Models for diffusion and island growth in metal monolayers

Ofer Biham*, Itay Furman, Majid Karimi, Gianfranco Vidali, Rosemary Kennett, Hong Zeng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


A model which describes self-diffusion, island nucleation and film growth on fee (001) metal substrates is presented. The parameters of the model are optimized to describe Cu diffusion on Cu(001) by comparing activation energy barriers to a full set of barriers obtained from semi-empirical potentials via the embedded-atom method. It is found that this model (model I), with only three parameters, provides a very good description of the full landscape of hopping-energy barriers. These energy barriers are grouped in four main peaks. A reduced model (model II) with only two parameters is also presented, in which each peak is collapsed into a single energy value. From the results of our simulations, we find that this model still maintains the essential features of diffusion and growth on this model surface. We find that hopping rates along island edges are much higher than for isolated atoms (giving rise to compact island shapes), and that vacancy mobility is higher than adatom mobility. We observe substantial dimer mobility (comparable to the single-atom mobility) as well as some mobility of trimers. The mobility of small islands affects the scaling of island density N versus deposition rate F (N ≈ Fγ) as well as the island size distribution. In the asymptotic limit of slow deposition, scaling arguments and rate equations show that γ = i/(2i* + 1), where i* is the size of the largest mobile island. Our Monte Carlo results, obtained for a range of experimentally relevant conditions, show γ = 0.32 ± 0.01 for the EAM barrier, 0.33 ± 0.01 for the model I barrier and 0.31 ± 0.01 for the model II barrier. These results are lower than the anticipated value of γ ≥ 0.4 due to dimer (and trimer) mobility.

Original languageAmerican English
Pages (from-to)29-43
Number of pages15
JournalSurface Science
Issue number1-3
StatePublished - 12 Mar 1998

Bibliographical note

Funding Information:
O.B. would like to thank Oded Millo and Nira Shimoni for helpful discussions. We would like to acknowledge partial support from the NSF under grants DMR−9217284 and DMR−9119735 at Syracuse University during the initial stages of this work, and partial support from the Intel–Israel college relations committee during the final stages.


  • Computer simulations
  • Growth
  • Nucleation
  • Surface diffusion


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