Dynamics of surface profile evolution through surface diffusion.

Abstract

We have studied the evolution, mediated by surface diffusion, of periodic corrugations on a surface using Monte Carlo simulations on a solid-on-solid (SOS) model. Above the roughening temperature ${\mathit{T}}_{\mathit{R}}$, for both unidirectional and bidirectional sinusoidal corrugations of wavelength L, the amplitude h decays exponentially with time h/${\mathit{h}}_{0}$\ensuremath{\approxeq}exp(-\ensuremath{\alpha}t), with t/${\mathit{L}}^{4}$ scaling in agreement with Herring-Mullins theory. Below the roughening temperature, there is a gradual transition to a power-law decay of the amplitude as the temperature is lowered. The wavelength scaling varies with the substrate temperature and the periodicity of the corrugation in the two orthogonal transverse directions. Well below ${\mathit{T}}_{\mathit{R}}$, the amplitude in unidirectional sinusoidal corrugations evolves with time according to h/${\mathit{h}}_{0}$\ensuremath{\approxeq}(1+\ensuremath{\lambda}t${)}^{\mathrm{\ensuremath{-}}1}$, with t/${\mathit{L}}^{5}$ scaling for diffusion-limited kinetics, in agreement with the theory of Ozdemir and Zangwill [Phys. Rev. B 42, 5013 (1990)]. In bidirectional sinusoidal corrugations, profile decay is driven by a combination of line-tension and step-step entropic repulsion, in agreement with the theory of Rettori and Villain [J. Phys. (Paris) 49, 257 (1988)]. \textcopyright{} 1996 The American Physical Society.