Competition between particle formation and burrowing: Gold on bismuth

We discuss Au vapor deposition on polycrystalline Bi under conditions where particle formation and burrowing are competitive. Burrowing occurs because the surface free energy of Bi is lower than that of Au, the Au-Bi interface energy is small, and the kinetics, in terms of high surface and grain boundary diffusion rates, are favorable. For formation of Au particles on Bi, kinetic Monte Carlo simulations that include the relative rates of atom impingement, surface diffusion, and burrowing show a broadening of the overall size distribution. This occurs because burrowing continuously removes small particles from the surface, reduces the density of existing nuclei, and allows those that remain to grow by atom capture to larger sizes before they too are completely burrowed. These results are important for systems where nanostructures are assembled on low surface energy substrates.

Figure 1

Schematic of Au particle formation and burrowing in a (001) Bi grain. A particle burrows by displacing atoms, driven by capillary forces, which depend on the particle size as it grows from a cluster to a nanocrystal with distinct surface energies. The final size and distribution depends on the relative rates of the adatom impingement $\left(R_a\right)$, diffusion $\left(R_{\text{diff}}\right)$, and the particle burrowing rate $\left(R_{\text{burr}}\right)$. A partially buried particle can grow by adatoms attaching to it, while one that is completely buried cannot.

Figure 2

Typical plan view TEM image of nanoparticles formed when $5\text{Å}$ of Au was deposited on a 20-nm Bi film at room temperature. Fringes seen in some particles are Moiré patterns due to interference between the Au and Bi lattices. They can be used to determine the orientation of the particles.

Figure 3

Cross-sectional TEM images of Au particles buried within Bi films of thicknesses (a) 10 and (b) 30 nm. The images were obtained by breaking areas in the deposited film using a sharp tip and imaging portions of the free standing film that were oriented favorably. The particles were obtained by depositing $5\text{Å}$ Au. In plan view, the particles look like those in Fig. 2. (c) A high-resolution TEM image of the boxed area in (b), showing a single particle of Au in Bi with the lattice fringes in Au and Bi clearly visible.

Figure 4

Particle size distributions after deposition on 30 nm Bi films at room temperature. The deposition rate was $1\text{Å}/\text{min}$. The distributions are normalized and vertically displaced for clarity. The continuous lines are a guide to the eye. The deposition conditions and the average particle sizes are included (they are also marked on the plot). For a wait time of 2 min, the size distribution in (b) resembles (a), except at small sizes (1–2 nm). The wait time of 30 min in (c) allowed the particles to burrow and the size distribution resembles (d), despite the difference in the amount of material.

Figure 5

Representative TEM images and size distributions for the same amount of Au deposited on Bi at different temperatures. The average particle size and size distribution increases for $T=50°\text{C}$, broadens at $75°\text{C}$, and decreases for $100°\text{C}$. The distribution arises from the competition between adatom diffusion that forms the particles and burrowing that sinks them in the substrate. As the temperature rises, the higher diffusion and burrowing rates increase the average size and broaden the distribution. Once burrowing is dominant, there is a decrease in average size and a narrower distribution.

Figure 6

Changes in particle density with time and weighted size distributions obtained from kinetic Monte Carlo simulations with and without burrowing. In (a), without burrowing, the surface particle density constantly increases with time. When there is burrowing, as in (c), the instantaneous surface particle density initially increases and then decreases. The total number of surface and buried particles increases linearly, as shown in the inset in (c). This is because formed particles constantly burrow, making available new sites for nucleation. Burrowing also leads to bimodal size distribution, seen in (d), compared to the size distribution without burrowing (b). The first peak corresponds to the critical size for burrowing while the second corresponds to those that remained on the surface during impingement. The inset in (d) is the weighted experimental size distribution.

Figure 7

Simulations of the pause experiments and temperature changes shown in Figs. 4, 5. During the pause, no new atoms were deposited, but atoms remaining on the surface were allowed to diffuse. Particles on the surface and partially buried ones continued to burrow at a rate inversely proportional to the fourth power of their radius. The size distributions in (a) and (b) closely mimic the observed changes of Fig. 4 and described in Sec. 3B. The plot of peak radius vs ratio of the burrowing and diffusion rate, shown in (c), can be compared with the results from Fig. 5. Initially, the size increases but it then decreases with increasing burrowing rates, mirroring changes activated by increasing temperature. The line acts as a guide to the eye.