Linearity and additivity in cluster-induced sputtering: A molecular-dynamics study of van der Waals bonded systems

Using molecular-dynamics simulation, we study sputtering of a condensed-gas solid induced by the impact of atomic clusters with sizes $1⩽n⩽{10}^4$. Above a nonlinear onset regime, we find a linear increase of the sputter yield $Y$ with the total energy $E$ of the bombarding cluster. The fitting coefficients in the linear regime depend only on the cluster size $n$ such that for fixed bombardment energy, sputtering decreases with increasing cluster size $n$. We find that to a good approximation the sputter yield in this regime obeys an additivity rule in cluster size $n$ such that doubling the cluster size at the same cluster velocity amounts to doubling the sputter yield. The sputter-limiting energy ${ϵ}_s$ is introduced which separates erosion $(ϵ>{ϵ}_s)$ from growth $(ϵ<{ϵ}_s)$ under cluster impact.