The growth dynamics of the wedding-cake Interfaces

Abstract

In the limit where the ratio of the surfaces diffusion coefficient to the deposition rate D/F ∞ → , the surface consists of wedding-cake structures. In order to understand the growth dynamics and the scaling properties of theses interfaces, we have calculated the time evolution of its width ω(L,t) for both one and two dimensional lattice. By the use of the dynamic scaling approach, we find that ω(L,t) scales with time t and length L as ω(L,t)≈L^α f(t/L^α/β ) where f is a scaling function and α and β are respectively the roughening and the growth exponents. The values of theses exponents are in good agreement with the theoritical ones predicted by the Edwards-Wilkinson equation.