Analytical description of the sputtering yields of silicon bombarded with normally incident ions

Experimentally determined sputtering yields of silicon bombarded with normally incident ions were analyzed with the aim of deriving a complete analytical description of the data. The yields, covering a wide range of energies (from 50 eV to 540 keV) and primary ions of vastly different mass (from H to Xe), can be described in universal form using (i) two energy-dependent functions, the reduced nuclear stopping cross section ${s}_{n}$ and Bohdansky's threshold function \ensuremath{\eta}, (ii) a modified form of Sigmund's \ensuremath{\alpha} function, only dependent on the mass ratio of projectile and target atoms, and (iii) a constant calibration factor ${x}_{0}N/{E}_{s},$ where ${x}_{0}$ is the effective mean escape depth of sputtered atoms, N the number density of Si atoms, and ${E}_{s}$ an effective surface binding energy. Considering the fact that according to computer simulations the mean escape depth increases significantly with increasing projectile energy, the observed constancy of ${x}_{0}N/{E}_{s}$ requires the assumption that ${E}_{s}$ is not a constant but contains two terms, the ``true'' surface binding energy ${E}_{s}$ and an additional energy-dependent term presumably reflecting the fraction of deposited energy that is lost in inelastic processes as well as in creating phonons and damage. There are indications that the sputtering yields reported for H and D bombardment as well as for heavy-ion impact at very low energies are too small by factors up to about 2, presumably due to oxygen incorporation and/or growth of surface contamination layers under nonideal vacuum conditions.