Shift in the ferroelectric transition temperature of (001)-oriented STO as function of the in-plane lattice mismatch between substrate (or buffer) and STO layers. (Refs. 8 and 9) The structural mismatch was measured at room temperature, and the ferroelectricity was determined for electric field parallel to the film surface. Theoretical predictions are added. (Ref. 11)
Thickness dependence of the out-of-plane lattice parameter of STO (circles) and (, squares), and FWHM (triangles) of the (200) rocking curve of the STO layer, respectively. The dashed lines indicate the literature values of the lattice parameters for STO and .
Microscope images (area: ) of the surface of STO films of thickness (a), 525 nm (b), 740 nm (c), and 970 nm (d). The crystallographic orientations of the substrate, buffer, and STO layer are determined via XRD diffraction experiments, they are identical for all images and are indicated in [(c) and (d)].The dashed ellipses in (b) mark hardly visible cracks in the STO film of medium thickness.
(a) XRD pole figures [(001) STO, (001) , and (012) ] provide the in-plane crystallographic orientation of the different layers with respect to the orientation of the substrate; (b) 2D-plot of the dependence of characteristic diffraction peaks of the pole figures [(112) and of STO, of , and of ] obtained for the samples of different STO layer thicknesses. The characteristic shift in the STO diffraction peak with respect to the diffraction peak is shown in detail for a thick film (c) and a thin film (d). For a better comparison, the (112) STO peaks are shifted by 45° in [(c) and (d)].
Critical thicknesses for the generation of misfit dislocations according to van der Merwe (Ref. 18) (dotted black line) and Matthews theory [solid line, Eq. (3)], and critical thickness for crack generation according to Eq. (6) for different values of and . The vertical lines indicate the lattice misfit of STO with respect to various substrates.
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