Defects in epitaxial Ru(0001) on Al2O3(0001): Dislocations, stacking faults, and deformation twins

Defects in epitaxial Ru(0001) films on c-plane sapphire, with nominal thicknesses of 10–80 nm, deposited at 350 °C and step-annealed to 950 °C, were characterized using transmission electron microscopy. The variation of Ru and sapphire lattice parameters with temperature is such that the misfit strain for the observed 30° rotated-honeycomb epitaxial relationship is essentially constant with temperature at 1.5%, resulting in a biaxial stress of 10.0 GPa and an energy density of 150 MJ m−3 in unrelaxed films. Stress relaxation occurs by the formation of defects. For the 20–80 nm thick films, the defects are a- and c-type dislocations and stacking faults, argued to be of I 2 type. In addition, the films show the surprising presence of { 11 2 ¯ 1 } 1 / 3 ⟨ 11 2 ¯ 6 ¯ ⟩ deformation twins. The 10 nm-thick films were found to be defect free. The critical thickness for misfit strain relaxation via the formation of threading and misfit dislocations is computed as 7 ± 2 nm, depending on the choice of the dislocation core radius. Energetic analysis of twin formation, using both the infinite-matrix and the finite-matrix (Mori–Tanaka) approaches, provides values of the twin aspect ratios, assumed to be ellipsoidal, and shows that the latter but not the former approach can qualitatively explain the formation of the observed twins. In addition to providing the maximum strain relief compared to other potential twin types, { 11 2 ¯ 1 } 1 / 3 ⟨ 11 2 ¯ 6 ¯ ⟩ twins do not require lattice shuffles and have a boundary that is a special boundary, namely, a 35° tilt boundary with a-type dislocations every other {0002} plane, that may also favor their formation.