Morphological equilibration of a corrugated crystalline surface

We study the flattening of a corrugated crystal surface for the case when mass transport is driven by surface diffusion and the temperature is well below the roughening temperature of the equilibrium facet. For the considered geometry, the problem is one dimensional and the surface morphology consists of a collection of terraces separated by straight, parallel steps. In this situation, the kinetics is driven by step-step interactions alone. We obtain separated variable (shape-preserving) solutions to both the differential equation of motion for the surface profile z(x,t) and the discrete equations of motion for individual terraces’ widths ${\mathit{l}}_{\mathit{n}}$(t). Numerical solutions of these equations demonstrate that the analytic solution well describes the kinetics in the latter case. As morphological equilibration proceeds, we find that z(x,t)∼${\mathit{t}}^{\mathrm{-}1}$ and that ${\mathit{l}}_{\mathit{n}}$(t)∼${\mathit{t}}^{1/5}$ or ${\mathit{l}}_{\mathit{n}}$(t)∼${\mathit{t}}^{1/4}$ for the cases of diffusion-limited or step-attachment-limited step propagation, respectively. These predictions are amenable to direct experimental tests.