Highly ordered square arrays of nanoscale pyramids produced by ion bombardment of a crystalline binary material

A theory is developed for the nanoscale patterns formed when the (001) surface of a crystalline binary material with fourfold rotational symmetry is subjected to normal-incidence ion bombardment. The deterministic nonlinear continuum equations account for the Ehrlich-Schwoebel barrier, which produces uphill atomic currents on the crystal surface. We demonstrate that highly ordered square arrays of nanopyramids can form in a certain region of parameter space. An Ehrlich-Schwoebel barrier is required for patterns of this kind to develop. For another range of parameters, a disordered square array of nanodots forms and the pattern coarsens over time.