Strain, composition tuning and size effect in Pb$_{\mathrm{x}}$Sr$_{\mathrm{1-x}}$TiO$_3$ piezoelectric thin films and nanostructures

Optimizing the piezoelectric performance at the nanoscale is one of the main challenges for future piezoelectric applications, especially in the field of vibrational energy harvesting. In this work, we have investigated the combined influence of epitaxial strain, compositional variation and size reduction on the crystallographic structure, ferroelectric domain configuration and piezoelectric properties of Pb$_{\mathrm{x}}$Sr$_{\mathrm{1-x}}$TiO$_{3}$ thin films and nanostructures epitaxially grown by Pulsed Laser Deposition on SrRuO$_{3}$-buffered (110)-DyScO$_{3}$ substrates. Theoretical predictions on the PbTiO$_{3}$-SrTiO$_{3}$ solid solution show an interesting phase transition, expected to give rise to enhanced piezoelectric properties, as a function of composition when the films are grown under strain on (110)-DyScO$_{3}$. A series of high quality epitaxial thin films has been grown with various Pb/Sr ratios. We have experimentally confirmed the predicted phase transition. Highly periodic domains with purely in-plane polarization have been observed by both X-ray diffraction and piezoresponse force microscopy. The piezoelectric properties have then been studied as a function of composition and of the lateral dimensions of nano-objects defined by Electron Beam Lithography.