  Recently it was experimentally demonstrated that sputtering under normal
incidence leads to the formation of spatially ordered uniform nanoscale islands
or holes. Here we show that these nanostructures have inherently nonlinear
origin, first appearing when the nonlinear terms start to dominate the surface
dynamics. Depending on the sign of the nonlinear terms, determined by the shape
of the collision cascade, the surface can develop regular islands or holes with
identical dynamical features, and while the size of these nanostructures is
independent of flux and temperature, it can be modified by tuning the ion
energy.
