First Principles Dielectric Slab Model for Dielectric and Piezoelectric Response in Superlattices

Superlattice systems, experimentally realizable with the development of layer by layer epitaxial growth techniques, continue to be of great interest in the development of new or enhanced material functionalities. Searching this enlarged space of realizable materials can be facilitated by models that allow prediction of superlattice properties from knowledge of the bulk properties of the constituent layers. In the dielectric slab model, introduced in 2003 for $\mathrm{BaTiO_3/SrTiO_3}$ superlattices, the superlattice properties are determined by the bulk responses of the constituents to the electrical and mechanical boundary conditions in the superlattice. The displacement field formulation due to Stengel and collaborators allows for a definitive version of this model that incorporates electric field effects beyond the linear approximation. Here, we present first-principles results for the bulk properties, including strain and polarization, as a function of displacement field for constituent compounds including $\mathrm{PbTiO_3}$, $\mathrm{BaTiO_3}$ and $\mathrm{SrTiO_3}$, and discuss the application of the model to obtain dielectric and piezoelectric responses of superlattices based on these constituents.