Highly accurate nuclear and electronic stopping cross sections derived using Monte Carlo simulations to reproduce measured range data

Abstract

We have examined and confirmed the previously unexplored concept of using Monte Carlo calculations in combination with measured projected ranges of ions implanted in solids to derive a quantitative description of nuclear interaction and electronic stopping. The study involved 98 ranges of 11B in Si between 1 keV and 8 MeV, contained in 12 sets of 10 different groups. Systematic errors by up to ±8% were removed to establish a refined data base with 93 ranges featuring only statistical uncertainties (±1.8%). The Monte Carlo calculations could be set up to reproduce the refined ranges with a mean ratio 1.002 ± 1.7%. The input parameters required for this very high level of agreement are as follows. Nuclear interaction is best described by the Kr-C potential, but in obligatory combination with the Lindhard-Scharff (LS) screening length. Up to 300 keV, the electronic stopping cross section is proportional to the projectile velocity, Se = kSe,LS, with k = 1.46 ± 0.01. At higher energies, Se falls progressively short of kSe,LS. Around the Bragg peak, i.e., between 0.8 and 10 MeV, Se is modeled by an adjustable function serving to tailor the peak shape properly. Calculated and measured isotope effects for ranges of 10B and 11B in Si agree within the experimental uncertainty (±0.25%). The range-based Se,R(E) reported here predicts the scarce experimental data derived from the energy loss in projectile transmission through thin Si foils to within 2% or better. By contrast, Se(E) data of available stopping power tables exhibit deviations from Se,R(E) between −40% and +14%.