Model for the electronic stopping of channeled ions in silicon around the stopping power maximum

Analysis of random and channeled He stopping powers and of random and channeled B ranges in Si suggest that the non-local fraction x(nl) of the electronic stopping is energy dependent. It is proposed that x(nl) can be written as a power of the random stopping power S-e. For low energies, where the random stopping power may be described by a power law, this model reduces to the model previously proposed by Hobler. The model is in good agreement with published B ranges and with the range of new [110] B channeling implantations at 2-3 MeV. Moreover, it is found that employing the ZBL stopping power overestimates the random range of B implantations in Si between about 100 keV and 1 MeV. It is shown that the exponent in the power law at low energies for the random stopping power S-e is 0.5 rather than 0.375 as proposed by ZBL.