Island-size distributions for submonolayer epitaxy: Rate equations and beyond

D. D. Vvedensky, R. E. Caflisch, M. F. Gyure, B. Merriman, S. Osher, C. Ratsch, J. J. Zinck

Research output: Contribution to journalConference articlepeer-review


The scanning tunnelling microscope has revolutionized the quantitative analysis of epitaxial phenomena. This, in turn, has spawned a huge theoretical effort aimed at analyzing various aspects of the morphology of growing surfaces. One of the most important general approaches to have emerged from this effort is based on the application of scaling concepts to epitaxial island-size distributions in the regime of submonolayer coverage prior to coalescence. We first discuss the analytical basis for scaling solutions to rate equations. In the limit of irreversible aggregation, a solution is obtained in terms of the capture numbers which agrees with previous work. For reversible aggregation, we identify a new quantity that may be regarded as a continuous analogue of a critical island size. We then examine the influence of spatial correlations by introducing a method for modeling epitaxial phenomena in terms of the motion of island boundaries, which is implemented numerically using the level set method. This island dynamics model is continuous in the lateral directions, but retains atomic scale discreetness in the growth direction. Several choices for the island boundary velocity are discussed and computations of the island dynamics model using the level set method are presented.

Original languageEnglish (US)
Pages (from-to)261-274
Number of pages14
JournalMaterials Research Society Symposium - Proceedings
StatePublished - 1998
EventProceedings of the 1998 MRS Spring Meeting - San Francisco, CA, USA
Duration: Apr 13 1998Apr 14 1998

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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