Simple expression for vacancy concentrations at half ion range following MeV ion implantation of silicon

Mean concentrations CD of aggregated vacancy-type point-defect structures in float-zone Si implanted with H+, B+, Si+, O+, and Ge2+ ions at energies between 0.45 and 4.0 MeV have been measured as a function of ion dose φ at depths ∼RP/2 (half projected ion range) by beam-based positron spectroscopy. By adjusting φ to φA using factors given by the code TRIM, one arrives at the universal expression CD=(2.79×1010) φA0.63; CD (cm−3) can be estimated to ±50% for MeV ions implanted for φA from 109×1013 cm−2, which corresponds to an upper limit dose approaching 1014 cm−2 for 2 MeV Si+ implantation.