Secondary-ion emission probability in sputtering

It is shown that the experimentally observed correlations between the ionization probability of the ejected particles of a sputtered metal surface and the substrate work function $\phi$, the outward velocity $v$, and the ionization potential $I$ or affinity $A$ of the departing atom, can be accounted for by considering the probability that the initial occupation of the ionization or affinity level survives during the nonadiabatic passage of the surface. With reasonable models for the variation of the position and width of the ionization or affinity level with distance from the surface, the ionization probability is shown for a large class of systems to be roughly proportional to $\exp [-\frac{(I-\phi )}{cv}]$ (positive ions) or $\exp [-\frac{(\phi -A)}{cv}]$ (negative ions), where $c$ is a constant.