Recent experimental studies focusing on the morphological properties of
surfaces eroded by ion-bombardment report the observation of self-affine
fractal surfaces, while others provide evidence about the development of a
periodic ripple structure. To explain these discrepancies we derive a
stochastic growth equation that describes the evolution of surfaces eroded by
ion bombardment. The coefficients appearing in the equation can be calculated
explicitly in terms of the physical parameters characterizing the sputtering
process. Exploring the connection between the ion-sputtering problem and the
Kardar-Parisi-Zhang and Kuramoto-Sivashinsky equations, we find that
morphological transitions may take place when experimental parameters, such as
the angle of incidence of the incoming ions or their average penetration depth,
are varied. Furthermore, the discussed methods allow us to calculate
analytically the ion-induced surface diffusion coefficient, that can be
compared with experiments. Finally, we use numerical simulations of a one
dimensional sputtering model to investigate certain aspects of the ripple
formation and roughening.Comment: 20 pages, LaTeX, 5 ps figures, contribution to the 4th CTP Workshop
on Statistical Physics "Dynamics of Fluctuating Interfaces and Related
Phenomena", Seoul National University, Seoul, Korea, January 27-31, 199
