Tilting during island growth of In2O3 on Y-stabilized ZrO2(001) revealed by high-resolution x-ray diffraction

The growth of ${\text{In}}_{2}{\text{O}}_{3}$ islands on (001)-oriented Y-stabilized cubic ${\text{ZrO}}_{2}$ has been investigated using high-resolution x-ray diffraction and the results compared with those from atomic force microscopy and electron microscopy. Measurements were performed with wave-vector transfer both parallel to and perpendicular to the surface normal. Transverse scans around the epilayer (004) and (008) reflections gave a characteristic three-peak structure for wave-vector transfer along the [110] direction but a two-peak structure when the scan was performed along the [100] direction. These results suggest that the atomic planes of the islands are not parallel to those of the substrate but are tilted at an angle of about $0.7\ifmmode^\circ\else\textdegree\fi{}$ from the four different in-plane $⟨110⟩$ directions. Tilting was also observed in real space by high-resolution transmission electron microscopy. The tilt helps to relieve tensile strain arising from a $\ensuremath{-}1.6\mathrm{%}$ lattice mismatch between the epilayer and the substrate. The tilt direction is shown to be determined by the elastic constants of the epilayer, which favor strain along $⟨110⟩$ directions rather than $⟨100⟩$ directions. The x-ray results also indicated that the islands imaged by atomic force microscopy are each built up from microdomains so that the coherence length deduced from x-ray scattering is much smaller than the island size. Thus for islands with a thickness of $2500\text{ }\text{\AA{}}$ the coherence length was estimated to be about $500\text{ }\text{\AA{}}$.