The Investigation of Bunching and No Bunching Regions of Sinusoidal Mounds

Abstract

We studied the evolution of an initial surface which was sinusoidal mound shaped for Diffusion Limited (DL) regime. We supposed that there were two dimensional concentric circular steps on initial surface and attractive/repulsive interactions between these monoatomic steps. While following the surface's evolution, the equation of motion related to each step radius's change and diffusion equation have been solved. We obtained bunching and no bunching regions of studied initial surfaces in a parameter space with their scaling characteristics. Our results in this examination can be summarized as; bunching (no bunching) region expands (shrinks) with increasing of wavelength or amplitude of the initial surface. The curves separating bunching/no bunching regions scale with each other. In the case of the amplitude (wavelength) is changed, the scaling factor is (A_0⁄(A_0^' ))^(1/6) ((λ⁄λ^' )^(1/2)). When both the wavelength and amplitude of the surface are changed at the same time, the scaling factor is equal to (A_0⁄(A_0^' ))^(1/6)×(λ⁄λ^' )^(1/2).