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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
Summary
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.
- 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.
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