Theory of nanoscale surface ripple formation during oblique-incidence thin film deposition

We develop a theory of surface ripples that can emerge spontaneously when an amorphous thin film is grown by oblique-incidence sputter deposition. For simplicity, we consider the case in which two diametrically opposed, broad atomic beams are simultaneously incident on the substrate and focus on the angles of incidence just above the threshold angle for ripple formation. At early times, the ripples are roughly sinusoidal in form, but as time passes, they become increasingly faceted as their wavelength and amplitude grow. The facet slopes and the form of the ripple crests and troughs are found analytically at long times, and these predictions are in good agreement with our simulations. Ultimately, the ripples become highly ordered in the transverse direction and few dislocations remain. However, because the ripple wavelength and the amplitude vary in the longitudinal direction, the ripples are not perfectly ordered, even at long times.