Stochastic Mullins-Herring equation for a solid-on-solid crystal

Abstract

We derive a stochastic version of the Mullins-Herring equation---a continuum equation of motion for the relaxation of a solid surface to morphological equilibrium---for a two-dimensional solid-on-solid crystal. For Arrhenius-type desorption and surface diffusion kinetics, a linear Langevin equation describes the scaling behavior of the surface width. The final equation of motion is interpreted in terms of effective, macroscopic desorption and surface-diffusion parameters that reflect the full chemical activity of the surface.