Growth instability in Cu multilayer films due to fast edge/corner diffusion

The instability observed in $\mathrm{Cu}∕\mathrm{Cu}\left(100\right)$ epitaxial growth by Ernst et al. [Phys. Rev. Lett. 72, 112 (1994)] is studied using serial kinetic Monte Carlo (KMC) simulations as well as a recently proposed algorithm for parallel KMC. Our parallel algorithm allows us to simulate longer time scales which are not easily accessible by a serial Monte Carlo simulation. Two different sets of activation barriers were used—one based on effective medium theory and the other based on the embedded-atom method. In both cases, we find that the existence of very fast edge diffusion along close-packed step edges along with a slight enhancement of the rate of corner diffusion is crucial to explaining the experimental results. Some possible mechanisms for this enhancement are discussed.

Figure 1

Schematic diagram showing neighboring atoms affecting the energy barrier of a diffusing atom (filled circle) in (a) EMT and (b) EAM models.

Figure 2

Schematic diagram showing edge and corner diffusion with activation barriers $E_e$ and $E_c$, respectively, along with corner detachment barrier $E_d$.

Figure 3

Surface width vs film thickness for EMT model without enhanced corner diffusion for two different values of the ES barrier along with experimental results (circles) at (a) $T=160\mathrm{K}$ and (b) $T=200\mathrm{K}$.

Figure 4

Surface width vs film thickness for three different values of the corner diffusion barrier $E_c$ along with experimental results (filled circles) at $T=200\mathrm{K}$. Here the EMT model is used with $E_{ES}=0.02\mathrm{eV}$.

Figure 5

Surface mound morphology at $T=200\mathrm{K}$ after 20 layers have been deposited for EMT model with $E_{ES}=0.02\mathrm{eV}$ (a) without corner diffusion, (b) enhanced corner diffusion with $E_c=0.35\mathrm{eV}$, (c) same as (b) but with dimer and trimer corner diffusion allowed.

Figure 6

Surface width vs film thickness for EMT model with enhanced corner diffusion $(E_c=0.35\mathrm{eV})$ for three different values of the ES barrier along with experimental results (filled circles) at $T=200\mathrm{K}$. Straight line with slope $1∕2$ is guide to the eye.

Figure 7

Surface width vs film thickness for EMT and EAM models with enhanced corner diffusion at 160 and 200 K along with experimental results (circles). Solid lines and symbols correspond to $E_{ES}=0.02\mathrm{eV}$ while dashed line corresponds to EMT model with $E_{ES}=0.1\mathrm{eV}$.

Figure 8

Mound angle ratio as function of film thickness for EMT model with $E_{ES}=0.02\mathrm{eV}$ and enhanced corner diffusion at $T=160$ and 200 K.

Figure 9

Log-log plot of surface roughness vs film thickness for EMT model with enhanced corner diffusion $(E_c=0.35\mathrm{eV})$ and $E_{ES}=0.02\mathrm{eV}$ at 200 K for different values of edge-diffusion reduction factor $R$.

Figure 10

Surface width vs film thickness for different values of corner attraction ratio $\delta$ at 160 and 200 K for EMT model with enhanced corner diffusion $(E_c=0.35\mathrm{eV})$ and $E_{ES}=0.02\mathrm{eV}$ along with experimental results (circles). The inset shows a schematic diagram of the edge atom one step away from a corner site.