Analyzing of the Evolution and the Scaling Properties of a Sinusoidal Mound

Abstract

The evolution of an initial surface (below its roughening temperature) bounded by a sinusoidal function and consisting of concentric circular steps in two dimensions has been investigated in the Diffusion Limited (DL) regime. Assuming that there were entropic interactions between steps and the local mass transfer took place due to the surface diffusion, the solution of the diffusion equation has been obtained by using polar coordinates in two dimensions. The results obtained in this investigation with analyzing the surface height’s evolution as a function of time are as follows: The surface’s height approximately decreases as τ^α (α≈0.35) and α is independent of the amplitude and the wavelength of the initial surface. The variations in the heights of the surfaces which have different amplitudes (A_01,A_02 ) and wavelengths (λ_1,λ_2 ) scale as (A_01⁄A_02 ) (λ_1⁄λ_2 )^3.