Enhancing piezoelectricity through polarization-strain coupling in ferroelectric superlattices

Short-period ferroelectric/ferroelectric ${\text{PbTiO}}_3$ (PTO)/${\text{BaTiO}}_3$ (BTO) superlattices are studied using density functional theory. Contrary to the trends in paraelectric/ferroelectric superlattices the polarization remains nearly constant for PTO concentrations below 50%. In addition, a significant decrease in the $c/a$ ratio below the PTO values was observed. Using a first-principles superlattice model we predict an enhancement in the $d_{33}$ piezoelectric coefficient peaking at $\sim 75\%$ PTO concentration due to the different polarization-strain coupling in PTO and BTO layers. Further analysis reveals that these trends are bulk properties which are a consequence of the reduced $P$ brought about by the polarization saturation in the BTO layers.

Figure 1

Polarization along the $z$ axis (top) and $c/a$ ratio (bottom) as a function of PTO concentration for BTO/PTO superlattices with varying superlattice periods. Solid squares represent DFT calculations, and the dashed lines are the values obtained using the superlattice model [see Eqs. (1, 3)]. Numerical model parameters can be found in Table .

Figure 2

Polarization along the $z$ axis as a function of in-plane strain for bulk BTO and PTO. Solid circles and squares represent DFT calculations for PTO and BTO, respectively. Dashed lines are the corresponding values obtained using Eq. (1) with the parameters of Table .

Figure 3

Dependence of $d_{33}$ on PTO concentration for PTO/BTO superlattices. The dashed line represents the results of the superlattice model at the bulk STO in-plane lattice constant of $3.863\text{Å}$, and the dotted line represents that for an in-plane lattice constant of $3.90\text{Å}$. The solid squares are computed from DFT.

Figure 4

Effective enthalpy (left) and $c$ lattice parameter (right) as a function of polarization for various compositions of PTO/BTO superlattices obtained from the superlattice energy functional. Dashed lines represent pure BTO, dashed-dotted lines are for pure PTO, and solid lines indicate the ferroelectric wells for the superlattices at 20% PTO intervals. Open circles mark the $c$ lattice parameter for each composition at the predicted $P$. The dotted line in the right figure indicates $c$ for epitaxially strained tetragonal PTO. Energies are relative to epitaxially strained bulk BTO.