Extension of Mean-Field Nucleation Theory with Long-Range Interactions

Mean-field nucleation theory is an important tool in understanding various adsorbate-substrate systems, particularly in the context of epitaxial growth. Conventional mean-field theory does not take into account nonlocal interactions, but these can be important in the nucleation and growth of various nanostructures. An approach due to Ovesson [1] is based on the assumption that the change of saddle-point energy in a potential field equals the average changes at the neighboring binding sites, but this assumption is not generally satisfied. We reformulate the theory in a more general sense, as an extension of the work of Grima and Newman [2] and Venables \textit{et al.} [3]. This leads to a continuum mean-field description in a general potential field, in which the transport coefficients are intrinsically connected with the interaction potential and with microscopic parameters. Computational examples are presented for Ge/Si(001) material parameters. \newline \newline [1] S. Ovesson, \textit{PRL} \textbf{88}, 116102 (2002);\newline [2] R. Grima and T.J. Newman, \textit{PRE} \textbf{70}, 036703 (2004);\newline [3] J.A. Venables \textit{et al.}, \textit{PRB} \textbf{74}, 075412 (2006)