Elsevier

Acta Materialia

Volume 60, Issues 6–7, April 2012, Pages 3047-3056
Acta Materialia

Anisotropic hole growth during solid-state dewetting of single-crystal Au–Fe thin films

https://doi.org/10.1016/j.actamat.2012.02.009Get rights and content

Abstract

Thin Fe–Au bilayers were deposited on c-plane sapphire substrates. The layers were found to be quasi-single crystalline, with a 〈1 1 1〉 texture and strong heteroepitaxy to the substrate. When annealed, these films dewetted from the substrate via the formation of faceted hexagonally shaped holes, which grow anisotropically with increasing annealing time. The studied Fe–Au films exhibited significantly higher thermal stability against dewetting than polycrystalline Au films prepared and annealed under identical conditions. We developed a thermodynamic diffusion model describing the growth kinetics of an individual hole. This model, in conjunction with experimental results, allows estimation of the effective surface self-diffusion coefficient.

Introduction

Solid-state dewetting, or agglomeration, of thin films is a process by which a thin continuous film exposes a substrate and transforms into an ensemble of isolated particles. The driving force for dewetting is the reduction of the total surface and interfacial energy of the system, and this process is well known for metal films on ceramic substrates, especially oxides [1]. This phenomenon has been the subject of extensive research over the years and the mechanisms of dewetting are well understood in most cases [1]: for a polycrystalline film to dewet, holes to the substrate must first be formed by some nucleation process (such as grain boundary or triple junction thermal grooving, heterogeneous nucleation on defects). This initial perturbation in film thickness subsequently grows due to capillary forces by some mass-transport mechanism (in solid-state dewetting – usually surface diffusion). For a system with an isotropic surface energy, the holes’ receding edges eventually develop morphological features which, over time, lead to “pinching off” and expose the substrate [2]. This mechanism results in islands and particles, the morphology of which can be manipulated by film or substrate patterning [3], [4].

The thermal stability of metallic thin films on ceramic substrate is of utmost technological importance. In many cases their adhesion to the substrate may become a “weak link” in the device, leading to its failure when exposed to a sufficient thermal budget [5]. Thus, achieving control of their microstructure as well as understanding the dewetting kinetics is a key to preventing device failure caused by film agglomeration. Additionally, such control is also desired when agglomeration is in fact encouraged, as in the case of producing arrays of particles of micron and sub-micron scales, for example for surface-enhanced Raman spectroscopy [6].

Most thin metallic film deposition methods usually yield polycrystalline films, with grain sizes of the order of the film thickness [7]. Thus, for such films the formation of particles in the course of dewetting is relatively fast due to an abundance of hole-nucleation sites and of short-circuit diffusion paths. However, the case of single-crystal metallic films is quite different and only few, recent works exist [8], owing to the difficulty of producing such films. The thermal stability of the deposited single-crystalline layers is expected to be much higher than that of their polycrystalline counterparts due to kinetic limitations: the formation of holes must rely on random defects, rather than on grain boundaries and their triple junctions. Moreover, most metals exhibit highly anisotropic surface properties (surface energy and diffusivity) at temperatures significantly lower than their melting point. The anisotropic surface energy often results in surface faceting – formation of atomically flat regions which do not exhibit any geometrical curvature. The theoretical description of the dewetting kinetics of anisotropic single-crystalline films presents a formidable challenge, since the standard concepts of morphology evolution controlled by curvature-driven surface diffusion [9] cannot be directly applied to the faceted surfaces. For example, in the classical model of solid-state dewetting of an isotropic thin film, accumulation of material around the receding hole edge leads to a characteristic hill followed by a depression, which deepens until it reaches the substrate and leads to the “pinching-off” of the hill [2], [9]. The first attempt of describing the kinetics of dewetting of thin films with faceted surfaces was based on a two-dimensional model, and it was shown that in the case of strong surface faceting the pinch-off mechanism of thin film dewetting does not come into play [10]. However, the formation of holes is essentially a three-dimensional process, especially at its initial stage, and there are only few attempts in the literature to describe the surface diffusion-controlled kinetics of shape change of faceted three-dimensional crystals [11], [12], [13], and these are mainly limited to high-symmetry polyhedra.

In this work, we studied the morphological stability and initial stages of dewetting of quasi-single-crystalline Fe–Au thin films. Our primary goals were to compare the thermal stability of this quasi-single-crystalline film with the stability of its polycrystalline counterpart, to determine the kinetics of holes growth in this strongly anisotropic film and to extract the relevant kinetic parameters (surface diffusivity) with the aid of a suitable theoretical model.

Section snippets

Sample preparation

Electron-beam deposition was used to deposit Fe and Au layers (5 N purity) of 3 and 9 nm in thickness, respectively, on c-plane-oriented sapphire ((0 0 0 1) single-crystal α-Al2O3) substrates. The polished wafers were 5 cm in diameter and 430 μm in thickness (University Wafer). Pieces approximately 1 cm2 in size were cleaved from each wafer and cleaned by standard procedures in a clean room prior to deposition. Deposition took place in a vacuum chamber with a base pressure of 5 × 10−7 torr and at room

Experimental results

The as-deposited samples were found to be quasi-single crystalline, meaning that the grain size was several orders of magnitude larger than the film thickness. This was confirmed by obtaining EBSD patterns and maps, indicating large (100 μm and more) areas of the same three-dimensional crystallographic orientation. An example is given in Fig. 1, which shows an EBSD map overlaid on an SEM micrograph. The empty pixels indicate that the software was unable to determine a crystal orientation;

Model

We developed a thermodynamic model describing the kinetics of the two-dimensional growth of holes, as well as the shape change of the holes in the course of their growth. The model is based on a weighted mean curvature approach [18], which was recently applied for describing the one-dimensional motion of a single edge of a faceted hole [10]. The weighted mean curvature is defined as “the rate of decrease of surface free energy with respect to volume swept out by the motion of the surface” [19].

Comparison with experiment

From the model, the perimeter of a hole, Pmod, normalized to the original film thickness, h0, is obtained as a function of dimensionless time, τ, defined by:τ=D111v111Ω2γh04kT·tS·twhere γ is the surface energy of {1 1 1} planes. For the purpose of comparison with the experiment, we assume, for simplicity, that the diffusivities of all facets are identical. Otherwise, the diffusion anisotropy can be taken into account by an additional fitting parameter (see Fig. 8). has to be determined from

Discussion and conclusions

As the main result of our model applies to a one-component system, its relevance to the binary Au–Fe system studied in the present work must be clarified. Our TEM, EBSD and XRD data all confirmed that the initial Au–Fe bilayer structure fully homogenized after the shortest annealing time of 4 h. According to the Au–Fe phase diagram, this Au–32 at.% Fe homogeneous solid solution phase is in thermodynamic equilibrium at the annealing temperature of 650 °C. The dissolution time can be estimated by

Acknowledgements

This work was supported by the Israel Science Foundation, Grant No. 775/10, and by the Russell Berry Nanotechnology Institute at the Technion. Helpful discussions with Prof. R. Shneck are heartily appreciated.

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