Representation of ion implantation projected range profiles by Pearson distribution curves for silicon technology

Several authors have reported difficulties in fitting Pearson curves to implants into amorphous targets. However, we show that accurate Pearson curve fitting to simulations of projected range profiles in amorphous targets is possible when implant profiles are available for which optimised moments can be generated. In previous literature few comparisons can be found between Pearson curve fits and the original implant profiles whereas, in the current paper, comparisons are made with high-resolution simulated profiles for B, P and As implanted into amorphous Si. These profiles were derived using Monte-Carlo simulations each of 1,000,000 ion trajectories. Fit coefficients that allow the regeneration of Pearson curves, optimised to fit Monte-Carlo implant profiles, are provided for the ions, B, P, As and Sb implanted, with energies in the range 25–300 keV, into targets of amorphous Si, silicon dioxide and silicon nitride. Comparisons of infinite and optimised moments, for B and P implants, show that the best fit moments (and corresponding Pearson type) can only be determined as part of an optimisation process, and not from infinite moments directly (such as moments from a backward Boltzmann transport equation solver).