Langevin formalism in the continuum limit.provides a fruitful way to approach the fluctuations of isolated
steps on surfaces. There are three well-characterized limiting cases, denoted EC, TD, and PD, in which atomic
motion is limited by [2D] evaporation/condensation (attachment/detachment) at the step edge, diffusion across
the terrace, or motion along the step edge, respectively, each with a distinctive power-law signature in the
wavevector dependence of the relaxation time of a capillary mode. All three processes can be included in a
single unified formalism, allowing examination of the [narrow] crossover regions between these 3 regime. The
formalism has been generalized to vicinal surfaces, where there are additional limiting cases, most notably
diffusion between steps, for which TD-like behavior changes to EC-like for small interstep separation;
experimental ramifications are discussed. Similar Langevin analysis has been applied to the Brownian motion
of single-layer clusters of adatoms or vacancies (describable as fluctuations of nearly circular steps).
When the islands are subjected to electromigration, we find that there are several new qualitative differences
depending on the dominant mode of atomic transport. These ideas are applied to, and so tested by, experimental
examples and Monte Carlo simulations.
Work supported by NSF MRSEC at U. of Maryland, done in collaboration primarily with S.V. Khare, N.C. Bartelt,
and E.D. Williams, and also with O. Pierre-Louis, S.D. Cohen, R.D. Schroll, D.B. Dougherty, and others at Maryland,
with M. Giesen and H. Ibach at FZ-Juelich (via Humboldt Foundation), and with J.-J. Métois at Marseilles.