THE EQUILIBRATION OF TERRACE WIDTH DISTRIBUTIONS ON STEPPED SURFACES

Many recent attempts to understand step structure have been based on the assumption of thermal equilibrium. In order to aid such analyses, we present calculations of the order of magnitudes of equilibration times for step structure. In particular, we discuss the equilibration of the distribution of terrace widths when step motion occurs through the exchange of atoms with a reservoir of adatoms on the terraces. By solving the appropriate continuum Langevin equation we give simple expressions for the time dependence of the terrace width distribution in terms of attachment/detachment rates at the step edge. We show that equilibration times should scale as the fourth power of the equilibrium width of the distribution (which can usually be expected to be proportional to the average terrace width). We verify this prediction for a discrete model of step dynamics with a Monte Carlo simulation, When equilibration occurs only through diffusion along the step edge, the equilibration times are much longer: they scale as the eighth power of the equilibrium width.