T. Salditt et H. Spohn, KINETIC ROUGHENING OF A TERRACE LEDGE, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 47(5), 1993, pp. 3524-3531
We study the motion of an isolated terrace ledge on a crystalline surf
ace within the framework of the terrace-ledge-kink model. We argue tha
t for length scales larger than the diffusion length the step roughnes
s is governed by the Kardar-Parisi-Zhang (KPZ) equation that predicts
a broadening as t1/3. For smaller length scales a variety of possibili
ties are explored. Their occurrence depends sensitively on the rates f
or the adsorption and desorption processes both on the terraces and at
the ledge. The ledge could be unstable, developing a fractal, dendrit
ic type of structure. If the ledge is stable, we obtain a crossover fr
om a t1/6 (conserved dynamics, model B) to a t1/4 (nonconserved dynami
cs, model A) and a t1/3 (KPZ) broadening.