Morphology of crystalline surfaces under various step interaction potentials

We study the morphological equilibration of a periodically corrugated one-dimensional crystalline surface under various forms of interaction between neighbouring atomic steps on the surface. The surface under consideration is assumed to be below its roughening temperature and only surface diffusion is considered as a means of mass transport. Both continuum and discrete equations of motion for surface evolution are derived and compared. Continuum equations and discrete equations of motion in the limit of 'diffusion limited growth' lead to the same form of the variation of the height of the surface. The discrete equations provide additional information on the evolution of crystal height and terrace separations in the limit of 'step attachment/detachment limited growth'. While the shape of the evolving surface is determined by the dominant type of step-step interaction between neighbouring steps on the surface, the time dependence of terrace widths and thus of the height of the crystal depends on the dominant surface process for a given type of the step-step interaction. The variation of height of the corrugation depends on time as t, e(-1), t(-1), t(-1/2) and t(-1/3) and the height variation scales with the period of the corrugation wavelength lambda as lambda(3), lambda(4), lambda(5) and lambda(6) in connection with the type of interaction between steps and the dominant atomic processes on the surface.