Periodic surface profiles under the influence of anisotropic surface energy: A steady-state solution

Abstract

The steady-state shape of surface profiles under the influence of anisotropic surface energy was calculated. All shape changes were assumed to occur by surface self-diffusion at elevated temperature. The orientation-dependent surface energy γ(θ) was allowed to contain a local minimum of very high curvature (cusp). The orientation of this cusp was equal to the macroscopic-orientation of a single crystal surface. No assumptions were made about the shape of the original profile. Only boundary conditions concerning the amplitude of the profile and several derivatives entered the calculation for the integration of the differential equations. The resulting profiles showed nearly flat regions centered at the cusp orientation. These results agree well with experiments and with previously published profile shapes which had been calculated dynamically. A big advantage of the steady-state calculation were short computing times, even in the case of very high curvature in γ(θ). Hence it could be shown that the profile shape converged towards a limit with increasing curvature of γ(θ). The anisotropy of γ(θ) can be evaluated from experimental shape data of faceted profiles.