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Island nucleation and growth with anomalous diffusion.

Jacques G Amar1, Mikhael Semaan1,2

  • 1Department of Physics & Astronomy, University of Toledo, Toledo, Ohio 43606, USA.

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|July 15, 2016
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Summary

This study explores island nucleation and growth beyond standard monomer diffusion, introducing general expressions for various diffusion behaviors (μ). Results align with kinetic Monte Carlo simulations across different dimensions.

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Area of Science:

  • Surface science and condensed matter physics.
  • Investigating nanoscale phenomena and material growth dynamics.

Background:

  • Most island nucleation studies assume ordinary monomer diffusion (μ=1).
  • Subdiffusive (μ<1) and superdiffusive (μ>1) diffusion behaviors can occur, impacting growth dynamics.

Purpose of the Study:

  • To develop general expressions for island and monomer densities under varying diffusion exponents (μ).
  • To analyze the flux dependence of nucleation and growth across different substrate dimensions and critical island sizes.

Main Methods:

  • Derivation of general scaling exponents for island nucleation and growth.
  • Kinetic Monte Carlo (KMC) simulations for irreversible island growth (i=1).
  • Validation across multiple substrate dimensions (d=1, 2, 3, and 4) and diffusion exponents (0≤μ≤2).

Main Results:

  • General expressions for flux-dependent island and monomer densities were derived.
  • Excellent agreement was found between theoretical results and KMC simulations.
  • The study covers a broad range of diffusion behaviors (0≤μ≤2) and substrate dimensions.

Conclusions:

  • The presented framework accurately describes island nucleation and growth for various diffusion regimes.
  • This work extends the understanding of surface processes beyond the ordinary diffusion assumption.
  • The findings are applicable to diverse systems exhibiting anomalous diffusion during thin film growth.