EHRLICH-SCHWOEBEL INSTABILITY IN MOLECULAR-BEAM EPITAXY - A MINIMAL MODEL

The instability of a growing crystal Limited by a high-symmetry surfac e in molecular-beam epitaxy is studied in the limit where terrace size is very large compared to the atomic distance. In that case, everythi ng is deterministic except the nucleation of new terraces. Moreover, e xchange of atoms between steps is ignored. If the typical terrace size l(c) is chosen as length unit, the model depends on a single paramete r (l(s)/l(c)) which characterizes the strength of step-edge barriers ( ''Ehrlich-Schwoebel effect''). Numerical simulations are supported by nonlocal evolution equations relating the time and space derivatives o f the surface height, The first mounds which appear have a radius lamb da(c)(inf) proportional to l(c) root l(c)/l(s). In contrast with other authors who studied different models, coarsening is found to become e xtremely slow after the mounds have reached a radius lambda(c)(sup) of order l(c)(2)/l(s).