Diffusion of the Cu monomer and dimer on Ag(111): Molecular dynamics simulations and density functional theory calculations

Abstract

We present results of molecular dynamics ͑MD͒ simulations and density functional theory ͑DFT͒ calculations of the diffusion of Cu adatom and dimer on Ag͑111͒. We have used potentials generated by the embedded-atom method for the MD simulations and pseudopotentials derived from the projected-augmentedwave method for the DFT calculations. The MD simulations ͑at three different temperatures: 300, 500, and 700 K͒ show that the diffusivity has an Arrhenius behavior. The effective energy barriers obtained from the Arrhenius plots are in excellent agreement with those extracted from scanning tunneling microscopy experiments. While the diffusion barrier for Cu monomers on Ag͑111͒ is higher than that reported ͑both in experiment and theory͒ for Cu͑111͒, the reverse holds for dimers ͓which, for Cu͑111͒, has so far only been theoretically assessed͔. In comparing our MD result with those for Cu islets on Cu͑111͒, we conclude that the higher barriers for Cu monomers on Ag͑111͒ results from the comparatively large Ag-Ag bond length, whereas for Cu dimers on Ag͑111͒ the diffusivity is taken over and boosted by the competition in optimization of the Cu-Cu dimer bond and the five nearest-neighbor Cu-Ag bonds. Our DFT calculations confirm the relatively large barriers for the Cu monomer on Ag͑111͒-69 and 75 meV-compared to those on Cu͑111͒ and hint a rationale for them. In the case of the Cu dimer, the relatively long Ag-Ag bond length makes available a diffusion route whose highest relevant energy barrier is only 72 meV and which is not favorable on Cu͑111͒. This process, together with another involving an energy barrier of 83 meV, establishes the possibility of low-barrier intercell diffusion by purely zigzag mechanisms.

Diffusion of Cu adatoms and dimers on Cu(111) and Ag(111) surfaces

“…Therefore, we can derive a general formula for the monomer and then substitute specific values for both Cu(111) and the Ag(111) surfaces in order to calculate the diffusion coefficients. As it is apparent from the first-principles calculations [12,16] and from the experiments [8][9][10], Cu monomers are slightly more stable at fcc sites than at hcp sites. For Cu(111) surface the difference between energies at those two sites is equal to 5 meV [12] and for the Ag(111) lattice it is equal to 6 meV [16].…”

“…Its behavior is a bit more complex than for the monomer's case, what is not surprising since the dimer's map of transitions is also more complex as is the diffusion coefficient. At low temperatures the activation energy for the dimer is 75 meV compared to 73 meV in the experiment [8] and the molecular dynamics calculations [16]. Between 0 and 100 K activation energy for dimer diffusion is higher than this for monomers and for higher temperatures E a for dimers decreases below value of E a for monomers.…”

“…According to Ref. [16] there are four types of transitions between Cu/Ag(111) sites. The geometry of jumps on this lattice is significantly different than that on Cu/Cu(111) and it requires a separate consideration.…”

“…These are the energies that are found by means of ab-initio calculations [16]. Variable ν is the diffusion prefactor, whose exact value is a subject for a separate study, however, its value is very often assumed to be of order of 10 13 /s.…”

“…[13,16] by means of ab-initio calculations. We get analytical expressions for diffusion coefficients from which general relations between different diffusion modes at various temperatures are derived.…”