trilayer) stacking sequence is used. The size-dependent mechanism of flexoelectricity, which couples gradients of strain to polarization, allows such a possibility. We present closed-form analytical expressions for the response of various thin-film and superlattice configurations. We also clarify some of the subtleties that arise in considering interface boundary conditions in the theory of flexoelectricity as well as the relationship of flexoelectricity to the frequently used polarization gradient terms used in modeling ferroelectrics. We find that for certain (optimum) material combinations and length scales, thin-film superlattices yielding apparent piezoelectricity close to 75% of ferroelectric barium titanate may be achievable.