Towards self-organization of decaying surface corrugations: A numerical study

We study numerically the interplay of surface topography and kinetics in the relaxation of crystal surface corrugations below roughening in two independent space dimensions. The kinetic processes are isotropic diffusion of adatoms across terraces and attachment-detachment of atoms at steps. We simulate the corresponding anisotropic partial differential equation for the surface height via the finite element method. The numerical results show a sharp transition from initially biperiodic surface profiles to one-dimensional surface morphologies. This transition is found to be enhanced by an applied electric field. Our predictions demonstrate the dramatic influence on morphological relaxation of geometry-induced asymmetries in the adatom fluxes transverse and parallel to step edges.