Epitaxial Sr(Sn, Ge)$_{x}$Ti$_{1-x}$O$_{3}$ buffer layers for continuous strain engineering on SrTiO$_{3}$ substrates

Abstract: Epitaxial strain plays a key role in determining the structure and functionality of thin films, with the choice of substrate being traditionally used to control the magnitude of the applied strain. However, even in the large family of perovskite materials, this allows for only a limited, discrete set of strain states to be achieved. Here we report on an approach to controlling epitaxial strain for the growth of perovskite materials by involving a single SrTiO${3}$ substrate (the most available perovskite in single crystal form) and a buffer layer that consists of the solid solution Sr(Sn, Ge)${x}$Ti${1-x}$O${3}$, of which the lattice parameter can be tuned in a continuous fashion, from 3.880 Å up to 4.007 Å, while maintaining coherent epitaxial growth on SrTiO${3}$ with high quality interfaces. Using a BaTiO${3}$ overlayer as a model system, we show that changes to the buffer layer composition, i.e. increase of in-plane lattice parameter, change the strain state of BaTiO$_{3}$ from fully relaxed, through highly compressively strained, to an exotic state showing 'inverted' epitaxy in which the buffer layer is relaxed from the substrate but lattice matched to the overlayer.