Hillock formation of Pt thin films on single-crystal yttria-stabilized zirconia

The stability of metal thin films on a dielectric substrate is conditioned by the magnitude of the interactive forces at the interface. In the case of a nonreactive interface and weak adhesion, the minimization of the free surface energy gives rise to an instability of the thin film. In order to study these effects, Pt thin films with a thickness of 50 nm were deposited via ion-beam sputtering on yttria-stabilized zirconia single crystals. All Pt films were subjected to heat treatments up to 973 K for 2 h. The morphological evolution of Pt thin films has been investigated by means of scanning electron microscopy, atomic force microscopy, and standard image analysis techniques. Three main observations have been made: (i) The deposition method has a direct impact on the morphological evolution of the film during annealing. Instead of hole formation, which is typically observed as a response to a thermal treatment, anisotropic pyramidal-shaped hillocks are formed on top of the film. (ii) It is shown by comparing the hillocks’ aspect ratio with finite element method simulations that the hillock formation can be assigned to a stress relaxation process inside the thin film. (iii) By measuring the quasiequilibrium shapes and the shape fluctuations of the formed Pt hillocks the anisotropy of the step free energy and its stiffness have been derived in addition to the anisotropic kink energy of the hillocks’ edges.

Figure 1

Illustration of the experimentally observed regimes of hillock formation. (a) During thermal treatment of a dense flat film (b) hillocks form on the film surface with a regular hexagonal shape (c) due to further annealing holes and secondary hillocks form in the vicinity of the primary hillock.

Figure 2

Schematic drawing of an elastically strained film including a hillock in the shape of a frustum, rotationally symmetric around the axis $M$, with the top radius $R_1$, the bottom radius $R_2$, and the height $h$.

Figure 3

SEM images of different stages of hillock formation on Pt(111) with corresponding annealing temperature. (a) Hillock formation on top of the dense film. (b) Additional hillock growth and holes forming in the vicinity of the hillock.

Figure 4

(a) 3D AFM image ($750\times 750$ nm${}^2$) of a hillock on Pt(111) annealed at 923 K. (b) Hillock perimeter of the formed hillock obtained via standard image analysis techniques; the differing radii $r_A$ and $r_B$ indicate an anisotropy in the line tensions for $A$ steps and $B$ steps.

Figure 5

Strain energy density balance calculated using a thermoelastic FEM model of a 50 nm Pt thin film on ZrO${}_2$ for rotationally symmetric hillocks with increasing aspect ratio $a$.

Figure 6

(a) Total free energy change as function of the aspect ratio $a$ as determined from the FEM model. (b) Evolution of the total free energy as function of the aspect ratio $a$ (FEM) including the experimentally determined aspect ratio distribution of hillocks (AFM).

Figure 7

(a) AFM image of a hexagonal-shaped hillock on Pt(111) film annealed at 923 K. (b) Measured quasiequilibrium hillock shape plotted in polar coordinates radius $R$ vs angle $\theta$ (open circles) fitted with Eq. (6) (solid line). (c) Polar plots of the fitted equilibrium shape $R\left(\theta \right)$ and the step free energy $\beta \left(\phi \right)$ with $\lambda =1$.