EVOLUTION OF TERRACE SIZE DISTRIBUTIONS DURING GROWTH ON STEPPED SURFACES.

Using a model based on step-mediated growth, we present an analytical derivation of the approach to uniform terrace lengths on a stepped surface, given a terrace length distribution of finite width at the outset. The results show that growth interruption is of no advantage and that in general the approach to uniform terrace lengths is quite slow. The width of the terrace length distribution varies approximately as the inverse 4-th root of the deposited coverage. This will only occur if the atoms attach themselves predominately at the up-step of each terrace. Otherwise the width of the distribution will grow without bounds. The model further predicts characteristic oscillations of terrace lengths in the vicinity of multiple height steps.