The Bradley-Shipman theory explains the genesis of the highly ordered hexagonal arrays of nanodots that can result from normal-incidence ion bombardment of a binary material [R. M. Bradley and P. D. Shipman, Phys. Rev. Lett. 105, 145501 (2010)]. To facilitate experimental testing of the theory, we generalize it to oblique-incidence bombardment with two diametrically opposed beams. Using analytical methods valid in the weakly nonlinear regime and computer simulations, we demonstrate that an unusual “dots-on-ripples” topography can emerge for nonzero angles of ion incidence $\theta$. In such a pattern, nanodots arranged in a hexagonal array sit atop a ripple topography. We find that if dots-on-ripples are supplanted by surface ripples as $\theta$ or the ion energy are varied, the transition is continuous rather than hysteretic.

• Received 8 March 2014
• Revised 31 July 2014

DOI:https://doi.org/10.1103/PhysRevB.90.085428