GROWTH OF MULTI-DIMENSIONAL SUPERLATTICES USING STEP ARRAY TEMPLATES; EVOLUTION OF THE TERRACE SIZE DISTRIBUTION.

The process of step-mediated growth in molecular beam epitaxy, where deposited atoms move along surface terraces until they eventually bind at a surface step, is currently being explored as a mechanism for forming two-dimensional periodic structures. To succeed such schemes require a periodic step distribution, i.e., uniform terrace lengths. A model, based on step-mediated growth, is presented, which yields 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 the approach to uniform terrace lengths with increasing deposition 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 terrace length distribution will grow without bounds.