Shape Transitions of Epitaxial Islands during Strained Layer Growth: Anatase ${\mathrm{TiO}}_2(001)$ on ${\mathrm{SrTiO}}_3(001)$

Extended annealing in UHV causes the surface region of ${\mathrm{SrTiO}}_3(001)$ to become enriched with ${\mathrm{TiO}}_2$, resulting in the formation of epitaxial islands of anatase ${\mathrm{TiO}}_2(001)$. The islands are studied using UHV scanning electron microscopy (SEM), which reveals the changes in morphology during growth induced by misfit strain. Starting from a square island, two types of shape transition are observed. In the first, between 1000 and $1030°\mathrm{C}$, the anatase islands elongate in length and narrow in width. This growth behavior follows the Tersoff-Tromp model [Phys. Rev. Lett. 70, 2782 (1993)]. In the second growth mode, between 930 and $1000°\mathrm{C}$, the islands relieve strain by the formation of trenches in the middle of each side of the square, thereby evolving into crosses. This shape arises because the lower annealing temperature imposes a kinetic constraint on the detachment of atoms necessary for island narrowing.

Figure 1

Secondary electron UHV SEM images of anatase islands on ${\mathrm{SrTiO}}_3$, which are formed at annealing temperatures between 1000 and $1030°\mathrm{C}$. In (a) a square island is shown. Beyond a critical size the islands elongate and narrow, forming rectangles (b),(c).

Figure 2

Plot of anatase island lengths (solid triangles) and widths (open circles) versus surface area of the islands. The thick line represents the theoretically derived growth behavior of an island of average height 30.8 nm, with a bifurcation point at the critical width of $1.3\mu \mathrm{m}$. The thin lines show the bounds due to the standard deviation of the island heights $\pm 4.0\mathrm{nm}$. The dashed parabolic line indicates how growth would proceed for unrelaxed islands. The error of measurement of individual data points is of the order of their size.

Figure 3

UHV SEM images of anatase islands at various stages of growth formed at an anneal temperature of $930°\mathrm{C}$. In (a) one side of the island forms a trench after the square reaches the critical size. In (b), another island is shown in which the shape transition has occurred, where the island symmetrically splits developing trenches in the middle of each of its four sides. Further annealing produces an island shape as shown in (c), which shows significant widening of the trenches and also shows growth from the tips of the cross.

Figure 4

Plot of island perimeters (triangles) versus their surface area for the types of island shown in Fig. 3. The thick line shows how growth would proceed according to Tersoff’s model, Eq. (1), for a rectangular island of 22.5 nm height and a critical transition area of $0.53\mu {\mathrm{m}}^2$. The thin lines correspond to the bounds due to the standard deviation in height of $\pm 2.7\mathrm{nm}$. The dashed parabolic line shows unrelaxed island growth.