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

Mean concentrations C-D 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 phi at depths similar toR(P)/2 (half projected ion range) by beam-based positron spectroscopy. By adjusting phi to phi(A) using factors given by the code TRIM, one arrives at the universal expression C-D=(2.79x10(10)) phi(A)(0.63); C-D (cm(-3)) can be estimated to +/-50% for MeV ions implanted for phi(A) from 10(9)x10(13) cm(-2), which corresponds to an upper limit dose approaching 10(14) cm(-2) for 2 MeV Si+ implantation. (C) 2002 American Institute of Physics.