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Fokker-Planck equation for lattice deposition models.

C Baggio1, R Vardavas, D D Vvedensky

  • 1The Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
PubMed
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A new Fokker-Planck equation accurately models lattice deposition height fluctuations. This provides an analytic and computational alternative to kinetic Monte Carlo simulations for surface growth models.

Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Lattice deposition models are crucial for understanding surface growth phenomena.
  • Kinetic Monte Carlo (KMC) simulations are commonly used but computationally intensive.
  • Analytical methods for describing height fluctuations are needed.

Purpose of the Study:

  • To derive an asymptotically exact Fokker-Planck equation for height fluctuations in lattice deposition models.
  • To provide an analytical and computational alternative to KMC simulations.
  • To validate the derived equation using an Edwards-Wilkinson-type model.

Main Methods:

  • Derivation of the Fokker-Planck equation using a Van Kampen expansion of the master equation.
  • Solving the equivalent Langevin equation for the derived model.

Related Experiment Videos

  • Comparison of results with kinetic Monte Carlo (KMC) simulations.

    • Main Results:

    • The derived Fokker-Planck equation accurately describes height fluctuations.
    • The solution of the equivalent Langevin equation reproduces surface roughness.
    • Lateral height correlations match those obtained from KMC simulations.

    Conclusions:

    • The derived discrete equations of motion offer an exact analytic and computational alternative to KMC.
    • This work provides a more efficient method for studying surface growth dynamics.
    • The approach is applicable to various lattice deposition models.