Order improvement of surface nanopatterns via substrate rocking under ion bombardment: Experiments and nonlinear models

Surface nanopatterns formed by ion beam sputtering (IBS) frequently include a high density of structural defects, which seriously limit their practical applications. Recent theoretical work [M. P. Harrison and R. M. Bradley, Phys. Rev. E 93, 040802(R) (2016)], based on the anisotropic Kuramoto-Sivashinsky (aKS) equation, proposes that rocking a substrate during IBS can produce defect-free patterns under certain requirements. We find experimentally, via low-energy ${\mathrm{Kr}}^{+}$ irradiation of Si and amorphous carbon targets, that rocking the substrates generally improves the order of the ripple patterns. Indeed, order is improved even when conditions required in the aKS model may not be satisfied. Through numerical simulations, we show that a suitable generalization of this equation, in which conserved nonlinear effects are incorporated, reproduces satisfactorily the pattern order in our experimental conditions.