Origin of nonlinear sputtering during nanocluster bombardment of metals

Recent experiments [S. Bouneau et al., Phys. Rev. B 65, 144106 (2002)] show that the sputtering of atoms from surfaces by cluster impacts behaves differently from what is expected in the classical stopping theory. The most significant unresolved questions are that the sputtering yield divided by cluster nuclearity squared (Y∕N²) is independent of N in the size range $N=2--13$ and that the energy maximum is not at the position expected from the nuclear stopping power. We use classical molecular dynamics simulations to examine the energy deposition from 0.1--18.50.3em0exMeV Au₅ and Au₁₃ clusters to the Au(111) surface to investigate this question. The simulations show that only a portion of the energy deposited from the cluster atoms to the crystal contributes to the formation of the displacement cascade because either the cluster channels through the surface layers as one entity or, if strong collisions occur, the energy deposited in these collisions is mostly carried away from the collision region by fast knock-on atoms. Based on the observations in the simulations, we develop an analytical model that explains the N² effect and an energy maximum that differs from the nuclear stopping.