Solution of Master and Fokker-Planck equations by propagator methods, applied to Au/NaCl thin film nucleation

J. B. Adams, W. N.G. Hitchon

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

Novel numerical solutions of Master and Fokker-Planck equations are described and compared for equivalent discrete and continuous problems. The two methods involve the calculation of long-time-step propagator matrices, whose single application is equivalent to many iterations of a finite difference scheme. For the discrete method we present two analytic propagators which are exact for growth-only (no decay) processes, and two approximate propagators for growth and decay processes. The continuous method couples a discrete boundary condition for small clusters with an efficient continuous description for large clusters. These two methods are applied to the nucleation and growth of vapor-deposited thin films whose atoms cluster together to form islands (Volmer-Weber growth). Mobility coalescence of islands is included to show how "slow" nonlinear processes may be included in the model.

Original languageEnglish (US)
Pages (from-to)159-175
Number of pages17
JournalJournal of Computational Physics
Volume76
Issue number1
DOIs
StatePublished - May 1988
Externally publishedYes

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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