Harmonically-Interacting Step Approach to the Relaxation Process of Vicinal Surface: III. Universal Relations

Abstract

The relaxation process of vicinal surface induced by the attachment-detachment mechanism is described in terms of the Ginzburg-Landau-Langevin (GLL) equation based on the harmonically-interacting step picture. To analyze the relaxation process, we pay attention to the three quantities, the step deformation width, the step diffusion length and the diffusion length of the system. These quantities are expressed in terms of two universal scaling functions and five system-specific constants. The GLL equation contains only three system specific parameters. Therefore, there must be two relations among the five constants and the relations do not depend on the details of vicinal surface. The two relations are verified by a Monte Carlo simulation. It shows the quantitative validity of the GLL equation. The GLL equation is rewritten in a universal form not depending on the microscopic dynamics by regarding the (squared) diffusion length of the system as the time.