Analytical properties of Stoyanov step bunches: Solutions, scaling, stationary profiles

Abstract

Within the framework of the Stoyanov–Tonchev equation, which describes the surface height evolution during the vicinal sublimation process affected by the electromigration of the adatoms, we explore further the stationary profiles of step bunches towards obtaining a closed-form solution. For this particular case, we derive an explicit analytical result for the slope-height relation for the bunches, and many of the well-known scaling results for the height and width of the bunch. A novel analytical approximation for the bunch profile $h\left(x\right)$ is derived, leading to a scaling relation for the minimal step-step distance in the bunch formed as a product of two parts - a special combination of the initial parameters, with the dimension of length, and a complementary one that contains only the number of steps in the bunch.