Smoothing of perturbed vicinal surfaces

The decay rate of a periodic profile in an arbitrary direction on a vicinal surface is calculated on the basis of the following assumptions: (i) isotropic step energy and step interaction energy, the latter being proportional to the square of the step density, (ii) small slopes of the perturbation compared to the vicinal angle alpha, and (iii) surface migration limited kinetics. These assumptions are also generalized for two special perturbation directions (parallel and normal to the unperturbed steps) to include anisotropy of step energies, a general law of step-step interaction, and slopes not restricted to being small. In the latter case, numerical calculation yields profiles that are blunter at the top and bottom than sinusoids and decay rates that increase (at a declining rate) with amplitude A. Following Cahn and Taylor (Acta Metall. Mater. 42 (1994) 1045), a treatment of profile decay is also given that incorporates attachment-detachment kinetics together with surface migration kinetics, providing a formal comparison of the two processes. A corresponding treatment, presented for an isolated step, gives a unified description of the fluctuation spectrum and shows that the rang of wave numbers q for which surface migration kinetics (q(4)) holds for a vicinal surface is substantially greater than for the corresponding isolated step.