Agglomeration of Pt thin films on dielectric substrates

The agglomeration of metal thin films on dielectric materials is a topic of high technological importance. In this contribution, a coupled morphology-agglomeration approach has been chosen to reveal the basic mechanism of rupture, mass transport, and the substrate dependence of agglomeration. The morphological evolution of Pt thin films has been investigated by means of scanning electron microscopy, atomic force microscopy, and focused ion-beam (FIB) etching techniques. Pt thin films were deposited on amorphous ${\text{Si}}_3{\text{N}}_4$ and polycrystalline yttria stabilized ${\text{ZrO}}_2$ substrates and subjected to heat treatments up to 1193 K for 2 h. Three main observations have been made: (i) the early stage of rupture can be described via basic thermodynamics as an order-disorder transition. The dominating mechanism of initial film rupture is a defect associated barrierless nucleation of holes in the spinodal regime of the Pt thin film as shown by means of Minkowski measures. (ii) Up to 1073 K the hole growth is found to be a surface-diffusion limited process, and in first approximation it is in agreement with Brandon and Bradshaw’s theory for the morphological evolution of thin metal films at elevated temperatures. Values for mass transport have been derived. (iii) It is shown that two in general independent physical processes control the morphological evolution and kinetics of thin-film agglomeration: one attributes to the film-ambient interface and the other to the film-substrate interface. Void formation at the film-substrate interface is enhanced by a factor of 9 in the case of the amorphous-crystalline interface due to a lower adhesion energy of the film. The corresponding adhesion energies have been determined experimentally using FIB techniques and the Wulff-Kaishew theorem for equilibrium crystal shapes.

Figure 1

$\left(h_{\text{film}}<h_{\text{film}}^{\prime }<h_{\text{film}}^{″}\right)$ Schematic description of thin-film agglomeration of a dense thin film (a). Temperature treatment leads to grain-boundary grooving at both interfaces (b) triggered by the chemical potential difference in the film, grooves are enlarged by diffusion and form holes (c).

Figure 2

Illustration of two possible agglomeration regimes (a) formation of a aperiodic hole pattern via nucleation at randomly distributed defects and (b) formation of periodic hole pattern due to spinodal dewetting with a continuous distribution of heights.

Figure 3

(a) Schematic illustration of the Wulff-construction of an isolated particle on a random substrate and necessary measurands like the truncation depth $\Delta h$ and surface energies ${\gamma }_{i,j}$ to determine the adhesion energy $E_{\text{ad}}$. (b) Cross section of a 50-nm-thick Pt film on polycrystalline ${\text{ZrO}}_2$ annealed at 923 K with grooves formed in a vicinity of a triple junction that links the surface and substrate.

Figure 4

SEM images of different stages of agglomeration with corresponding annealing temperature $T_a$ of Pt on ${\text{Si}}_3{\text{N}}_4$ (thickness 15 nm, annealed 2 h in air). (a) 673 K $\left(T_a<T_c\right)$ dense film, (b) 773 K $\left(T_a\ge T_c\right)$ onset of rupture and hole formation, (c) 798 K $\left(T_a>T_c\right)$ coalescences of holes, and (d) 1193 K $\left(T_a⪢T_c\right)$ disintegration in separated islands.

Figure 5

(a) Order parameter $\xi$ vs temperature $T$ for 15 nm and 50 nm thick Pt films on ${\text{Si}}_3{\text{N}}_4$ with marked critical temperature $T_c$. (b) Free energy curves as function of the order parameter $\xi$ of 15-nm-thick Pt on ${\text{Si}}_3{\text{N}}_4$.

Figure 6

(Color online) (a) AFM image of agglomeration morphology of Pt on ${\text{Si}}_3{\text{N}}_4$. (b) The Minkowski functionals, i.e., the normalized area $m_0\left(h\right)$, the boundary length $m_1\left(h\right)$, and the Euler characteristic $m_3\left(h\right)$, as a function of the gray-scale threshold for agglomeration pattern shown in Fig. 3a. (c) Effective measures $s\left(h\right),u\left(h\right),\kappa \left(h\right)$ according to Eq. (8) which are in good agreement with a Gaussian model (dashed lines).

Figure 7

Plot of the hole radius distribution (solid line) of Pt thin film (50 nm) on ${\text{Si}}_3{\text{N}}_4$ annealed 986 K for 2 h (inset) and a normal distribution with $\mu =0.34\mu \text{m}$ and ${\sigma }^2=0.006$ (dashed line).

Figure 8

(Color online) (a) Platinum surface self-diffusion coefficients as derived from the Brandon-Bradshaw model and (b) comparison of measured surface self-diffusion coefficients with literature data of Pt surface self-diffusion (Refs. 58, 59).

Figure 9

(a) Three-dimensional (3D) reconstruction of an agglomerated 180-nm-thick Pt film on ${\text{Si}}_3{\text{N}}_4$ obtained via FIB nanotomography with associated top views on (b) the Pt/ambient interface and (c) the $\text{Pt}/{\text{Si}}_3{\text{N}}_4$ interface.

Figure 10

(a) 3D reconstruction of a facetted Pt particle on a ${\text{Si}}_3{\text{N}}_4$ substrate with cross sections {1}{2} through particle’s mass center obtained by FIB nanotomography. (b) Cross section {2} of reconstructed Pt particle and fitting Wulff-Construction of the particle with indicated truncation depth $\Delta h_s$. (c) Schematic illustration of the Wulff-Construction of an isolated particle on a random substrate and necessary measurands to determine the adhesion energy $E_{\text{ad}}$. (d) SEM image of FIB-etched Pt particle and apparent Wulff-Construction.

Figure 11

Schematic illustration of the hole formation according to the Brandon-Bradshaw model.

Figure 12

Log-log graph of the mean hole radius $r$ as function of the film height $h$. Fitted slopes $n$ are shown for data with differing temperature and substrate, the predicted slopes for the Brandon-Bradshaw model $n_{BB}=-\frac{3}{5}$ and the model by Jiran and Thompson $n_{JT}=-3$ are plotted.