Rapid-relocation model for describing high-fluence retention of rare gases implanted in solids

It has been known for a long time that the maximum areal density of inert gases that can be retained in solids after ion implantation is significantly lower than expected if sputter erosion were the only limiting factor. The difference can be explained in terms of the idea that the trapped gas atoms migrate towards the surface in a series of detrapping-trapping events so that reemission takes place well before the receding surface has advanced to the original depth of implantation. Here it is shown that the fluence dependent shift and shape of implantation profiles, previously determined by Rutherford backscattering spectrometry (RBS), can be reproduced surprisingly well by extending a simple retention model originally developed to account only for the effect of surface recession by sputtering ('sputter approximation'). The additional migration of inert gas atoms is formally included by introducing an effective shift parameter Y-eff as the sum of the sputtering yield Y and a relocation efficiency Psi(rel). The approach is discussed in detail for 145 keV Xe+ implanted in Si at normal incidence. Y-eff was found to increase with increasing fluence, to arrive at a maximum equivalent to about twice the sputtering yield. At the surface one needs to account for Xe depletion and the limited depth resolution of RBS. The (high-fluence) effect of implanted Xe on the range distributions is discussed on the basis of SRIM calculations for different definitions of the mean target density, including the case of volume expansion (swelling). To identify a 'range shortening' effect, the implanted gas atoms must be excluded from the definition of the depth scale. The impact-energy dependence of the relocation efficiency was derived from measured stationary Xe concentrations. Above some characteristic energy (similar to 20 keV for Ar, similar to 200 keV for Xe), Y exceeds Psi(rel). With decreasing energy, however, Psi(rel) increases rapidly. Below 2-3 keV more than 90% of the reemission of Ar and Xe is estimated to be due to bombardment induced relocation and reemission, only the remaining 10% (or less) can be attributed to sputter erosion. The relocation efficiency is interpreted as the 'speed' of radiation enhanced diffusion towards the surface. The directionality of diffusion is attributed to the gradient of the defect density on the large-depth side of the damage distribution where most of the implanted rare gas atoms come to rest. Based on SKIM calculations, two representative parameters are defined, the peak number of lattice displacements, N-d,N-m, and the spacing, Delta z(r,d), between the peaks of the range and the damage distributions. Support in favour of rapid rare gas relocation by radiation enhanced diffusion is provided by the finding that the relocation efficiencies for Ar and Xe, which vary by up to one order of magnitude, scale as Psi(rel) = kN(d,m)/Delta z(r,d), independent to the implantation energy (10-80 keV Ar, 10500 keV Xe), within an error margin of only +/- 15%. The parameter k contains the properties of the implanted rare gas atoms. A recently described computer simulation model, which assumed that the pressure established by the implanted gas drives reemission, is shown to reproduce measured Xe profiles quite well, but only at that energy at which the fitting parameter of the model was determined (140 keV). Using the same parameter at other energies, deviations by up to a factor of four are observed. (C) 2009 Elsevier .V. All rights reserved.