Relaxation of Terrace-width Distributions: Physical Information from Fokker-Planck Time

TL;DR

This paper clarifies the physical significance of the Fokker-Planck relaxation time for terrace-width distributions on vicinal surfaces, demonstrating through simulations that it exhibits activated behavior and correlates with real physical time.

Contribution

It establishes a physical interpretation of the Fokker-Planck relaxation time and confirms its quantitative relation to actual physical time via kinetic Monte Carlo simulations.

Findings

Relaxation time shows activated behavior with a physically plausible energy barrier.

Fokker-Planck time semiquantitatively tracks actual physical time.

Simulation results support the physical relevance of the Fokker-Planck formalism.

Abstract

Recently some of us have constructed a Fokker-Planck formalism to describe the equilibration of the terrace-width distribution of a vicinal surface from an arbitrary initial configuration. However, the meaning of the associated relaxation time, related to the strength of the random noise in the underlying Langevin equation, was rather unclear. Here we present a set of careful kinetic Monte Carlo simulations that demonstrate convincingly that the time constant shows activated behavior with a barrier that has a physically plausible dependence on the energies of the governing microscopic model. Furthermore, the Fokker-Planck time at least semiquantitatively tracks the actual physical time.