Diffusion of small two-dimensional Cu islands on Cu(111) studied with a kinetic Monte Carlo method

Abstract

Diffusion of small two-dimensional Cu islands ͑containing up to 10 atoms͒ on Cu͑111͒ has been studied using the newly developed self-learning Kinetic Monte Carlo ͑SLKMC͒ method which is based on a database of diffusion processes and their energetics accumulated automatically during the implementation of the SLKMC code. Results obtained from simulations in which atoms hop from one fcc hollow site to another are compared with those obtained from a parallel set of simulations in which the database is supplemented by processes revealed in complementary molecular dynamics simulations at 500 K. They include processes involving the hcp ͑stacking-fault͒ sites, which facilitate concerted motion of the islands ͑simultaneous motion of all atoms in the island͒. A significant difference in the scaling of the effective diffusion barriers with island size is observed in the two cases. In particular, the presence of concerted island motion leads to an almost linear increase in the effective diffusion barrier with size, while its absence accounts for strong size-dependent oscillations and anomalous behavior for trimers and heptamers. We also identify and discuss in detail the key microscopic processes responsible for the diffusion and examine the frequencies of their occurrence, as a function of island size and substrate temperature.

Particle-resolved dynamics during multilayer growth ofC60

“…Note that this contrasts with the situation for atomic systems where growth phenomena for both, monolayers and multilayers have been studied intensely for a wide range of systems [38][39][40] . These studies include even subtle phenomena such as concerted gliding of islands 41 or direction-resolved step-edge diffusion 42,43 . In our recent study we have obtained, together with real-time experiments 13 , a consistent set of energybarrier parameters for KMC simulations which describe measurable morphological quantities such as island density and layer coverage as functions of time.…”

Diffusion and submonolayer island growth during hyperthermal deposition on Cu(100) and Cu(111)

“…The most spectacular difference is the almost complete absence of oscillations in the diffusion coefficient with size for the smaller islands (1 − 10 atoms) [26]. This is seen to occur when small islands Ref.…”

Effect of Temperature on Diffusion Parameters for 2-Dimensional Copper 5-Atom Island

“…The small difference between the two calculated values might be due to the fact that the experimental barrier relates mainly to fcc↔fcc hoping whereas that from MD simulations stems largely from fcc↔hcp hopping. Therefore, keeping the barrier for fcc↔hcp hopping smaller than that for fcc↔fcc hopping [16,17] , it is good to hope that fcc↔hcp hops little bias our calculated effective energy barrier toward small values.…”

“…From several sets of simulations we find the error in D to be less than 4%. Extraction of the effective diffusion energy barrier ∆E and the diffusion prefactor D 0 for the Cu pentamer is enabled by the smooth Arrhenius behavior [17] of the diffusion coefficient D Figure 5. The negligible temperature dependence of the prefactors between ~300 and 600 K is well understood since this temperature range is low enough that the potential energy of the entire crystal can be considered harmonic [27,28] and the atomic vibrations treated as small oscillations, while high enough that quantum effects may be neglected [27] .…”

“…It was found that the diffusion coefficient of island nicely fits the Arrhenius curve. The diffusion prefactor can hence safely be considered temperature independent in the range 300-700 K. A useful point to consider the diffusional kinetics of Cu pentamer on Ag(111) surface, is the contrast with the corresponding homoepitaxial case of Cu/Cu(111), for which a considerable body of theoretical and experimental work is already available [14][15][16][17][18][19][20][21][22][23][24] . In the light of The interpretation of our results (summarized below) as well as in a recent study on Ag 27 Cu 7 core-shell nano-particle [25] , it is suggested that there is a bond-strength hierarchy among homo-bonds and hetero-bonds that mediates the minimum-energy structure of any particular system.…”