Thickness effect on ferroelectric domain formation in compressively strained K0.65Na0.35NbO3 epitaxial films

In this paper, the influence of thickness in epitaxial ${\mathrm{K}}_{0.65}{\mathrm{Na}}_{0.35}{\mathrm{NbO}}_{3}$ ferroelectric thin films grown on a (110) ${\mathrm{TbScO}}_{3}$ substrate was systematically studied. Detailed atomic force microscopy revealed a complex change in growth mode with increasing film thickness, with the surface roughness remaining 0.30 nm throughout. By combining piezoresponse force microscopy and high-resolution x-ray diffraction, the occurrence of 90\ifmmode^\circ\else\textdegree\fi{} stripe domains was demonstrated for the films with a thickness of \ensuremath{\ge}11 nm, while the domain periodicity is in good agreement with Kittel's law. Furthermore, up to the thickness of 93 nm, elastic strain relaxation induced by the formation of ferroelectric domains was observed, whereas plastic strain relaxation plays only a minor role. As the film thickness increases, three successive phases of ferroelectric domains were observed: (i) irregularly arranged orthorhombic $c$ domains in the thinnest film, (ii) periodically arranged 90\ifmmode^\circ\else\textdegree\fi{} monoclinic ${M}_{C}$ domains up to a thickness of 25 nm, and (iii) a flux closure vortexlike structure in thicker films to achieve the lowest equilibrium energy. These results demonstrate the importance of understanding the lattice relaxation mechanism for intentional tuning of ferroelectric thin film properties.