Universal Equation for Argon Gas Cluster Sputtering Yields

An analysis is made of the sputtering yields of materials for argon gas cluster ion beams used in SIMS and XPS as a function of the beam energy, E, and the cluster size, n. The analysis is based on the yield data for the elements Si and Au, the inorganic compound SiO2, and the organic materials Irganox 1010, the OLED HTM-1, poly(styrene), poly(carbonate), and poly(methyl methacrylate). The argon primary ions have cluster sizes, n, in the range 100–16 000 and beam energies, E, from 2.5 to 80 keV. It is found that the elemental and compound data expressed as the yields, Y, of atoms sputtered per primary ion may all be described by a simple universal equation: Y/n = (E/An)q/1 + (E/An)q−1 where the parameters A and q are established by fitting. The sputtering yields of the three organic materials are given as yield volumes expressed in nm3. For these, an extra parameter B is included multiplying the right-hand side of the equation where B is found by fitting to be of the order (0.18 nm)3 to (0.26 nm)3. This universal equation exhibits no threshold energy, and no deviation was observed from the equation, indicating that any threshold energy would have to be significantly below E/n = 1 eV per atom. The equation also shows that doubling the cluster size at the same energy per atom simply doubles the sputtering yield so that in this sense, and probably this sense alone, the sputtering effects are linearly additive. The parameter A is related, inversely, to the mean sputtered fragment size, and the low A values for organic materials are indicative of high yield volumes. For materials with low A values, the universal equation is close to a linear dependence on energy, and if that linear dependence is assumed, an apparent threshold energy is predicted and observed experimentally.