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We propose and study a continuum model for the dynamics of amorphizablesurfaces undergoing ion-beam sputtering (IBS) at intermediate energies andoblique incidence. After considering the current limitations of more standarddescriptions in which a single evolution equation is posed for the surfaceheight, we overcome (some of) them by explicitly formulating the dynamics ofthe species that transport along the surface, and by coupling it to that of thesurface height proper. In this we follow recent proposals inspired by``hydrodynamic'' descriptions of pattern formation in aeolian sand dunes andion-sputtered systems. From this enlarged model, and by exploiting thetime-scale separation among various dynamical processes in the system, wederive a single height equation in which coefficients can be related toexperimental parameters. This equation generalizes those obtained by previouscontinuum models and is able to account for many experimental features ofpattern formation by IBS at oblique incidence, such as the evolution of theirradiation-induced amorphous layer, transverse ripple motion with non-uniformvelocity, ripple coarsening, onset of kinetic roughening and other.Additionally, the dynamics of the full two-field model is compared with that ofthe effective interface equation.

Coupling of morphology to surface transport in ion-beam irradiated surfaces. I. Oblique incidence